No title

Synthese (2011) 180:317–335 DOI 10.1007/s11229-009-9704-8

In defense of true higher-order vagueness Susanne Bobzien

Received: 17 November 2009 / Accepted: 19 November 2009 / Published online: 5 December 2009 © Springer Science+Business Media B.V. 2009

Abstract Stewart Shapiro recently argued that there is no higher-order vagueness. More specifically, his thesis is: (ST) ‘So-called second-order vagueness in ‘F’ is nothing but first-order vagueness in the phrase ‘competent speaker of English’ or ‘competent user of “F”’. Shapiro bases (ST) on a description of the phenomenon of higher-order vagueness and two accounts of ‘borderline case’ and provides several arguments in its support. We present the phenomenon (as Shapiro describes it) and the accounts; then discuss Shapiro’s arguments, arguing that none is compelling. Lastly, we introduce the account of vagueness Shapiro would have obtained had he retained compositionality and show that it entails true higher-order. Keywords Vagueness · Higher-order vagueness · Contextualism · Qualified individuals Reviews and discussions of Stewart Shapiro’s excellent recent book Vagueness in Context1 have mostly focused on Shapiro’s ‘open-texture’ theory and his contextualism, with relative neglect of his theory of higher-order vagueness.2 The present paper aims to fill this gap. Shapiro argues that “there is no higher-order vagueness, strictly so-called” and that “so-called ‘higher-order vagueness’ is actually ordinary first-order vagueness in different predicates”.3 More specifically, Shapiro’s Thesis is:

1 Shapiro (2006). 2 Cf. e.g. Keefe (2007), Sorensen, (2008), Eklund, M. (2006), Gross (2009). 3 Shapiro (2005) 147; Shapiro, (2006) 163.

S. Bobzien (B) Yale University, New Haven, CT, USA e-mail: [email protected]

123

318

Synthese (2011) 180:317–335

(ST) So-called second-order vagueness in a predicate ‘F’ is nothing but first-order vagueness in the phrase ‘competent speaker of English’ or ‘competent user of the word “F”.4 Instead of true higher-order vagueness, Shapiro maintains, all we have is surrogate higher-order vagueness.5 He bases (ST) on a description of the phenomenon of higherorder vagueness and two accounts of ‘borderline case’, and supports it with several arguments. We briefly present the phenomenon (as Shapiro describes it) and Shapiro’s accounts of vagueness; then show that none of Shapiro’s arguments for (ST) is compelling; finally, we introduce the account of vagueness that Shapiro would have obtained had he consistently abided by the rules of compositionality, and show that this account both entails true higher-order vagueness and does not turn on the vagueness of ‘competent speaker’. 1 The phenomenon of higher-order vagueness and the accounts of ‘borderline case’ For Shapiro “[h]igher-order vagueness is vagueness concerning borderline cases of vague predicates.”6 He describes the phenomenon as follows, assuming a series of men lined up according to how much hair they have: The first … has no hair whatsoever, and the last, … has [a] full head of hair. After [the first], each man in the series has slightly more hair than his predecessor. Intuitively, there is no (sharp) border between the men that are bald … and those that are not …. The fellows in the middle are the borderline cases. … Intuitively, it also seems that there is no sharp boundary between the (determinately) bald men at the start and the borderline bald men in the middle, nor … between the borderline men in the middle and the (determinately) non-bald men at the end.7 Shapiro identifies as second-order the borderline cases of ‘determinately bald’ with ‘borderline bald’ and the borderline cases of ‘borderline bald’ with ‘determinately non-bald’. He identifies as third-order the borderline cases of ‘determinately determinately bald’ with ‘borderline borderline bald’, etc. (there are four categories for these); higher orders can be introduced in the same way.8 The phenomenon is the one most commonly discussed under the heading of ‘higher-order vagueness’.9 Shapiro provides two accounts of ‘borderline case’. The first is10 : 4 Shapiro (2005) 161: “on the present option, what passes for second-order vagueness is vagueness in the phrase ‘competent user of the word “bald”’; ibid. 155 “If there is vagueness in ‘borderline bald’, it turns on the vagueness of ‘competent speaker of English”’. Cf. Shapiro (2006) 163. Instead of ‘competent speaker of English’ Shapiro also uses ‘competent user of the language’ and similar phrases. 5 Shapiro (2005) 161, or, as he states in Shapiro (2006), 161 and 163, analogs to higher-order vagueness. 6 Shapiro (2006, p. 125). 7 (Shapiro, 2006, pp. 125–126), cf. Shapiro (2005, pp. 147–148). 8 Shapiro (2006, pp. 126–127), cf. Shapiro (2005, pp. 147–148). The number of categories of borderline

cases doubles with each order. 9 Besides Shapiro, Fine (1975), Keefe (2000), Greenough (2005), Sainsbury (1991). 10 It is based on McGee and McLaughlin (1995), Sect. 2.

123

Synthese (2011) 180:317–335

319

(1) a is borderline F if it is not the case that (i) the thoughts and practices of competent English speakers determine the conditions of application for F and (ii) the facts about a determine that these conditions are met.11 Shapiro introduces a variation of (1) which indicates the location of indeterminacy: (2) a is a borderline case of F if (i) the thoughts and practices of speakers of the language do determine the conditions of application for F and for ¬F and (ii) the non-linguistic facts do not determine that either of these conditions are met.12 As a specification of (1) and (2) tailored to his open-texture account, Shapiro offers: (3) The borderline cases for a predicate like ‘bald’ are just those for which there is no consensus among competent speakers … even after the external context … is fixed.13 He further specifies (3) as: (4) If at least one competent speaker of the language would judge a man to be bald … and at least one competent speaker … would judge the same man to be not bald, then the man is borderline [bald].14 Shapiro works with the following relation between ‘borderline case’ and ‘vague’: (5) F is vague if there is a borderline case a of F.15 In the next three sections we discuss the points Shapiro produces in support of (ST). These are (i) his reference to Timothy Williamson’s theory of higher-order vagueness; (ii) and (iii) his arguments regarding the facts that borderline red is not a colour and that the meaning of ‘borderline red’ makes reference to competent speakers; (iv) the argument by elimination which he puts forward in order to identify the source of so-called higher-order vagueness. We employ the following terminological conventions: we use F for atomic vague predicates such as ‘is bald’ and a for designators such as ‘Baldwin’. We abbreviate ‘borderline’ as BL. BL2 is short for ‘borderline borderline’, etc. We occasionally make use of the letter  for predicates constructed from F by prefixing zero or more occurrences of ‘borderline’ and of ‘not’. Like Shapiro, we use ‘a is a borderline case of “F”’ and ‘a is borderline F’ interchangeably. We abbreviate both as BLFa.16 11 Cf. Shapiro (2005, pp. 151–152). 12 Shapiro (2005, p. 155), italics ours. 13 Shapiro (2005, p. 157). Shapiro assumes that “a competent speaker is someone that understand the language and is employing normal perceptual mechanisms under the fixed, favourable conditions” (ibid.). The competence is thus not merely linguistic. 14 Ibid. Here and later we disregard Shapiro’s references to conversational contexts, since they are irrelevant to the questions discussed in this paper. 15 Cf. Shapiro (2005, p. 148), Shapiro (2006, pp. 125–127). 16 This terminology translates easily into standard nomenclatures for vague predicates in terms of deter-

minacy, clarity, etc.: BLFa iff ¬DFa & ¬D¬Fa.

123

320

Synthese (2011) 180:317–335

2 The brittle alliance with Timothy Williamson In support of his thesis (ST) that so-called higher-order vagueness is nothing but vagueness in “competent speaker”, Shapiro four times quotes the following sentences from Timothy Williamson’s paper on higher-order vagueness17 : (i) It may be misleading to think of higher-order vagueness in α as a species of vagueness in α. (ii) Higher-order vagueness in α is first-order vagueness in certain sentences containing α.18 However, the quote does not support (ST), and Shapiro does not have a supporter in Williamson. The context of the quote reveals clearly the specific point Williamson intends to make.19 To begin with, in his whole paper α stands for a closed sentence, more precisely for a closed propositional formula of the modal systems he discusses. Thus unlike (ST), Williamson’s claim is not about predicates. We consider Williamson’s two sentences individually. Sentence (i) takes issue with the potential misunderstanding that higher-order vagueness in α might be a species of vagueness in α. Williamson reasonably assumes that if higher-order vagueness in α were a species of vagueness in α, the following principle would hold: ‘In any theorem of the system we can substitute BLn for each occurrence of a single BL salva validitate.’ For instance, assume that BL[α1 &α2 ] → [BLα1 vBLα2 ] is a theorem. (This is Williamson’s example.) Then, if BL2 in α was a species of BL in α, the following formula would also be a theorem: BL2 [α1 &α2 ] → [BL2 α1 vBL2 α2 ]. Yet, as Williamson correctly points out, this is not so. The same holds for higher orders. Hence higher-order vagueness in α is not a species of vagueness in α. Sentence (ii) is meant to describe the relation between first-order and higher-order vagueness in an accurate way; that is, in a way that does not lead to the consequences entailed by the false assumption that higher-order vagueness is a species of vagueness. Taking the case Williamson himself is discussing, we get as an example for (ii): If we have BL2 [α1 &α2 ], (which is second-order vagueness in the sentence [α1 &α2 ]), then we have first-order vagueness in the sentence BL[α1 &α2 ]20 (which is a sentence which contains [α1 &α2 ]). Understood in the way Williamson intends, (ii) is true in all theories of higher-order vagueness we know. Generalized, it comes to the following: Having higher-order vagueness in α is nothing but having BLn α with n > 1. In that case we always, necessarily, also have first-order vagueness in BLn−1 α, a sentence we obtain by replacing BLn by BLn−1 . Evidently, this sentence is always a sentence that contains α. Thus (ii) comes to: nth-order vagueness in a sentence α is first-order vagueness in the sentence BLn−1 α. (The sentence containing α stands to the sentence in which there is higher-order vagueness as BLβ stands to β.) Williamson’s point 17 Williamson (1999, p. 140). Roman numerals ours. 18 Shapiro (2005, p. 153), “So I agree with Williamson”; Shapiro (2006, p. 125), as motto for the chapter

on higher-order vagueness; Shapiro (2006, p. 132) “So I agree with the passage from Williamson”; Shapiro (2006, p. 163) “my endorsement of … Williamson”. 19 Cf. Williamson (1999, pp. 139–140) for detail. 20 And in the logical equivalents of BL[α &α ] in terms of definiteness, e.g. ¬D[α &α ] & ¬D¬[α &α ]. 1 2 1 2 1 2

123

Synthese (2011) 180:317–335

321

is purely formal. It is fully compatible with the assumption of compositionality for higher-order vagueness. Shapiro offers Williamson’s (ii) as support for (ST). They indeed sound similar. Nevertheless, they are very different. Moreover, Shapiro’s thesis is much stronger in that in most theories of vagueness it does not hold. If we formulate Shapiro’s thesis in a way similar to Williamson’s (ii), we get: So-called higher-order vagueness in a predicate F is nothing but first-order vagueness in a predicate CS where (a) (b) (c) (d)

CS stands for ‘competent speaker of English’; F does not contain CS; CS is a meaning component21 of BL; BLn Fx = BL[BLn−1 CSx].

Using an example: higher-order vagueness in ‘bald’ is first-order vagueness (a) in the predicate ‘competent speaker’,22 where (b) ‘bald’ does not contain ‘competent speaker’; (c) ‘competent speaker’ is a meaning component of ‘borderline’ and (d) ‘borderline-borderline bald’ is not equivalent to ‘borderline case of “borderline competent speaker”’. None of (a)–(d) has anything to do with Williamson’s point. Thus, whereas the logical relations Williamson commented about in the quoted passage did not involve any predicates (or any expressions beyond those explicit in BLn−1 α), and concerned the relation between modalized closed formulae, Shapiro’s thesis involves a predicate (‘competent speaker’) which is not explicit in BLn−1 Fx, but makes explicit a meaning component of BL. Moreover, whereas Williamson’s rejection of the genus–species relation for higher-order and first-order vagueness is uncontroversial and retains compositionality of the borderline-operator, and thus preserves true higher-order vagueness, Shapiro’s thesis is highly controversial as it violates the compositionality of the borderline-operator (details below), and thus eliminates true higher-order vagueness. In short, Williamson’s quote does not support (ST).

3 The argument based on the fact that ‘borderline red’ is not a colour(-predicate) Shapiro’s second point in support of (ST) is an argument from the fact that ‘borderline red’ is not a colour(-predicate). He maintains that for any a to be a true borderline borderline case of ‘red’, ‘borderline-red’ would need to be a colour (sic).23 However, he claims, the meaning of ‘borderline-red’ includes a linguistic component, in that it makes reference to the judgement of competent speakers, whereas the meanings of

21 Shapiro does not define ‘meaning component’. He seems to assume that if x is a constituent of the definition of y, then x is a meaning component of y (e.g. Shapiro 2005, p. 152). 22 For brevity, we will use ‘competent speaker’ for ‘competent speaker of English’. 23 Shapiro (2005, pp. 147, 152). We assume that Shapiro intends ‘colour-predicate’ here, and speaks loosely.

123

322

Synthese (2011) 180:317–335

colour terms never do.24 Therefore, Shapiro infers, borderline-red is not a colour (-predicate). Hence no a can be a true borderline borderline case of ‘red’. Shapiro offers no general argument, but we can reconstruct his reasoning: He claims that for true higher-order vagueness there must not be a “difference in kind” between predicates F and BLF. If one is a colour(-predicate), or height(-predicate), etc., so must be the other.25 Hence for each ordinary language vague term (‘red’, ‘tall’) there is a kind-term KF so that (i) we can say ‘F is a KF ’ and (ii) the meaning of this kind-term does not make reference to competent speakers. Then, for it to be possible that a is a true borderline borderline case of F, BLF would have to be a KF . But the meaning of any predicate BLF does make reference to competent speakers, and thus BLF is not a KF . Thus F and BLF are of relevantly different kinds, since no BLF is ever a KF and all BLF, but no KF , make reference to competent speakers. Hence no a can be a true borderline borderline case of ‘F’. Hence there can be no true higher-order vagueness. Shapiro’s argument fails in several respects. First, it matters that the philosophically relevant type of borderline cases that Shapiro discusses are not red/orange or red/purple borderline cases, but red/not red borderline cases. The Sorites paradox as well as the so-called paradoxes of higher-order vagueness would disappear, if the red/not red borderline cases were replaced by red/orange borderline cases. Shapiro himself repeatedly notes that borderline cases are of the kind F/not F or F/non-F.26 But ‘not red’ and ‘non-red’ are not colour(-predicate)s, and it would be a stretch to say they are on a par with ‘red’ and ‘orange’. Moreover, ‘not red’ and ‘non-red’ contain a meaning component that makes reference to the absence of a color, which color terms (other than ‘black’) definitely don’t. Shapiro’s own line of argument would then imply that there can be no borderline cases of ‘not red’. Thus the generalized result of his argument is incompatible with his own theory.27 Second, true higher-order vagueness is not precluded by the fact that the meaning of BLn F, but not the meaning of F, makes reference to competent speakers. To show this, we suppose that (ST) is grounded solely on the fact that ‘borderline F’, but not ‘F’ makes reference to competent speakers. Now consider the predicate ‘borderline H’. Applying Shapiro’s own thesis, we get the result that second-order vagueness in ‘borderline H’ is not true higher-order vagueness, since the meaning of ‘borderline borderline H’, but not the meaning of ‘borderline H’ makes reference to competent speakers. But this is obviously false. Both the meaning of ‘borderline H’ and the meaning of ‘borderline borderline H’ make reference to competent speakers. Thus, if we skip the simply bald and simply non-bald men and start with the borderline bald men, we get perfectly good higher-order vagueness by Shapiro’s own lights.28 24 Shapiro (2005, p. 152). Shapiro’s underlying assumption here, that meanings and linguistic expressions are structured in the same way, is of course in itself controversial. 25 Shapiro (2005, p. 152). 26 Shapiro (2005, pp. 147–148, passim). In fact, every borderline case of F is also a borderline case of

not-F. Cf. e.g. Shapiro (2006, pp. 62–63, 101). 27 The fact that ‘not red’ applies to the same kind of objects as ‘red’ and ‘orange’ doesn’t help, since so

does ‘borderline red’ (see below). Shapiro might retort: but neither ‘borderline red’ nor ‘not borderline red’ are colors, but one of ‘red’ and ‘not red’ is. Still he’d have to tell us why this matters. 28 Perhaps Shapiro’s thesis is only that there are no true higher-order borderline cases of predicates that do not have ‘judgement of competent speakers’ as meaning component, so that there is an insurmountable

123

Synthese (2011) 180:317–335

323

Our foregoing two arguments are but playful banter. Philosophically more significant is the following point: Shapiro appears to confound two distinct questions: (i) whether ‘borderline-red’ is a colour predicate and (ii) whether the objects that satisfy the predicate ‘borderline-red’ have a colour. Take the predicate H ‘is yellower than the Gouda your father brought but less yellow than the tulip the cat ate’. The meaning of H makes reference to your father and the cat and the notions of less and more. The meanings of colour terms quite definitely don’t. Hence, according to Shapiro, H is not a colour predicate. Still, the objects that satisfy H all have a colour. More than that, H allows us to place the objects that satisfy it on a colour dimension (from more yellow to less yellow, left to right, say), in the minimal sense that they are to the right of all objects yellower than the tulip the cat ate and to the left of all objects less yellow than the Gouda your father brought. The same general point can be made about the predicate ‘borderline-red’. ‘Borderline-red’ may not be a colour predicate. Still, the objects that satisfy ‘borderline-red’ all have a colour.29 More than that, given basic penumbral connections,30 we can locate those objects on the dimension made up by a section of the colour spectrum (with decreasing nanometers from 700 to 600, say) in the minimal sense that they would not be to the left of any non-borderline case of ‘red’ we can identify and not to the right of any non-borderline case of ‘not red’ we can identify. What matters is not whether ‘borderline-red’ is a colour predicate, but that satisfaction of BLn F places a on a dimension on which—in the first instance—objects that satisfy Fx would also be placed. The objects that satisfy F, BLF, BLn F are all the same kind of objects insofar as they are the kind of objects that can but need not be F (e.g. for ‘tall’, ‘borderline tall’, ‘borderlinen tall’, objects with a measurable height). Shapiro is thus correct in requiring some shared feature of F and BLn F. But it is neither that both are colour predicates (etc.) nor that it must not be that one, but not the other, makes reference to competent speakers. For there to be true higher-order borderline cases, it is sufficient (and necessary) that F and BLF, and any BLn F, are alike in that they each place the objects that satisfy them on one and the same dimension D, a dimension which—in the standard case—has F objects at one end, non-F objects at the other. Baldemar, Haribald and Little Harry are all placeable, by ‘bald’, ‘borderline bald’ and ‘borderline borderline bald’ respectively, on the dimension of increasing amounts of hair, with hairless men at one end, men with abundant scalp hair at the other. Footnote 28 continued divide between ‘red’ and ‘bald’, for which there are no higher-order borderline cases, and ‘borderline red’ and borderline bald’, for which there are. Thus Baldwin may be truly borderline borderline-bald, and Hariman may be truly borderline-borderline borderline-bald, but Baldwin is not truly borderline-borderline bald, and Hariman is not truly borderline-borderline-borderline bald (with Baldwin located somewhere between the borderline bald men and the clearly bald men, and Hariman located somewhere between Baldwin and the clearly bald men). Curiouser and curiouser. 29 Naturally, we are not here concerned with a case in which something is borderline-red in a derivative sense, i.e. because it is borderline-coloured. An example of derivative borderline-red would be this: we put increasing numbers of drops of a red coloured essence into clear containers filled with clear water (rather than drops of red paint into yellow paint). Here the relevant kind would be things that can, but need not, be coloured. 30 For penumbral connections see e.g. Fine (1975), Shapiro (2006, p. 67).

123

324

Synthese (2011) 180:317–335

The upshot of this section is that neither the fact that ‘borderline-red’ is not a colourpredicate nor the fact that ‘red’ does not make reference to the judgement of competent speakers lends support to (ST). 4 The argument by elimination Shapiro’s only other argument for (ST) has the form of an argument by elimination. Shapiro presents the argument with his first account of ‘borderline case’: So our man is borderline bald if the thoughts and practices of competent language-users, together with the non-linguistic facts, do not determine whether the man is bald or whether he is not bald. I assume here that there is no vagueness in the relevant non-linguistic facts (such as the number and arrangement of hairs on our man’s head). I also assume, just for the sake of simplicity, that there is no relevant vagueness in what counts as a ‘thought’ and a ‘practice’. There is only one more place to look. If there is vagueness in ‘borderline bald’, it turns on the vagueness of ‘competent speaker of English’.31 The underlying structure of the argument appears to be something like this: 1. Implicit compositionality premise: If an expression  is vague, then at least one of ’s meaning components (or components of the definition of ) is vague.32 2. Implicit elimination premise: The meaning components of ‘borderline bald’ are the expressions ‘the non-linguistic facts’, ‘thoughts’, ‘practices’ and ‘competent speaker’. 3. ‘The non-linguistic facts’ is not vague. 4. ‘Thoughts’ is not vague. 5. ‘Practices’ is not vague. 6. If ‘borderline bald’ is vague, then ‘competent speaker’ is vague. (From 1.–5.) 7. Any vagueness in ‘borderline bald’ turns on the vagueness in ‘competent speaker’. (From 6.) There are two problems with Shapiro’s elimination argument. The first concerns the elimination premise. It seems that Shapiro has not listed all the meaning components of ‘borderline bald’. In particular, there is no mention of ‘bald’. At first blush, this seems baffling. Isn’t ‘bald’ part of the account of ‘borderline bald’ and doesn’t it by assumption have borderline cases, and is thus vague? How can ‘bald’ be ruled out as a 31 Shapiro (2005, p. 155). Shapiro provides a much abbreviated version of this argument by elimination for his second account of ‘borderline case’: “If at least one competent speaker of the language would judge a man to be bald (…) and at least one competent speaker (…) would judge the same man to be not bald, then the man is borderline. Once again, we see that any vagueness of ‘borderline bald’ must turn on vagueness in ‘competent speaker”’. Shapiro (2005, p. 157). We assume that, in parallel to his first argument, Shapiro would eliminate the expressions ‘at least one’ and ‘not’ as not vague and would declare any vagueness there may be in ‘to judge’ as irrelevant, before drawing the conclusion that “any vagueness of ‘borderline bald’ must turn on vagueness in ‘competent speaker”’. 32 With this strong assumption of compositionality Shapiro has lost the support of many philosophers of

language (e.g. those who accept unarticulated constituents), but this is not our concern here.

123

Synthese (2011) 180:317–335

325

possible source of the vagueness in ‘borderline bald’? Shapiro doesn’t say. Still, this is unlikely to be a simple oversight. There is one possible explanation, viz., that for Shapiro (i) ‘borderline’ is a meta-linguistic expression, short for something like ‘borderline case of (the predicate) “F”’, and (ii) an account of it needs to be non-disquotational. We can modify Shapiro’s account of ‘borderline bald’ from above accordingly: So our man is a borderline case of ‘bald’ if the thoughts and practices of competent language-users, together with the non-linguistic facts, do not determine whether the man satisfies ‘bald’ or whether he does not satisfy ‘bald’. Since Shapiro defines ‘borderline case’ in terms of a determinacy operator, and treats this operator sometimes explicitly as meta-linguistic, and since he often uses the phrase ‘borderline case of “F”’, we assume that the above is Shapiro’s view. For him, it then follows that, although there are borderline cases of the predicate ‘bald’, and the predicate ‘bald’ is vague, there are no (relevant) borderline cases of ‘the predicate “bald”’, and ‘the predicate “bald”’ is not vague. Given the assumption of ‘borderline’ as a meta-linguistic expression, we can see how ‘competent speaker of English’ may appear to be left as the only plausible source for the vagueness in ‘borderline bald’. However, it is Shapiro’s choice to use ‘borderline’ as a meta-linguistic expression with a non-disquotational account. Shapiro himself seems to agree with this, when he says that in the philosophy of language the word ‘borderline’ is becoming a term of art, and that what he is concerned with is this term of art.33 We see no independent philosophical reasons that would force us, or Shapiro, to make ‘borderline’ a meta-linguistic expression with a non-disquotational account. The truth of the elimination premise thus rests on Shapiro’s choice to use ‘borderline’ as a meta-linguistic expression. Without this choice, the conclusion that the vagueness of ‘borderline bald’ turns on the vagueness of ‘competent speaker’ cannot be drawn. But making an otherwise unmotivated terminological choice that undercuts the possibility of true higher-order vagueness is not the same as demonstrating that there is no higher-order vagueness. We conclude that Shapiro has not provided sufficient reason for eliminating the vagueness of ‘bald’ as a potential source for the vagueness of ‘borderline bald’. In fact, we can show that, if an expression ‘borderline F’ is vague, the vagueness of F is a necessary condition for the vagueness of ‘borderline F’. Consider the cases of ‘child*’ and ‘child’.34 Both satisfy Shapiro’s general criterion for vagueness. Both are such that for some individuals a, the thoughts and practices of competent languageusers, together with the non-linguistic facts, do not determine whether a is a child*, or child, respectively. Now consider the expressions ‘borderline child*’ and ‘borderline child’. The generally accepted view is that the first is not vague, but the second is. Why? In Shapiro’s terms, there are no borderline borderline cases of ‘child*’, since there are no objects such that the (relevant) non-linguistic facts do not determine whether the application conditions for ‘borderline child*’ or for ‘non borderline-child*’ are 33 Shapiro (2005, p. 153), Shapiro (2006, p. 133). 34 ‘Child*’ (like ‘oldster’, smidget, ‘dommal’) is an artificially concocted predicate which exhibits seman-

tic indeterminacy with sharp boundaries. For discussion of such predicates see e.g. Sainsbury (1991, pp. 172–174), Hyde (1994, pp. 35–36), Soames (1999, chap. 6), Glanzberg (2003, pp. 168–171).

123

326

Synthese (2011) 180:317–335

met. By contrast, the phenomenon of higher-order vagueness suggests that there are objects such that the (relevant) non-linguistic facts do not determine whether the application conditions for ‘borderline child’ or for ‘non borderline-child’ are met. So the difference between the expressions ‘borderline child’ and ‘borderline child*’ (that the first is vague, the second not) cannot lie in their shared component ‘borderline’. Hence the vagueness of ‘child’ is a necessary condition for the vagueness of ‘borderline child’.35 The factors on which the (true or so-called) second-order vagueness of ‘child’ turns cannot be reduced to the vagueness in (a meaning component of the) expression ‘borderline’.36 Hence Shapiro’s choice of ‘borderline’ as a meta-linguistic expression with non-disquotational definition is unfounded and clashes with the phenomenon of higher-order vagueness. Consequently, it should be rejected. As a result, the elimination premise falters, and so does the elimination argument as a whole. 5 The reduction of higher-order to first-order vagueness and the shift to meaning components of ‘borderline’ Even if Shapiro’s argument by elimination was successful, it would not prove (ST). At most, it would demonstrate that vagueness in the phrase ‘competent speaker’ is a necessary condition for vagueness in the predicate ‘borderline F’ (and hence for so-called second-order vagueness in ‘F’).37 By contrast, what is needed for (ST) is a proof that vagueness in ‘competent speaker’ is a necessary and sufficient condition for vagueness in ‘borderline F’. Only then could so-called second-order vagueness in F be reduced to first-order vagueness in ‘competent speaker’. It is unclear where in his argument Shapiro makes this step from necessary to necessary and sufficient condition.38 In any case, the inference from (i) ‘ψ is the only vague component of the complex expression ’ to (ii) ‘ψ is necessary and sufficient for the vagueness of ’ is invalid. Take the complex expression T ‘tall & more than 6 high’. ‘tall’ is the only vague 35 This argument assumes that the way the words ‘borderline’ and ‘child’ combine is not itself vague. If we drop this assumption, we can only infer that either the vagueness of ‘child’ is a necessary condition for the vagueness of ‘borderline child’ or the way ‘borderline’ combines with ‘child’ is vague, but the way ‘borderline’ combines with ‘child*’ is not. Again, the factors on which the second-order vagueness of ‘child’ turns cannot be reduced to vagueness in (a meaning component of the) expression ‘borderline’. 36 A similar point can be made regarding the number of higher orders of a vague expression. For all we know, different vague predicates may have a different number of higher orders of borderline cases. Again, this cannot simply be based on the relation between the expression ‘borderline’ and non-linguistic facts concerning objects which may satisfy this expression. In particular, it cannot be based on the relation between the expression ‘competent speaker’ and non-linguistic facts concerning objects which may satisfy this expression—as Shapiro would have it. For, by assumption, the number of higher orders depends on which first-order vague predicate is at issue. Naturally, if all vague predicates have an infinite number of higher orders, this point becomes void. However, Shapiro does not assume an infinite number of higher orders. 37 Shapiro uses the phrase ‘x turns on y’ for ‘y is a necessary condition for x’, see e.g. Shapiro (2006, p. 41). 38 In Shapiro (2005, p. 161) and Shapiro (2006, p. 126) this step seems completed. Cf. also the motto in

Shapiro (2005, p. 147).

123

Synthese (2011) 180:317–335

327

component in T. It is a necessary condition for T to be vague (to have borderline cases) that the component expression ‘tall’ is vague (has borderline cases). But it is not sufficient. Borderline cases, and hence vagueness, are context-sensitive.39 In a context C1 in which all borderline cases of ‘tall’ are below 6 feet, ‘tall & more than  6 high’ is not vague. By contrast, in a context C2 in which some borderline cases of ‘tall’ are above 6 feet, ‘tall & more than 6 high’ is vague. Thus it depends on a nonvague component of T whether T is vague. Hence, even if the elimination argument were sound, Shapiro would not have proved (ST), since his argument does not reduce higher-order vagueness to first-order vagueness. The general idea that higher-order vagueness of F reduces to vagueness in ‘competent speaker’ seems to originate in the implicit compositionality premise of the elimination argument. It said that, if an expression  is vague, then at least one of ’s meaning components (or components of the definition of ) is vague. The problem is not that the premise may be false; rather, that it is misleading, insofar as it encourages the assumption that the vagueness of a meaning component of an expression  provides any useful insight regarding the form the vagueness of  would take. Consider for comparison ‘bald’ or ‘red’. These are vague predicates. They lead to borderline cases. But we do not usually ask ‘where in the account of ‘bald’ does its vagueness reside?’—nor does Shapiro. Take the definition of ‘bald’ which Shapiro picked from a dictionary: “having little or no hair on the scalp”.40 Does the vagueness of ‘bald’ reside in ‘to have’ or ‘little or no’ or ‘hair’ or ‘on the scalp’? Presumably ‘little or no’ is vague; but so are the other expressions. In any event, this is not how Shapiro himself progresses towards a philosophical explanation of Sorites-vagueness of ‘bald’. Rather, Shapiro progresses by taking account of the fact that the Sorites-proneness of ‘bald’ is based on the fact that there are borderline cases of ‘bald’. There are cases where the ascription of ‘bald’ is not straightforward.41 a is borderline bald, since, although (i) the thoughts and practices of speakers of the language determine the conditions of application for ‘bald’ and for ‘non-bald’, (ii) the non-linguistic facts regarding a do not determine that those conditions are met.42 No word about any phrase from the definition of ‘bald’—and wisely so. In the case of ‘borderline bald’, surely the first hypothesis must be that the very same is true: ‘borderline bald’ should be vague because there are borderline cases of ‘borderline bald’43 ; i.e. because there are cases a for which the ascription of ‘borderline bald’ is doubtful; or, in Shapiro’s terms: cases for which neither the application conditions for ‘borderline bald’ nor those for ‘not borderline bald’ are met by the non-linguistic facts regarding a!

39 Shapiro repeatedly emphasizes this. See Shapiro (2005, pp. 152, 154), Shapiro (2006, pp. 134, cf. 3, 64). 40 Shapiro (2005, p. 152). 41 Cf. e.g. Shapiro (2006, p. 44). 42 Shapiro (2005, p. 151) “the facts about a” (drawing on McGee and McLaughlin); Shapiro (2005,

p. 155) “non-linguistic facts such as the number and arrangement of hairs”; cf. Shapiro (2006, p. 135) ((2) above). 43 Cf. Shapiro (2005, p. 148) “by definition, a second-order borderline case of ‘bald’ is a borderline case

of ‘borderline bald”’.

123

328

Synthese (2011) 180:317–335

Instead, Shapiro strays from the path he had previously paved himself. The route he takes is that ‘borderline bald’, if vague, is vague (because ‘competent speaker is vague, and that is) because there are speakers of English s for whom it is doubtful whether the expression ‘competent speaker’ applies to them; and that is, because neither the application conditions for ‘competent speaker’ nor the application conditions for ‘non-competent speaker’ are met by the non-linguistic facts regarding some speakers of English s.44 Shapiro moves away from the series of objects that would feature in the Sorites series for ‘bald’, or for ‘red’, etc., to a target group of objects that would feature in a Sorites series for ‘competent speaker’. It is this shift towards the vague meaning component of ‘borderline’ which seems to have prompted the endeavour to reduce higher-order vagueness to first-order vagueness. 6 Shapiro’s accounts of ‘borderline case’ and compositionality The most significant consequence of Shapiro’s reduction of the vagueness of ‘borderline bald’ to the vagueness of ‘competent speaker’ is that it does away with the compositionality of the account of ‘borderline case’.45 Shapiro himself had stated: (6) By definition, a second-order borderline case of ‘bald’ is a borderline case of ‘borderline bald’.46 Hence we would expect that a is second-order borderline-bald iff a is a borderline case of ‘borderline bald’. Instead, Shapiro argues (unsuccessfully) that a is second-order borderline-bald iff some speaker s is a borderline case of ‘competent speaker’. We now show that, if we use Shapiro’s own account of ‘borderline case’ and construct the account for higher-order borderline cases in a way that strictly preserves compositionality, we obtain a workable account of true, as opposed to merely socalled, higher-order vagueness. We use Shapiro’s specification of his second account: (7) a is a borderline case of F iff (in some conversational context) there is a competent speaker who would judge that a is F and (in some conversational context) there is a competent speaker who would judge that it is not the case that a is F.47 In line with our remarks above, we understand BL as an object-language operator48 and express (7) slightly more formally: (8) BLF a iff there is a competent speaker who would judge that Fa and there is a competent speaker who would judge that it is not the case that Fa. 44 Cf. Shapiro (2005), Sect. IV. 45 Note that the compositionality of vagueness dealt with in the previous two sections is different from the

compositionality of the account of ‘borderline case’ or compositionality of the BL-operator. 46 Shapiro (2005, pp. 148, 157); cf. Shapiro (2006, p. 126). 47 Cf. above (4) and Shapiro (2005, p. 157). We have replaced ‘the man’ by a and ‘bald’ by F. 48 Thus we avoid any pitfalls of disquotation and of the elimination argument (see above). As Shapiro

frequently uses ‘borderline’ non-metalinguistically, we preserve the core elements of Shapiro’s theory.

123

Synthese (2011) 180:317–335

329

Making use of (6), we introduce second-order borderline cases thus: We substitute BLFa for Fa on the side of the definiendum, and we substitute the account of BLFa for Fa on the side of the definiens. In this way we get: (9) BLBLF a iff there is a competent speaker who would judge that (there is a competent speaker who would judge that Fa and there is a competent speaker who would judge that it is not the case that Fa) and there is a competent speaker who would judge that it is not the case that (there is a competent speaker who would judge that Fa and there is a competent speaker who would judge that it is not the case that Fa). With this we are almost there. All we need to add is the scope of the competence of the speaker. Shapiro himself is keenly aware that the scope matters.49 We believe that the question of scope has a straightforward answer, once we acknowledge that it varies systematically with the sentence the competent speaker is asked to judge. It is common sense to require that the competence of the speakers must be competence regarding the object of their judgement. Thus, if they are to judge whether Fa, they need to be competent with regard to Fa.50 It is obvious that their qualifications must cover no less than this. At the same time there are no good reasons why their qualifications should go beyond this. We indicate the scope of competence by adding an index to the expression ‘competent speaker’: (10) BLFa iff there is a competent speakerFa who would judge that Fa and there is a competent speakerFa who would judge that it is not the case that Fa. (Based on the ordinary language use of ‘whether’, we assume that competence as to whether Fa is equivalent to competence as to whether ¬Fa.) For second-order vagueness, there will be two different indices: (11) BLBLFa iff there is a competent speaker(there is a competent speaker (Fa) who would judge that Fa and there is a competent speaker (Fa) who would judge that it is not the case that Fa) who would judge that (there is a competent speakerFa who would judge that Fa and there is a competent speaker(there is a competent speaker (Fa) who would judge that Fa and there is a competent speaker (Fa) who would judge that it is not the case that Fa) who would judge that it is not the case that Fa) and there is a competent speaker who would judge that it is not the case that (there is a competent speakerFa who would judge that Fa and there is a competent speakerFa who would judge that it is not the case that Fa). Don’t complain this is too complex.51 All we did is construct an account of second-order vagueness that satisfies the requirement of compositionality. This is a necessary condition for true higher-order vagueness. Still, for convenience, we 49 He discusses the issue in Shapiro (2006, at 164), though without reaching a conclusive result. 50 We discuss elsewhere what exactly this would involve. For present purposes, it suffices that there is a

straightforward relation between the competence of the speaker and the object to be judged by the speaker. (The competence still has a linguistic component, since Shapiro’s criterion for borderlinehood requires a conversational context.) 51 Compare the accounts of higher-order vagueness in Fine (1975), Section 5 and Williamson (1999) and

then come back ….

123

330

Synthese (2011) 180:317–335

introduce some simplifications. We use the index ‘BLFa ’ as an abbreviation for the index‘(there is a competent speaker (Fa) who would judge that Fa and there is a competent speaker (Fa) who would judge that ¬Fa)’ , keeping in mind that this mixing of elements of the definiendum into the definiens, though harmless, is not entirely correct. We also replace BLBLFa with the equivalent BL2 Fa, and abbreviate ‘it is not the case that’ by ‘¬’. Thus we get the more manageable: (12) BL2 Fa iff there is a competent speakerBLFa who would judge that (there is a competent speakerFa who would judge that Fa and there is a competent speakerFa who would judge that ¬Fa) and there is a competent speakerBLFa who would judge that ¬(there is a competent speakerFa who would judge that Fa and there is a competent speakerFa who would judge that ¬Fa). The account for third-order borderline cases is obtained by substituting BLFa for Fa on the side of the definiendum of BL2 Fa, and substituting the account of BLFa for Fa on the side of the definiens of BL2 Fa. The accounts for higher orders are obtained in the same way.52 We have, thus, starting from Shapiro’s own account of ‘borderline case’ and his own definition of ‘second-order borderline case’ constructed an account for higherorder vagueness that preserves compositionality and should define true, as opposed to merely so-called, higher-order vagueness. 7 Shapiro’s account of ‘borderline case’ does not entail (ST) Of course we cannot rule out that Shapiro believes that the account of ‘second-order borderline case’ we thus got entails that ‘competent speaker’ is vague. For he himself offers something close to an account that is gained from substituting the account of ‘borderline Fa’ for Fa in his first account of ‘borderline Fa’: A man is a borderline case of ‘borderline bald’ if the thoughts and practices of speakers of the language determine conditions of application for ‘determinately bald’ and for ‘borderline bald’, and the non-linguistic facts do not determine that either of these conditions are met.53 Here Shapiro has substituted ‘determinately bald’ (which entails ‘not borderline bald’) and ‘borderline bald’ for ‘not bald’ and ‘bald’ in a variant of his first account. We next show that the compositionally obtained account of ‘second-order borderline case’ ((12) above) does not entail that second-order vagueness turns on the vagueness of ‘competent speaker’. For this purpose, we want to bring out more clearly the logical structure of the embedded existential clauses in the definiens (13) … there is a competent speakerBLFa who would judge that (there is an x who is a competent speakerFa and who would judge that Fa and there is an x who is a 52 Thus we disagree with Shapiro’s statement “[t]he higher and higher orders correspond to deeper and deeper embeddings of “competent user of ‘competent user of “competent user of …””’ (Shapiro 2006, p. 163). The deeper and deeper embeddings are not of ‘competent user of’. They are of the whole account of ‘borderline case’—just as it should be. 53 Shapiro (2005, p. 155).

123

Synthese (2011) 180:317–335

331

competent speakerFa and who would judge that ¬Fa) and there is a competent speakerBLFa who would judge that ¬(there is an x who is a competent speakerFa and who would judge that Fa and there is an x who is a competent speakerFa and who would judge that ¬Fa). We can expose the structure further by formalizing the existential clauses (14) … there is a competent speakerBLFa who would judge that [∃x[CSx&Hx] & ∃x[CSx&Ix]] and there is a competent speakerBLFa who would judge that ¬[∃x[CSx&Hx] & ∃x[CSx&Ix]] with CSx for ‘x is a competent speakerFa ’, Hx for ‘x would judge that Fa’ and Ix for ‘x would judge that ¬Fa’. We can now easily show that it is possible for the account of ‘second-order borderline case’ to be true with ‘competent speakerFa ’ being not vague. All we need is an interpretation I1 based on the following assumptions: (i) in our domain there are only competent speakersBLFa ; (ii) all competent speakersBLFa judge all objects in the domain to be competent speakersFa ; hence ‘competent speakerFa ’ is not vague; (iii) one competent speakerBLFa in addition judges that ∃xHx&∃xIx; (iv) another competent speakerBLFa in addition judges that [∃xHx&¬∃xIx] v [¬∃xHx&∃xIx]. In Interpretation I1 , a is BL2 Fx, but this fact does not turn on the vagueness of ‘competent speakerFa ’. Hence the (compositional) account of ‘second-order borderline case’ we obtained from Shapiro’s own account of ‘borderline case’ and his own definition of ‘secondorder borderline case’ does not entail that ‘competent speaker’ is vague. Shapiro’s belief that (ST) is “how the notion of ‘borderline case’ in [his] own account of vagueness plays itself out, as we move to what passes for higher-orders [sic]”54 is thus false. 8 Can higher-order vagueness ever turn on the vagueness of ‘competent speaker’? The compositionalized and properly indexed version of Shapiro’s second account of ‘borderline case’ still seems to allow for a weakened form of Shapiro’s thesis: (STw ) It is possible that there are individual higher-order borderline cases whose being borderline turns on the vagueness of ‘competent speaker’. For example, it seems possible that the reason why Baldwin is borderline-borderline bald is the fact that there are borderline cases of ‘competent speaker(Baldwin is bald) ’, and that ‘competent speaker(Baldwin is bald) ’ is hence vague. All we need to grant is (15) Every competent speakerBLFa is a competent speakercompetent speaker (Fa) . (15) is likely true.55 With it granted, the following Interpretation I2 provides a case in which some a’s being second-order borderline-F turns on the vagueness of ‘competent 54 Shapiro (2005, p. 151). Shapiro himself discards the alternative that competent speakers must be competent with respect to the entire language as leading to a circular account of ‘competent speaker’ at ibid., pp. 164–165. 55 Recall that ‘competent speaker BLFa ’ is short for ‘competent speaker(there is a competent speaker (Fa) who would judge that Fa and there is a competent speaker (Fa) who would judge that it is not the case that Fa)’ . Thus in

123

332

Synthese (2011) 180:317–335

speakerFa ’. Consider again the partially formalized account (14), but this time with Interpretation I2 : (i) (ii) (iii) (iv)

The domain is {b, c, d, e}. d and e are competent speakersBLFa . b and c are not competent speakersBLFa . All competent speakersBLFa judge that Hb, Hc, ¬Hd, ¬He, Id, Ie, ¬CSc, CSd, CSe. (Thus by CSd and CSe, competent speakersBLFa judge themselves to be competent speakersFa .) (v) d judges that CSb. (vi) e judges that ¬CSb.

In I2 there is a competent speakerBLFa , i.e. d, who judges that [∃x[CSx&Hx]&∃x[CS x&Ix]]: She judges that CSb, Hb, CSd and Id and then judges by inference that [∃x[CSx&Hx]&∃x[CSx&Ix]]. And there is a competent speakerBLFa , i.e. e, who judges that ¬[∃x[CSx&Hx]&∃x[CSx&Ix]]: She judges that ¬CSb, ¬CSc, ¬Hd and ¬He (which makes the first conjunct of the conjunction with the largest scope false) and then judges by inference that ¬[∃x[CSx&Hx]&∃x[CSx&Ix]].56 Hence the condition for BL2 Fa is satisfied, that is, a is borderline borderline Fx. Since in I2 all competent speakersBLFa agree upon everything except their judgement regarding CSb, that is whether b is a competent speakerFa , BL2 Fa turns on the disagreement of the competent speakersBLFa as to whether b is a competent speakerFa . Since, by (15), all competent speakersBLFa are also competent speakersCS(Fa) , BL2 Fa turns on the disagreement of competent speakersCS(Fa) as to whether b is a competent speakerFa . In other words, it turns on the fact that there is a borderline case of competent speakerCS(Fa) , or, what is the same, on the fact that ‘competent speakerCS(Fa) ’ is vague. Thus the compositionalized and properly indexed modification of Shapiro’s second account of ‘borderline case’ allows for there being individual higher-order borderline cases whose borderlinehood turns on the vagueness of ‘competent speaker’. Worse, this modification seems to lead to two wholly unrelated criteria for second-order vagueness: one based on disagreement about how competent speakers would judge Fa; the other based on disagreement about whether some individuals are competent speakers. Nothing in the phenomenon of higher-order vagueness suggested such a thing, and it seems rather bizarre. Let’s call this problem the Two-Criteria Problem.57 Should an a’s being borderline-borderline F ever depend wholly on the fact that some competent speakersCS(Fa) would disagree about whether someone (who is a competent speakerFa ) is a competent speakerFa ? Should it be possible that Baldwin is borderline-borderline bald because competent judgeCS(Fa) Jude would not judge Footnote 55 continued order to be a competent speakerBLFa , a speaker needs to be competent with respect to ‘competent speakerFa ’. Hence every competent speakerBLFa is also a competent speakercompetent speaker (Fa) . 56 We assume that competent speakers—or in any case d and e in I —have basic rational skills. 2 57 Could the two criteria be unified by making the second dependent on the first? That is, by assuming

that whether someone is a CSFa would depend on how they would judge Fa? This suggestion fails. For, in Shapiro’s view, if Fa is borderline, even a CSFa could legitimately go either way in their judgement of Fa. So how they would judge Fa cannot determine whether they are competent.

123

Synthese (2011) 180:317–335

333

competent judgeFa Judy competent? That makes no sense. Either Judy is competent, whatever Jude says; then she should count just as every other competent speakerFa , regardless of what Jude thinks. Or the fact that Jude would not judge Judy competent takes somehow away from her competence; in that case, we shouldn’t want her to be criterial at all for whether Baldwin is borderline bald. Moreover, the weakened thesis (STw ) seems to allow for the unappealing possibility that there are borderline-borderline cases of F without there being borderline cases of F. Imagine that all competent speakersFa1 , competent speakersFa2 , …, competent speakersFa100 agree about Fa1 , Fa2 , … Fa100 , respectively, but that there is disagreement among competent speakersCS(Fa24) about one of the competent speakers Fa24 as to whether she is competent. Then a24 is borderline-borderline F, but neither a23, nor a24 , nor a25 is borderline F. (This is possible, however fine-grained the series a1 to an .) This clearly clashes with the phenomenon of higher-order vagueness with which Shapiro (and we) started out.58 But it seems that as long as individual cases of secondorder vagueness can turn on the vagueness of ‘competent speaker’, this possibility cannot be avoided. At this point, the most reasonable thing to conclude is that the borderline-competence of individual competent speakers should never be the decisive factor for higher-order borderlinehood.59 Given this conclusion, there are two ways in which the Two-Criteria Problem can be avoided. The first alternative: For each level (the levels of Fa, BLFa, BL2 Fa, etc.) considerations are restricted to all and only the relevant competent speakers (i.e. those with the index Fa, BLFa, BL2 Fa, etc., respectively). It is stipulated that the competent speakers are to count as part of the criterion, even if they are borderline competent.60 We then get for the first three orders: • BLFa iff, in the domain D1 of competent speakersFa there are x who judge that Fa and there are x who judge that ¬Fa. • BL2 Fa iff, given the domain D1 of competent speakersFa and the domain D2 of competent speakersBLFa , there are x in D2 who judge that in the domain D1 of competent speakersFa there are x who judge that Fa and there are x who judge that ¬Fa; and there are x in D2 who judge that it is not the case that in the domain D1 of competent speakersFa there are x who judge that Fa and there are x who judge that ¬Fa. • BL3 Fa iff, given the domains D1 of competent speakersFa , D2 of competent speakersBLFa and D3 of competent speakersBL2 F a , there are x in D3 who judge that there are x in D2 who judge that in D1 there are x who judge that Fa and there are x who judge that ¬Fa; and there are x in D2 who judge that it is not the case that in D1 there are x who judge that Fa and there are x who judge that ¬Fa and there are x in D3 who judge that it is not the case that there are x in D2 who judge that in D1 there are x who judge that Fa and there are x who judge that ¬Fa; and there are x 58 It also clashes with the result of the argument based on the child* example above, that the vagueness of ‘borderline F’ has the vagueness of ‘F’ as necessary condition. 59 Of course excepting the cases in which the predicates at issue are of the kind ‘is a competent speaker x’. a 60 Evidently, borderline competent speakers who are not competent speakers do not count. Fa Fa

123

334

Synthese (2011) 180:317–335

in D2 who judge that it is not the case that in D1 there are x who judge that Fa and there are x who judge that ¬Fa. This alternative could be justified thus: If someone is fully competent with respect to a, then that suffices for them to count as criterial, even if there is some disagreement among competent speakersCS(a) as to whether they are fully competent. This is a kind of epistemicism about speaker competence. It is possible that speakers are fully competent, despite the fact the some speakers who are fully competent with regard to them may not be able to detect that they are. Competence is then not transparent. The second alternative: It is stipulated that, if there is disagreement among the competent speakersBLa , as to whether someone is a competent speakera , then that person is to be discounted as competent speakera . The justification would be this: First, according to (15), any competent speakerBLa is also a competent speakerCS(a) . The competent speakersCS(a) are by definition the best qualified competent individuals with regard to competent speakersa . Hence, if even the best qualified competent individuals cannot agree about whether the competent speakersa are appropriate judges regarding a, then we don’t want those competent speakersa as judges for a.61 This alternative assumes the transparency of competence.62 9 Concluding remarks None of the four points Shapiro adduced in support of his thesis (ST) that—in an opentexture theory like his, at any rate— so-called higher-order vagueness is nothing but first-order vagueness in ‘competent speaker’ held up against scrutiny. (1) The quote from Williamson concerns a different theoretical point. (2) The fact that borderline red is not a colour is irrelevant to higher-order vagueness. (3) The fact that ‘borderline case’ makes reference to the judgement of competent speakers proved to be no impediment to the existence of true higher-order borderline cases. (4) Shapiro’s argument from elimination is grounded on an unsubstantiated premise and does in any case not support the reduction of higher-order vagueness to first-order vagueness necessary for proving (ST). By starting out from Shapiro’s own account of ‘borderline case’ and his own formal definition of ‘second-order borderline case’, we constructed an account of higher-order vagueness that is compositional and truly higher-order. We showed that the undesirable possibility that with this account, in some cases, higher-order borderlinehood 61 Competent speakers Fa who are borderline competent speakersFa can be excluded from being criterial

for the borderlinehood of Fa by the addition of a suitable series of conjuncts into the definiens of (6). We abbreviate ‘x is a competent speaker’ as ‘CSx’, ‘x would judge that y’ as ‘Jx(y)’: (6 ) BLFa = df [∃x[CSFa x&Jx(Fa)]&∃x[CSFa x&Jx(¬Fa)]] &[∀y[CSCS(Fa)x y → Jy(CSFa x)]v∀y[CSCS(Fa)x y → Jy(¬CSFa x)]] &[∀z[CSCS(CS(Fa)x)y z → Jz(CS(CS(Fa)x) y)] v ∀z[CSCS(Fa)x y → Jz(¬CS(CS(Fa)x) y)]] &[[∀w[CSCS(CS(CS(Fa)x)y)z w → etc....]. 62 Logically, the second alternative would favour a modal system with the S4 axiom, the first alternative

would favour a modal system without the S4 axiom. Cf. Bobzien (2010, forthcoming).

123

Synthese (2011) 180:317–335

335

may turn on the vagueness of ‘competent speaker’ can be eliminated in two ways. One’s choice would depend on whether one favours an account of higher-order vagueness with, or without, the S4-axiom. Plausible arguments were presented for either alternative. In sum, we have every reason to believe that, even with an open-texture theory of vagueness like Shapiro’s, there is true higher-order vagueness.63 Acknowledgements I thank Zoltan Gendler Szabo for helpful comments on a draft version of this paper and wish to acknowledge support from the Institute for Advanced Studies, Princeton and from the National Endowment for the Humanities.

References Bobzien, S. (2010). If it’s clear, then it’s clear that it’s clear, or is it? - Higher-order vagueness and the S4 Axiom. In K. Ierodiakonou (Ed.), Essays in Honour of Jonathan Barnes. Oxford: OUP (forthcoming). Eklund, M. (2006). Review of vagueness in context. Notre Dame Philosophy Reviews. http://ndpr.nd. edu/review.cfm?id=6624. Fine, K. (1975). Vagueness, truth and logic. Synthèse, 30, 265–300. (Reprinted in Vagueness: A reader, by R. Keefe & P. Smith, Eds., 1997, Cambridge: CUP). Glanzberg, M. (2003). Against truth-value gaps. In J. Beall (Ed.), Liars and heaps (pp. 151– 194). Oxford: OUP. Greenough, P. (2005). Higher-order vagueness. Proceedings of the Aristotelian Society, 105(Suppl), 167–190. Gross, S. (2009). Review of vagueness in context. Philosophical Review, 118, 261–266. Hyde, D. (1994). Why higher-order vagueness is a pseudo-problem. Mind, 103, 35–40. Keefe, R. (2000). Theories of vagueness. Cambridge: CUP. Keefe, R. (2007). Vagueness without context change. Mind, 116, 275–292. McGee, V., & McLaughlin, B (1995). Distinctions without a difference. Southern Journal of Philosophy, 33(Suppl), 203–251. Sainsbury, M. (1991). Is there higher-order vagueness?. Philosophical Quarterly, 41, 167–182. Shapiro, S. (2005). Context, conversation, and so-called “higher-order” vagueness. Proceedings of the Aristotelian Society, 105(Suppl), 147–165. Shapiro, S. (2006). Vagueness in context. Oxford: OUP. Soames, S. (1999). Understanding truth. New York: OUP. Sorensen, R. (2008). Semivaluationism: Putting vagueness in context in context. Philosophy and Phenomenological Research, 76, 471–483. Williamson, T. (1999). On the structure of higher-order vagueness. Mind, 108, 127–142.

63 Shapiro’s arguments are important, since they generalize to all accounts of vagueness that use some kind of qualified individuals as a criterion for borderlinehood (i.e. the majority of accounts of vagueness). Our replies generalize as well. We show this in a different paper.

123

Synthese (2011) 180:337–356 DOI 10.1007/s11229-009-9705-7

How Galileo dropped the ball and Fermat picked it up Bryan W. Roberts

Received: 14 July 2009 / Accepted: 19 November 2009 / Published online: 28 November 2009 © Springer Science+Business Media B.V. 2009

Abstract This paper introduces a little-known episode in the history of physics, in which a mathematical proof by Pierre Fermat vindicated Galileo’s characterization of freefall. The first part of the paper reviews the historical context leading up to Fermat’s proof. The second part illustrates how a physical and a mathematical insight enabled Fermat’s result, and that a simple modification would satisfy any of Fermat’s critics. The result is an illustration of how a purely theoretical argument can settle an apparently empirical debate. Keywords Foundations of physics · History of mathematics · Freefall · Acceleration · Galileo · Fermat 1 Introduction The modern textbook concept of uniform acceleration is given as a definition: it is a constant change in velocity over time. This definition is in accord with experience; for example, it correctly describes objects falling freely near the surface of the earth. However, the nature of uniform acceleration was once a mammoth foundational problem. At the birth of modern mechanics, there was neither an obvious definition nor a body of experimental data to characterize the concept. Nevertheless, the problem turned out have a theoretical solution, through a proof that one side of the debate was in contradiction with a well-known empirical fact. That proof is the subject this paper. One part was easy. Namely, it was clear that uniform acceleration is characterized by a constant change in velocity. The challenge was in answering the question, change

B. W. Roberts (B) Department of History and Philosophy of Science, University of Pittsburgh, 1017 Cathedral of Learning, Pittsburgh, PA 15260, USA e-mail: [email protected]

123

338

Synthese (2011) 180:337–356

with respect to what: distance, or time? The correct answer is time. But why isn’t it distance? And can a convincing argument be established in the absence of empirical data? The seeds of an argument were suggested in a notoriously terse passage of Galileo’s Two New Sciences. However, as modern scholars have pointed out,1 the first convincing argument was actually given by Pierre Fermat, of ‘Fermat’s last theorem’ fame. Scholars have announced scattered conclusions about Fermat’s analysis. Galluzzi calls Fermat’s proof “rigorously geometrical,” and a “deduction of the Galilean proportion of the acceleration of natural motion” (Galluzzi 2001, p. 258). Drake has said that there is “no getting around Fermat’s argument” (Drake 1989, p. 75). However, these conclusions have not only been superficial; they have often been incorrect. Fermat’s proof is not geometrical; it does not deduce any Galilean proportion; and there do seem to be clear ways to get around Fermat’s argument. I would like to correct the story of the Galileo–Fermat analysis of acceleration. This story reveals several surprising results about how a concept of empirical significance, which lies at the heart of a physical theory, can be settled through theoretical analysis alone. The four central results that I will argue for are the following: 1. The physical insight behind the analysis of acceleration was that the well-known law of constant velocity actually places restrictions on motion that is not constant. 2. The mathematical insight behind the analysis was that if velocity increases in discrete jumps, then as we scale those jumps down, the result becomes more and more like a continually increasing quantity. 3. There is an objectionable part to the Galileo–Fermat analysis, from the point of view of a critic that would reject any argument involving infinite sequences. 4. Nevertheless, a slight modification of the argument appears capable of satisfying any such critic. The result was a theoretical argument, showing that the traditional empirical characterization of freefall was in contradiction with the law of uniform velocity. The paper has two main sections. The first section sketches the background of the analysis, by recounting some key events leading up to Fermat’s proof. Here I briefly sketch the debate between two schools of freefall, as well as Galileo’s argument in response to this debate. In the second section, I’ll describe the analysis that Fermat presents. In particular, I’ll draw out a physical and a mathematical insight, and show how they enabled Fermat’s argument. Finally, I’ll point out some possible objections that Fermat’s contemporaries might have given, and illustrate a simple modification that addresses these concerns. 2 How Galileo dropped the ball Let’s begin with a little narrative. There were two competing schools of freefall in the years leading up to Fermat’s analysis: a Galilean school and a Jesuit school. The views of these schools were logically incompatible, and a curious dispute arose between 1 See especially Mahoney (1973, pp. 384–387), but also Drake (1975a, p. 360; 1975b, p. 45; 1989, p. 75).

123

Synthese (2011) 180:337–356

339

them. This dispute was exacerbated by a cryptic argument of Galileo, which suggested that the controversy could be settled by purely theoretical considerations. However, Galileo’s argument was generally thought to be incomplete and unconvincing. The following four subsections fill in the details of this story. The goal is to understand how this foundational issue arose, as a debate over two empirical characterizations of freefall. We will then be prepared to see Fermat’s proof, which shows how one of these characterizations contradicts a well-known fact.

2.1 Two schools of freefall The death of Galileo in 1642 marked the birth of a vigorous debate over the nature of freefall. The traditional position was upheld most loudly by French Jesuits. They stated that the velocity of an object in freefall is proportional to the distance fallen. More precisely, their claim was that: d2 v2 = , v1 d1

(1)

where d1 , d2 are any two distances below the point from which an object is released, and v1 , v2 are the velocities of the object at those positions.2 For ease of reference, let’s call Eq. 1 the Jesuit law of freefall. In contrast, the Galilean law of freefall maintained that velocity in freefall is proportional to time fallen: v2 t2 = , v1 t1

(2)

where t1 , t2 are any two times after the object is released, and v1 , v2 are the respective velocities at those times. The Galilean claim is equivalent to the time-squared law.3 So, Galileo’s commitment to Eq. 2 was already implicit in the Dialogue of 1632, where he famously wrote that in freefall, “the spaces passed over are to each other as the squares of the times” (Galilei 1967, p. 222). But the time-squared law apparently did not generate much controversy until 1638, when it made an explicit appearance as a logical consequence of the Galilean law (2).4 A lively debate then ensued, and lasted for nearly a decade. 2 Throughout this paper, I use equality of fractions as shorthand for the language of compound ratios. In particular, a sentence like ‘A is to B as C is to D’ will be simply written A/B = C/D. If there is any question, the reader can always substitute the original language. 3 There is an easy proof of this in modern language: let s be the distance traveled, t the time passed, and v the velocity of a body dropped from rest at t = 0. If s ∝ t 2 , then v = ds/dt ∝ 2t ∝ t. Conversely, if v ∝ t, then s = 0t tdt = t 2 /2 ∝ t 2 . 4 See Drake (1989, Chap. 7) for a discussion.

123

340

Synthese (2011) 180:337–356

2.2 Incompatibility of the two schools Marin Mersenne, a heavy-weight of French intelligentsia, applauded Galileo’s timesquared law in his 1639 notes on the Two New Sciences. He also picked up on a now-notorious suggestion of Galileo: that if the Jesuit law were true, then motion would be instantaneous. Quite a damning conclusion. But Mersenne didn’t buy it, suggesting that the Jesuit law “can nevertheless be understood in a correct way; for can we not say that the speed is greater in proportion to the greater spaces traversed?”.5 Mersenne had nailed precisely the part Galileo’s remark that seems to lack justification (more on this in Sect. 2.4). However, Mersenne’s comment also betrays some confusion. Once one has accepted the Galilean law of freefall, there is no ‘correct way’ to understand the Jesuit law, because these two laws are incompatible. One proof of this is the following. Suppose, for reductio, that both (1) v2 /v1 = d2 /d1 , and (2) v2 /v1 = t2 /t1 . Then: t2 d2 = by substituting (1) into (2) t1 d1 (t2 )2 by substituting the time-squared law. = (t1 )2 Simplifying this equation, we get the strange result that t2 = t1 . In other words, not rejecting either (1) or (2) would entail that any two distances traveled in freefall are traversed in the same amount of time. But that’s obviously false: drop any object, and observe that it reaches your knees before it reaches your ankles. So, by reductio, a view that supports (1) is incompatible with a view that supports (2). This argument is just one of innumerable other ways of illustrating this incompatibility. Of course, Mersenne was not a mathematician, and so his apparent failure to deduce this result is perhaps not surprising. But a more adept theoretician could have easily reached this conclusion. And that might explain some of the vigor with which the participants in this debate went after each other. We will now discuss one particularly vigorous such exchange, which directly inspired Fermat’s work. 2.3 Une Bataille de Pierres By the 1640’s, the disagreement between the Galilean and the Jesuit schools had developed into a lengthy published debate. Among the most hard-headed debaters were Pierre Gassendi (who supported the Galilean school of freefall), and Pierre Cazré (who upheld the Jesuit school). From 1642 to 1646, these two Pierres kept a long written correspondence of courteous defamation. It unfolded roughly as follows. 5 “neantmoins cecy se peut entendre d’une veritable façon; car pourquoy ne peut-on pas dire que la vitesse

est plus grande à proportion des plus grands espaces parcourus?” (Mersenne 1973a, p. 184).

123

Synthese (2011) 180:337–356

341

Gassendi (1642) set out to show, among many other things, that the Galilean law of freefall was a consequence of the impellent force of air, combined with the attractive force of the earth. Cazré (1645a) responded to Gassendi with a scathing criticism of the Galilean school. In this letter, Cazré described a balance experiment with which he claimed to have verified the Jesuit law. Gassendi (1646) shot back with a meticulous response to Cazré’s critique, and Cazré (1645b) replied with a counter-argument.6 And the exchange could have continued, had Gassendi not withdrawn. Part of the curiosity of the episode is that, although one might have expected a simple experiment to provide quick resolution of the controversy, such an experiment was not soon to arrive. Both Gassendi and Cazré described experiments that they claimed would allow anyone to verify their respective views. Each decried that the other’s experiments as fallacious. So, little progress was made by either Gassendi or Cazré on the empirical front. On the other hand, the problem was an excellent candidate for pure theoretical resolution. Both Gassendi and Cazré agreed about one substantive physical fact: if the velocity of a body is uniform, then d2 t1 v2 = . v1 d1 t2

(3)

This law is easy to verify experimentally. Perhaps that’s why Gassendi and Cazré managed to agree. Perhaps it was simply because this law was as old as the Physics of Aristotle, or because it enjoyed the irrefutable status of what Lakatos called the ‘hard core’ of a research program. Either way: the uniform velocity law provided a hopeful starting point for the theoretician. Any argument that assumed nothing more controversial than Eq. 3 would be sure to convince members of both schools of freefall. In what follows, we will see that this is exactly the rhetorical strategy that Fermat pursued. 2.4 Galileo’s ‘very clear proof’ Could the Jesuit law be disproven, without assuming the Galilean law? Could it be disproven without assuming anything more controversial than the uniform velocity law? (Take a moment to try this before you read on—it’s easier said than done!) Galileo seemed to think so, and provided a notorious sketch of a proof in the Two New Sciences: Sagredo: That the falling heavy body acquires force in going, the speed increasing in the ratio of the space… appear to me as propositions to be granted without repugnance or controversy. Salviati: And yet they are as false and impossible as that motion should be made instantaneously, and here is a very clear proof of it. When the speeds have the same ratio as the spaces passed or to be passed, those spaces come to be passed in 6 This debate has been discussed in detail by numerous authors; see Clark (1963), Drake (1975b), Galluzzi

(2001), and Palmerino (2002, 2004).

123

342

Synthese (2011) 180:337–356

equal times; if therefore the speeds with which the falling body passed the space of four braccia were the doubles of the speeds with which it passed the first two braccia, as one space is double the other space, then the times of those passages are equal; but for the same movable body to pass the four braccia and the two in the same time cannot take place except in instantaneous motion. (Galilei 1974, p. 160.) Salviati’s response to Sagredo would appear to stretch the meaning of ‘very clear proof.’ The second part is not so bad: if all spaces really were passed in equal times during freefall, then one might be able to conclude that freefall would be instantaneous (more on this in Sect. 3). But why should we believe that, if the Jesuit law of freefall is true, then all spaces are passed in equal times in freefall? Galileo leaves this problem to his readers. Galileo’s readers did not generally find an answer forthcoming. Marin Mersenne raised early doubts, as we have discussed above. But many modern commentators have also found themselves at a loss. Indeed, some have suggested that Salviati’s terseness is simply a “trait de plume,” or even that Galileo was committing the novice error of “applying the law of uniform motion to a motion which is not so”.7 The most compelling of all such speculations was given around 1646, with the entrance of a third Pierre into the debate. Pierre Fermat agreed that Galileo’s conclusion remained “undemonstrated,” but suggested that Galileo might actually have had a correct proof in mind.8 Fermat wrote down what he thought Galileo meant in a lengthy letter to Gassendi. At the end of the letter, Fermat implored Gassendi: “dismiss any troubles from Cazré or any other adversary of Galileo, as well as the innumerable volumes that might crop up, which by a single demonstration will be either refuted or proven useless and superfluous, by the confessions of the authors themselves”.9 It was a bold suggestion. In the next section, we’ll get to the bottom of Fermat’s argument.

3 How Fermat picked the ball up Let’s begin with a wide-angle overview of the proof. I’ll then follow through on my promise, to show how Fermat’s result hinges on a physical insight and a mathematical insight. Next, I’ll run through a step-by-step review of Fermat’s proof, in order to understand the machinery of how it works. Finally, we’ll turn to some of the objections that Fermat’s contemporaries might have given.

7 “Précisons que l’erreur de Galilée consiste à appliquer la règle des mouvements uniformes à un mouvement qui ne l’est pas” (Mersenne 1973b, p. 250). 8 Sed concedatur, si placet, viro perspicaci et Lyncaeo indemonstrata conclusio, dummodo sit vera (Fermat 1894, p. 268). 9 “ne tibi in posterum facessat negotiuim aut Cazraeus aut quivis alius Galilei adversarius, et in immensum excrescant volumina, quae unica demonstratione, vel fatentibus ipsis auctoribus, aut destruentur aut inutilia et superflua efficientur” (Fermat 1894, p. 276).

123

Synthese (2011) 180:337–356

343

Fig. 1 a A geometric sequence F A, F B, FC, . . . , set out along the path of a falling body. b Three bodies in motion: B is in freefall, while B + and B − move with constant velocity v + and v − , respectively

3.1 Fermat’s proof: a wide angle view In a debate between two incompatible empirical laws, Fermat proposed a theoretical resolution. How can such an argument be carried out? One way to do it is to show that one of the two empirical laws contradicts something that everybody accepts. This was the core of Fermat’s argument: although it’s not obvious, the Jesuit law of freefall actually contradicts the law of constant velocity.10 Here’s a wide-angle view of how the argument runs. Fermat’s proof has a two-step structure, which superficially follows Galileo’s ‘very clear proof.’ The first step shows that the Jesuits are committed to the claim that a falling body travels different distances in the same amount of time. The second step argues that as a consequence, motion in freefall occurs instantaneously. Like Galileo, Fermat takes this result to be absurd. So, he concludes by reductio that the Jesuit law of freefall is false. Both of Fermat’s two main insights went into the first part of the proof, and it’s the trickiest part of the argument. Fermat began with an arbitrary geometric sequence of segments,11 drawn along the path traveled by a falling body (Fig. 1a below). He then considered time required for a freely falling body to traverse any two consecutive lengths in the sequence, say AB and BC. Fermat was then able to prove the following: “The time for the accelerated motion through AB is therefore not less than the time for the accelerated motion through BC; but neither is it greater…; therefore it is equal”.12 In short: a freely falling body traverses each segment in the sequence in the same amount of time. The second part of the proof was comparatively easy. There, Fermat showed that the first step implies instantaneous motion. To see why, he simply noted that a finite 10 That is, that velocity is proportional to distance/time. 11 A geometric sequence is one in which the ratio of successive terms is constant. 12 Non ergo tempus motus accelerati per AB est minus tempore motus accelerati per BC; sed nec majus,

ut supra demonstratum est : ergo est aequale (Fermat 1894, p. 274).

123

344

Synthese (2011) 180:337–356

interval can contain as many segments of a (converging) geometric sequence as you want. So, if the time required to traverse each of these segments is finite and non-zero, then a freely falling object will require an arbitrarily long amount of time to traverse the entire finite interval. Fermat thus concluded that the interval is traversed in no time at all. In sum: Fermat showed that the Jesuit law of fall implies an absurd conclusion, that motion in freefall can occur instantaneously. Mahoney has given a lovely overview of Fermat’s steps, pointing out that the proof “rests on the clever use of continued proportion” (Mahoney 1973, p. 387). But one would like to dig more deeply into the machinery of Fermat’s proof. What was Fermat’s physical insight? And, if ‘continued proportions’ were his main mathematical tool, then how did he use them? Fermat’s physical insight was to use facts about uniform velocity to place upper and lower bounds on the velocity of a falling body. I call this insight physical, because it’s the only step in the argument that makes use of an empirical assumption: the law of uniform velocity. Fermat’s mathematical insight was, as Mahoney suggests, to make use of continued proportions, known today as geometric sequences. In particular, Fermat used facts about these sequences to ‘tighten’ his upper and lower bounds on the velocity of a falling body. Indeed, the tighter these bounds were made, the closer they got to approximating the continuous acceleration of a falling body. The details of these techniques are the subject of the next two subsections. 3.2 Physical insight Fermat’s central physical insight is easy to overlook, buried deep in lengthy mathematical prose. Even worse, Fermat introduces the upper and lower bounds at different points in the proof, and does so with very little discussion. So, let’s begin with a clearer illustration of the basic idea. Fermat considers a vertically standing segment A R of length d, with R toward the top. Suppose that a body B is dropped somewhere above A R, accelerates downward in freefall, and traverses A R in a certain time t. Let’s say that B has initial velocity v − when it gets to R. We’ll say it has final velocity v + by the time it gets down to A. Next, Fermat asks us to consider the “imaginary motions”13 of two more bodies, B − and B + . Neither of these two bodies are in freefall. Instead, Fermat takes that initial velocity v − , and imagines the body B − moving with constant velocity v − across A R. Let’s say that B − traverses A R in time t − . Similarly, Fermat takes the final velocity v + , and imagines the body B + moving with uniform velocity v + . Let’s say it traverses A R in time t + . The situation is illustrated in Fig. 1b above. The interesting fact about this construction, Fermat says, is that “the time [t] for the accelerated motion through A R is less than the time [t − ] for the uniform motion through A R with the velocity at R [v − ]”.14 This provides him with an upper bound 13 motus fictitii (Fermat 1894, p. 272). 14 Sed tempus motus accelerati per A R est minus tempore motus per A R uniformis juxta velocitatem in

R (Fermat 1894, p. 271).

123

Synthese (2011) 180:337–356

345

on the time t for the accelerated body B to cross the segment. Similarly, he concludes that the time for the accelerated motion “is greater than”15 the time t + . This provides him with a lower bound. In summary: t + ≤ t ≤ t −.

(4)

This simple insight is the key to Fermat’s result. He has in effect taken a quantity that people disagreed about (time elapsed in accelerated freefall), and bounded it using quantities that everyone agreed about (time elapsed in uniform motion). Notably, this strategy is much in the spirit of the Archimedean double-reductio, which often sought to calculate controversial quantities like areas under curves, by bounding them with more tractable shapes like rectangles (Archimedes 1912, pp. 251–252). Let’s now take this a step further. The bounds stated in Eq. 4 certainly make intuitive sense. But suppose an objector were to challenge these inequalities. Could any further justification be given? Curiously, Fermat suggests the further justification is that “by the hypothesis, the velocity would continually increase from R to A”.16 What does Fermat mean here? I suggest we adopt two interpretive views of Fermat’s claim. First, let’s assume Fermat is using “the hypothesis” in the same way that he uses it throughout proof: to refer to the reductio hypothesis, the Jesuit account of freefall. Second, let’s take the phrase “continually increase” [crescat] to mean increase whenever distance and time increase. (This is similar to what we now call a monotonic increase). These two interpretations are certainly plausible. But they are also fruitful, in that they allow us take Fermat’s suggestion seriously, and deduce Eq. 4 from the Jesuit law of freefall. This derivation can be carried out in two steps. First, let’s see how Fermat can get ‘continually increase’ from the Jesuit law. We can take the ‘increasing’ part for granted, since no one believed that an object slows down once released into freefall. More interestingly, observe that the Jesuit law of freefall d2 v2 = , v1 d1 implies immediately that if d1 < d2 , then v1 < v2 . So the Jesuit law does indeed come with an assumption of monotonicity or ‘continual increase’ built in. Next, consider what a ‘continual increase’ means in the example of three bodies in motion (B, B + and B − ). All three of these bodies are imagined to traverse a particular, vertically oriented segment of length d. They arrive at the top of the segment at the same time (let’s say t0 = 0), and proceed to move down it. In particular, B, B + and B − traverse the segment in times t, t + and t − , respectively. Their motions are illustrated in Fig. 2. 15 est majus (Fermat 1894, p. 274). 16 cum enim a puncto R usque ad punctum A perpetuo, ex hypothesi, velocitas crescat (Fermat 1894,

p. 271).

123

346

Synthese (2011) 180:337–356

Fig. 2 If the velocity of B increases monotonically, then the requirement that the areas under these three curves be equal guarantees that t + < t < t −

Now, the path of the falling body B can be drawn almost arbitrarily, since we know little about how its velocity is changing. However, we do know that its velocity will ‘continually increase’ over distance and time. However, each of the three bodies travel the same distance d. So, no matter how much time each one requires to make the trip, they will all have the same area under the curve (as illustrated). Given this constraint, it’s easy to deduce the bounds given by Eq. 4 from Fig. 2. If t + were any greater than t, then the area under B + would be greater than the area under B. That’s impossible, so t + ≤ t. Similarly, t − < t is only possible if the area under B is greater than the area under B − . So it must be that t − > t. These graphs offer a convenient way to illustrate how the bounds in Eq. 4 follow from the Jesuit law, as Fermat suggested. However, one must remember that this is almost certainly not the way that Fermat made the argument. (For example, it is unlikely that he thought of distance as area under a curve.) On the other hand, one can check that an isomorphic argument is available using only simple algebra.17 So although Fermat left us sparingly little to work with, this reconstruction may offer a glimpse into the kind of argument he had in mind. Fermat’s physical insight, in summary, is that bodies moving with constant velocity can provide upper and lower bounds on the time that elapses during accelerated freefall. These bounds make intuitive sense, but they also follow directly from the Jesuit law (and, incidentally, from the Galilean law as well). So the force of this insight would have been felt by both schools of freefall. Of course, to get a more precise fix on the time t of the freely falling body, one would like to squeeze these upper and lower bounds as close together as possible. Fermat chose to do this using a mathematical construction of which he was a master: the method of constant proportions. Fermat’s use of this construction is the subject of the next section. 17 Define v¯ := d/t, the average velocity of the falling body on the interval. Since v is continually increasing, v − ≤ v¯ ≤ v + . Therefore, d/t − ≤ d/t ≤ d/t + , which implies that t + ≤ t ≤ t − .

123

Synthese (2011) 180:337–356

347

3.3 Mathematical insight Recall again the Jesuit law of freefall: for a falling body that begins at rest, d2 v2 = . v1 d1

(5)

This claim is formulated in terms of ratios. So, in order to apply Fermat’s upper and lower bounds on time in freefall, the bounds constructed in the discussion above must also be formulated as ratios. This is achieved by simple division. If t1 and t2 are the times a falling body takes to travel two respective distances d1 and d2 , then it follows from Eq. 4 that t2+ t1−

≤

t− t2 ≤ 2+ . t1 t1

By the uniform velocity law, this in turn implies that d2 v1− t2 d2 v1+ ≤ ≤ . d1 v2+ t1 d1 v2−

(6)

But there is a problem. Equation 5 is supposed to hold for a falling body that begins at rest, v − = 0 (remember, v − is the minimum velocity of the falling body on a given interval). In this case, (6) implies the trivial result that 0≤

t2 ≤ ∞. t1

(7)

These bounds are not very informative; they are in a sense ‘infinitely wide.’ Fermat’s strategy is thus to ‘tighten’ them as much as possible, through the clever manipulation of geometric sequences. Here is the mathematical trick that is the basis for this strategy. Consider a body that falls from rest at a point F, down to a point A. Divide this interval F A up into segments by marking off the points B through E, such that the sequence F A, F B, FC, . . .

(8)

is set out in constant proportion. Following (Euclid 1956, books XIII–IX), a sequence is in constant proportion if the ratio of any two consecutive terms in the sequence is fixed (i.e., the sequence is geometric). Fermat draws particular attention to one property that the elements of such a sequence share: “their differences will be in the same ratio”.18 What he means is that for any two terms in the sequence, say F A and F B, 18 earum intervalla erunt in eadem ratione (Fermat 1894, p. 268).

123

348

Synthese (2011) 180:337–356

Fig. 3 A geometric sequence F A, F B, FC, . . . , has a corresponding ‘scaled-down sequence’ AB, BC, C D, . . .

FA FA − FB BA = = FB F B − FC CB

(9)

Fermat states this claim without argument, but it has a simple proof.19 This property is evidently important to Fermat, as it is the only mathematical fact that he sets apart as a separate proposition in his letter. Indeed, it’s really the mathematical heart of Fermat’s proof. The fact allows Fermat to construct a new, finer geometric sequence, B A, C B, DC, . . . , which by Eq. 9 is in the same constant proportion as the original sequence. The construction is illustrated in Fig. 3. Here are the two reasons it’s so important in Fermat’s argument. First, a falling body that begins at F has non-zero velocity on every segment of this construction. So, since v − = 0 on the segments, we’ll get finite (instead of ‘infinitely wide’) bounds on the time it takes a body to fall across them. Indeed, as we’ll see in the next subsection, if we imagine a body with constant velocity that increases in discrete ‘jumps,’ then we can get bounds on this time that are as tight as we want. 19 Suppose a /b = a /b = · · · = a /b . Then for any i, a b = b a . Summing over i, it follows that n n n i n i 1 1 2 2

nbn (a1 + a2 + · · · + an ) = nan (b1 + b2 + · · · + bn ). Therefore, for any i, an ai a1 + a2 + · · · + an = = . b1 + b2 + · · · + bn bn bi

123

(10)

Synthese (2011) 180:337–356

349

Second, this new construction is nothing more than a scaled-down copy of the original.20 It is the combination of this fact with the Jesuit law of freefall that is the central step in Fermat’s reductio. Fermat calls his construction as a “sub-proportion”.21 But for our purposes, it is more appropriate to call it the scaled-down sequence with respect to the original. The significance of this is that we can substitute the ratio of two segments of a geometric series interchangeably with the segments of a scaled-down sequence, since scaled-down sequences preserve ratios of terms. To recap: in the last subsection, I claimed that Fermat’s physical insight was to set particular bounds on the time it takes a freely falling body to traverse an interval. I’ve now suggested that his mathematical insight was to construct a scaled-down sequence along that interval, in order to tighten the bounds. It’s now time to see precisely how these insights work together in Fermat’s proof.

3.4 The first step: equal times Fermat begins by asking us to imagine a body released at a point F, which accelerates in freefall down to a point A. As described above, Fermat constructs a sequence F A, F B, FC, . . . in constant proportion along the path of this falling body. He states his goal: “We will demonstrate first that the spaces C B, B A are traversed in the same time, given the supposition [i.e., the Jesuit law] about their motion”.22 In other words, Fermat will deduce in this first step that the Jesuit law implies that tB A = 1. tC B This step makes use of an Archimedean double-reductio. Fermat first shows that t B A /tC B > 1, and then shows that t AB /t BC < 1. Since both halves of the reductio follow exactly the same steps, let’s just review the first half. Suppose, for the purposes of reductio, that t B A /tC B > 1. Fermat begins by embedding the original sequence F A, F B, FC . . ., in a new sequence F A, F R, F M, . . ., as shown in Fig. 4. Call the ratio of consecutive terms in the new sequence ρ (= F A/F R). Then since ρ can be made arbitrarily close to 1, the sequence can always be constructed so as to have the property that

1<ρ<

tB A . tC B

(11)

20 Just take any geometric sequence ak i ; Fermat’s new sequence ak i − ak i−1  = (1 − 1/k)ak i  is just

the original sequence scaled by a factor of (1 − 1/k).

21 proportio sub (Fermat 1894, p. 270). 22 Demonstrabimus primo spatia C B, B A eodem tempore in supposito motu percurri (Fermat 1894, p.

269).

123

350

Synthese (2011) 180:337–356

Fig. 4 A body falls from F to A. The segments A R, R M, M N , . . . form a geometric sequence, of which AB, BC, C D, . . . is a subsequence

Fermat remarks, “Who doesn’t see that this will indeed occur out of necessity, even from a single term, this operation having been iterated as often as need be?”23 —but he does not prove the claim.24 That’s the basic construction. Now, here’s the trick. We’ve constructed a new sequence of segments, with the ratio of consecutive segments ρ < t B A /tC B . But as we discussed above, Fermat had the physical insight to see that the law of uniform velocity restricts the fraction on the right. In particular, we know that t− tB A < B+A . tC B tC B

(12)

Fermat’s trick is to show that, if the Jesuit law is true, then the right side of the inequality is less than ρ. This would imply the left side of the inequality is also less than ρ. And that contradicts Eq. 11, completing the reductio. So, how does Fermat get this result out of the Jesuit law? Recall our notation from + the previous sections: v − I and v I are the minimum and maximum velocities of a falling − body on an interval I . And t I and t I+ are the times that would be required for bodies + traveling with uniform velocity v − I and v I to traverse the interval. Then Fermat’s argument can be summarized: t R−A

+ tO B

= = = = =

R A v+ OB (by the uniform velocity law) O B v− RA R A vB (by definition of v + and v − ) O B vR F A vB (substituting the ‘scaled-down’ sequence) F B vR FA FB (by the Jesuit law of freefall) FB FR FA = ρ (by the definition of ρ). FR

23 quod quidem necessario eventurum, vel ex sola mediae inventione ejusque iterata, quoties opus fuerit, operatione, quis non videt? (Fermat 1894, p. 270). 24 However, Fermat’s remark does suggest a simple proof. We must show that any geometric sequence ak i  can be embedded in a finer sequence ah i , with the ratio of consecutive terms ρ = ah n+1 /ah n = |h| as close to 1 as we like. But ak i  can be embedded in any sequence ah i , as long as h = k 1/n . So we can just check, for a given n, if |h| is small enough. If it’s not, then we can increase n, which has the effect make h closer to 1. Therefore, by iterating this procedure ‘as often as need be,’ we can make |h| be as close to 1 as we like, and thus less than t B A /tC B .

123

Synthese (2011) 180:337–356

351

But then, as Fermat observes, “the time for the accelerated motion through A R is less than the time [t R−A ] for the uniform motion through A R with the velocity at 25 A similar upper bound can be placed on the time for the accelerated R [v − R A ]”. motion through each of the other intervals. Therefore, Fermat concludes, t R−A + · · · + t B−N tB A < + . tC B t O B + · · · + tC+X

(13)

In effect, Fermat has shown how uniform acceleration across an interval is bounded from above, by uniform motion that increases in discrete ‘jumps’ across each of the intervals R A, M R. . .. It follows immediately that since each t − /t + is equal to ρ, t R−A + · · · + t B−N

+ + tO B + · · · + tC X

= ρ.

But, combining this result with Eq. 13, we have now shown that tB A ≤ ρ. tC B That contradicts Eq. 11. So by reductio, t B A /tC B > 1. Exactly the same kind of argument can be used to complete the other horn of the reductio, and show that t B A /tC B < 1. Thus, we have by double-reductio that t B A = tC B . Indeed, this argument can be made for any pair of consecutive intervals in the sequence, B A, C B, DC, . . .. So, Fermat concludes, as a body falls freely from F to A, the Jesuit law implies that “each and every one of the spaces is traversed in the same time”.26 3.5 The second step: instantaneous motion Fermat’s second step is comparatively easy. Here, one simply shows that the above conclusion leads to an absurdity: that motion in freefall is instantaneous. Fermat begins by imagining a body falling from rest at a point A down to a point H , and then continuing further down to a point K (Fig. 5). We are instructed to assume, for the purposes of reductio, that this motion “does not in fact occur instantaneously,” but that it “will require a certain definite time”.27 Then there is some integer n such that (n)t H K > t AH .

(14)

25 Sed tempus motus accelerati per A R est minus tempore motus per A R uniformis juxta velocitatem in

R (Fermat 1894, p. 271). 26 omnia omnino spatia eodem tempore percurri (Fermat 1894, p. 275). 27 Si enim motus per H K non fiat in instanti, fiet in tempore aliquo determinato (Fermat 1894, p. 275).

123

352

Synthese (2011) 180:337–356

Fig. 5 A body at rest at A falls down to a point K . The sequence K H , H G, G F is a geometric sequence that converges before getting to A

As before, Fermat now constructs a geometric sequence in which the first term is K H , the second term is H G, and so on. But this time, he must suppose in addition that the first n + 1 segments of the series H G + G F + F E + · · · sum to less than the length of H A (where Fermat has assumed the fact discovered by Archimedes that a geometric series can converge). Now, by the first step of Fermat’s proof, the falling body takes the same amount of time to traverse these n + 1 of these segments. So if H B is the union of the n + 1 segments, then the time it takes the falling body to traverse all of them is t H B = (n + 1)t H K .

(15)

Substituting Eq. 15 into 14, we now get that n tH B > tH A ⇒ tH B > tH A. n+1 Fermat thus writes that, “a fortiori, the time of the motion through H B is greater than the time of the motion through all of H A, which is absurd”.28 Having produced an absurdity, Fermat now finally rejects the reductio hypothesis, and infers that the Jesuit law implies that freefall occurs instantaneously. He concludes: “Thus, the assertion of Galileo is true, even though he did not himself demonstrate it”.29 3.6 Objections Drake wrote that “There is no getting around Fermat’s argument in support of Galileo’s position” (Drake 1989, p. 75). That is certainly correct from a modern perspective, since we now know that Galileo was right and the Jesuits were wrong. But from a more historically sensitive perspective, Drake’s conclusion here is a bit too hasty. Fermat deduced an absurdity, as Galileo indicated was possible, by assuming (i) the Jesuit law of freefall; (ii) the law of uniform velocity; and (iii) the validity of a set of mathematical techniques. By reductio, one of these assumptions must be rejected. Fermat chose to reject the Jesuit law. But an objector might just as well reject one of his other assumptions, and thus ‘get around’ Fermat’s purported vindication of the Galilean school. But would any of Galileo’s contemporaries have been willing to reject one of these assumptions? I will argue in defense of Drake, that although there are ways to get around Fermat’s result, none of them are reasonable options for any of Fermat’s contemporaries. 28 ergo a fortiori tempus motus per H B tempore motus per totam H A est majus. Quod est absurdum (Fermat 1894, p. 275). 29 Ergo vera remanet Galilei illatio quamvis eam ipse non demonstrarit (Fermat 1894, p. 276).

123

Synthese (2011) 180:337–356

353

The law of uniform velocity was simply too well established in Fermat’s time to have been objectionable to anyone. So the only real target available to an objector was option (iii), Fermat’s mathematical techniques. Of course, most of these techniques were Euclidean and uncontroversial. But Fermat might have heard some complaints about what appears to be ‘infinitary reasoning’ in his argument. In the seventeenth century, the many methods of ‘indivisibles’ and of ‘infinitesimals’ were only just beginning to be understood. They were often viewed with distrust, as these methods appeared to be wrought with paradoxes. Galileo himself, even in his later work, urged caution in considerations of the infinite, when “paradoxes are at hand” (Galilei 1974, p. 28). These were matters of serious concern to potential objectors, and so there are at least two parts of Fermat’s proof that might have been deemed worrisome. The first worry, I think, is a clear red herring; it only superficially appears to deal with the infinite. The second worry is less superficial; however, I argue that an easy modification of Fermat’s argument would have been accepted even by mathematical conservatives. The first worry comes in Fermat’s conclusion to his first step. Here, Fermat writes, the time for the accelerated motion through C D is equal to the time for the accelerated motion through AB, and to the time for the accelerated motion through BC, and continuing the reasoning, if desired, to the infinite, each and every [omnia omino] one of the spaces is traversed in the same time.30 While the language ‘omnia omnino’ might have sent up warning flags for some critics of ‘infinite quantities,’ Fermat never actually uses this claim about the infinite in any quantitative way. Recall that this claim only gets used in the second step, when Fermat picks out n +1 segments in a geometric sequence (where n is finite), and concludes that they are all traversed in the same amount of time. Thus, although Fermat’s language here is suggestive of infinity, his reasoning is not. The second worry is somewhat more interesting. This is about the assumption that a geometric series can converge. Fermat assumes here that, given any finite interval AK , a geometric sequence exists that begins with a particular segment H K , and can be continued through arbitrarily many terms without every reaching A (as in Fig. 5 above). Fermat does not explain why this assumption should be true. So it appears that an objector is free to complain that Fermat is making illegitimate use of infinitary reasoning: he has claimed that a particular, infinite geometric sequence can occupy a finite length. However, there are two responses available to Fermat. First, infinite geometric sequences would hardly have constituted ‘fringe’ calculations using infinity. Indeed, the notion of a convergent geometric series played a central role in Archimedes’s well-known letter on the quadrature of the parabola (Archimedes 1912, Proposition 23–24). So this objection would perhaps only have held sway among extreme mathematical conservatives. But in fact, Fermat’s position was even stronger. Even if Fermat grants this worry, there appears to be an easy modification of Fermat’s proof that avoids this ‘infinitary 30 Eadem ratione patet tempus motus accelerati per CD aequari tempori motus accelerati per AB, et tempori motus accelerati per BC, et, continuatis, si placet, in infinitum rationibus, omnia omnino spatia eodem tempore percurri (Fermat 1894, p. 275).

123

354

Synthese (2011) 180:337–356

assumption’ altogether. Go back to end of the first step, in which Fermat showed that a falling body takes the same amount of time to traverse any two lengths in a geometric sequence. One immediate consequence is that any two lengths at all are traversed in the same amount of time in freefall. To see why, let a1 be an arbitrary length, which is the first element in some geometric sequence. Any two segments in this sequence are traversed in the same amount of time, according to Fermat’s first step. Moreover, all the elements are determined as soon as we choose a2 . But a2 can be any arbitrary length. Therefore, any arbitrary length is traversed in the same amount of time as a1 . So, since a1 was also chosen arbitrarily, any two lengths are traversed by a falling body in the same amount of time. Now, in particular, we can conclude that any two halves of a unit segment are traversed in the same amount of time as the segment itself. Therefore, 2t = t, a contradiction. This argument is obviously much easier than the one that Fermat actually gives in his second step. Furthermore, it seems to avoid any possible worries about infinitary reasoning. I can only speculate that Fermat took a more complicated route because he wanted to do more than disprove the Jesuit law: he wanted to prove Galileo’s suggestion down to the very letter. Thus, it seems that Drake was almost correct. There appears to be just one serious objection that could have been leveled against Fermat’s construction of a convergent geometric series. But as it turns out, that part of the argument could have been avoided altogether. So the would-be objector to Fermat’s result would not have gotten very far.

4 Conclusion The debate between the Jesuit and the Galilean schools of freefall was eventually settled empirically, as Newtonian mechanics began to amass evidence at the end of the seventeenth century.31 But remarkably, Fermat managed to produce solid evidence in favor of the Galileans, independently of any empirical discovery, by proving that the Jesuit account was inconsistent. We have now seen that this unlikely result required only a very simple insight into the physics of falling bodies, together with some very clever mathematical techniques. It is only unfortunate that the density of Fermat’s argument seems to have prevented it from drawing much commentary. Gassendi, the original recipient of Fermat’s letter, never responded to Fermat’s argument in print. Fermat apparently made no efforts to further publicize his work. And so Fermat’s contemporaries, as well as modern scholars, seem to have largely ignored this curious little argument. This kind of historical episode suggests some care be taken in our philosophical accounts of confirmation and theory change. Certainly, a picture in which empirical claims are measured only by their ability problem-solve or determine research agendas

31 It’s not clear precisely when the Galilean law of freefall definitively gained widespread acceptance. While still controversial in the 1640s, it was treated as an established fact in the (1673) Horologium of Huygens. Understanding the evaporation of the conflict over this 30-year period appears to be an open project for investigation.

123

Synthese (2011) 180:337–356

355

would be too blunt.32 As we have seen, Fermat’s refutation of the Jesuit law followed a different strategy. Fermat’s proof made a connection that wasn’t obvious: that the Jesuit characterization of freefall contradicts the law of uniform velocity. This theoretical solution was enough to settle an empirical debate—a result that I hope both historians and philosophers of science might find of interest. Acknowledgements I would like to thank Paolo Palmieri for many stimulating discussions during the development of this work.

References Archimedes. (1912). The works of Archimedes. New York: Dover. Cazré, P. (1645a). Physica demonstratio qua ratio, mensura, modus ac potentia accelerationis motus in naturali descensu gravium determinantur, adversus nuper excogitatam a Galilaeo Galilaei Florentino philosopho ac mathematico de eodem motu pseudoscientiam. Ad clarisimum virum Petrum Gassendum Cathedralis Ecclesiae diniensis praepositum dignissimum. Paris: J. du Brueil. Cazré, P. (1645b). Vindiciae demonstrationis physicae de proportione qua gravia decidentia accelerantur. Paris: Ad clarissimum D. Petrum Gassendum Cathedralis Ecclesiae diniensis praepositum dignissimum. G. Leblanc. Clark, J. (1963). Pierre Gassendi and the physics of Galileo. Isis, 53, 352–370. Drake, S. (1975a). Free fall from Albert of Saxony to honoré Fabri. Studies in History and Philosophy of Science, 5, 347–366. Drake, S. (1975b). Impetus theory reappraised. Journal of the History of Ideas, 36, 27–46. Drake, S. (1989). History of freefall (Chap. 7). Toronto: Wall and Emerson Inc. Euclid. (1956). The thirteen books of the elements (Vol. 2). New York: Dover Publications Inc. Fermat, P. (1894). Fermat a Gassendi (1646?). In P. Tannery & C. Henry (Eds.), Oeuvres de Fermat (Vol. 2, pp. 267–276). Paris: Gauthier-Villars et Fils. Galilei, G. (1967). Dialogue concerning the two chief world systems (2nd revised edition). Berkeley and Los Angeles: University of California Press. Galilei, G. (1974). Two new sciences. Madison: University of Wisconsin Press. Galluzzi, P. (2001). Gassendi and l’Affaire Galilée of the Laws of motion. In J. Renn (Ed.), Galileo in context (pp. 239–275). New York: Cambridge University Press. Gassendi, P. (1642). De motu impresso a motore translato: Epistolae duae in quibus aliquot praecipuae, tum de motu universe, tum speciatim de motu terrae attributo, difficultates explicantur. Paris: V. de Lanville. Gassendi, P. (1646). De proportione qua gravia decidentia accelerantur: Epistolae tres quibus ad totidem epistolas R. P. Cazraei, Societatis Iesu, respondetur. Paris: L. de Heuqueville. Huygens, C. (1673). Horologium oscillatorium sive de motu pendulorum ad horologia aptato demonstrationes geometricae. Paris: Apud F. Muguet. Lakatos, I. (1968). Criticism and the methodology of scientific research programmes. Proceedings of the Aristotelian Society, 69, 149–186. Laudan, L. (1981). A problem-solving approach to scientific progress. In I. Hacking (Ed.), Scientific revolutions (Chap. vii, pp. 144–155). Oxford: Oxford University Press. Mahoney, M. S. (1973). The Mathematical Career of Pierre de Fermat, 1601–1655 (2nd ed.). Princeton: Princeton University Press. Mersenne, M. (1973a). Les nouvelles pensées de Galilée, mathématicien et ingénieur (Vol. 1, critical edition). Paris: J. Vrin. Mersenne, M. (1973b). Les nouvelles pensées de Galilée, mathématicien et ingénieur (Vol. 2, critical edition). Paris: J. Vrin.

32 In particular, the Fermat–Galileo episode may require a more refined development of Lakatos (1968) ‘research programmes,’ or Laudan (1981) ‘research traditions,’ although a more detailed discussion lies outside the scope of this paper. Thanks to an anonymous referee for suggesting this avenue of research.

123

356

Synthese (2011) 180:337–356

Palmerino, C. R. (2002). Two Jesuit responses to Galilei’s science of motion: Honoré Fabri and Pierre Le Cazre. In M. Feingold (Ed.), The new science and Jesuit science seventeenth century perspectives, No. 6 in New studies in the history and philosophy of science and technology. (pp. 187–227). Dordrecht: Kluwer. Palmerino, C. R. (2004). Galileo’s theories of free fall and projectile motion as interpreted by Pierre Gassendi. In C. R. Palmerino & J. M. M. H. Thijssen (Eds.), The reception of the Galilean science of motion in seventeenth-century Europe, No. 239 in Boston Studies in the Philosophy of Science (pp. 137–164). Dordrecht: Kluwer.

123

Synthese (2011) 180:357–389 DOI 10.1007/s11229-009-9707-5

A role for abstractionism in a direct realist foundationalism Benjamin Bayer

Received: 30 June 2009 / Accepted: 24 November 2009 / Published online: 10 December 2009 © Springer Science+Business Media B.V. 2009

Abstract Both traditional and naturalistic epistemologists have long assumed that the examination of human psychology has no relevance to the prescriptive goal of traditional epistemology, that of providing first-person guidance in determining the truth. Contrary to both, I apply insights about the psychology of human perception and concept-formation to a very traditional epistemological project: the foundationalist approach to the epistemic regress problem. I argue that direct realism about perception can help solve the regress problem and support a foundationalist account of justification, but only if it is supplemented by an abstractionist theory of concept-formation, the view that it is possible to abstract concepts directly from the empirically given. Critics of direct realism like Laurence BonJour are correct that an account of direct perception by itself does not provide an adequate account of justification. However a direct realist account of perception can inform the needed theory of concept-formation, and leading critics of abstractionism like McDowell and Sellars, direct realists about perception themselves, fail to appreciate the ways in which their own views about perception help fill gaps in earlier accounts of abstractionism. Recognizing this undercuts both their objections to abstractionism and (therefore) their objections to foundationalism. Keywords Epistemology · Justification · Epistemic regress problem · Foundationalism · Direct realism · Abstractionism · Internalism

B. Bayer (B) Colorado College, Colorado Springs, CO, USA e-mail: [email protected]

123

358

Synthese (2011) 180:357–389

1 Introduction The epistemic regress problem challenges us to reconcile the requirement that our beliefs be justified with the widely accepted conviction that we do not have an infinite series of reasons justifying these beliefs. It is this problem that usually motivates a foundationalist account of justification, which holds that we should, in principle, expect some beliefs to be basic, in need of no justification of their own. But foundationalism’s solution to the regress problem is anything but uncontroversial. In this paper I propose that a novel and compelling defense of foundationalism is possible if we draw on appropriate accounts of human perception and concept-formation which help characterize the nature of basic beliefs. This proposal is novel because most epistemologists, traditionally, do not regard psychological facts as relevant to their discipline. But I think this material is relevant, and much of this paper will be an effort to show how it is. Fundamental to the solution I will propose is a direct realist account of perception. According to direct realism, perception is direct insofar as (a) it involves no awareness of mental intermediaries, and (b) it does not provide justification for our beliefs through a (conscious or subconscious) process of inference from the awareness of these intermediate objects (BonJour 2007).1 “Indirect” accounts of perception, by contrast, have included the classical sense data theory as well as other more recent representationalist theories. I will draw on a theory of direct perception that is realist insofar as the objects of perception are taken to be ordinary mind-independent physical objects, as opposed to sensory qualities or properties of objects.2 Because direct realism describes perception as a direct form of awareness of these objects, it should be seen as an ideal source of support for a foundationalist account of basic beliefs. Direct realism can explain why basic beliefs count as basic, by reference to their relationship to perceptual states which do not themselves require inferential justification. In combining direct realism with foundationalism, I am in something of a philosophical minority. While many epistemologists have claimed that there are sensory foundations for human knowledge, usually their accounts of the nature of sensory perception involve indirect realist positions about perception (Schlick 1959; Moser 1985; Fumerton 1995). The most prominent direct realists about perception, on the other hand, usually propose reliabilist or other non-foundationalist approaches to justification (Reid 1969/1785; McDowell 1996; Alston 1999; Schantz 2001). A few brave philosophers combine these positions in the way I propose (Huemer 2001; Porter 2006), but even in these cases, their account of direct perception will differ from mine in important ways. In particular, I argue that the most plausible case for foundationalism 1 The “mental intermediaries,” the primary awareness of which direct realism rejects could be sense data, or adverbial contents, or other information-theoretic representations. Note that the direct realist need not reject the possibility of the awareness of mental intermediaries, only the claim that awareness of them is necessary to perceive the external world in the ordinary way. It may be that while we require no awareness of intermediaries to be aware of the external world in the first place, we can engage in reductive phenomenological focus and become aware of our states of consciousness only after we are first aware of the world. 2 In this paper I will leave unexamined questions about what counts as a “physical object,” and assume, for my purposes, that it includes other perceivable occurrences that fall into the same epistemic category as paradigmatic objects, things such as rainbows, shadows, etc.

123

Synthese (2011) 180:357–389

359

can be advanced by assuming that the content of perception is non-conceptual and also non-representational (which means, in this context, that it is not the kind of content that can be either true or false). Conceived in this way, direct realist foundationalism has only a few obscure allies (e.g., Kelley 1986). Part of the reason direct realism and foundationalism are not usually seen as requiring each other is that critics argue that even if direct realism’s portrait of perception is correct, it does not imply foundationalism or any other theory of justification. I will argue that direct realism about perception does provide auxiliary support for a foundationalist account of justification, but only in conjunction with a particular theory of how concepts can be formed from non-conceptual awareness. As critics rightly point out, an account of perceptual awareness alone does not imply an account of epistemic justification, because it is our conceptual awareness, held in propositional form, which is in need of justification. A complete account of justification must consider both the nature of perceptual awareness and of conceptual awareness, as well as their relationship to each other. As we shall also see, accounts of concept-formation are themselves inadequate to the task of providing an account of foundational justification unless they are informed by a direct realist view of perception. By providing an account that demonstrates how a theory of perception informs the requisite theory of concepts, I answer critics who say that direct realism does nothing to support a theory of justification. In order to show how theories of perception and concepts are relevant to a theory of justification, I begin, in the section that follows, by describing the basic outlines of the epistemic regress problem, and the issue at stake between foundationalist and antifoundationalist theories concerning the regress problem. The issue is whether we can make sense of a basic form of awareness that justifies our knowledge without needing justification of its own. I then outline the anti-foundationalist’s most prominent reason for thinking we cannot make sense of epistemically basic beliefs: the view that the existence of a regress-halting basic form of awareness would be incompatible with the fact that human knowledge requires a kind of reflective epistemic perspective. Subsequently, I argue that viewing justification as justifiable concept-application allows one to see how there is an epistemically basic form of awareness that can explain the justifiable origin of both the content of our beliefs and our reflective perspective on them. In my final section, I note with critics of foundationalism that this form of basic awareness makes sense as such only if it is possible to abstract basic concepts from perception, but I criticize their arguments against its possibility. In the end, I suggest that the most prominent critiques of this “abstractionist” view of concepts fail to realize how a direct realist account of perception improves the case for abstractionism, insofar as it enriches our understanding of the data from which concepts are abstracted, and helps clarify which concepts count as basic in relation to this data. Showing how an appropriate theory of perception and of concepts underpins a foundationalist theory of justification will have the incidental effect of challenging an old shibboleth among epistemologists. Philosophers of many stripes have long maintained that facts about human psychology are largely irrelevant to traditional questions in normative epistemology about the justification of our beliefs. Traditionalists insist that facts about the causes of our beliefs are not relevant to an account of how our beliefs ought to be formed. Modern naturalistic epistemologists do see human psychology

123

360

Synthese (2011) 180:357–389

as relevant to their project, but they produce accounts of knowledge and justification which depart significantly from the normative epistemological tradition. Externalist reliabilists like Goldman (1979) and naturalistic pragmatists like Quine (1969a) have, in one way or another, abandoned Descartes’ and Locke’s original goal of presenting an account of epistemic normativity that offers the individual believer prescriptive guidance in the formation of beliefs. On my account, however, a view of epistemic normativity more in keeping with the goals of Descartes and Locke ignores facts of human psychology at its peril. Attention to basic facts about the nature of our cognitive processes can indeed bear on a guidance-oriented account of epistemic norms.3 But my point about the relationship between psychology and epistemology is not the main focus here. I am primarily interested in presenting a solution to a traditional problem about justification, the epistemic regress problem. It just so happens that my solution provides an object lesson in the relevance of psychology to epistemology. 2 Direct realism and the epistemic regress problem Cling (2007) aptly summarizes the epistemic regress problem by characterizing it in terms of an inconsistent triad of propositions concerning epistemic support. (In Cling’s terminology, an “S-ordered sequence” is a sequence of propositions every member of which is supported by its successor4 ): (1) Reasons are supported. Only supported propositions provide support. (2) No Proposition is Supported only by Endless Regresses. Propositions supported only by endless S-ordered sequences are unsupported. (3) Some Proposition is Supported. At least one proposition is supported by a proposition. According to this presentation, a proposition P2 provides evidential support for a proposition P1 just in case P2 implies or stands in some epistemic relation to P1 , and P2 is itself epistemically non-arbitrary. But if P2 is a reason, then stating the requirement (1), that reasons be supported by other propositions, is the usual approach to explaining the non-arbitrariness of reasons: they are non-arbitrary because they themselves are supported by further reasons held in the form of propositional beliefs. So (1) implies 3 An epistemology informed by psychology is not necessarily a “naturalized” epistemology. I do think scientific insight can help dislodge long-standing philosophical prejudices that obscure our understanding of knowledge and justification, and my defense of foundationalism will sometimes refer to contemporary work in psychology (usually in the footnotes), to challenge what I take to be mistaken views of perception and concept-formation. But I do not think that a correct epistemology requires specialized discoveries in the rigorous empirical sciences; it requires only careful, first-person introspection of the operations of our own minds. There is room, in short, for an epistemology which draws on “folk” or “ordinary” psychology without collapsing into naturalism. 4 Cling states the problem in terms of support, rather than justification, because the support regress problem is the weakest version of the problem. Associated problems for both knowledge and justification arise on the assumption that knowledge requires justification, and that justification requires support. Support is distinct from justification in that justification may require some propositions to reach a particular threshold of support before they are to count as justified.

123

Synthese (2011) 180:357–389

361

that P2 must be supported by P3, which in turn requires P4 , and so on. On the assumption that reasons cannot support themselves, (1) and (3) are then jointly inconsistent with (2). If every reason requires support, and some proposition is supported, then it cannot be the case that no proposition is supported only by endless regresses. Yet for a variety of reasons, (2) still seems right. Either we abandon the conjunction of (1) and (3), or we abandon (2). The usual foundationalist solution to the problem of this inconsistent triad is to reject (1), that reasons are supported by further propositions. According to the foundationalist, there are basic beliefs that offer support but do not themselves require support by further beliefs. This eliminates the problem of a regress, but does not require basic beliefs to be entirely unsupported, if something other than beliefs can be found to provide support. The natural candidate for an alternative source of support is sensory perception. But there are many ways of understanding how sensory perception provides justification for basic beliefs, each of which depends on how we understand the nature of perception itself. The traditional approach through much of the twentieth century was to understand perception as awareness of sense data or other internal mental states, but the existence of sense data is now highly controversial, if not widely discredited. Arguments for the existence of sense data (which often turn on facts about conflicting appearances, illusions, and hallucinations) are not regarded as cogent (Austin 1962; Le Morvan 2004). Making sense of the semantics of claims about sense data, let alone their metaphysics, is an even heftier challenge (Sellars 1997/1956). Even if there is an internal state we may regard as the object of awareness, there are long-standing problems about how knowledge of the external world can be inferred from awareness of such internal objects, problems concerning whether the existence of external objects is the best explanation for the character of internal experiences, and whether naïve subjects have the knowledge necessary to make these inferences. There are, of course, many recent representationalist theories of perception which abjure any commitment to sense data. Computationalist theories like Marr’s (1982), or functionalist theories like Dretske’s (1995) are each “representational” in the sense that they invoke information-bearing states to explain the semantic properties of cognition. Whatever the merit of these theories, it is not obvious that they were formulated for the sake of solving any epistemological problems; mainly they aim at formulating an account of perceptual content that aids in psychological explanation. As such, these theories could be integrated into an externalist theory of epistemic justification, but are of little use in providing an account of the states of awareness in relation to which beliefs might count as epistemically basic and which would serve as basic standards guiding one’s inquiry. Sense data theory at least afforded an account of awareness which was intended to serve this justificatory role in a foundationalist epistemology (Schlick 1959), but given the shortcomings of sense data theory, any epistemologist looking to offer a guidance-oriented, internalist account of justification must look beyond contemporary representationalism. For this reason, direct realism is increasingly regarded as a viable alternative account of the nature of sensory perception, and I will argue that it is one which might serve robust epistemological purposes. As indicated earlier, direct realism rejects the view that the primary objects of perceptual awareness are intermediate, internal objects,

123

362

Synthese (2011) 180:357–389

and the view that knowledge of external objects derives from inferences from those intermediate objects; it reaffirms the “naïve” attitude that external objects present themselves directly to the mind.5 Often, the direct realist’s main task is simply to answer arguments purporting to establish the impossibility of this direct awareness (usually the same arguments purporting to establish the existence of sense data), but independent arguments for direct realism from its explanatory value are also offered. Recent years have seen a proliferation of such theories (Kelley 1986; Putnam 1994; Huemer 2001; Campbell 2002; Noë 2002; Travis 2004; Le Morvan 2004). Apart from its common sense plausibility, direct realism is attractive from the perspective of psychological theory. A persuasive defense of one version of this theory was famously advanced by the psychologist J. J. Gibson (1966, 1986). Gibson insisted that a theory of vision which treats two-dimensional retinal images as the only source of perceptual information is an impoverished account of the biological nature of perception. Instead of the retinal image, Gibson argues that the source of perceptual information is the “ambient optic array,” the totality of structured light surrounding the organism, which, he argues, uniquely specifies the layout of the organism’s environment. Perception of objects in an environment works through “information pickup” from this ambient array, via the total organism’s active interaction—involving all of its sensory modalities—with that light. Through this active interplay, the organism latches onto the “invariant” properties of the perceived world such as the regular rate of the recession of equidistant points as distance increases. The organism is not aware of the information itself, e.g. of the regular recession of equidistant points, but through a physiological process, rather than a process of conscious or subconscious inference, it uses information in the light to achieve awareness of its environment, e.g. of distance.6 Gibson assembled an impressive array of further experimental evidence supporting the explanatory value of this account (1986, pp. 147–202). His theory spawned an entire discipline, “ecological” psychology, which continues to generate active research to this day.7 5 I believe direct realism would support a theory of justification compatible with some version of inter-

nalism, but “internalism” here should not be read too literally. While internalism is often associated with the view that one counts as being justified in virtue of having access to internal mental states (and is hence often associated with forms of representationalism), the broadest essence of the view distinguishing it from paradigmatic forms of externalism is that one counts as being justified in virtue of having access to or awareness of the factors that contribute to this justification. This is the version of internalism targeted by prominent externalists, such as Goldman (1999). Direct realism is consistent with this kind of access internalism, provided that the objects or facts of which one is directly aware contribute to one’s justification. The rest of this paper is concerned with showing that they do. 6 See the sixth paragraph of Sect. 4, and the second paragraph of the concluding section of this essay for

interesting implications of the importance of the distinction between information used and the awareness achieved. 7 Here it is important to emphasize, in keeping with my anti-naturalistic framing, that the proper role for a specialized psychological theory like Gibson’s is not as evidence for direct realism. On a foundationalist account, this would be circular since it is precisely the justifiability of scientific knowledge that needs to be established. Naturalists such as Quine make free use of empirical data without worries of circularity, because they have abandoned the project of offering a foundational justification of science. But the circularity problem is very real if one does not abandon that project. I see the use of specialized empirical data as important mainly for breaking the grip of the philosophical prejudices of sense data theory and representationalism, which were themselves made plausible by other specialized empirical data. The claim

123

Synthese (2011) 180:357–389

363

Direct realism and Gibson’s science are not entirely uncontroversial. Elsewhere I have argued that scientifically-oriented objections to Gibson (such as those registered by Fodor and Pylyshyn 1981) rely on unwarranted philosophic assumptions or beg important questions against direct realism (Bayer 2007a, pp. 240–250). But it is not the task of this paper to lay out a detailed defense of the direct realist view of perception. In my view, at least, the position has significant first-person plausibility. One comes to know that the objects which one perceives are mind-independent through a variety of introspective discoveries: that the world is still there even after one closes one’s eyes, that there is a difference between the motion experienced by moving one’s body and that which is experienced as external, etc. This ordinary evidence is undermined mainly by philosophic arguments for sense data, arguments that now seem dubious. Direct realism is not only prima facie plausible, but independently plausible as a solution to the regress problem. As we shall see in the next section, the most interesting objections to direct realism are not those directed against its scientific merit or even its philosophic account of the objects of perception, but those directed against its ability to counter the regress problem. We can find philosophic agreement with direct realism in especially surprising quarters. Although I present the view as a source of support for foundationalism, some of the most prominent direct realists of the past fifty years have been anti-foundationalists. Sellars (1997/1956), famously a critic of empirical foundationalism, was nonetheless a leading critic of the sense data theory of perception, and is properly understood as a direct realist (Levine 2007).8 Much the same is true of McDowell (1996), who carries on Sellars’ legacy as a critic of “Myth of the Given” foundationalism. Both contend that perception is of external objects, and that it is direct, i.e., that it requires no inference from internal mental objects (especially since they regard talk of these internal objects as a linguistic artifact). Both differ from direct realist foundationalists in arguing that a non-inferential form of awareness such as perception is still a conceptual form of awareness (in virtue of its ability to be justified by further reasons) and hence not absolutely epistemically basic.9 Sellars’ and Footnote 7 continued that perception is indirect was inspired not only by arguments from illusion, but in large part by the philosophical misinterpretation of early modern discoveries in optics and physiology. Yolton (1979) presents the widely accepted view that classical empiricists’ theory of experience was in large part influenced by their reading of early modern theories of optics and vision. Sense data theory and its kin are best viewed as resulting from a reductio ad absurdum of direct realism in conjunction with empirical facts about the physical makeup of the senses. Bringing in a wider body of empirical data can help emphasize that this reductio is not inevitable. The goal of making free use of this specialized empirical data is not to prove direct realism, but simply to demonstrate that if we accept it, it does not contradict other scientific data, the acceptance of which our foundationalist theory would otherwise justify. 8 Consider Sellars’ statement in Science, Perception and Reality: “physical objects are really and directly perceived, and that there is no more basic form of (visual) knowledge than seeing physical objects and seeing that they are, for example, red and triangular on this side” (1991, p. 87). 9 Sellars may also endorse a version of adverbialism, which leaves it open that perceptual experience may exist in the absence of an object. This is at odds with the version of direct realism that I endorse, and probably at odds with seeing perception as providing a foundational role in justification. But the dispute between adverbialism and an object-dependent theory of direct perception is not at issue at present. The point is simply to emphasize that Sellars does not call into question the fact that when we perceive objects,

123

364

Synthese (2011) 180:357–389

McDowell’s position enables a response to the regress problem which is not foundationalist, but contextualist. They can reject proposition (1) of the regress problem, the premise that only supported propositions provide support, without positing basic beliefs that never require support. Rather than identifying an alternative form of basic support, they contend that not all support-providing propositions need to be supported in every context.10 Because the very critics of foundationalism we are about to challenge are themselves direct realists, we can simplify our defense of foundationalism by taking for granted, at least for this paper, that perception is of physical objects and that perceptual beliefs do not require previous inferential support. The interesting question then becomes whether a direct realist can still be a foundationalist. In the next section, I will examine claims that direct realism cannot solve the regress problem in foundationalism’s favor. We shall see that the epistemological shortcomings of recent versions of direct realism can be supplemented by a greater appreciation of the psychology of concept-formation which I have been urging. Ironically, if we appreciate these points of psychology, we will find that Sellars’ and McDowell’s criticisms of foundationalism rely on assumptions at odds with their own concessions to direct realism.

3 A dilemma for contemporary direct realist foundationalism BonJour (2004, 2007) is probably the leading contemporary critic of direct realist foundationalism. Though he is a foundationalist himself, he views “pure reason” rather than perception as the source of basic beliefs. Even though BonJour’s positive alternative is therefore very different from Sellars’ and McDowell’s positions, his reasons for rejecting direct realist foundationalism are virtually identical to theirs.11 Especially Footnote 9 continued these objects are perceived directly and as existing in the world, not inside our minds. This means that we should expect less resistance on this point when we show how conceding it ironically weakens Sellarsian objections to the epistemological role of perception. 10 Suppose that we take as P “This tie is green.” According to the contextualist, P does not require 1 1

support by reference to any other proposition P2 unless its standing as knowledge is challenged socially. To use Sellars’ example, we can and must justify our claim that a tie is green, if appropriately challenged, by stating that we are perceiving it under standard conditions of perception, and claiming that perceptual reports with that content under these conditions are reliable, etc. In contexts missing such challenges, we can be said to know that the tie is green provided that we would be able to offer this support if challenged. Having previously inferred this belief from another belief (or having previously done anything else justificatory) is not required. 11 Though neither Sellars nor McDowell present their objections to the “myth of the given” in the form of

a dilemma, I think BonJour’s dilemma is implicit in their arguments. As we shall see below, the dilemma amounts to claiming that either perception is “representational” and capable of being true or false, and therefore in need of justification, or it is not representational, in which case it is incapable of providing justification. Both Sellars and McDowell agree that it is at least possible for observation reports to require justification in the correct context (see my discussion of contextualism above), challenging their status as epistemologically basic. And both emphasize that a non-inferential, merely causal connection between perception and beliefs would not count as a justificatory relationships. (As McDowell puts it, it would at best count as “exculpatory,” not justificatory.) For more on the second half of the dilemma, see my discussion below of Sellars’ view of epistemic perspective.

123

Synthese (2011) 180:357–389

365

because he presents his reasons very clearly, it is worth evaluating them as representative of the broader position targeted in this paper (and we will get back to Sellars and McDowell specifically in the next section). In essence, BonJour contends that even if direct realism is a correct theory of perception, it does not supply its own theory of epistemic justification, let alone a foundationalist version of such a theory: Even if the perceptual awareness of material objects is arrived at without inference, and even if the objects in question are from a phenomenological standpoint simply presented in our perceptual experience, neither of these forms of directness or immediacy seems in any very obvious way to yield a good reason or basis for thinking that the resulting claims about the physical world are true or likely to be true. (BonJour 2004, p. 356) BonJour goes on to examine the details of several prominent versions of direct realism, and concludes that none of these provides an adequate account of epistemic support. It is worth briefly examining each of these views and BonJour’s responses to them.12 Huemer’s (2001) direct realism holds that perceptual knowledge is non-inferentially justified on the basis of perceptual experiences. Huemer maintains that perceptual experiences have propositional, representational content, which content justifies our basic beliefs in accordance with the “rule of Phenomenal Conservatism”: “If it seems to S as if P, then S thereby has at least prima facie justification for believing that P.” Though he takes perceptual experience to have propositional content, he also insists that it is not conceptual content. It is non-conceptual because it represents objects in a manner that is highly determinate and enriched compared to our conceptualization of the same objects, but it is propositional because it represents the world as being in this highly determinate way, which representation may be true or false.13 BonJour wonders, if perceptual experience really is the basis for justified beliefs, why 12 Whether or not BonJour interprets these theories correctly or anticipates every possible objection they might give in response to his criticism is not so important. What emerges from his criticism is a distinctive dilemma about foundationalist justification, and examining his criticism is useful for seeing why he takes there to be such a dilemma. 13 Like BonJour, I have serious doubts about whether it makes sense to call content both propositional and non-conceptual. On anybody’s view of the nature of propositions, the possibility of truth or falsehood arises because of the possibility of misidentification of subject and predicate, where at least the predicate needs to be conceptualized. In predicate logic, the implicit subject is x in ∃(x) Fx, and the predicate F needs to be true of x in order for the proposition to count as true—that predicate is surely represented conceptually. In a more traditional subject-predicate logic (which I favor), both the subject and predicate need to be conceptualized, or, in the case of indexically-represented subject terms, at least presuppose prior conceptualization [“This (man) is F”]. Later, I propose that perception is neither propositional nor conceptual, but, contra Huemer (2001, pp. 72–74), I contend it is nonetheless a source of justification. As a direct realist myself, I am sympathetic with Huemer’s view that perceptual content has a richer content than conceptual content, but I do not think one needs to think of it as perceptual or even as representational in order to capture this view. It is a legitimate to loosely describe someone’s perceptual experience as, for example, “representing a stick to be bent.” But we can describe it this way without assuming that the experience itself is propositional or true or false. When describing it this way, we could simply mean that a perceiver’s experience is such that, if we who have conceptual beliefs were to have it, we would assert on its basis the proposition that the stick is bent. Or we might only mean that a preconceptual perceiver perceives it in a way that looks similar to an actually bent stick. There is still room for a distinction between non-propositional experience and conceptual/propositional interpretations of that experience, even if our descriptions of experience are as Huemer suggests.

123

366

Synthese (2011) 180:357–389

do we have reason to think it is justified? Huemer thinks it is a mistake to suggest that perceptual experiences are either justified or unjustified, because they occur as automatic responses to stimuli. But BonJour contends that this misses the point, since by Huemer’s admission, perceptual experiences are either true or false and we need a reason to believe they are true to justify anything on their basis. BonJour also contends that invoking the rule of Phenomenal Conservatism at this point adds nothing more to Huemer’s case, because we still need a reason to think it is true. The putative fact that we invariably rely on the rule as a matter of default or presumption does not justify reliance on it or justify reliance on the perceptual experience to which it refers. BonJour’s response to Bill Brewer’s version of direct realism (1999) is similar. Brewer also assumes that perceptual experience possesses some kind of propositional content. His theory focuses on how direct perception makes possible the determinate reference of perceptual beliefs. BonJour thinks this is fine as far as it goes, but wonders what questions about the reference of perceptual beliefs have to do with the justification of perceptual beliefs. In whatever way veridical direct perception might contribute to the reference of perceptual beliefs, our inability to distinguish between qualitatively indistinguishable veridical and non-veridical experiences (such as hallucinations) would eliminate the possibility of internalistic justification. Brewer thinks he can set this question aside by insisting that justification does not require the ability to distinguish infallibly between veridical and non-veridical cases. But BonJour thinks this is a red herring: his point is not that we lack an infallible internal criterion for distinguishing between the veridical and the non-veridical, but that we have no criterion at all. As in his response to Huemer, then, BonJour wants to know what reason we have to believe that our perceptual experience represents the world accurately—a point that is plausible as long as direct realists maintain that perceptual experience has something like propositional content. Brewer himself later recognizes this difficulty, and revises his position to show how perceptual experience might count as both non-propositional and non-conceptual (Brewer 2006)—the type of revision we will have occasion to revisit. For the time being, it is useful to examine BonJour’s third direct realist candidate, Reynolds (1991), who initially opts for a non-propositional view of perceptual content. According to Reynolds, perceptual content (in this example, of a visual kind) consists in an arrangement of various color patches of different shapes and sizes in a subject’s external visual field. There are correlations between types of arrangements and claims about external objects made by one’s epistemic community. When one’s own claims about material objects exhibit this correlation, Reynolds says one’s claims are justified. BonJour complains that if the subject does not actually have a good reason to believe that his claims reliably match this correlation, he cannot be said to be internally epistemically justified in believing that his claims are true. At best, our beliefs are causally explained insofar as they conform to a truth-conducive rule, but this does not make them justified. BonJour’s objection here is reminiscent of a standard Sellarsian objection to externalist theories of justification: that it is not enough for a subject’s claims to have authority—the subject must also, in some sense, recognize that authority (Sellars 1997/1956, pp. 74–75). According to BonJour, then, direct realist foundationalism faces a dilemma. On one hand, perceptual experience might have propositional content and present something

123

Synthese (2011) 180:357–389

367

true or false, in which case its role in justifying other beliefs would be clear, but the acceptance of what it presents would itself require justification and a regress problem would remain. On the other hand, perceptual experience might have no propositional content, in which case there would be no problem of needing to justify the acceptance of a perceptual presentation (it would be neither true nor false), but there would be a new problem of explaining how our non-propositional experiences could justify our propositional beliefs. In either case, we are faced with a version of Sellars’ problem about the need to recognize the authority of our evidence, what we might call the problem of epistemic perspective. In earlier work, BonJour claims that this is a dilemma for any version of foundationalism based on “the empirically given”: [T]he proponent of the given is caught in a fundamental and inescapable dilemma: if his intuitions or direct awarenesses or immediate apprehensions are construed as cognitive, at least quasi-judgmental…, then they will be both capable of providing justification for other cognitive states and in need of it themselves; but if they are construed as noncognitive, nonjudgmental, then while they will not themselves need justification, they will also be incapable of giving it. In either case, such states will be incapable of serving as an adequate foundation for knowledge. This, at bottom, is why empirical givenness is a myth. (BonJour 1985, p. 69) My aim is to show the direct realist foundationalist a way to slip between the horns of this dilemma. To avoid the need to justify perception itself, we should, contra Huemer and the early Brewer, take its content as non-propositional and thus neither true nor false. But then we also need to find some rudimentary way in which a subject could have an epistemic perspective on the relationship between direct, non-propositional perception of objects and one’s basic beliefs. To show how this could be done, we need to find some support relationship between the non-propositional and the propositional, the grasping of which is also non-propositional (and thus not itself in need of further meta-justification). If there is no such support relationship, the direct realist cannot avoid a regress or meta-regress problem without compromising internalism or adopting Sellarsian contextualism. But if there is such a support relationship, there can be a version of foundationalism that rivals Sellars while maintaining internalism and avoiding the inconsistent triad. Interestingly, BonJour himself considers possible ways of escaping the dilemma in his earlier work. He considers the possibility of a “quasi-cognitive (or semi-judgmental) state, which resembles a belief in its capacity to confer justification while differing from a belief in not requiring justification itself” (1985, p. 77). BonJour thinks that positing such a state is “ad hoc,” and needs to be established independently of the need to avoid the dilemma. But if the existence of this state is a genuine possibility, then the dilemma mentioned above is not “inescapable.” So we need to consider whether it is a genuine, rather than ad hoc possibility. For his part, BonJour rules it out as genuine because he thinks the direct realist appeal to the mind’s immediate confrontation with the facts is just a “metaphor” because “the mind is…not an eye, or…anything like an eye” (p. 77). This is a curious response because the eye is quite a lot like an eye, and direct realists about perception should not be deterred from making reference to

123

368

Synthese (2011) 180:357–389

“immediate confrontation.” The question is whether such confrontation is justificatory. BonJour addresses this question when he says that so long as the quasi-cognitive state “involves anything like a representation, the question of justification can still legitimately be raised: is there any reason to think that the representation in question is accurate or correct?” (p. 78). Here, BonJour begs the question against the kind of direct realism we are now entertaining, which of course rejects the idea that direct awareness has content that can be true or false.14 Granted, many philosophers, including direct realists like Huemer, have raised problems for the idea that perceptual content is neither true nor false, but this protest has been registered mainly on the grounds that non-propositional content would be incapable of justifying beliefs. In what follows, however, I contend that considering the psychology of concept-formation does help to show how non-propositional content might justify the propositional. 4 Foundational justification as justifiable concept-application We need to find a non-propositional mode of awareness (other than the direct perception of objects) that counts as an awareness of the relationship between one’s non-propositional perceptual awareness and one’s propositional beliefs. Curiously, BonJour himself also considers the possibility of just this type of awareness in his earlier work. At one point he critiques Quinton’s view (1973) that we can understand the justification of basic beliefs as closely related to our grasp of their meaning. According to BonJour’s characterization of Quinton, if the meaning of some statements can be established ostensively (which seems required by a regress argument of its own), then …ostensive statements are…introduced into language by correlating them with external states of which one is directly aware; and a subsequent direct awareness of the same sort of external state of affairs would provide an adequate, noninferential justification for the assertion of a statement whose meaning was thus specified. (BonJour 1985, p. 71) If Quinton’s proposal is right, one has a non-propositional grasp of epistemic perspective on one’s belief as long as one has some kind of non-propositional grasp of the perceived objects’ “sameness of sort” with objects perceived in the past, those by reference to which one ostensively established the meaning of the same belief type in the first place. This grasp would be a form of meta-awareness, an awareness of one’s present perceptual awareness in relation to previous perceptual awareness. If it is non-propositional, then there would be no question of whether it is accurate or not, and grasping it would require no further regress-generating justification. So, can there be a non-propositional grasp of an object’s being of the “same sort” as another?15 14 Above I have made some use of the fact that both Sellars and McDowell are direct realists and that we can take heart in their concession to the view that perception is both non-inferential and of external objects. For the sake of full disclosure, it is worth remembering that they reject the idea that direct realism requires the non-conceptual content of perception. We will deal with their contention of this requirement later. 15 I should mention that at this point BonJour makes two objections to Quinton’s proposal. The first deals with whether it is even possible to grasp meaning ostensively, as through perception (1985, p. 71). Though I will have much to say on this topic in the next section, I will only mention that I think BonJour’s

123

Synthese (2011) 180:357–389

369

Whether or not Quinton’s view includes this point, it is important that direct realist foundationalism insist on the possibility of a non-propositional, non-conceptual form of awareness of the something like the sameness of sort. The best candidate for this form is the grasp of perceptual similarity relationships. A perceived similarity is not literally an awareness of the sameness of sort: one who pre-conceptually perceives two objects as similar does not yet grasp a “sort” over and above the objects of perception. But perceived similarity, the ability to see two or more objects as resembling each other, is the preconceptual precursor of concept-formation, the explicit grasp of “sorts.” In the next section, I will say much more about what perceptual similarity consists of, and how it forms the basis for concept-formation. For now, the first point to make is that the grasp of such similarity is akin to the perceptual grasp of objects affirmed by direct realism. Without this point, my proposal would fall prey to Sellars’ objection that the grasp of similarity presupposes further concepts, such as that of “similarity,” and that of the respect in which things are said to be similar (Sellars 1997/1956, p. 63). Similarity is a relationship rather than an object, but at least in the Gibsonian direct realist tradition, one can directly perceive particular relationships just as well as one can perceive particular objects without the need of additional conceptualization, e.g., one can perceive a particular distance or a particular location. I think Gibson is right about this.16 One can see the difference in length between a pencil and a toothpick and one can see the pencil next to the toothpick, without judging that the pencil is longer than the toothpick, or that the pencil is next to the toothpick. One does not need to be aware of something as the kind of thing it is in order to perceive it; nor does one need to grasp something as a kind of relationship to

Footnote 15 continued specific objection here begs the question against direct realism, in that he explicitly assumes, without argument, that grasping meaning must be propositional. Also BonJour assumes that if content cannot be grasped propositionally, it cannot suffice to provide a basis for propositional content. This is a non-sequitur, since the reason non-conceptual content might not be fully propositionally graspable is that it is may be too rich for that: but this would mean that non-conceptual content is more than sufficient to provide a basis for the conceptual kind. BonJour’s second objection to Quinton (pp. 71–72) tries to separate questions about the sources of meaning and the sources of justification. Though his point is not stated clearly, BonJour seems to suggest that the source of content is irrelevant to whether its assertion is justified: one might form a concept or belief through electrode stimulation, and still eventually justify the belief. This objection is not really an objection to our particular proposal, but to any evidentialist theory claiming that justification must find its source in (usually perceptual) evidence. It assumes the plausibility of the pragmatist-coherentist view that only the consequences of a belief, only its eventual testing or integration into a system of beliefs, determine its justificatory status. For present purposes, I abstain from defending the view that foundational justification is necessary, and simply defend the view that it is possible. Whether it is possible is the primary question at issue in BonJour’s dilemma, and related regress problems. 16 Agreeing with Gibson on this does not imply agreeing with him about every relationship he thinks can be directly perceived. In particular I think most of the relationships Gibson characterizes as “affordances” are probably not directly perceived, but are the result of various kinds of post-perceptual processing, not direct perception. Arguably, the grasp of similarity itself is not the most fundamental kind of perception (perception of objects is), but it is still prior to the kinds of post-perceptual processing that Gibson mistakes for perception.

123

370

Synthese (2011) 180:357–389

perceive the relationship, provided that it is a sufficiently simple relationship.17 This is so, even if the relationship in question is that of similarity, the awareness and retention of which may help one later develop an awareness of sameness of kind. There is no reason to deny that particular similarity relationships might be perceived in the same way as other relationships, provided that the similarity in question is sufficiently simple. One can see the similarity between the toothpick and the pencil in comparison to a ball, as well as the even greater similarity between two pencils in comparison with the toothpick—even if one cannot easily see,e.g., the similarity between whales and other mammals. Count this as the first way in which direct realism about perception informs the theory of concepts underwriting an associated theory of epistemic justification. How then does the perception of a particular similarity relationship form a basis for the awareness of a kind as a kind? Probably the formation of the first concept on the basis of a perceived similarity coincides with the formation of the first justified belief on the same basis.18 One does not use concepts except in the context of propositions, and one does not form a concept except in the process of forming—and asserting—a proposition. One forms a concept when perceived similarities become important enough in one’s cognitive life that knowledge of the similarity is worth retaining. So one only comes to possess the concept TABLE, for instance, when one first becomes aware of a cognitively important similarity between two tables, using the holophrastic sentence, “Table!” (implicitly, “This is a table”). Of course one doesn’t need to perceive a similarity between two immediately present tables in order to justifiably assert “Table!” One could perceive a single table and be aware of the similarity between it and previously perceived tables through non-propositional, episodic memory. Foundational justification, on this proposal, is justifiable concept-application in virtue of a perceived similarity—and justifiable concept-application, following Quinton’s proposal, is essentially a kind of rehearsal of the same cognitive act whereby one originally formed a concept. It is worth mentioning, briefly, that there is an important sense in which the formation of the concept itself is justified on the basis of the perceived similarity (Salmieri 2007). As mentioned above, we need concepts to highlight cognitively important similarities, those worth retaining as enduring forms of awareness, and only the sorts reflective of this requirement count as justified. There are many cognitively unimportant similarities (e.g., that between everything that is both orange and round, or that which Goodman suggested to hold between anything that is either a bag or a naval fleet). Early in one’s cognitive life, it is probably difficult to form unjustifiable 17 Confusion between universals and particulars is at the root of many errors in the theory of concepts. There seems to be a bias that any type of existent apart from entities is “abstract,” that such things as properties, qualities, and relationships are by their very nature universal. I don’t see any reason to believe this, though it may be true that many of the properties, qualities and relationships we know of we cannot perceive as particulars. This is also true of entities: some are too big or too small to perceive, and we would not question their status as particulars for this reason. Just as there can be particular entities and particular actions, there can be particular relationships and properties, at least some of which we can perceive. Metaphysicians sometimes call particularized properties “tropes.” 18 For intriguing developmental evidence concerning children’s use of one-word utterances and how they correlate with learning of their first words (and concepts), see Bloom (1993) and especially (1973). For an important discussion of how this evidence helps undermine a variety of inscrutability of reference problems from Quine, see Modee (2000).

123

Synthese (2011) 180:357–389

371

concepts that highlight baroque similarities: the most obvious, unavoidable similarities are those that are cued toward our immediate survival needs, and we probably do not even have access to the baroque similarities. But as our knowledge grows, the choices we exercise over the process of conceptualization also grow, and more guidance is needed to navigate between justified and unjustified concepts. What, then, makes for an important similarity, and how can one be aware of its importance nonpropositionally? One issue is the mere frequency of perceived similarities, and plausibly one could possess rough non-propositional episodic memory of relative frequency, given enough repetition. The more important issue is the causal import one attaches to similarities. Some similarities are merely superficial, and conceptualizing them would not generate new inferences—a point appreciated by recent cognitive and developmental psychology.19 Real cognitive importance is attached to those similarities which are perceived as causally significant. For example, one perceives a human being’s shape as relevant to his actions, or the shape and size of a table as relevant to its function of supporting human artifacts.20 That these causal relationships might be perceived in addition to similarity relationships is of course 19 Here one is reminded of Rosch’s (1999/1978) reference to Borges’ portrayal of an animal taxonomy in an ancient Chinese encyclopedia, the Celestial Emporium of Benevolent Knowledge: “(a) those that belong to the Emperor, (b) embalmed ones, (c) those that are trained, (d) suckling pigs, (e) mermaids, (f) fabulous ones, (g) stray dogs, (h) those that are included in this classification, (i) those that tremble as if they were mad, (j) innumerable ones, (k) those drawn with a very fine camel’s hair brush, (l) others, (m) those that have just broken a flower vase, (n) those that resemble flies from a distance” (1999/1978, p. 189). Many of these categories comprise patently superficial similarities, such as “those that have just broken a flower vase,” from which nothing of causal or cognitive significance follows. On the basis of this and other examples, Rosch formulates a principle of “cognitive economy,” according to which “an organism…wishes to gain from one’s categories…a great deal of information while conserving finite resources as much as possible[,]… to reduce the infinite differences among stimuli to behaviorially and cognitively usable proportions” (p. 190). Recent years have also shown an increased appreciation for the so-called “psychological essentialism” displayed by young children, who have a surprising ability to categorize objects on the basis of inner properties which exhibit causal significance (Medin and Ortony 1989). Many psychologists take this psychological essentialism to be represented in “theoretical” form (Keil 1992), but others suggest that the simplest appreciation of essence is available through perceptual similarity (Gelman 2004; Namy and Gentner 2002), and that this is the initial awareness of essences that makes possible the appreciation of higher-level, theoretical essences. Part of the reason “similarity” theories are seen as being at odds with “causal” theories is the longstanding bias that causal relationships are not available, perceptually. Contra this assumption, see footnote 21. 20 Understanding similarity in light of this requirement of the cognitive significance of causal import helps answer Quine’s objection to similarity as a basis for understanding natural kinds (1969b). Quine says there is something “logically repugnant” about similarity, because of the inability to identify the properties in terms of which this similarity should be formulated. Quine repeats the familiar point that two objects are similar in any number of regards, which threatens a promiscuity of natural kinds. Quine speculates that standards of similarity are innate, determined by evolution. I agree, but the types of similarity standards he takes to be most salient primarily concern color-similarity, which is an age-old empiricist bias that has long been contradicted by developmental evidence (see the next section). Children are far more impressed by similarities in shape than they are by color, and we can now understand this in evolutionary terms by reference to Gibson’s understanding of ecological properties as forming the basis for the information pickup of perception. And when similarity is understood first in terms of shape, similarity also becomes much more respectable, scientifically. The shapes of objects have far greater causal import, which makes concepts formed on the basis of perceptual similarity “natural kind” concepts from the beginning, not just superficially-held “nominal essences.” Science itself, then, to the extent that it begins, developmentally, with similarity concepts, is not, as Quine says “rotten to the core.”

123

372

Synthese (2011) 180:357–389

controversial, especially in light of Hume’s critique. But direct realist and other Gibsonian approaches to perception have at least made this possibility increasingly plausible.21 On this theory, we perceive not only entities, but some simple actions and relationships. At least on this point, I think the direct realists have convincingly shown how the content of perception is richer than many might suspect (even if their position sometimes makes it too rich). I cannot defend their view here, but as I’ve emphasized before, my purpose in this paper is not to defend direct realism but to show how, if it is permitted its usual resources, it can support a theory of concepts in conjunction with which it yields a theory of justification. Count this point about direct realism’s resources for explaining our awareness of causality, then, as the second way in which direct realism about perception informs the theory of concepts needed for a theory of justification. While it is true that concepts formed on the basis of perceived similarities are in need of justification—as are the basic beliefs whose formation is a kind of rehearsed concept-formation—this does not mean that perceptual similarity itself needs justification. As a form of direct, non-propositional awareness, the perception of similarity needs no justification for the same reason that direct perception of objects needs none: it is not the kind of awareness that can be true or false. This might seem perplexing at first, since it seems that our ability to identify and classify things conceptually, on the basis of perceived similarities, is by no means infallible. At a distance we might erroneously identify a mule as a horse. But notice that even in this circumstance, there really is a perceived similarity between the mule and other horses we have seen and conceptualized. Granted, it is not the same similarity relationship as we see among horses: this is why the belief that it is a horse is an error. But in viewing foundational justification as justifiable concept-application, we are only giving a theory of justification. Judging a mule as a horse is an error, but in the situation in question it is a justifiable error.22 The view of justification I have described above and its implications for our understanding of epistemic perspective is in some respects unique as an internalist view of justification. Both BonJour and Sellars are right that, to be justified, we need to recognize the authority of our evidence, not just have evidence—that is, we need to grasp the “epistemic perspective” on our evidence. But I believe there is potential equivocation in what it is to grasp epistemic perspective. Here it helps to distinguish between what I call “particular-particular perspective” and “particular-categorical 21 See Michotte (1963) for the original psychological work, and Harré and Madden (1975) for a neo-Aristo-

telian theory of agent causation based in part on Michotte and Gibson. For more contemporary psychological work influenced by Michotte, see Leslie and Keeble (1987), Scholl and Tremoulet (2000), and Prinz (2002, pp. 173–177). 22 Conceivably under other special circumstances, a very vague similarity between horses and mules would not justify the judgment in question. If a subject knows that the perceptual conditions are impoverished, and if he still refuses to hedge his judgment, conceivably his judgment would count as unjustified. But this possibility presupposes that the subject knows a great deal more about conditions of perception. Of course not just any degree of similarity is sufficient to justify the application of a concept, even in the absence of knowledge of perceptual conditions and the like. At the same time, not just any degree of similarity is sufficient to generate erroneous belief. We make erroneous identifications when we are taken in by a similarity. To believe a proposition to take it for granted for the sake of practical and theoretical reasoning. If a proposition conflicts with too much of the rest of what we already know, we won’t believe it.

123

Synthese (2011) 180:357–389

373

perspective.” So far the recognition of authority I have considered amounts to the grasp of “particular-particular perspective,” in which the awareness of a particular object has the authority to justify a judgment about the object because through this awareness one can make a direct comparison between this object and another (e.g., a similar, previously observed object). But when BonJour and Sellars talk about recognizing the authority of evidence, it seems they are concerned with the grasp of what I will call “particular-categorical perspective,” in which one’s awareness of a particular object has the authority to justify a judgment about the object only because one subsumes this particular state of awareness under a higher category of awareness which one judges to be generally reliable (e.g. sensory perception as such). There is sometimes a need for particular–categorical perspective. We cannot live our cognitive lives without the need to assent to the merit of some very general methods of cognition. Reliance on testimony is a good example. We need to be able to identify rudimentary reasons for a general reliance on the words of other people. Much of this needs to be held explicitly and conceptually if we are to have justified beliefs on the basis of testimony. This kind of particular–categorical epistemic perspective is necessary because it enables particular–particular perspective: it helps us to see why the content of a given bit of testimony is relevantly similar to objects of past states of awareness—a similarity which is not perceptually available. Obviously if the only form of epistemic perspective were particular–categorical perspective, a regress would ensue. One could judge instances of testimony as reliable only by subsuming them under the general reliability of testimony, which one could judge as reliable only by subsuming under another more generally reliable category of cognition, etc. This is why it is important that the most basic form of epistemic perspective be particular–particular, both because particular–categorical perspective is a means to achieving particular–categorical perspective, and because one would come to acquire the knowledge of the reliability of a general form of cognition only through a kind of induction from particulars, made possible by particular–particular perspective. So for instance, to grasp the general reliability of (simple forms of) testimony, we would need other general knowledge that we perceive things and remember what we perceive, that we can communicate our perceptual knowledge verbally, and that other people are conscious beings like ourselves who can do the same things.23 Ultimately each of these generalizations would need to be acquired by observing the similarities and differences

23 As critics of foundationalist approaches to testimony (such as Coady 1992) have rightly noted, we cannot reduce our reliance on all testimony directly to our reliance on observation and judgments about it. Too much of our testimony is itself dependent on the reliability of other testimony. I do not think, however, that this implies we must be coherentists about testimony. As long as we can identify certain basic, general kinds of testimony whose reliability can be judged on a first-hand basis (e.g., testimony about simple observable facts that anyone would be in a position to report about accurately, and would have little reason to lie about), these kinds of testimony can then be used in bootstrapping fashion to justify less obviously reliable forms of testimony. I think an overall foundational structure of testimony can be preserved. Part of the reason that Humean reductivism about testimony fails on its own terms is that it assumes that the reliability of testimony can be determined only through the observation of constant conjunctions of testimony and testified-to facts. I would suggest that it largely the Humean approach to induction that is at fault here, not a foundational approach to testimony in general (but it is beyond the scope of this article and this note to argue for this point).

123

374

Synthese (2011) 180:357–389

among our particular conscious states as well as the perceptual similarities between ourselves and other people.24 However, when anti-foundationalists argue that the grasp of epistemic perspective sometimes requires a particular–categorical perspective, they assume that a faculty as basic as perception itself requires justification, that we must subsume this faculty under some generalizations that would justify our reliance on it. Note that demanding justification for reliance on testimony is relatively uncontroversial: on just about anyone’s terms, it has propositional content and can be true or false. But to ask for the justification of perceptual awareness per se is quite a different matter, and is to beg the question against direct realism. It is only on a representationalist view that some account is needed of why internal sense data accurately represent external objects. But if perception is a direct, non-propositional awareness of objects, there is no question of justification of this kind (or of any other).25 Now I doubt that BonJour or Sellars would beg the question against direct realism this blatantly, especially when Sellars himself is a kind of direct realist. Indeed, skeptical worries about hallucination or dreaming do not demand a justification of perception itself. They demand a justification for the claim that one is perceiving (rather than hallucinating). But then the question becomes why one needs this kind of justification in order to have knowledge, why one needs to eliminate, e.g., the possibility of hallucination.26 This approach to epistemic perspective mimics the need to justify that one is seeing a table rather than a chair (a kind of particular–particular perspective) but applies it to general sources of belief (the usual subjects of particular–categorical perspective). Whether this assimilation is justifiable or some kind of category mistake is a serious question. I will make two brief responses to suggest that it is not obviously justifiable. First, the minimalist response: suppose that when one is hallucinating, there is no obvious way to differentiate genuine perception from hallucination. Then the kind of epistemic perspective I have described is incapable of providing the justification one needs to answer the skeptic. But I think it is important not to confuse making a case for foundationalism with making a case against skepticism. The regress arguments that motivate anti-foundationalism do not necessarily involve ruling out skeptical alternatives: they concern whether it is possible to find a type of rudimentary awareness that requires no further justification. The question of what counts as adequate justification is a putatively separable question. In identifying the grasp of perceptual similarity as a kind of epistemic perspective, I have at least shown where we can find the source 24 There is, of course, much controversy in the philosophy of psychology about whether or not we come to understand other minds through the kind of induction and analogy that I am briefly describing here. But I tend to think that the objections to this proposal from “simulation theory” cannot entirely eliminate reference to epistemological generalizations, and I have illustrated this in an unpublished paper on the subject (Bayer 2007b). 25 Huemer actually makes this point against BonJour in a later reply (Huemer 2007a, pp. 50–54). I do think, however, that since Huemer regards perceptual experience as having a propositional content, he remains subject to BonJour’s criticism, unless he can defend his rule of Phenomenal Conservatism, and its accessibility to ordinary believers. 26 There is a tradition of direct realist criticism of arguments from hallucination (Ghate 1998, pp. 76–91;

Le Morvan 2004, pp. 227–228; Johnston 2004), but these are too various to examine here.

123

Synthese (2011) 180:357–389

375

of an important kind of justification that meets internalist criteria, even if it is not the kind of justification needed to answer the skeptical challenge, a challenge that could be posed without consideration of the regress problem. In case this minimalist response is not fully persuasive, I would like to leave the question of answering skeptical challenges to others. But I don’t think I’m taking too much for granted in doing so, because answers are available in quarters that are otherwise sympathetic to the anti-foundationalist regress arguments we’ve been examining. The usual social contextualist response to arguments from hallucination is the appeal to “relevant alternatives.” To know that p is to be able to rule out alternatives to p. Contextualists usually specify that only a subset of alternatives to p are relevant to establishing knowledge, and skeptical scenarios arise only in special philosophic contexts (Wittgenstein 1969; Williams 1996). Contextualists say that what counts as relevant is determined by context. The same approach is evident in externalist epistemology. To borrow an example from Dretske (1970), to know that animals we see in the zoo are zebras, we should know that they are not mules. But we may be unable to rule out that zebras we see in the zoo are cleverly disguised mules. Does it follow that to know that the animals are zebras, we must know they are not cleverlydisguised mules? It is not obvious that this follows, or that being a cleverly-disguised mule is a relevant alternative that must be ruled out. And relevant alternatives theories are available outside of contextualist and externalist theories of justification. Michael Huemer himself, an internalist foundationalist, has proposed a theory according to which brain-in-the-vat alternatives may be ruled out as genuine epistemic possibilities on the grounds that one’s perceptual experiences offer prima facie evidence against these possibilities (Huemer 2007b). I think a more refined internalist foundationalism should also support a burden of proof requirement for claims of epistemic possibility, a burden to be shouldered by specific evidence (as proposed, most notably, by Austin (1946)).27 I shall not say more about the kind of internalist justification my proposal would underwrite, because the leading objection to it—especially from contextualist quarters—is that it presupposes a view about concept-formation that is unacceptable: the view that we can form concepts from mere perception in the first place, the view I will call abstractionism. I address this objection in the next section.

27 Austin of course approaches epistemology as a social contextualist, but I think his requirement of specific evidence can be interpreted along internalist foundationalist lines. The emphasis would not be so much that entertaining possibilities not grounded on evidence would be an unjustified form of cognition, but that it would not really be cognition at all. In the same way that virtue ethicists critique consequentialism for alienation of values from the concerns of the individual valuer (someone who acts for the sake of impersonal consequences in not really acting on the basis of his values) I would critique the acceptance of possibilities without special evidence as the acceptance of alien “beliefs.” Someone who reasons on the basis of imagined possibilities is not drawing consequences using the same device, evidence, that he would otherwise demand for the sake of the acceptance of probabilities and certainties. By introducing this dichotomy into his mental life, he develops a fractured epistemic character, and these hypotheses cannot be said to be his own beliefs, let alone justified beliefs.

123

376

Synthese (2011) 180:357–389

5 A defense of abstractionism Sellars and McDowell, direct realists but anti-foundationalists, are also aware of the proposal to explain epistemic perspective by appeal to abstractionism. This is no surprise, since their general approach to justification is to characterize it in terms of the justifiability of concept-application. Only, in their tradition, the justifiability of concept-application is understood as a kind of socially-conditioned language game. The idea that justifiable concept-application might be understood on the basis of firstperson cognitive factors independent of social sanction is regarded as an instance of the “Myth of the Given.” In a crucial and revealing passage, McDowell notes a condition under which propositional beliefs might count as justified on the basis of non-conceptual perception, but claims that the condition does not hold. We could not begin to suppose that we understand how pointing to a bit of the Given could justify the use of a concept in judgment…unless we took this possibility of warrant to be constitutive of the concept’s being what it is, and hence constitutive of its contribution to any thinkable content it figures in… …The supposed requirement is reflected in a familiar picture of the formation of such concepts. The idea is that if concepts are to be even partly constituted by the fact that judgments in which they figure are grounded in the Given, then the associated conceptual capacities must be acquired from confrontation with suitable bits of the Given: that is, occasions when pointing to an ultimate warrant would have been feasible. But in any ordinary impingement on our sensibility, it would have to be a manifold Given that is presented to us. So in order to form an observational concept, a subject would have to abstract out the right element in the presented multiplicity. (McDowell, 1996, pp. 6–7) Here McDowell is considering our proposal in its essence: the idea that there is a strong link between understanding the justifiable application of a concept and understanding its meaning (its being “constitutive of the concept’s being what it is”). And, for the Given to partially constitute our concepts, concepts must have been acquired from “suitable bits of the Given.” But neither McDowell nor Sellars thinks it is possible to “abstract out the right element” without presupposing other conceptual capacities. This is why they reject foundationalism while accepting the possibility of non-inferential knowledge: what non-inferential knowledge we have still presupposes other concepts and cannot result ultimately from a form of awareness that involves direct confrontation with the Given. In this regard, McDowell makes special reference to Peter Geach’s “trenchant” Wittgensteinian critique of abstractionism in his book Mental Acts (1957). It is not clear whether he intends Geach’s work as offering a conclusive refutation of abstractionism, but it is worth examining Geach’s arguments as representative of skepticism about the view. Should they turn out to be less than trenchant, McDowell’s objection to my proposal will be threatened. I will argue that Geach’s objections are less than persuasive. Ironically, they fail to persuade precisely because they neglect the possibility of a direct realist theory of perception—the very theory that Sellars and McDowell themselves take for granted.

123

Synthese (2011) 180:357–389

377

According to Geach, “abstractionism” is the doctrine that “a concept is acquired by a process of singling out in attention some one feature given in direct experience— …and ignoring the other features simultaneously given.” On this view, “all acts of judgment are to be accounted for as exercises of concepts got by abstraction” (1957, p. 18). Geach acknowledges that abstractionists will not always contend that every concept is gotten by abstraction from perceptual awareness. Even still, Geach insists that no concept is acquired this way.28 In most of the sections cited by McDowell, Geach surveys the hardest cases for abstractionism: logical operator concepts, arithmetical concepts, and relational concepts. Most of the abstractionist proposals he considers for these concepts are in fact wildly implausible. But as Geach admits, it is not incumbent upon the abstractionist to account for every type of concept by direct abstraction from perceptual awareness. We might abstract some basic concepts from experience, and then widen, subdivide, or recombine them into new, more abstract concepts singling out similarities that are more distant from perception. What matters to the case for foundationalism is the foundational, observational concepts. Therefore, it is not surprising that Geach says that “concepts of sensible things” are of “special interest.” These, he thinks, are “formed by picking out features directly given in sense-experience” and used to form “concepts of kinds of substance, like gold and water…by piecing together …concepts of their characteristic sensible features” (p. 19). Geach even devotes a special chapter to what he takes to be paradigm examples of concepts of sensible things: concepts of color. Presumably a refutation of abstractionism about these, allegedly the most basic of concepts, would defeat abstractionism about any concepts at all. McDowell and Sellars both rely on a similar strategy when critiquing the idea that the exercise of concepts might be “self-standing,” when they assume that the foundationalist would privilege the position of color concepts (Sellars 1997/1956, pp. 75–76; McDowell 1996, p. 12). Geach does raise thought-provoking problems for abstractionist accounts of color concepts. For example: a sensation of red could serve as data for both the concept of COLOR and of CHROMATIC COLOR (i.e., colors other than white, grey, and black). Yet a sensation of red is but one sensation, and there seems to be no way to divide its chromatic color from its color, more generically conceived. What’s more, as Locke observed, there is also no way to 28 Interestingly, while Geach situates his critique in the Wittgensteinian tradition, he begins with a point that might seem alien to Wittgensteinians, but useful to foundationalists. Geach rejects the contention that individual concepts have no meaning to call their own, as one might think on the grounds that meaning is use, and concepts are used only in the context of an overall sentence. He notes that sentences as a whole do not acquire meaning through use, for many sentences are entirely original. Here he is referring to what we now call “compositionality”: “It is words and phrases that have an established usage; a language is mastered not by learning whole sentences out of a guidebook but by learning to make up sentences in it and to understand sentences not previously heard…The ability to express a judgment in words thus presupposes a number of capacities, previously acquired, for intelligently using the several words and phrases that make up the sentence” (Geach 1957, p. 12). I will assume that Geach is right about this; I have long thought that there is a tension between two related Fregean points in this regard: the emphasis on compositionality, and on the “context principle” (that words have meaning only in the context of a sentence). Obviously there are some terms in our language which are meaningful only in the context of a sentence. Logical concepts like IF, THEN, NOT, AND, and OR are the most notorious examples. But the fact that some concepts have no separable meaning does not imply that none do. So Geach agrees with “the old logic-books” that judgments presuppose the exercise of concepts, though the exercise of a concept in judgment is not a “definite, uniform sort of mental act” (1957, p. 15).

123

378

Synthese (2011) 180:357–389

separate RED from COLOR, as there is no differentia that can be added to something’s being colored to specify what it is to be RED. In virtue of what do we grasp red qua RED, rather than red qua COLOR? The main question to ask of Geach’s critique here is if the foundationalist— especially the direct realist foundationalist—should assume that color concepts, or any other concepts of sensory qualities, are the most basic concepts, epistemically. Indeed Geach’s contention that these concepts are concepts of “sensible things” betrays an assumption that is at odds with direct realism about perception. In fact, the version of direct realism I have been assuming should deny that the most basic concepts are concepts of sensory qualities (or qualities of any kind), because the direct realist should maintain that we are first aware of entities, of physical objects. The connection between the most basic objects of perception and the most basic types of concepts can be understood better by looking back to Gibson. More obvious to us than similarities among the qualities of objects are those among the objects as object-types. Recall that central to Gibson’s theory is the distinction between information that is “picked up” from the ambient optic array on the one hand, and the things or properties of the world that are actually perceived, on the other. Information about properties such as shape and resistance to deformation are picked up unconsciously, and “invariant” relationships among these are extracted in a way that automatically and non-inferentially produces an awareness of the object as a whole. The awareness which this information helps produce does not at first constitute an ability to focus attentively on the attribute of shape, for example, even though some of the information unconsciously drawn upon is with regard to shape. In my view, it is natural to think that the same information with respect to which our perceptual systems detect differences—and hence become aware of distinct objects—should soon become the respect in which we come to be aware of similarities.29 We first use perceptual similarities in three-dimensional shape, for example, to form concepts of object types, concepts like TABLE, CHAIR, and CAT, each of which we recognize especially for its distinctive shape.30 Only once we form concepts of objects can we then attend to their qualities and attributes, and form concepts like SQUARE, RED, and FUZZY, by noting how objects of fundamentally different types can all possess the same attribute. So, 29 Prinz (2002) comments on how his theory of concepts (see footnote 39) predicts just what we would expect about similarity in light of Gibson’s findings about perception: “The basic level generally lies at an intermediate [middle-sized] level of abstraction…. This suggests that shape similarity confers an advantage in learning and categorization. Proxytype theory predicts this because proxytypes are perceptually derived and shape plays a very dominant role in object perception” (p. 163). Prinz is probably not a direct realist about perception, himself. The noteworthy lesson to take from his position here is to see the connection he notes between a point from Gibsonian direct realism and a point about basic-level concepts. 30 Drawing in part on the work of Gibson, Pollock and Oved (2005) understand that we can recognize middle-sized objects, like cats, even when we cannot articulate a description of cats in terms of shape (or color) concepts. They speculate about how this recognition might result from a “cat detector” cognitive “module,” that is acquired after seeing how the various parts of cats fit and move together in a certain uniform way, in just the same way that chicken-sexers learn their skill on the basis of an implicit learning of chicken-parts. Perhaps this results from the formation of a connectionist “neural network” that permits a sophisticated form of pattern recognition (pp. 333–338). But one does not have to accept the modularity theory of cognition or connectionism to realize that what Pollock and Oved are gesturing toward is the acknowledgement that we have something like an innate capacity to recognize perceptual similarities among objects with three-dimensional shapes.

123

Synthese (2011) 180:357–389

379

some similarities are more readily available to perception than others, and concepts of object-types, not of quality-types, are the ones formed first.31 Recognizing that some similarities are automatically more accessible early on helps solve, in part, the problem of how we are to abstract out the “right” element: as young children, at some point we simply have no choice. This is another respect in which the perceptual awareness of similarity is neither justified nor unjustified. We cannot help but form concepts of object-types first, because salient similarities in three-dimensional shape single them out for us. And then, even though the attributes with respect to which these similarities hold are not the first things to be conceptualized, we eventually can’t help but form concepts of shapes and colors themselves, because the possession of concepts of objects enables us to focus perceptually on these qualities and attributes (by noticing, for example, how the object type can vary while the color stays the same, or vice-versa).32 For all of these reasons, I maintain that the direct realist about perception should expect the most basic concepts of “sensible things” to be concepts of “middle-sized objects,” of animals, of plants, of simple artifacts, etc. If this is true, a point that Geach takes to be a criticism of abstractionism actually lends further strength to the view: There is however no reason to think that this gives ‘sensory’ concepts an epistemological primacy over others; for the description of sensations is a highly sophisticated exercise of concepts, and is secondary to the application of ‘sensory’ concepts to the material environment. In this primary, outward-looking application, ‘sensory’ concepts have not in fact any privileged position; a child with only a few concepts and only a small understanding of language may easily possess concepts like door and book…before it has any colour concepts at all. (pp. 41–42) “But of course!”, the direct realist should insist. The child is able to use these physical object concepts first because they are epistemically basic, they are the ones the child needs to abstract first in order to form the others. If the exercise of concepts of sensory qualities is sophisticated, it is no surprise, because this exercise will presuppose the acquisition of more basic object concepts. Curiously, earlier in his book, Geach proclaimed that he would not critique abstractionism by resorting to the findings of developmental psychology, but on the grounds that abstractionism stems from a “wrong analysis about what is done when the concept is exercised” (p. 18). Yet here 31 It does seem that the most salient similarities children conceptualize are those among objects (types

of animal, people, food, artifacts, etc.) in regard to their shape (Anglin 1977, p. 71). Arguably this would be for evolutionary reasons. Differences in shape make the most difference to us qua animals, since these differences make the biggest difference to organisms that must locomote to obtain nutrition. The particular scientific story about how our capacity as shape detectors came about is not important. Further confirmation is found in the work of Rosch (1999/1978), who discovered that the “basic level concepts” for adults, those concepts which designate things at the highest taxonomic level (level of generality) with maximum perceptual resemblance, are physical object concepts, are likewise the first to be categorized by children (p. 195). For a survey of more recent work confirming Anglin and Rosch, see Sloutsky (2003). For further philosophical points about the necessary order in which types of concepts are formed, see my later discussion (using the example of blueberries and blackberries) of how a series of concepts of object-types are needed to recognize the range of variation encompassed by an attribute concept. 32 Again, see more about this in the section 11 paragraphs from this point about blueberries and blackberries.

123

380

Synthese (2011) 180:357–389

his critique does refer to a seemingly relevant point from a kind of common sense developmental psychology.33 So concepts of middle-sized object-types are much better candidates for the basiclevel concepts that would feature in the foundationalist’s basic beliefs, as they do not presuppose other concepts in the way that quality or attribute concepts do.34 Direct realism’s role in identifying the proper basic-level concepts is thus the third major way in which its view of perception helps support a view of epistemic justification. (The first two roles involved its support for the possibility of a non-conceptual grasp of similarity, and of causal connections.) In what remains, I will say what more besides a direct realist theory of perception is needed to inform the foundationalist’s theory of concepts. So far, I have only shown that it is more plausible that concepts are abstracted on the basis of perceived similarities than Geach thinks. I have not yet suggested how abstraction from that basis would work. To see the way to an explanation, it is useful to consult Sellars’ own critique of abstractionism. Sellars sees a particular view about abstraction as fundamental to all versions of the Myth of the Given: “all have in common the idea that the awareness of certain sorts… is a primordial, non-problematic feature of ‘immediate experience”’ (Sellars 1997/1956, p. 59). He thinks this view amounts to treating sensations as involving “absolutely specific, and infinitely complicated, thoughts,” and illustrates the view by reference to the theories of the classical British empiricists. Sellars observes that Locke takes for granted that we have 33 Perhaps he regards it as too obvious even to require special scientific evidence. But that is further to my point that the kind of psychological evidence we need to develop a theory of concepts needn’t be specialized or experimental. In this case, it is something any parent could observe, perhaps something any individual could remember about his own conceptual development. Certainly many of us remember learning color words later than words for types of middle-sized objects. 34 Critics could object that abstractionism’s allegedly basic level concepts, physical object concepts (like DOOR and BOOK) might still presuppose other concepts, and that for this reason, the abstraction and reapplication of said concepts could not deliver truly epistemically basic propositions (see Fumerton 1998). In my mind, the most plausible case for this claim would be the Kantian position that physical object concepts presuppose the concepts of space and time, the principles of individuation of objects. But I also think that Gibsonian theory affords many of the resources we need for understanding, at the very least, how spatial relationships might be perceived directly (at least given the direct perception of entities). As for temporal relationships, I would argue for the relevance here of an Aristotelian perspective on time as a way of grasping motion, and motion is clearly grasped perceptually. But Kantianism about space and time is controversial, and more plausible objections are likely to come from more standard contextualist considerations. Sellars says that a knowing subject needs to recognize the authority of his observational report by, say, recognizing that it has been made in the “standard conditions” of perception (in broad daylight rather than under artificial lighting, for instance.) Or as Sellars summarizes it, the subject recognizes that “utterances of ‘This is green’ are reliable indicators of the presence of green objects in standard conditions of perception.” Hence in knowing “This is green,” one presupposes concepts such as UTTERING ‘THIS IS GREEN,’ and the concept of STANDARD CONDITIONS OF PERCEPTION. What concepts might be presupposed in recognizing the authority of physical object reports? That is, what concepts might be components of “X” and “Y” for the corresponding “X is a reliable symptom of Y” for physical object reports? It seems much less likely that Sellars could invoke questions about “standard conditions” for the perception of physical objects. The need to speak of standard conditions arises mainly for identifying attributes of objects, especially “secondary quality” attributes that vary more with the state of the perceiver. The only conditions that would seem to determine the reliability of the perception of objects would be whether or not one is hallucinating. But see my comments on skeptical alternatives in Sect. 4.

123

Synthese (2011) 180:357–389

381

awareness of “determinate sense repeatables” like particular shades of red (CRIMSON, SCARLET, etc.) and only sees a problem in explaining how we are to abstract “determinable repeatables” (like RED) from determinate ones. What is the problem with this view, and how shall we evaluate Sellars’ response to it? First, Sellars observes that Locke attempts to account for abstraction by understanding determinate concepts as conjunctions of separate properties. CRIMSON, for example, might be understood as a conjunction of (A) RED and (B) some additional characteristic distinguishing CRIMSON from SCARLET.35 The determinable concept RED would then be formed by simplifying the conjunction of A and B, isolating A from the distinguishing characteristic B. The trouble is that there is no such characteristic B that separates CRIMSON from other shades of red. That is because there is no “pure” identical red that forms a part of shades like crimson which can be isolated from other non-red aspects of the shade. The shade is one form of red, through and through, although nothing qualitatively identical can be found in common among all shades of red, all of which differ continuously in hue. (This is the same problem as determining what distinguishes RED from COLOR, or CHROMATIC COLOR from COLOR.) Sellars suggests that a disjunctive rather than a conjunctive approach would obviate the need to find a characteristic like B to isolate determinate concepts. One could think of RED as (CRIMSON or SCARLET or ROSE or MAROON, etc.) This would also permit an answer to the objection Berkeley posed for Locke’s theory of abstraction, that there is something incoherent in an idea of TRIANGLE which is “neither oblique, nor rectangle, neither equilateral, equicrural, nor scalenon; but all and none of these at once” (Locke 1979/1690, IV, Chap. vii, Sect. 9). However, the likely response here is that no finite number of completely determinate concepts could possibly go to form the concept of a determinable, since something like a color continuum can be cut into an infinite number of discrete shades. Hume’s “missing shade of blue” example also shows that no such disjunction of determinate concepts is necessary or sufficient to understand BLUE (or RED), since the concept might be seen as applying to the missing shade even if it doesn’t make it onto the original list of disjuncts. Later Sellars comes to consider a version of “psychological nominalism” inspired by Hume, according to which red particulars fall under determinate and determinable concepts only in virtue of an association between the word “red” and particulars which are in fact similar. This association is engendered ultimately through social conditioning, rather than cognitive awareness, since Sellars assumes that grasping similarity requires conceptualizing objects as similar, and conceptualizing the respects in which they are similar.36 35 Both Sellars and Locke make Geach’s mistake of assuming that concepts of sensible qualities like color are basic, but the point Sellars raises here, though it involves an example about color, raises a problem that is more general. 36 Eventually Sellars acknowledges that this simple formula is “impossibly crude and inadequate as an account of the simplest concept.” His more fully developed view explains how concepts might be acquired holistically as the result of a coalescence of non-conceptual habits, habits of reliable linguistic expression in response to sorts of physical objects. A concept is formed when enough such habits coalesce that one is able to relate one’s various reliable responses, i.e. place them in a “space of reasons.” As I discuss in footnote 34, he takes this to mean that concepts are formed not singly, but in holistic batteries simultaneously. Ultimately his holism stems from his demand for epistemic perspective: to have a piece of perceptual

123

382

Synthese (2011) 180:357–389

Is there an alternative to the Lockean view of the formation of concepts of determinables apart from Sellars’ holistic “psychological nominalist” view? We have already seen a glimpse of one way in which the perceptual similarity approach bypasses Sellars’ alternative. Since an enriched (Gibsonian) view of perception allows for the direct perception not just of objects, but of some basic relationships, it should allow for the perceptual grasp of basic similarity relationships, without presupposing that such a grasp requires any conceptual abilities. Of course, simply noting how perceptual similarity is available as a basis for concept-formation does not give us a theory of abstraction from this similarity. But Sellars’ criticism of the Lockean view of abstraction gives us clues about how to articulate an alternative approach to abstraction. Locke’s error is to assume that the awareness of a repeatable depends on the awareness of qualitatively identical parts or aspects of entities. If there were such qualitatively identical parts, such as a “pure” red found in every shade of red, we would need no more than the comparison of two particulars possessing it to conceptualize the repeatable—but there are no such pure identities. A non-Lockean approach should embrace awareness of the variability of shades as essential to the very process of abstraction. Indeed the awareness of similarity itself is to be understood not as grasping an identity surrounded by differences, but as grasping a form of comparative difference. We grasp the similarity between a particular shade of crimson and a particular shade of scarlet—the basis for thinking of them as determinations of a repeatable—only because we see these two shades as different, but as less different than each is from, say another particular shade of yellow. Perception of similarity arises from active perceptual interrelation of the similars in contrast to “foils” which differ more from the similars than they do from each other. Without the foil, we might only see the similars as irreducibly different (Kelley 1984, pp. 336–342). This point addresses Huemer’s concern that if perceptual content were nonpropositional, it would be “intrinsically meaningless” and incapable of being the basis for concept-formation (2001, pp. 72–74). It is correct that single, isolated percepts would indeed be conceptually meaningless on my account. So, it seems, would pairs of them. The solution is to recognize that conceptual meaning comes from the active interrelation of at least two perceived objects with a foil. The concept of TABLE does presuppose some recognition of the contrast between tables and non-tables. Contrary to Sellars, however, the only “holism” involved in this process is with regard to one’s perceptual knowledge: one must see the difference between tables and nontables to grasp the similarity among tables. But it is not even necessary that we form TABLE by forming some complementary concept, like CHAIR: it is enough that tables are contrasted with as yet-unconceptualized chairs and entities of many other kinds. This allows us to accept Hegel’s wisdom that we form concepts through comparison

Footnote 36 continued knowledge demands the conceptual recognition of its authority. As should be evident from my earlier section, the need for epistemic perspective does not entail holism, as long as nonconceptual forms of perspective are available.

123

Synthese (2011) 180:357–389

383

and contrast, without embracing his anti-foundationalist rejection of the relevance of “sense certainty” (or Sellars’ updated “Meditations Hegeliennes”). Understanding similarity in terms of the paradigm-foil model, which embraces similarity as a matter of comparative difference, is crucial not only to understanding similarity itself, but to understanding the process of abstraction on the basis of similarity.37 The problem with Sellars’ “disjunctive” view of concepts (the contention that a concept of RED could be equated with “either CRIMSON or SCARLET or etc.…”), is that a universal concept stands for more than a finite number of relatively determinate disjuncts. How does a cognitive state capture the whole range of possibilities, the whole span of the determinable? Part of the problem, I believe, is expecting abstract conceptual awareness to be a static form of awareness. But we need not and should not think of concepts as mere mental states. We should approach them in the same way that the direct realist approaches perception of both objects and similarities: as a form of awareness enabled and even constituted by an active process of cognition.38 The processing involved in the perceptual grasp of entities as such is often strictly physiological and unconscious, but even still active discrimination and attention is sometimes needed to perceive a given entity. The role of conscious activity increases as we move up the scale of cognition. We have just seen how a form of active interrelation is needed to grasp perceptual similarity, when it is understood as a form of comparative difference. This should lead us to expect abstraction from similarity to require even more conscious activity. Finding the form of active conscious activity needed for abstraction will improve upon Sellars’ disjunctive proposal, which could not account for how concepts integrate

37 The paradigm-foil model of similarity helps address a problem for foundationalists originally formulated by Moser (1985). If a foundationalist wishes to show how an unconceptualized perception of a cold, pink surface could support a belief about cold, rather than a belief about pink, subjects making an appeal to perception must be able to direct their attention just to the cold and not to the pink (Cling 2007, p. 410). Moser and Cling assume that one can simply direct one’s attention to the color rather than the temperature, but it is not clear how this would work since the same surface has both properties. The problem is intensified if the two properties in question are graspable only through the same sensory modality, such as PINK and SQUARE. We cannot attend to PINK rather than SQUARE if we stare at a single pink, square object. We cannot do it even if we compare two square pink objects to each other, as Locke might urge. But it is more plausible to say that we can abstract PINK rather than SQUARE if we compare two square pink objects to a square white object. (To abstract SQUARE rather than PINK, we compare two square pink objects to a circular pink object.) Perceiving a similarity works something like a “method of difference” experiment: holding the color constant, we vary the shape, bringing one attribute rather than the other to the forefront of consciousness. Cling also raises the problem of how we are to abstract WATER rather than H20 from samples of water, or any concept which nomologically or conceptually implies other concepts we do not seem to be in a position to grasp (pp. 410–411). I think this problem is much easier to solve than the attention problem, which Cling thinks is easier. Simply stated, nobody thinks that crude deductive closure is true of knowledge generally (“If person S knows p, and p entails q, S knows q.”) Obviously people can know scattered premises of complicated mathematical deductions without yet knowing the conclusions. A similar crude principle of closure should fail for concept-possession, as well. This is underscored by the present account of concept-formation, which reminds us that while we have automatic awareness of similarity in regards to shape and color (which enable us to form a concept of WATER), we do not have such awareness of similarity in regards to hydrogen or oxygen atom possession. 38 For more in support of this point, and its implications for understanding the nature of a truly prescriptive

conception of epistemology, see Salmieri and Bayer (2009).

123

384

Synthese (2011) 180:357–389

a potentially infinite range of referents. Consider an analogy: there is a potentially infinite number of points between one end of a room and another, and Zeno could not conceive of reaching each point along the way while still reaching the other end of the room. We know, of course, that one can make the trip in one swift, active motion. We should think of conceptual reference along the same lines. As long as a concept is understood as having to embrace each “point” of reference separately, its ability to do so for potentially infinite such points is inconceivable. But if to grasp a concept is to make an “active motion,” rather than to hold a static number of representations, there is no conceptual Zeno’s paradox. What is the nature of this “active motion” for concepts? Consider the pre-conceptual ability to transform objects in imagination. We can imagine the color crimson turning into scarlet by mere changes in degree, or even a table turning into a chair. Not every color in the universe counts as red, and not every artifact as a piece of furniture: the range is finite, even if the boundaries of the range can be vague. There is potentially infinite variability within the scope of that finite range, but we don’t need to “stop” mentally at each such possibility to grasp the range. To be sure, we may never actually imagine transformations from one end of the spectrum of reference to the other along every possible dimension of variability. What is important is that we can, and that after perceiving similarities, we can, in virtue of this ability, identify new referents as falling inside or outside the scope of these similarities (depending on the “distance” from the paradigm or foil). Here I have by no means fully articulated or defended the proposal that imaginative transformation plays a role in abstracting from similarity, but I believe that considering it is the most promising avenue to explaining a fully direct realist version of abstractionism.39 It is worth mentioning that it is not enough to be able to imagine a single type of object changing from one color to the next in order to form concepts of attributes, such as color. To completely grasp color as an attribute in abstraction from objects, one must be able to comprehend that blueberries differ from blackberries in precisely the same way that bluebirds differ from blackbirds, that the referents of many types of physical object concepts may differ in this way of being. One must be able to understand conceptually that the range of possible differences may apply. This is part of the reason that color concepts are not, in the end, the most basic concepts—their grasp does presuppose the possession of physical object concepts in terms of which the range of differences may be understood.40 Physical object concepts can be abstracted in much the same way in which we have described color concepts being formed, but the range of possibilities to be imagined will vary along axes of three-dimensional

39 Prinz (2002) has formulated a new theory of “concept empiricism” that explains how concepts of middle-sized objects are abstracted from perceptual experience, which exploits mental devices he calls “proxytypes,” products of “long-term memory networks” which permit the grouping together of quantitatively-varied percepts. Simple examples of these networks include “hierarchical” representations, which encode and integrate changes in experience as one “zooms” in or out on an object, “transformational” representations, which do the same for moving objects, and most importantly, “predicative” representations, which exploit the other types to group objects on the basis of similarity (as if a similarity range could be grasped as a transformation from one similar to another) (2002, pp. 141–144). See also Kelley (1984, p. 345). 40 I owe this point to Greg Salmieri (personal conversation).

123

Synthese (2011) 180:357–389

385

shape and associated types of perceived motions and/or causal powers (the awareness and imagination of which can be pre-conceptual, according to direct realists). One last point, especially important to combating Sellars’ nominalism, is that the awareness of similarity on this model is not a wholly psychological, subjective phenomenon. There are objective facts that make it possible for us to see similars as falling along the same range in the first place. Recently Salmieri (2008) has argued persuasively, contrary to conventional wisdom, that Aristotle’s theory of concepts explains the relationship between determinables and determinates by reference to objective facts, without falling into the trap of the Lockean view of abstraction. Color and shape are just distinct from each other in a way that red and blue are not. They are “incommensurable” and cannot be compared directly. Red and blue, on the other hand, are not merely distinct. They differ from each other in a comparable way, existing as determinates under the same determinable. As Aristotle puts it, “difference and otherness are distinct. For while the other and that which it is other than are not necessarily other in something… the different differs from something in something.”41 Kind members differ “in the more and the less,” according to Aristotle (1055a3), in merely quantitative ways with respect to a commensurable characteristic. Salmieri offers an intriguing account of the connection between Aristotle’s conception of kinds and his conception of “intelligible matter.” Members of kinds which differ in the “more and the less” differ only in their potential to be transformed intellectually from one determinate member to another, and as such, their sameness of kind consists in this potential. But clearly there exist real commensurability relationships among them (relationships which do not exist between, say, colors and shapes). What’s more, members of the kind must have an objective causal unity that provides explanatory connections among the defining characteristics of the concept. Rather than being arbitrary groupings, concepts formed in this way designate groups that are held together by objective relations in reality, if not by the possession of qualitatively identical characteristics (as the conventional reading of Aristotle suggests). Even if this is not Aristotle’s real position, it is a provocative proposal in its own right, and similar proposals have been advanced by a number of other contemporary neo-Aristotelian theories of concepts (Rand 1990; Kelley 1984; Gotthelf 2007). Only if Sellars could eliminate from consideration such theories would his nominalism be the only alternative to failed Lockean theories of abstraction, and only then would his contextualism be the best alternative to the foundationalist solution to the regress problem. Even if I have identified a basic form of awareness that avoids various regress problems concerning our most basic concepts and beliefs, much more research is needed to show how the use of these basic concepts provides a foundation for large portions of the rest of our knowledge. Showing this requires a more in-depth and systematic survey of the range of our concepts and of how concepts of increasing abstraction derive from lower-level concepts. In particular, to account for the validity of scientific induction, we would need an explanation of the abstraction of concepts of causal relations (not just an account of how particular causal relations are perceived, as Gibson

41 Salmieri translation quoted in Salmieri (2008, p. 79), of Metaphysics I.3-4 (1054b22-a12).

123

386

Synthese (2011) 180:357–389

and others have given). But I think I have at least provided a compelling case to pursue this research project, because its basics fit the bill needed to avoid the most pressing philosophical problem for foundationalism: not whether basic beliefs can support all of our knowledge, but whether they can support any of it. 6 Conclusion In closing, I need to mention that there is one last respect in which direct realism about perception helps inform not only a theory of concepts but an overall theory of justification built upon a theory of concepts. One of the mistakes that direct realists cite as responsible for the popularity of representationalism is the confusion between the form and the object of cognition.42 If, for example, one notices that the proverbial stick in water looks bent, and infers that there must be some intermediate object of awareness that is actually bent (unlike the non-bent stick), one is mistakenly conflating the form of awareness of the stick with the object of awareness. In fact, one is aware of a stick, not of a bent stick sense datum, even if one is aware of it in a way that more strongly resembles the way in which one is aware of bent sticks (and even if to some in certain contexts this may be misleading). Representationalists often seem to assume that if awareness is made possible by some process, it is only the final stage of the process that is the object of awareness, as if awareness must be an unmediated magical state. But as Huemer points out, the fact that one uses an axe to chop wood does not mean that one is only “indirectly” chopping the wood, and only directly chopping the axe (Huemer 2001, pp. 81–82). Likewise the fact that human consciousness involves and is constituted by a definite process with a definite identity does not disqualify it from being conscious of an object distinct from that process. Finally, then, I want to briefly urge a point that most direct realists do not acknowledge, that the form/object distinction applies not only to perceptual forms of awareness, but to conceptual forms, as well. Taking the distinction seriously helps address the concern that our approach to concepts is too psychological to undergird a theory of epistemic justification. This returns me to the concern I mentioned at the end of my introductory section, about the alleged dichotomy between the psychological and the epistemological. There is no prima facie rationale for this distinction. To propose an epistemology without a thinking, psychological subject is incoherent. One may be concerned that a theory of concept-formation that stresses the psychological conditions needed to grasp similarities (e.g., foil and paradigms) might only describe human mechanisms that “filter” rather than cognize reality. But this (vaguely Kantiansounding) position also conflates the form of conceptual awareness with its object.43 42 See Adler invoking Aquinas (1987, pp. 15–19) and Kelley (1986, pp. 44–51). For more contemporary counterparts to this distinction, see Campbell’s idea of the “standpoint” of perception (2002). 43 Most likely it was a Kantian anti-psychological view that influenced Frege to de-psychologize his distinction between Sinn and Bedeutung. Frege’s concept of Sinn is best understood as the “mode of presentation” of an object—much like the concept of “form” I have articulated above. But Frege thought that a psychological mode of presentation would relativize or subjectivize the identity of our thoughts: since subjects’ thoughts may be more or less similar in respect to “mode of presentation,” they would not share

123

Synthese (2011) 180:357–389

387

Like perception, conceptual awareness is an active process, and one would expect that, as an act, it has a definite identity, operating under definite conditions. As before, we should not confuse the identity of the act, the how (or the form) of cognition, with its referent in the world, its what (the object). The fact that our cognition involves a definite process should not be seen as a barrier to cognition, but as its enabler. We achieve conceptual awareness of, say, a range of tables by perceiving a similarity made possible by the physiology and psychology of our perceptual and imaginative capacities. But it is still the range of past, present and future tables in the world that we are aware of by means of these psychological capacities. The sum total of the above should raise questions about the longstanding assumption that the consideration of human psychology is irrelevant to the establishment of genuine epistemic norms. Though I have drawn on psychology to explain the nature of perception and concept-formation, my purpose has been to explain the nature of internalistic foundational justification—contrary to the usual naturalistic preference for externalism. I do not take the same approach to perception or abstraction championed by Descartes and Locke, but my internalistic, foundationalist approach here is firmly within the guidance conception of justification those figures long ago established as central to the Western epistemological tradition. Acknowledgements I am indebted to several parties for commentary on various versions and drafts of this paper. Attendees at the Anthem Foundation conference on the theory of concepts at the University of Pittsburgh in the Spring of 2004 provided useful feedback on a presentation representing my nascent views on this topic. My interest was developed further in early drafts of my dissertation. Gary Ebbs and Jonathan Waskan provided feedback at all stages of this process, and Jon offered feedback on a more recent draft. The Colorado Springs Philosophy Discussion Group also read and commented on the first draft of the present paper. Anonymous reviewers at Synthese and at one other journal provided indispensible suggestions for improving the more recent draft, as did Matt Bateman and Stacey Swain. Stacey and Keri S. Kahn also helped improve the style and readability of the paper.

References Adler, M. (1987). Ten philosophical mistakes. New York: Collier Books. Alston, W. (1999). Back to the theory of appearing. Philosophical Perspectives, 13, 181–203. Anglin, J. (1977). Word, object, and conceptual development. New York: Norton. Austin, J. L. (1946). Other minds. Proceedings of the Aristotelian Society, 20, 148–187. Austin, J. L. (1962). Sense and sensibilia. London: Oxford University Press. Bayer, B. (2007a). The varieties of naturalized epistemology: Criticisms and alternatives. Doctoral dissertation, The University of Illinois, Urbana-Champaign.

Footnote 43 continued the same thought if Sinn was taken to partially individuate thoughts. I doubt, however, that the variations in psychological mode of presentation are enough to make “sharing a thought” impossible in any meaningful sense. Obviously different subjects can still share the same objects of thought. And while it is true that their thoughts would be token non-identical, this would not force them to be type-non-identical. Surely even within the scope of a type, there would be individual variations, but as my theory of concepts stresses, variation is essential to falling under a determinable anyway, so this is no problem unless one thinks that items must be identically determinate in order to fall under the same concept. McDowell (2005, p. 49) has stressed that Frege’s concept of mode of presentation could be made to involve psychology, provided that the psychology was not that of the anti-normative psychologism preached by the naturalists of 19th century German philosophy.

123

388

Synthese (2011) 180:357–389

Bayer, B. (2007b). From folk psychology to folk epistemology: The status of radical simulation. Unpublished manuscript. http://www.benbayer.com/simulationtheory.pdf. Bloom, L. (1973). One word at a time: The use of single word utterances before syntax. Janua linguarum, series minor, 154. The Hague: Mouton. Bloom, L. (1993). The transition from infancy to language. Cambridge: Cambridge University Press. BonJour, L. (1985). The structure of empirical knowledge. Cambridge, MA: Harvard University Press. BonJour, L. (2004). In search of direct realism. Philosophy and Phenomenological Research, 69(2), 349–367. BonJour, L. (2007). Epistemological problems of perception. In E. N. Zalta (Ed.), The Stanford encyclopedia of philosophy. http://plato.stanford.edu/entries/perception-episprob//. Brewer, B. (1999). Foundations of perceptual knowledge. American Philosophical Quarterly, 34, 41–55. Brewer, B. (2006). Perception and content. European Journal of Philosophy, 14(2), 165–181. Campbell, J. (2002). Reference and consciousness. New York: Oxford University Press. Cling, A. (2007). The epistemic regress problem. Philosophical Studies, 140(3), 401–421. Coady, C. A. J. (1992). Testimony: A philosophical study. New York: Oxford University Press. Dretske, F. (1970). Epistemic operators. The Journal of Philosophy, 67(24), 1007–1023. Dretske, F. (1995). Naturalizing the mind. Cambridge, MA: MIT Press. Fodor, J., & Pylyshyn, P. (1981). How direct is visual perception?: Some reflections on Gibson’s ecological approach. Cognition, 9, 139–196. Fumerton, R. (1995). Metaepistemology and skepticism. Lanham, MD: Rowman and Littlefield. Fumerton, R. (1998). Externalism and epistemological direct realism. The Monist, 81(3), 393–406. Geach, P. (1957). Mental acts: Their content and their objects. London: Routledge and Kegan Paul. Gelman, S. (2004). Psychological essentialism in children. Trends in Cognitive Sciences, 8(9), 404–409. Ghate, O. (1998). The argument from conflicting appearances. Doctoral dissertation, The University of Calgary, Alberta. Gibson, J. J. (1966). The senses considered as perceptual systems. Boston: Houghton-Mifflin Co. Gibson, J. J. (1986). The ecological approach to visual perception. Hillsdale, NJ: Lawrence Earlbaum Associates. Goldman, A. (1979). What is justified belief ?. In G. Pappas (Ed.), Justification and knowledge: New studies in epistemology. Boston: D. Reidel. Goldman, A. (1999). Internalism exposed. The Journal of Philosophy, 96(6), 271–293. Gotthelf, A. (2007). Ayn Rand on concepts: Another approach to abstraction and essence. Metaphysics of science project conference at the University of Birmingham on nature and its classification, 13 October 2007. http://www.bristol.ac.uk/metaphysicsofscience/naicpapers/gotthelf.pdf. Harré, R., & Madden, E. (1975). Causal powers: A theory of natural necessity. Oxford: Basil Blackwell. Huemer, M. (2001). Skepticism and the veil of perception. Lanham, MD: Rowman & Littlefield. Huemer, M. (2007a). Compassionate phenomenal conservatism. Philosophy and Phenomenological Research, 74(1), 30–55. Huemer, M. (2007b). Epistemic possibility. Synthese, 156, 119–142. Johnston, M. (2004). The obscure object of hallucination. Philosophical Studies, 120, 113–183. Keil, F. (1992). Concepts, kinds, and cognitive development. Cambridge, MA: MIT Press. Kelley, D. (1984). A theory of abstraction. Cognition and Brain Theory, 7(3&4), 329–357. Kelley, D. (1986). The evidence of the senses: A realist theory of perception. Baton Rouge: Louisiana State University Press. Le Morvan, P. (2004). Arguments against direct realism and how to counter them. American Philosophical Quarterly, 41(3), 221–234. Leslie, A., & Keeble, S. (1987). Do six-month-old infants perceive causality ?. Cognition, 25, 265–288. Levine, S. (2007). Sellars’ critical direct realism. International Journal of Philosophical Studies, 15(1), 53–76. Locke, J. (1979/1690). In P. H. Nidditch (Ed.), An essay concerning human understanding. New York: Oxford University Press. Marr, D. (1982). Vision. San Francisco: Freeman Press. McDowell, J. (1996). Mind and world. Cambridge, MA: Harvard University Press. McDowell, J. (2005). Evans’ Frege. In J. Bermudez (Ed.), Thought, reference, and experience: Themes from the philosophy of Gareth Evans (pp. 42–65). New York: Oxford University Press. Medin, D. L., & Ortony, A. (1989). Psychological essentialism. In S. Vosniadou & A. Ortony (Eds.), Similarity and analogical reasoning (pp. 179–195). Cambridge: Cambridge University Press. Michotte, A. (1963). The perception of causality. New York: Basic Books.

123

Synthese (2011) 180:357–389

389

Modee, J. (2000). Observation sentences and joint attention. Synthese, 124, 221–238. Moser, P. (1985). Empirical justification. Dordrecht: D. Reidel. Namy, L., & Gentner, D. (2002). Making a silk purse out of two sow’s ears: Young children’s use of comparison in category learning. Journal of Experimental Psychology, 131(1), 5–15. Noë, A. (2002). On what we see. Pacific Philosophical Quarterly, 83, 57–80. Pollock, J., & Oved, I. (2005). Vision, knowledge and the mystery link. Philosophical Perspectives, 19, 309–351. Porter, S. (2006). Restoring the foundations of epistemic justification: A direct realist and conceptualist theory of foundationalism. Lanham, MD: Lexington Books. Prinz, J. (2002). Furnishing the mind: Concepts and their perceptual basis. Cambridge, MA: MIT Press/Bradford Books. Putnam, H. (1994). Sense, nonsense, and the senses: An inquiry into the powers of the human mind. Journal of Philosophy, 91(9), 445–517. Quine, W. V. O. (1969a). Epistemology naturalized. In W. V. O. Quine (Ed.), Ontological relativity and other essays (pp. 69–90). New York: Columbia University Press. Quine, W. V. O. (1969b). Natural kinds. In W. V. O. Quine (Ed.), Ontological relativity and other essays (pp. 114–138). New York: Columbia University Press. Quinton, A. (1973). The nature of things. New York: Routledge & Kegan Paul. Rand, A. (1990). Introduction to objectivist epistemology (2nd ed.). New York: Meridian. Reid, T. (1969/1785). Essays on the intellectual powers of man. Cambridge, MA: MIT Press. Reynolds, S. (1991). Knowing how to believe with justification. Philosophical Studies, 64, 273–292. Rosch, E. (1999/1978). Principles of categorization. In E. Margolis & S. Laurence (Eds.), Concepts: Core readings (pp. 189–206). Cambridge, MA: MIT Press. (Originally published in E. Rosch & B. Lloyd (Eds.), Cognition and categorization (pp. 27–48). Hillsdale, NJ: Lawrence Erlbaum Associates.) Salmieri, G. (2007, 12 June). Justification as an aspect of conceptualization. Paper presented at Workshop on Normativity and Justification in Epistemology and Ethics, Harvey Mudd College, Claremont, CA. Salmieri, G. (2008). Aristotle and the problem of concepts. Doctoral dissertation, The University of Pittsburgh. Salmieri, G., & Bayer, B. (2009). How we choose our beliefs. Unpublished manuscript. http://www. benbayer.com/how-we-choose-our-beliefs.pdf. Schantz, H. (2001). The given regained. Philosophy and Phenomenological Research, 62(1), 167–180. Schlick, M. (1959). The foundation of knowledge. In A. J. Ayer (Ed.), Logical positivism. New York: Free Press. Scholl, B., & Tremoulet, P. (2000). Perceptual causality and animacy. Trends in Cognitive Science, 4(8), 299–305. Sellars, W. (1991). Science, perception and reality. Atascadero: Ridgeview. Sellars, W. (1997/1956). Empiricism and the philosophy of mind. Cambridge, MA: Harvard University Press (Originally published as Empiricism and the philosophy of mind. In H. Feigl & M. Scriven (Eds.), Minnesota studies in the philosophy of science, volume I: The foundations of science and the concepts of psychology and psychoanalysis (pp. 253–329). Minneapolis: University of Minnesota.) Sloutsky, V. (2003). The role of similarity in the development of categorization. Trends in Cognitive Sciences, 7(6), 246–251. Travis, C. (2004). The silence of the senses. Mind, 113(449), 57–94. Williams, M. (1996). Unnatural doubts: Epistemological realism and the basis of skepticism. Princeton, NJ: Princeton University Press. Wittgenstein, L. (1969). In G. E. M. Anscombe & G. H. von Wright (Eds.), On certainty. New York: Harper Torchbooks. Yolton, J. (1979). As in a looking-glass: Perceptual acquaintance in eighteenth-century Britain. Journal of the History of Ideas, 40(2), 207–234.

123

This page intentionally left blank z

Synthese (2011) 180:391–417 DOI 10.1007/s11229-009-9708-4

The cognitive act and the first-person perspective: an epistemology for constructive type theory Maria van der Schaar

Received: 16 July 2007 / Accepted: 1 December 2009 / Published online: 27 December 2009 © The Author(s) 2009. This article is published with open access at Springerlink.com

Abstract The notion of cognitive act is of importance for an epistemology that is apt for constructive type theory, and for epistemology in general. Instead of taking knowledge attributions as the primary use of the verb ‘to know’ that needs to be given an account of, and understanding a first-person knowledge claim as a special case of knowledge attribution, the account of knowledge that is given here understands first-person knowledge claims as the primary use of the verb ‘to know’. This means that a cognitive act is an act that counts as cognitive from a first-person point of view. The method of linguistic phenomenology is used to explain or elucidate our epistemic notions. One of the advantages of the theory is that an answer can be given to some of the problems in modern epistemology, such as the Gettier problem. Keywords Constructive type theory · Theory of knowledge · Cognitive act · Judgement · Truth and error

1 Introduction Current accounts of propositional knowledge (knowledge that) take knowledge attributions as their starting-point, asking what the truth-conditions are for sentences such as ‘John knows that S’. Such accounts of knowledge do not capture all relevant aspects of propositional knowledge, because it has an exclusive focus on knowledge as state. Knowledge as state is standardly understood as a species of the state of belief, which is taken to be a disposition or capacity to act in certain ways. Besides the notion of knowledge as state one needs to acknowledge what may be called the cognitive act.

M. van der Schaar (B) Faculty of Philosophy, Leiden University, Leiden, The Netherlands e-mail: [email protected]

123

392

Synthese (2011) 180:391–417

The cognitive act is not a special case of belief; it is an insight gaining deed, or an act of perception; it is an act, not a disposition or capacity to act. A cognitive act may be expressed by exclamations such as: ‘Now I understand it’, ‘Now I see it’, or ‘Now I know it’. Although there are two types of cognitive acts, judgemental (the act of perceiving that the hawk is catching a bird) and non-judgemental (the act of perceiving the hawk), the paper focuses on the judgemental cognitive act. Constructive type theory (CTT) may be understood as a formal system among others to which meaning can arbitrarily be given. This is not the way, though, that Per Martin-Löf understands his theory. Logic is, for him, the theory of demonstrative knowledge: “Logic studies, from an objective point of view, our pieces of knowledge as they are organized in demonstrative science, or, if you think about it from the act point of view, it studies our acts of judging, or knowing, and how they are interrelated” (Martin-Löf 1985, p. 20). On such an account, one cannot understand logic without understanding such basic concepts as judgement and knowledge. To put it in phenomenological terms: formal logic is grounded upon rational, subjective activity. Martin-Löf explains these concepts in a different way than is generally done today. One of the two aims of this paper is to elucidate these notions by means of concepts developed in linguistic philosophy by Zeno Vendler and J.L. Austin, on the one hand, and by means of the epistemic concepts that one may find in the early phenomenologists, such as Franz Brentano and Edmund Husserl. Austin once called his philosophical method linguistic phenomenology, and that term suits the method that I use here to develop an epistemology for constructive type theory. The other aim of the paper is to evaluate the epistemology presented in this paper. How can it be used to give an answer to some of the philosophical problems that we are struggling with today? Section 2 introduces the notion of cognitive act without presupposing Per MartinLöf’s interpretation of CTT. In Sect. 3 I argue that the notion of cognitive act, when used for an epistemology for CTT, is preferably understood to be a primitive notion in terms of which the other epistemic notions are to be explained. And I argue that the idea of a first-person perspective is essential to understand the notion of cognitive act. Section 4 makes a comparison between the notion of cognitive act introduced here and the account of the cognitive act given in Husserl’s sixth Logical Investigation; notwithstanding the similarities, it will turn out that there is an important difference. Section 5 gives an analysis of the concepts of knowledge, judgemental correctness and evidence in terms of the cognitive act. Section 6 raises the question whether such a theory does not imply a relativism with regard to truth; the concept of error plays an important role here. Finally, Sect. 7 gives an evaluation of the cognitive notions developed in this paper by applying these notions outside the field of logic and mathematics. It is argued that these notions can be used to make sense of some of our pre-theoretical uses of the verb ‘to know’. Furthermore, these cognitive notions can fruitfully be applied to some of our philosophical problems. I give an answer to the following questions: To what extent can the concept of knowledge as state be defined in terms of the cognitive act, and would this be an improvement of the explanation of knowledge in terms of belief? To what extent can the concept of fallible knowledge introduced in this paper be used to give an answer to the problem of skepticism? Presupposing that if one asserts that S one claims to know that S, one may ask: ‘What sort of knowledge is claimed in

123

Synthese (2011) 180:391–417

393

assertion?’ And, given that the theory as it is presented here uses an internalist notion of justification: What is the answer to the Gettier problem?1 2 Knowing as achievement versus knowledge as state We know because we discover, demonstrate, understand, realize, perceive, see, spot, descry or recognize.2 As Gilbert Ryle once said, such cognitive verbs signify a special type of actions: they signify achievements (Ryle 1949, p. 130). Like ‘to win’, to arrive’ and ‘to find’, ‘to discover’, ‘to perceive’, and ‘to demonstrate’ are success or achievement verbs. And although it is now sometimes said that ‘to know’ is a success verb too, Ryle does not give the verb ‘to know’ as an example of an achievement verb. In most uses, ‘to know’ signifies a state or capacity, whereas the cognitive verbs just mentioned signify an action, which is characteristic of being an achievement verb. By introducing these verbs, Ryle wants us to understand that someone who has won the race or has proved a theorem has not done two things, running the race and winning it, or making certain derivations and proving the conclusion, he has done one thing with a certain upshot (Ryle 1949, p. 150). Zeno Vendler uses Ryle’s notion of achievement verb to elucidate a distinction regarding the verb ‘to know’. In most cases, ‘to know’ is used as a state verb. There are cases, though, in which the verb ‘to know’ is used as an achievement verb, for example, when someone exclaims ‘Now I know it!’. Later one may refer to such an achievement, and say: ‘And then suddenly I knew’ (Vendler 1967, p. 112). This ‘insight’ sense of knowing is not the same as the state sense of knowing. Knowing as insight is not related to the state of knowing as to start running is related to the activity of running, Vendler says, for knowing as insight does not start an activity. The two notions are related as getting married is related to the state of being married: knowing as insight is an achievement that initiates a state of knowing. Similarly, a flash of understanding, that is, understanding as achievement, initiates a state of understanding. ‘Knowing’ in the achievement sense is related to ‘knowing’ in the state sense as the present tense of a verb is related to its perfect form. ‘Understanding’ is in this way related to ‘ having understood’, and ‘seeing’ that the hawk catches the bird to ‘ having seen’ that the hawk catched the bird. It is a pity that the English language has only one verb ‘to know’, where most European languages have two verbs. German, for example, has the verbs ‘(er)kennen’ and ‘wissen’.3 The verb ‘wissen’, which is derived from the old form wizzan (originally meaning the perfect having seen; 1 See Gettier (1963). Except for the answer to the Gettier problem, the answers to these questions are meant as first proposals. They are meant to give an idea how an epistemology for CTT can be used outside logic and mathematics. Ranta (1994) has already given extensive applications of CTT in linguistics; I have developed a semantics of linguistic mood for constructive type theory in van der Schaar (2007). 2 I leave the problem of knowledge by testimony (deferred knowledge) for another occasion. The question

whether, and if so, in what sense, we can be said to know what we have learned from others will not be addressed here, either. 3 The Oxford English Dictionary, though, gives two older forms of knowledge verbs, namely ‘to ken’ and

‘to wit’, which correspond roughly to the German ‘(er)kennen’ and ‘wissen’.

123

394

Synthese (2011) 180:391–417

cf. the Duden dictionary), is used for the state of knowing; knowing as achievement is signified by the verb ‘(er)kennen’. According to Vendler, achievement verbs can be predicated only for single moments of time, whereas state verbs can be predicated for shorter or longer periods of time (Vendler 1967, p. 102). The actions introduced at the beginning of this section, such as to demonstrate, to discover, and to perceive may themselves, though, be stretched out in time. An act of demonstration takes time, depending upon the number of steps that is necessary to reach the conclusion from already known premises. The achievement itself of actually reaching the conclusion after all the steps have been made, happens at a single moment of time, and we could therefore restrict the term ‘act of demonstration’ to this final moment, but generally we call the whole process an ‘act of demonstration’. Cognitive acts, whether of demonstration, of insight, or of perception, can therefore not be distinguished from knowledge as state by saying that the act happens at a single moment of time. The distinction between the cognitive act and knowledge as state can best be understood as a special case of the distinction between an act or process and a state in the sense of a disposition to act. The distinction between act and disposition or ability to act regarding knowledge has a long tradition, going back to Aristotle’s De Anima (417a21–417b2). Apart from the capacity a human being has to become a knower, Aristotle distinguishes two meanings of the term ‘being a knower’. A man may be called a knower because he has knowledge of grammar (which is a ‘hexis’, often translated as ‘state’ or ‘disposition’), or he may be called a knower, because he is contemplating, that is, he “is actually and in the proper sense knowing this particular A”. An act of contemplating is an actuality; it is an end (telos) in itself [cf. Metaphysica  (= Book IX) 1050a9–1050a10]. In contemplating, the man is exercising or actualising his knowledge as disposition (De An. 417a21–417b2).4 A man has knowledge as disposition, when: “he can if he so wishes contemplate, as long as nothing external prevents him” (idem). According to the Aristotelian order of explanation, actuality is conceptually prior to potentiality (cf. De An. 415a14–415a22), for potential means potentially actual (Metaphysica  1049b13–1049b14). This principle means with respect to knowledge that knowledge as ability is fully to be explained in terms of its exercises. A man knows Greek grammar precisely means that he is able to make and understand grammatical sentences in Greek. We therefore may call him a knower of Greek grammar also when he is at the moment not exercising this ability. Knowledge of grammar is probably not a case of propositional knowledge . It is an ability, namely the ability to apply the grammatical rules correctly.5 Did anyone apply the Aristotelian distinction between actuality and potentiality to propositional knowledge? The Aristotelian distinction was common in the Scholastic tradition. The Thomistic terminology, ‘first’ and ‘second actuality’, for, respectively, the ability 4 Hamlyn (1968, p. 23), whose translation I use, gives a clarifying note (with respect to another passage): “It is noteworthy that Aristotle believes that there is an activity of knowing, and that knowledge is not merely dispositional. In contemplating the objects of the intellect we are engaged in this activity, and it is this which the Nicomachean Ethics ultimately sets out as the end for the rational man” (Hamlyn 1968, p. 85). 5 The contrast between knowledge as ability and propositional knowledge is elucidated in Ryle (1949, Chap. II), where it is called the contrast between knowing how and knowing that.

123

Synthese (2011) 180:391–417

395

(habitus) and its exercises, is perhaps better known than the Aristotelian terminology, but Aquinas does not explicitly mention propositional knowledge in this context. John Locke is perhaps the first to apply the distinction to propositional knowledge. He introduces the distinction between actual and habitual knowledge in the fourth book of An Essay Concerning Human Understanding (1689). According to Locke, actual knowledge is an act of perception, which may be an act of insight, an act of demonstration, or an act of sensual perception. For Locke, habitual knowledge is a form of propositional knowledge. I reconstruct Locke’s definition of habitual knowledge as follows, where any meaningful declarative sentence may be substituted for S: P has habitual knowledge that S, precisely if: • P has once had the act of perceiving that S; • the perception that S is stored in the memory of P, in such a way that: whenever P thinks of the proposition that S, he assents to S, and is certain of the truth of S.6 For Locke, like for Aristotle, it is important to understand habitual knowledge as a potentiality, to be defined in terms of its actualities or exercises. Locke also adds a new point: without a first act of perception there is no habitual knowledge. The act of perception marks the beginning of knowledge as state. What Locke calls the ‘act of perception’, is here called the ‘cognitive act’. Concerning propositional knowledge, current analytic epistemology has exclusively focused on knowledge as state, and has neglected the cognitive act. As far as I know, only Paul K. Moser distinguishes the two forms of knowledge introduced above, and applies the distinction to propositional knowledge.7 Moser starts with distinguishing between the dispositional state of belief and the act of assent. S believes that P—Moser uses S for the speaker, and P for the proposition, which is to have declarative form here—means that “(i) S has assented to P (consciously or unconsciously) either before t or at t, and (ii) as a nondeviant result of his assenting P, S is in a dispositional state at t whereby he will assent to P in any circumstance where he sincerely und understandingly answers the question whether it is the case that P” (Moser 1989, p. 18). And, “One’s genuinely assenting to a proposition is simply one’s sincerely and understandingly affirming it” (Moser 1989, p. 15). He understands assenting and affirming in a non-epistemic sense (Moser 1989, p. 46). Such affirming, Moser says, need not be a verbal utterance or inscription, and one need not be aware of it. In dispositional knowledge one is related to the known proposition by a dispositional belief. In what Moser calls nondispositional knowledge, one is actually related to the 6 “There are several ways wherein the Mind is possessed of Truth; each of which is called Knowledge.

1. There is actual Knowledge, which is the present view the Mind has of the Agreement, or Disagreement of any of its Ideas, or the Relation they have one to another. 2. A Man is said to know any Proposition, which having been once laid before his Thoughts, he evidently perceived the Agreement, or Disagreement of the Ideas whereof it consists; and so lodg’d it in his Memory, that whenever that Proposition comes again to be reflected on, he, without doubt or hesitation, embraces the right side, assents to, and is certain of the Truth of it. This, I think, one may call habitual Knowledge” (Locke 1689, IV.i.8: 527/8). 7 Kevin Mulligan acknowledged the cognitive act, both in its propositional and in its nominal sense (the act of seeing the hawk), in a lecture held at Leiden, December 2006. The next note shows that Franz von Kutschera also makes the relevant distinction.

123

396

Synthese (2011) 180:391–417

known proposition not by a dispositional belief, but by genuine assent (Moser 1989, p. 21); nondispositional knowledge is not a species of belief, but a species of assent. Moser explains dispositional knowledge as true justified belief, and nondispositional knowledge as true justified act of assent. Nondispositional knowledge standardly results in dispositional knowledge, but it may also be merely transitory, perhaps because of some defect in the knower’s memory system, as is the case in Moser’s Mr. Lawless, who can affirm P, but who cannot obtain any disposition to affirm P. According to Moser, Mr. Lawless may be said to ‘know’ in the transitory, nondispositional sense, although he cannot have dispositional knowledge. Although Moser does not use the term ‘cognitive act’, what he calls ‘the true justified act of assent’ is an example of a cognitive act. Conceptually, there are three ways to relate the concepts cognitive act and knowledge as state. First, one may explain both the cognitive act and knowledge as state in terms of more primitive notions, as Moser has done. Second, the cognitive act may be explained in terms of knowledge as state: the cognitive act is characterized as a coming or getting to know, that is, the cognitive act is explained as the act or process through which one comes or gets into a state of knowledge.8 The third way to relate the two notions is by explaining knowledge as state in terms of the cognitive act, as Locke for example has done. If one relates the notions of cognitive act and knowledge as state in this third way, the notion of cognitive act is given the most prominent place. In this paper, I argue that the cognitive act is of importance for an epistemology that suits constructive type theory, and for epistemology in general. Because knowledge as state is a disposition, it needs to be explained in terms of its actualisations, that is, in terms of the cognitive act. If one asserts in a dialogue situation ‘(I know that) S’, an interlocutor is entitled to ask ‘How do you know that?’, that is, one has to be able to give an account of the way one has obtained one’s knowledge state. One obtains a state of knowledge by means of an act of demonstration, an act of discovery, an act of understanding, an act of perceiving, or an act of recognizing; these are some of the sorts of cognitive act that may result in knowledge. Below I argue that the cognitive act is preferably not to be explained as (1) an act of judgement, (2) that is justified and (3) right. I take the notion to be primitive. Although it is thus not possible to define the notion of cognitive act, it is possible to elucidate the notion by giving examples, as I have done already above, and by showing how the notion is related to other notions, which will be done below. In this paper, the notion of belief does not form part of the explanation of knowledge. A dispositional notion such as belief cannot be understood as primitive, because we

8 Franz von Kutschera (1981, p. 9) gives an explanation of cognizing (erkennen) in terms of knowledge as

state (wissen): “Die Person a erkennt, im Zeitpunkt t, dass p, genau dann, wenn a in t von einen Zustand des Nichtwissens, dass p, in einen Zustand des Wissens, dass p übergeht.” From this definition he draws the conclusion that an analysis of the concept of knowledge as state, being the more primitive notion, suffices for epistemology. In contrast, defining knowledge as state in terms of cognizing (the act of cognition) brings the act of cognition into focus.

123

Synthese (2011) 180:391–417

397

need to explain a disposition in terms of its actualisations. Besides, the term ‘belief’ is an ambiguous notion, which may mean: a disposition or ability to judge; (a certain degree of) conviction; or faith. One should not explain knowledge in terms of ‘belief’, as long as it is not clear what is understood by that term.9 Below, knowledge (as state) is not explained in terms of belief, but in terms of the cognitive act. Because knowledge and the cognitive act are not explained in terms of belief and the act of judgement, the conceptual order of these notions is essentially different from the order in modern analytic philosophy, and another method is needed to explain the relation between these notions. This method I call linguistic phenomenology, and modification and etiolation of meaning play a certain role in it, which ideas will be explained below. 3 The cognitive act and the first-person perspective In the explanation of the epistemic notions that are essential to understanding Per Martin-Löf’s interpretation of constructive type theory, the notion of cognitive act, or act of knowing, plays a central role. How the notion of cognitive act is to be understood is not unproblematic, though. I understand the notion of cognitive act to be identical with the notion of justified or grounded judging, but I do not explain the notion in terms of the act of judging and being grounded. A cognitive act may be an act of demonstration or an act of (immediate) insight. The act of demonstration is an act of judgement based upon known premises; this act of judgement is therefore a cognitive act. An act of insight is an act of understanding, for example, that 0 is a natural number. One sees that 0 is a natural number as soon as one understands that 0 is a natural number. One cannot make the judgement without understanding the concepts involved, and thereby knowing that 0 is a natural number. The cognitive act plays an important role in the epistemology that is developed here for constructive type theory, because other epistemic notions are explained in terms of it. The cognitive act is prior in the order of explanation to, for example, the concept of knowledge as state. Science does not consist in a unified whole of cognitive acts, but in a whole of pieces of knowledge or of knowledge states in the individual scientist. Pieces of knowledge are, for Martin-Löf, the product of an act of knowing. One may thus apply the traditional distinction between act or process and product to the concept of knowledge10 : the act of knowing or the cognitive act results in knowledge as product.11 How is this relation between cognitive act and knowledge as product to 9 I criticize the way the term ‘belief’ is used in modern epistemology in van der Schaar (2009). 10 The distinction between act and product is acknowledged in the scholastic tradition, especially the Tho-

mistic one. In Aquinas the product is called the terminus (ad quem). The terminus of an act of knowing, the ‘inner word’, the known proposition (in the old-fashioned sense, having declarative form), is distinguished from the external object of knowledge. More on the distinction between act and product in van der Schaar (2006). 11 The German term is ‘(eine) Erkenntnis’, which is preferably translated as ‘(a) cognition’, as is done by Werner S. Pluhar in his translation of Kant’s Kritik der reinen Vernunft from 1996. Because Martin-Löf does not use the term ‘(a) cognition,’ but the term ‘knowledge’ for the product of the act of cognition, I conform to that usage; cf. Martin-Löf (1985, pp. 19, 20).

123

398

Synthese (2011) 180:391–417

be understood? The relation between the act of cognition and knowledge as product is not a natural, causal relation; it is an internal relation: knowledge as product is inevitably constituted in a cognitive act. Knowledge as product, a piece of knowledge, is an abstract entity, and has as such an enduring existence from the moment on that it is made in the cognitive act. Theorems are typical examples of knowledge products. Knowledge as product, being an abstract entity, is not to be identified with the knowledge state of an individual knower. Regarding knowledge as state, Martin-Löf makes the following equation: “to know = to have understood, comprehended, grasped, seen” (Martin-Löf 1985, p. 20). The act of understanding is an example of a cognitive act resulting in (knowledge of) an axiom. Knowledge as state can thus also be understood in terms of the cognitive act. The cognitive act that inevitably results in knowledge as product, may also result in a knowledge state of the individual knower. The relation between the cognitive act and knowledge as state is not an internal one. As the example of Mr. Lawless has shown (see the introduction), there may be exceptions to the rule that the cognitive act results in knowledge as state. A man’s cognitive act standardly initiates in him knowledge as state, but there may be physical or psychic hindrances. The relation between cognitive act and knowledge as product is thus tighter than the relation between cognitive act and knowledge as state. One may either explain the notion of cognitive act by means of the notion of judgemental act together with the notion of justification and perhaps a truth notion, or the notion may be understood as primitive in the sense that it cannot be explained in terms that are prior in the order of explanation, and the act of judgement is then understood as being, in a certain sense, identical with the cognitive act. Martin-Löf has understood the notion of cognitive act to be primitive in his earlier writings, but he has now changed his position: the act of knowing is explained as justified, or grounded, judging, and the act of judgement is identified with the act of assertion.12 The notion of truth is missing in the explanation of cognitive act, because being justified implies being correct, where correctness is epistemic correctness (see Sect. 5). The identification of judgemental act and cognitive act is not unproblematic, as we will see below, but the identification of act of judgement and act of assertion creates problems of its own, for when we lie we make an assertion without the corresponding judgement. I argue here for the identification of judgemental act and cognitive act, because this way of relating the two notions shows something important about the constructive notion of knowledge. Below I understand a mere act of judgement as a modification of a cognitive act.13 To understand what modification is, it is important to understand what modifying adjectives are, such as ‘fake’, ‘mock’, or ‘sham’. If an attributive (non-modifying) adjective precedes a general term in a singular, atomic sentence, one may validly draw the conclusion that the subject falls under (the concept denoted by) the general term. From the assertion ‘He has a German pistol,’ in which ‘German’ is used 12 As he writes to me in a letter from 17 August 2007. His early identification of act of judging and act of knowing can be found in Martin-Löf (1985, p. 19, 1991, p. 144); cf. also Sundholm (1998, p. 183). 13 Compare Husserl in Erfahrung und Urteil: “blosses Urteilen [ist] eine intentionale Modifikation von

erkennendem Urteilen” (Husserl, 1939, Sect. 5, p. 15).

123

Synthese (2011) 180:391–417

399

attributively, one may validly draw the conclusion ‘He has a pistol.’ If a modifying adjective precedes a general term, as does the term ‘sham’ in the assertion ‘He has a sham pistol,’ one cannot validly draw the conclusion that he has a pistol. One may have doubts regarding the identification of the judgemental act with the cognitive act, for it seems that there is no conceptual space for error on this account. After all, some of our judgemental acts will turn out to be unjustified and incorrect, and such an act of judgement cannot be identified with a cognitive act, that is, an act of knowing. There are cases in which we are not entitled to judge, while making the judgement nonetheless. I do think, though, that one can give an account of error, even though the cognitive act is understood as primitive, and the judgemental act is, in a certain sense, identified with the cognitive act. In what follows I presuppose that there is a distinction between making a guess and making a judgement: without having a justification or ground, one does not judge, one is merely making a guess. This means that for someone to count as a judger he needs to have a ground for the judgement he is making. (Below I will explain the point that the ground is to be understood as what counts as a ground from a first-person perspective.) Prima facie, the act of judgement is grounded, and is in this sense a cognitive act. Later, it may turn out that there was something wrong with the ground, and the act of judgement is considered to be a misfire, because something essential is missing. As soon as the judger realizes that his ‘ground’ can no longer be considered as ground, he withdraws his judgement. Now that he considers what he used to call a ‘ground’ no longer to be a ground, he may still say that he made a judgement in the past, but then the term ‘judgement’ is used in a modified sense (a full account of error is given in Sect. 6). The concept of judging without a ground is thus secondary in the order of explanation to the notion of grounded judging, and the latter is precisely identical with the primitive notion of cognitive act. The cognitive act may thus be understood as the primitive notion, and mere judgement (without a ground) is a notion that can be understood as a modification of the cognitive act. Perhaps this sounds like Henry VIII’s denial that there has been a marriage, notwithstanding the fact he and his first wife went through all the procedures, simply because it didn’t bring him the right kind of offspring. I do think, though, that the point is important for understanding what epistemic concepts one needs for constructive type theory. Primary cases on the basis of which the concept of knowledge is explained on this account are not knowledge attributions, but first-person knowledge claims. And from a first-person perspective, there is no distinction between the act of judgement and the cognitive act, the grounded act of judgement. I understand my judgement to be grounded; it is not merely a guess. I understand it to have epistemic value, and this is so, because I take it to be grounded.14 The cognitive act is thus prima facie cognitive, or cognitive from a first-person point of view. Only someone else (or the same judger at another time), with his own first-person perspective, who evaluates the epistemic situation, may come to the conclusion that the act of judgement of the person introduced above is not grounded, and that it is therefore not a 14 A similar thesis I found in Adler (2002, p. 275): “From the first-person point of view, one treats one’s belief as factive, which is the central property of knowledge”. Throughout Belief’s Own Ethics, Adler stresses the importance of a first-person methodology.

123

400

Synthese (2011) 180:391–417

cognitive act. The notions of cognitive act and act of judgement may fall apart. If I see that the ground on the basis of which you make your judgement is defective, I am entitled to say, given my first-person perspective, that your act of judgement is not a cognitive act. The idea that the cognitive act counts as cognitive from a first-person perspective, has far-reaching consequences. It means that a ground or justification is always a ground or justification from a first-person perspective, and because (epistemic) truth will be explained in terms of justification (see Sect. 5), ‘being (epistemically) true’ means ‘being true-for-me’. This means that knowledge is understood as inherently fallible, and that there is a threat of relativism, which problem is addressed in Sect. 6. Not all judgemental acts seem to be equally cognitive. Some create a knowledge product, others do not, but initiate a new knowledge state in the person making the act. Finally, we sometimes merely bring to the occasion, for ourselves or aloud, a knowledge already obtained. There seems to be a difference between a first cognitive act that S that results in the abstract knowledge product S, and standardly initiates a corresponding state of knowledge, on the one hand, and subsequent acts of judging that S, on the other hand. These subsequent judgemental acts are the exercises or actualisations of knowledge as state or disposition. Although these repeated judgemental acts are still cognitive, in so far as they are exercises of dispositional knowledge, they are not full cognitive acts in the sense that they create a knowledge product or initiate a state of knowledge. As cognitive acts, these repeated judgemental acts are ‘etiolated’, to borrow a term from J.L. Austin. The term ‘etiolated’ before a term, diminishes the meaning of that term without changing the meaning in an essential way. An etiolated cognitive act is still a cognitive act. The concept of etiolation is not the same as that of modification introduced above. Both etiolation and modification involve a change in meaning, a kind of diminishing, but only in the case of modification the change is essential: when ‘stage’ works as a modifying term, a stage tree is not a tree, whereas an etiolated plant is still a plant. With respect to the cognitive act, there are two kinds of etiolation. The cognitive act may be etiolated because it does not result in a new knowledge product. Because the knowledge product already exists, the act is not original, but the act may still initiate a new knowledge state in the individual knower. Or, the cognitive act is etiolated in the full sense: it neither creates a new knowledge product, nor does it initiate a new knowledge state. It may still be called cognitive because the judgemental act is an exercise or actualisation of dispositional knowledge. The cognitive act is of importance for constructivism, for only when constructed in a cognitive act do proofs for propositions gain epistemic significance. Propositions are considered to be sets of their proof objects, but their meaning-explanation is given exclusively in terms of their canonical proof objects.15 Two questions are of importance in the explanation of a proposition: How are its canonical proofs formed? And, when are two such proofs equal? A non-canonical proof object for a proposition is a method which yields, when executed, a canonical proof object for that proposition (Martin-Löf 1998, p. 112). A proposition is true precisely if 15 On the relevance of the distinction between canonical and non-canonical proof object for CTT, cf. van der Schaar (2007).

123

Synthese (2011) 180:391–417

401

a proof of it exists. That is, on the presupposition that A is a proposition, the judgement A is true can be identified with the judgement there exists a proof of A, i.e., Proof (A) exists.16 The term ‘proof’ here means proof object.17 The idea that proofs of propositions are objects also finds expression in the thesis that these objects are the truth-makers for the relevant propositions.18 What is relevant here is that a proof object is an (abstract) object, not to be confused with the cognitive act, such as an act of demonstration. A proof object is an object to be denoted by a singular term. For example, a canonical proof object for a conjunction A & B is a pair of proof objects, the first being a proof of A, the second being a proof of B. A canonical proof object of an implicational proposition A ⊃ B has the form of a λ-abstract: (λ x) b(x), where b(x) : B (x : A), that is, where b(x) is a proof object of B, given that x is a proof object of A. These proof objects as such are non-epistemic objects. It is essential to constructivism that the person who asserts that there exists a proof of A is entitled to make that assertion only if he is entitled to make the assertion a is a proof of A. He is allowed to make the existential claim only upon possessing a proof for A (cf. Sundholm 2004, p. 449): existence is thus understood in the constructive sense. This means that the person who asserts that A is true is entitled to make that assertion only if he has constructed a proof object for A within a cognitive act, such as an act of demonstration. It is only in this way that proof objects gain epistemic significance. In order to obtain constructivism, the semantic talk in terms of propositions and proof objects needs to be embedded within a theory of the cognitive act, in which proof objects are constructed as proofs of their propositions. This point has both a meaningtheoretical aspect and an epistemic aspect, and it is the latter aspect that is dealt with in this paper.19 Although the constructive notion of knowledge may seem to be subjective because it is the result of a cognitive act that counts as cognitive from a first-person point of view, one cannot privately decide what counts as a proof for a certain proposition. The semantic notion of a proposition A, which is part of the judgement A is true, is 16 The notion of existence that is used in this judgemental form has to be different from the notion of

existential quantifier that is present in existential propositions. 17 Arend Heyting has introduced the idea to explain propositions in terms of proofs, and this has led to the idea that proofs for proposition are non-epistemic, mathematical objects, or proof objects. Cf. Sundholm (1994, p. 121). 18 Cf. (Sundholm, 2004, p. 438). The notion of truth for propositions can be explained in terms of truthmakers: the above ‘there exists a proof of A’ is then substituted by ‘there exists a truth-maker for A’, cf. (Sundholm, 1997, p. 117). 19 That a semantics in terms of propositions and proof objects needs to be embedded within a meaning

theory of assertion conditions given in epistemic terms is shown in van der Schaar (2007).

123

402

Synthese (2011) 180:391–417

explained in non-mentalist, public terms. As we have seen, the proposition A & B is explained by what its canonical proof objects are, pairs consisting of a proof object of A and a proof object of B. Equally, what counts as a non-canonical proof object for a proposition is determined independently of any judger’s act. Only the point whether there exists a proof object for the relevant proposition is dependent upon a first-person cognitive act, in which that proof object is to be constructed.

4 The cognitive act and the phenomenological account of knowledge In the former section, I introduced a methodology in which the ideas of modification and etiolation play a role in the explanation of the notions of cognitive act and act of judging. The terminology I took from Husserl and Austin, and I have introduced an explanation of the idea of modification and etiolation in logical and linguistic terms, thus introducing a new method to explain or eludicate our epistemic concepts. Regarding the concept of cognitive act as I have introduced it, there is also a close relation between constructive type theory and phenomenology. The notion of cognitive act can be elucidated by making a comparison with the elucidation Husserl has given of the cognitive act (das Erkennen) in the sixth Logical Investigation. According to Husserl, there are three moments involved in the cognitive act20 : (1) the act of empty meaning intention; (2) the act of intuition or perception, which is to function as the fulfilling act in (3); (3) the cognitive act, which is a single act that brings the former two acts into synthesis, in such a way that the act of perception fulfils the act of intention (only at this moment the second act is understood as a fulfilling act). In the case of cognizing (Erkennen) non-propositional objects, the fulfilling act is an act of sensual intuition, and the act of synthesis is a cognitive act in which the object intuited in the second act is identified with the object meant in the first act. Instead of an act of identification, the cognitive act may also be an act of classification, for example, when the object perceived in the second act is classified as inkpot, which meaning was intended in the first act; the object is thus cognized as inkpot (Husserl 1901, VI, Sect. 6). In a further cognitive act, the object may then be identified as my inkpot. The cognitive act thus brings the act of intention and the act of perception, the fulfilling act, into synthesis. The act of intuition or perception as such, without an act of cognitive interest, is epistemically irrelevant. The same perception can fulfil different meaning intentions, such as inkpot and my inkpot, and without such a meaning intention, there is no concept under which the perceived object can be taken, which means that the act of perception has no cognitive value. It is not the word, or its meaning, and the object that are primarily related to each other in the synthesising act, but the act of meaning 20 Cf. Husserl (1901, VI, Sects. 6 and 8). “Eben darum dürfen wir nicht bloss die Signifikation [first act] und Intuition [second act], sondern auch die Adäquation, d. i. die Erfüllungseinheit, als einen Akt bezeichnen, weil sie ein ihr eigentümliches intentionales Korrelat hat, ein Gegenständliches, worauf sie ‘gerichtet’ ist. Wieder eine andere Wendung derselben Sachlage ist, nach dem oben Gesagten, in der Rede vom Erkennen ausgedrückt” (idem, VI, Sect. 8, p. 568). Compare Husserl (1901, p. 1901, VI, Sects. 38 and 40).

123

Synthese (2011) 180:391–417

403

intention and the act in which the object is perceived. The cognitive act is a primitive phenomenological fact, and is not to be reduced to the mere sum of the other two acts; consciousness that the one act fulfils the other is essential to the cognitive act.21 In the case of judgemental cognition (Husserl 1901, VI, Sect. 38 ff.), the act of empty meaning intention (1) is, for example, an act of wanting to know whether the bird in the garden is a robin. The act of perception is (2) an act of non-sensory perception of an ideal entity, the state of affairs the bird in the garden being a robin. Finally, (3) there is a cognitive act that the bird in the garden is a robin, if and only if the perception of the state of affairs is apprehended as fulfilling the act of empty meaning intention. If the fulfilment is complete, the cognitive act is evident in the strict sense, and its correlate is (judgemental) truth.22 In the sixth Logical Investigation, judgemental truth is thus elucidated by means of evidence, and ultimately by means of the distinction between intention and fulfilment. Besides judgemental truth, Husserl acknowledges propositional truth, which he understands as truth pertaining to states of affairs (the bird’s being a robin/ that the bird is a robin), consisting in the correspondence of what is meant (a meaning intention not as act, but as content of an act) and what is given [fulfilment not as act, but as content of a (fulfilling) act] (cf. Husserl 1901, VI, Sects. 37 and 38; this is ‘the first concept of truth’). If one understands Husserl’s position in the sixth Logical Investigation in idealistic terms, truth pertaining to states of affairs cannot be understood without the evident cognitive act with its fulfilling synthesis, in which the truth of the intended state of affairs is determined. There is only truth in the sense of correspondence in so far as there is a fulfilling synthesis of subjective acts.23 Although Husserl considers the cognitive act to be a primitive phenomenological fact, it is possible to elucidate the notion of cognitive act. In order to compare the concept of cognitive act as introduced in this paper with the phenomenological concept of knowledge, a distinction between proposition and judgement candidate needs to be made.24 A proposition A, which was introduced above as a set of proof objects, has the form of a that clause; the judgement candidate of the judgement  A is true, where  is a sign of judgemental force, has the form A is true. A judgement may thus be understood as a judgement candidate to which judgemental force is added. The proposition as such, having the form of a that clause, does not have the right form to be judged or asserted. According to Martin-Löf, what a judgement is, “is fixed by laying down what it is that you must know in order to have the right to make the judgement in question” (Martin-Löf 1995, p. 188). The term ‘judgement’ is ambiguous: it may mean the judgement candidate together with

21 “Es ist eine primitive phänomenologische Tatsache, dass Akte der Signifikation und Intuition in dieses eigenartige Verhältnis treten können” (Husserl 1901, VI, Sect. 8, p. 567). 22 “Urteil [first act] und Urteilsintuition [second act] einen sich dabei zur Einheit des evidenten Urteils” (idem, VI, Sect. 44, p. 668). Cf. (idem, VI, Sects. 38 and 39). 23 Cf. Bernet et al. (1989, Chap. 6, esp. p. 174). According to Tugendhat, this idea can only be found in

Husserl’s Ideen, published in 1913, cf. Tugendhat (1970, pp. 89, 90). The first edition of the sixth Logical Investigation, though, forms already a transition to Husserl’s idealism. 24 I have argued for the importance of the judgement candidate in van der Schaar (2007), where it is called

the ‘assertion-candidate’.

123

404

Synthese (2011) 180:391–417

the judgemental force, or it may mean the judgement candidate as such, and it is the latter sense that is captured by the definition. A presupposition for putting forward the judgement candidate with assertive or judgemental force is that one understands the judgement candidate, that is, that one understands what one must know in order to have the right to make the judgement in question. It is essential to the judgement candidate that one can apprehend it without making the judgement oneself. Before one has constructed a proof object for A and judges/cognizes that A is true, one needs to apprehend the judgement candidate A is true, that is, one has to understand what proof object has to be constructed to make A true. The act of apprehending the judgement candidate and the act of cognition may happen at the same moment, but it is important to understand that they are conceptually different; one can have the former without the latter. There is an important difference between the notion of cognitive act as part of an epistemology for constructive type theory and Husserl’s notion of cognitive act. Within constructive type theory all objects come as typed. One cannot conceive of an act in which a proof object is found independently of the proposition for which it is a proof; there is an internal relation between proof object and proposition. Because all objects belong to a certain type, proof objects are not found or constructed independently of the question for what proposition they are a proof. The act of finding a proof-object is essentially an act in which a proof-object is found for the relevant proposition. For Husserl, the same act of intuition or perception may fulfil different intentions, for example, there is a bird, the bird flies away, or the black bird flies away. Thus, in Husserl, a separate act is needed to understand the act of perception as fulfilment of a certain intention: the cognitive, synthesising act. In an epistemology for CTT, one need not make a distinction between the act of intuition or perception and the cognitive act. The act in which a proof object is constructed for the relevant proposition, is precisely the cognitive act. The phenomenological threefold distinction thus becomes a twofold distinction in an epistemology for constructive type theory: (1) the act of apprehending the judgement candidate, such as A is true; (2) the act of cognition, in which a proof-object a (the fulfilment as object) for the proposition A (the intention as object) is constructed.25 The act described in (1) is needed, because we have to understand what we must know in order to have the right to make the judgement. The act in (2) can be understood as the fulfilment of the act in (1). One may also think of intention and fulfilment in terms of objects, as indicated in (2), but it is essential to constructivism that the distinction between intention as object and fulfilment as object is embedded in the distinction given in terms of acts, as in (1) and (2). Apart from the difference between Husserl’s and the constructivist’s account of the cognitive act given in this paper, there are also some important agreements. The cognitive act is understood as a primitive phenomenon, not to be explained in terms 25 Heyting already used the Husserlian distinction between intention and fulfilment for the explanation of intuitionistic ideas: “Die Behauptung einer Aussage bedeutet die Erfüllung der Intention” (Heyting 1931, p. 113).

123

Synthese (2011) 180:391–417

405

of truth, justification and belief. How knowledge is related to truth and justification on a constructivist account will be explained in the next section. 5 Knowledge, evidence and judgemental correctness Above, knowledge as product is defined as the internal result of the cognitive act, but Martin-Löf also elucidates the notion of knowledge as justified or evident judgement (Martin-Löf 1998, p. 110). A judgement candidate is made evident by an act of demonstration (Martin-Löf 1987, p. 417, 1998, p. 108), or an act of insight. A judgement made evident by a cognitive act can be considered both as knowledge in the sense of knowledge product and in the sense of knowledge as state. That a judgement is evident means that it is known, and it can be made known only through a cognitive act. Whether a judgement counts as knowledge is thus dependent upon the cognitive act of a judging agent. If the act of cognizing is not based on other judgements, that is, if the act is an act of insight, the judgement is traditionally called immediately evident, and the evident judgement is an axiom. If the act of cognition is based on other evident judgements, that is, if the act is a demonstration, the judgement is called mediately evident (Martin-Löf 1985, p. 30), and the evident judgement is a theorem.26 One may wonder whether there is a circle in the explanatory order of the notions knowledge and judgement: knowledge is characterized as justified judgement, and judgement in the sense of judgement candidate is defined in terms of what one has to know in order to be entitled to make the judgement. There is an important difference, though, in the meaning of the term ‘knowledge’ and that of the term ‘to know’ as it is used in the two explanations. When knowledge is characterized as justified judgement, it is knowledge as product that is explained. When the term ‘to know’ is used to define the judgement candidate, it is the cognitive act that is indicated. The judgement is defined by what one has to do in order to have the right to make it, and the act that one needs to have done in order to be entitled to make the judgement, is the cognitive act. If one puts the two explanations together, one obtains: knowledge as product is the judgement candidate justified by the cognitive act that is demanded by the explanation of the judgement candidate in order to be entitled to make it; in short, knowledge as product is the result of the cognitive act. A judgement is called correct, if it is possible to make it evident or justified, that is, if it is knowable (cf. Martin-Löf 1998, p. 109). After one has justified the judgement, one is entitled to assert that the judgement candidate that one had apprehended before the judgement was made evident, is correct. The judgement candidate is thus the bearer of correctness. The notion of correctness cannot be understood independently of the notion of being evident, because the two are related as potentiality to actuality: the former notion has to be explained in terms of the latter. Given this meaning of correctness, explaining knowledge as justified correct judgement, or ‘justified true belief’ in the standard formulation, is less apt, because the notion of being correct is here 26 Current epistemology uses the term ‘evidence’ primarily in the sense of evidence for a judgement. The evidence for a judgement that S consists of those judgements that justify the judgement that S. If one uses evidence in this sense, there is no evidence for an axiom. According to the use of the term ‘evident’ introduced here, where being evident is a characteristic of certain judgements, an axiom is an evident judgement.

123

406

Synthese (2011) 180:391–417

redundant: the judgement’s being evident or justified implies its being correct. The evidence of a judgement is not only a criterion for its correctness; the notion of evidence is part of the definition of judgemental correctness. Here, as in Husserl, judgemental correctness is not the same as truth of a proposition. The explanation of propositional truth in terms of ‘existence of a proof of A’ can be understood in a non-epistemic sense, whereas the notion of judgemental correctness is defined in epistemic terms. A judgement’s being evident has two aspects. On the one hand, the judgement is justified, grounded by a cognitive act. In this sense, axioms are also justified, namely by an act of insight. On the other hand, the judger is convinced of the correctness of the judgement. A judgement’s being evident is a subjective characteristic; a judgement is evident to a certain person. Being evident is not a purely subjective characteristic, though. The judger should be convinced of the correctness of the judgement because of the cognitive act. Strong conviction of the correctness of a judgement without the cognitive act to support this conviction is not to be identified with the evidence of the judgement. Conviction or sureness without the corresponding cognitive act is nothing but a feeling that may equally accompany our prejudices. Evidence is not a mere feeling. Under the influence of the criticism on the concept of evidence by the logical positivist Moritz Schlick (Allgemeine Erkenntnislehre, 1918) and the Neo-Kantian Leonard Nelson, the notion of a judgement’s being evident, the evidence of a judgement, has disappeared from analytical philosophy. Nelson, in his Über das sogenannte Erkenntnisproblem (1908), focuses on Meinong’s use of the term ‘evidence’, and criticizes the idea that evidence may be used as a criterion to distinguish judgements that are knowledge from those that are not. Nelson argues in general that such a criterion cannot be given, which he calls the problem of the criterion, and that this problem also applies to the idea that evidence may function as criterion. He formulates ‘the problem of evidence’ in such a way that it can be conceived of as the standard criticism on the notion of evidence: Either the concept of evidence entails the characteristic of truth, in which case it is impossible to decide whether a judgement is evident. Or ‘evident’ merely means an experience of consciousness that can psychologically be ascertained, in which case it is impossible to determine that an evident judgement is true. (Nelson 1908, p. 124) I will argue that the notion of evidence as it is introduced in this paper differs in an important sense from the notion of evidence introduced by the early phenomenologists, and that Nelson’s criticism therefore does not apply. The point is that the cognitive act that makes the judgement evident is essentially a cognitive act for me in the sense that the cognitive act counts as cognitive from a first-person point of view. Another person may look upon the act as not cognitive at all; this may effect the way I consider the act at a later moment, but only insofar as the other person is able to show me that I was wrong. The thesis that the cognitive act is cognitive from a first-person point of view has an important bearing on the notions of judgemental evidence and correctness: the evidence and the correctness of a judgement are fallible, and evidence and correctness mean evidence-for-me and truth-for-me. Later, the judgement may no longer count as

123

Synthese (2011) 180:391–417

407

evident, because the act on which the evidence of the judgement depends is no longer considered to be cognitive by the judger. Both in Brentano and Husserl one finds the idea that something is true if it is possible to judge it with evidence: a conceptual relation between the notions evidence and truth is affirmed. In contrast to Husserl, Brentano does not acknowledge degrees of truth, and his theory seems therefore more apt for making a comparison with the theory as it is presented here. Besides, in the Prolegomena zur reinen Logik of the Logische Untersuchungen Husserl defines evidence in terms of truth, whereas Brentano defines (judgemental) truth in terms of evidence, just as this is done above.27 I take Brentano’s later theory as starting-point, in which only persons and things are acknowledged. According to Brentano, a judger’s judgement is correct in the strict sense (right, richtig) precisely if the judger judges with evidence. And the right judgement is knowledge.28 The judgement of a judger may also be correct in a less strict, extended sense (true, wahr): truth belongs to the judgement of a judger who asserts what an evident judger would assert.29 The evident judger in this explanation of truth is to be understood as an ideal judger. For Brentano, the notion of ideal, evident judger is not a notion given in complete abstraction from actual, human judgers. According to Brentano, all knowing beings have the same proof grounds (Beweisgründe; Brentano 1930, p. 150), and, we are not entitled to assert anything about other beings having a different type of axiomatic knowledge (Brentano 1956, p. 171). Brentano’s explanation of truth in the extended sense corresponds to the idea of judgemental correctness introduced above: both notions are defined in terms of the possibility to make the judgement evident. There is also an important difference between the two truth notions. In Brentano, (judgemental) truth is explained in terms of the evident judgement of an ideal judger; the evident judgement is infallible: error is excluded.30 According to Brentano, if someone judges with evidence, the evidence transcends his judgement insofar as it corresponds, by definition, to the judgement of the ideal judger: truth and evidence are infallible. Brentano also says that if the judger’s judgement is evident, he is certain of its truth, that is, the judgement’s being evident is epistemically accessible to the judger.31 The judgement’s being evident is thus conceived of as being both transcendent to the judger and phenomenologically

27 Cf. Husserl (1901, Prol., Sect. 51), where evidence is explained as experience of the truth (‘Erlebnis’ der Wahrheit). 28 Denn die Logik […] soll uns das Verfahren lehren, das uns zu der Erkenntnis der Wahrheit führt, d.i. zum richtigen Urteil” (Brentano 1956, pp. 1, 2). 29 “dass die Wahrheit dem Urteile des richtig Urteilenden zukommt, d.h. …. der das behauptet, was auch der evident Urteilende behaupten würde” (Brentano 1930, p. 139). The definition is from 1915. More on Brentano’s theory of truth and evidence, and his distinction between truth in the strict sense and truth in the extended sense in van der Schaar (1999, 2003). In my (1999) paper it is shown that both Brentano and Martin-Löf defend a negative version of the law of excluded middle. 30 “Bei Evidenz ist Irrtum ausgeschlossen” (Brentano 1930, p. 144). In the sixth Logical Investigation (Sect. 39), Husserl says that if someone experiences the evidence of A, then it is evident that no one can experience the absurdity of the same A. In Formale und transzendentale Logik, published in 1929, Husserl has changed his position: evidence does no longer exclude the possibility of illusion or error (Täuschung, Husserl 1929, pp. 139, 140). 31 “Bei Evidenz ist Zweifel ausgeschlossen” (idem).

123

408

Synthese (2011) 180:391–417

accessible to him. Nelson’s criticism thus applies to Brentano’s theory: the thesis that evidence is transcendent in order to make evidence a guarantee of infallible truth is incompatible with the thesis that evidence is epistemically accessible to the judger, for the latter thesis implies that evidence is not a guarantee of infallible truth. The point is that one has to chose consistently for one side of Nelson’s dilemma. In this paper, the judgement’s being evident is understood as epistemically accessible to the judger; evidence is therefore understood as fallible evidence. This means that a judgement’s being evident does not give a guarantee for infallible truth: error is not excluded. Evidence obtains its fallibility from the cognitive act that makes the judgement evident. We trust our cognitive acts that bestow evidence upon our judgements. This does not imply that it does not make sense to doubt our cognitive act and the evidence of the judgement, but we should only do so when we have a reason for our doubt. The point is not that we have to explain why our cognitive acts make our judgements evident or justified, we simply take that for granted, and I take the two notions, that of cognitive act and that of the judgement’s being evident, to be conceptually related. What we do need to explain is the possibility that our cognitive act might be an illusion.

6 Truth and the possibility of error Regarding our going wrong, one should make a distinction between mistakes and errors. One may, for example, mistake one number, or one person, for another. As soon as someone shows that we mistook the one for the other, we know how to apprehend the right number or person. Such going wrong may be called a mistake. Truth and falsity are not necessarily involved in order to explain what a mistake is. Those who consider formal systems to be given prior to any meaning that can be given to them generally do not speak of the truth of the axioms and theorems of the system as such, but they acknowledge that mistakes can be made with respect to the system. There is also a form of going wrong that cannot be understood independently of truth. Suppose that I assert that it is snowing, and I am entitled to make that assertion because I have seen that it is snowing by looking through the window. Some time later, I realize that I am in a movie-setting, and I doubt whether it was really snowing. I realize that I might be wrong with respect to my act of perception. Such going wrong would be an error: one takes an illusion to be real. If one defends the thesis that truth means nothing but truth-for-me, that is, if one defends a relativism regarding truth, one is able to account for illusions to a certain extent. In the example given above, one may say that given that I now have information that what I thought to be falling snow was perhaps not real snow, it is no longer true-for-me that it is snowing. If truth is nothing but truth-for-me, it is not possible, though, to say that something is true-for-me now, but that what is true-for-me now might not be true at all. Or, to extend the first-person perspective to the perspective of our culture, there is no way to say that something is true-for-us, but that we all might live in error. There is thus a fundamental form of illusion that cannot be explained if one defends a relativism with respect to truth. If one defends the thesis that truth is nothing but truth-for-me, there is not a contradiction involved, if, on the presupposition that A is a proposition, one person judges A is true, and another judges ¬ A is true, for this would mean that, say, John judges

123

Synthese (2011) 180:391–417

409

that A is true-for-him, while Mary judges that A is true-for-her. The acknowledgement of the law of contradiction means that one denies a relativism regarding truth. Martin-Löf gives the following formulation of the law of contradiction: one and the same proposition cannot both be known to be true and be known to be false (Martin-Löf 1995, p. 194). To understand why this law holds, one has to go back to the meaning explanation of the proposition called absurdity. Absurdity is defined by its having no canonical proof object. It is thus impossible to know a proof of absurdity. This implies that it is impossible to know that absurdity is true. Martin-Löf thus arrives at one of the laws of knowability: Absurdity cannot be known to be true. In order to show that the law of contradiction holds we need both this law of knowability and the following rule of inference: A true A false ⊥ true (N.B. A is false is interderivable with ¬ A is true, Martin-Löf 1995, p. 192). If the judgements A is true and A is false were both knowable, then absurdity is true would be knowable. But, absurdity cannot be known to be true. Therefore, the two judgement candidates A is true and A is false cannot both be knowable, that is, they cannot both be correct. We are now entitled to say that if someone makes the judgement A is true, whereas someone else asserts that A is false (it may be the same person at different times), not both can be right. At least one of the cognitive acts on which these two judgements were based must have been an illusion. From a philosophical point of view, this implies that there is more to truth than the evidence of the judgement. We are in need of a notion of truth that makes it possible to say: my judgement is evident to me, but it may be the case that the cognitive act on which the evidence of the judgement is based is an illusion. In order to be able to make the distinction between a real and an illusory cognitive act, another notion of truth is needed. Martin-Löf calls this notion of truth the metaphysical notion of truth, and he also speaks of truth as reality, truth as rightness (rectitudo), or truth as infallibility. If one identifies the epistemic notion of correctness with the metaphysical notion of truth, as Brentano did, one is confronted with Nelson’s problem of the criterion. This leaves us two options. One may either explain the truth of a proposition in terms of the existence of a state of affairs, where the existence of the state of affairs is understood as truth as reality to which the proposition is said to correspond. This is the realist alternative. Or, one may understand truth as reality as pertaining to the cognitive act. Per Martin-Löf applies the notion of reality or rightness to the act, and in an epistemological context it applies to the cognitive act. “Is it that an act is right if the object of that act is right, or is it that an object is right if it has been rightly done? … rightness applies primarily to the action and only derivatively to the object” (Martin-Löf 1991, p. 146). By understanding rightness primarily to pertain to the cognitive act, Martin-Löf commits himself to a variant of idealism.32 32 That is, a form of idealism one may also find in Peirce, who introduces the notion of metaphysical truth or reality in his paper ‘How to Make Our Ideas Clear’: “The opinion which is fated to be ultimately agreed to by all who investigate, is what we mean by the truth, and the object represented in this opinion is the real. That is the way I would explain reality” (Peirce, 1878, p. 139).

123

410

Synthese (2011) 180:391–417

Whether one’s cognitive act is a ‘real’ one, is something we, being fallible creatures, are not able to determine. “[A]s a matter of fact, our demonstrations are not infallible: a demonstration purports to make something evident to us, and it is the best guarantee that we have, but it is not infallible” (Martin-Löf 1998, p. 110). According to MartinLöf, our concept of knowledge should not have the metaphysical notion of truth as part of its explanation, for that would make knowledge to be infallible and humanly inaccessible (Martin-Löf 1991, p. 144). If the metaphysical notion of truth were part of the explanation of knowledge, we would never be able to determine whether we know. Human knowledge is fallible in the sense that it does not exclude error; there is no guarantee that the cognitive act on which our knowledge is based, might not be an illusion.33 There is a danger in using the term ‘real cognitive act’: one should not understand it as denoting a special kind of cognitive act. ‘Real’ is not a characteristic that some cognitive acts have as opposed to others. There are not two types of cognitive act: the ordinary, prima facie one, and the real one. The term ‘real’ is not a determiner; it can only be made sense of when doubt is raised. Suppose someone wants to sell you a watch, which he asserts to be ‘golden’, for a small amount of money. Because of the price, you have reason to ask yourself: ‘Is it real gold?’ Only against the possibility of an illusion does the term ‘real’ make sense. According to Austin, “[t]he doubt or question ‘But is it a real one?’ has always (must have) a special basis, there must be some ‘reason for suggesting’ that it isn’t real” (Austin 1946, p. 87). Austin points to a contrast between standard terms and the term ‘real’. In standard cases, the affirmative use of a term is basic: to understand ‘x’, one needs to know what it is to be x. “But with ‘real’… it is the negative use that wears the trousers” (Austin 1962, p. 70). To understand the term ‘real (gold)’, one needs to know what it is for something not to be real (gold). 7 An evaluation of the constructivist account of knowledge I focus on two questions that may be asked to evaluate a philosophical theory. Does it throw any light on the problems that philosophy is struggling with, today? And, do the philosophical notions of the theory suit our use of these notions in daily life? It is usually said that constructivism may be apt for mathematics, but that there is no use for constructivism outside of mathematics. Charles Parsons argues that the constructivist explanation of knowledge and truth cannot be extended to empirical knowledge, because: “In intuitionism, possession of a proof of A guarantees the truth of A. But in most domains of knowledge even very strong evidence for a statement A might be called in question by additional evidence” (Parsons 2004, p. 193). 33 Current epistemology explains the fallibility of knowledge in different terms: a subject’s knowledge that S is fallible in so far as the knowing subject is not able to eliminate the possibility of it being true that not S, given the (pieces of) evidence that person has for S (cf. Lewis 1996, p. 549ff). This explanation of fallibility does not inherently effect all our judgements, as does the notion of fallibility used here. Martin-Löf’s concept of fallible knowledge is closer to Peirce’s, as Göran Sundholm pointed out to me. Peirce describes himself as a contrite fallibilist: there is no reason to suppose that any of our judgements might not involve error.

123

Synthese (2011) 180:391–417

411

I think, though, that the constructivist explanation of knowledge and truth can be used beyond mathematical knowledge. Above, knowledge is explained as a judgement made evident by a cognitive act. In the singular, empirical case the judgement is equally made evident by a cognitive act, namely an act of (judgemental) perception. For example, the judgement (candidate) there is a robin in my garden is made evident by an act of perception that there is a robin in my garden. Parsons is right that the act of perception may be called in question: if we know more about the situation, we may consider the act of ‘perception’ not to be cognitive: the perceptual act is no guarantee for the infallible truth of the judgement. This cognitive act does nevertheless make the judgement evident.34 The point is that there is in this respect no difference between an act of perception and an act of insight or an act of demonstration, the relevant cognitive acts within mathematics. The act of demonstration that makes a judgement candidate into a theorem might not be a real ‘act of demonstration’; the theorem is fallible knowledge. Parsons is not right insofar as he claims that within mathematics possession of a proof of A guarantees the (infallible) truth of A. Of course, there are important differences between the cognitive acts inside mathematics and logic and those outside these fields, but these differences do not constitute a difference in the explanation of knowledge and truth. The concept of knowledge as state that is introduced in this paper may be generalized beyond mathematics and logic. This means that (propositional) knowledge as state is understood as the result of a cognitive act. One need not remember the first cognitive act; the role of memory can be restricted in the way it is done by Locke. My reconstruction of Locke’s definition of habitual knowledge can be used, with some changes, to give an explanation of knowledge as state in general. P has knowledge that S, precisely if: • P has once had the cognitive act that S; • The cognitive act that S is stored in the memory of P, such that: whenever P apprehends the judgement candidate S, he judges that S. One of the advantages of this explanation of knowledge is that it does not make use of the ambiguous notion of belief (see the end of Sect. 2). Another advantage is that Gettier cases do not arise on this account (see below). Do we use in daily life a fallible notion of knowledge as explained in Sects. 5 and 6? Austin asserts in his paper ‘Other Minds’ that our ordinary concept of knowledge is that of fallible knowledge: “we are often right to say we know even in cases where we turn out subsequently to have been mistaken—and indeed we seem always, or practically always, liable to be mistaken… The human intellect and senses are, indeed, inherently fallible and delusive, but not by any means inveterately so” (Austin 1946, p. 98). Our daily concept of knowledge does not involve infallibility; it so often has happened that what was called ‘knowledge’, no longer is considered to be knowledge. Why should we think that this will not happen to what is today called ‘knowledge’? This does not imply that we continually have to speak about what we consider to be knowledge; it is simply what we call knowledge. In possession of the relevant stud-book papers, 34 Not infallibly evident, of course.

123

412

Synthese (2011) 180:391–417

you know that your stallion is Arabian. Because knowledge implies (epistemic) truth, it follows that it is true that the horse is a thorough-bred. If you cannot provide any documents that prove that it is a thorough-bred, I might doubt whether you know it, and, most likely, I will doubt whether it is true at all. Austin understands knowledge not in terms of knowledge attributions, but in terms of assertions of the form ‘I know that S’, which he does not conceive as special cases of knowledge attribution. To do so would be an example of the descriptive fallacy (Austin 1946, p. 103). “It is naturally always possible (‘humanly’ possible) that I may be mistaken …, but that by itself is no bar against using the expression(s) ‘I know’ … as we do in fact use [it]” (Austin 1946, p. 98). Austin thus defends the thesis, as I have done in this paper, that knowledge is what counts as knowledge from a first-person perspective. A topic that applies both to the question whether the knowledge concept defended here is apt for daily life, and to the question whether the constructivist concept of knowledge may throw light on the problems that philosophy is struggling with, is that of assertion. Several philosophers have defended a knowledge account of assertion, and this account suits constructivism, because judgement and its linguistic counterpart assertion are explained in terms of what one has to know in order to be entitled to make the relevant judgement or assertion. According to Timothy Williamson, the rule of assertion is that “One must: assert p only if one knows p” (Williamson 2000, p. 243). Bernard Williams has made a point against the knowledge account of assertion: knowledge is too strong a demand (‘norm’) for assertion. According to Williams, the speaker “may not be in the position himself to apply the norm effectively, because, at the point of asserting that P, he may reasonably think that he knows that P when he does not” (Williams 2002, p. 76). This criticism is applicable to those knowledge accounts of assertion that take knowledge that S to imply the infallible truth of S. How could we ever meet a demand of infallible truth? Since one never knows whether P is really true, the above-mentioned rule of assertion transcends the game and the players alike. If one defends a knowledge account of assertion, and understands that knowledge is always knowledge from a first-person perspective, the criticism does not apply. On the account of knowledge defended in this paper, the rule that ‘One is entitled to assert that S only if one knows that S’ demands of the asserter that he has perceived or demonstrated that S, but not that S is ‘really’, infallibly true. The point is that the knowledge claimed in assertion is what counts as knowledge from a first-person perspective. The constructivist concept of knowledge may be used to clarify two other problems in modern epistemology: the problem of skepticism, especially as it is dealt with by contextualism, and the Gettier problem. Austin’s paper ‘Other Minds’, already mentioned above, is presented as an answer to skeptical problems relating to other minds. According to Austin, fallibility is essential to knowledge: “It is futile to embark on a ‘theory of knowledge’ which denies this liability: such theories constantly end up by admitting the liability after all, and denying the existence of ‘knowledge”’ (Austin 1946, p. 98). One of the causes of skepticism is that philosophers have explained knowledge in terms of metaphysical or infallible truth. Because we are never able to determine whether our judgement is really, infallibly true, knowledge is impossible to determine on such an account. The modern answer to skepticism is contextualism: “Contextualists hold that the truth conditions of knowledge-ascribing and

123

Synthese (2011) 180:391–417

413

knowledge-denying sentences … fluctuate in certain ways according to the context in which they are uttered” (DeRose 2002, p. 168). According to contextualists, standards of justification vary relative to context. In most contexts, when we have reasonable evidence, our standards of justification are such that we do have knowledge according to those standards. In other contexts, especially that of the skeptical philosopher, standards are raised, they say, so that we do not have knowledge, although we are in possession of the same evidence as before. I think, though, that contextualism grants the skeptic too much. One should answer the skeptic in the Austinian manner: do not doubt, when there is no reason to doubt. According to Edmund Gettier and modern epistemology, the standard explanation of knowledge as justified true belief is problematic, because we can imagine cases, so-called Gettier cases, in which there is justified true belief without knowledge. I start with a simple Gettier case, Alvin Goldman’s description of a man perceiving a barn in barn facade county in Goldman (1976). Henry is driving along the road, sees a barn, and says to his young son ‘That is a barn’. In standard cases, we say that Henry knows that it is a barn. The Gettier case is created by adding extra information of which Henry has no knowledge. Henry happens to drive in a district that is full of papier-mache facsimiles of barns. They look like barns, but are incapable of being used as such; they have no back walls or interiors. By accident, the object that Henry takes to be a barn, is a real barn, not a barn facade, but, because it is merely by accident that he has hit upon a real barn, we seem to be reluctant to say that Henry knows that there is a barn. His belief that this is a barn is justified and true, but it seems not to be knowledge, because his belief seems to be the result of pure luck. The standard reaction to Gettier cases has been that the believer’s justification should not depend on pure luck. It also has been suggested, though, that Gettier cases can be formulated only when one tries to make a wedge between the notions being justified and being true. Already in 1974, Robert Almeder asks the question: “if the satisfaction of the evidence condition does not entail the satisfaction of the truth condition, then how could the truth condition be satisfied at all?” (Almeder 1974, p. 367). On the explanation of knowledge given here, in which the cognitive act on which one’s knowledge is based is understood to be a cognitive act from a first-person perspective, Gettier cases cannot consistently be formulated. The judgement that this is a barn is justified by Henry’s act of perception that this is a barn; he therefore knows that this is a barn. As long as he has no knowledge of barn facades, he is fully entitled to make the assertion that this is a barn, because he has no reason to doubt his perception; his perception counts as cognitive from his point of view. From the point of view of the attributor of knowledge, who has his own first-person perspective, and who knows about all the barn facades, Henry’s judgement does not count as justified, because he is not able to discriminate this case from the fake cases. From the attributor’s point of view, Henry does not have knowledge, but neither does he have a justification for his assertion. The moment Henry realizes that he is driving in barn facade county, he raises doubts concerning his act of perception, for he understands now that he cannot distinguish a barn from a barn facade. Given his new first-person perspective, he no longer considers himself to be knowing that this is a barn, and he considers his act of

123

414

Synthese (2011) 180:391–417

perception not to be cognitive in the sense that it makes the judgement that this is a bar justified. The second case in Gettier (1963) is the one where Smith judges that either Jones owns a Ford, or Brown is in Barcelona. Smith knows that Jones always had a Ford, and Jones just offered him a ride while driving a Ford, so he seems to be justified in his judgement that Jones owns a Ford. On the basis of the judgement that Jones owns a Ford, he infers the disjunction that Jones owns a Ford, or Brown is in Barcelona. Smith does not know that Brown is in Barcelona, but he is justified in the disjunctive judgement, because the judgement that Jones owns a Ford is justified. I am not sure that Smith’s judgement that Jones owns a Ford is justified, but let us suppose that it is. This means, on the account of knowledge in this paper, that he knows that Jones owns a Ford, and he therefore knows the disjunctive judgement as soon as he has made the inference step. The Gettier case is formulated as follows. Unknown to Smith, Jones does not own a Ford, but Brown is in Barcelona. This would mean that Smith’s belief in the disjunction is justified, because of the evidence he has concerning Jones, and true, because Brown is in fact in Barcelona. On a constructive account, in order for Smith to have knowledge that Jones owns a Ford, or Brown is in Barcelona, at least one of the two disjuncts needs to be justified, which makes this disjunct correct. From Smith’s, that is, the subject’s, point of view, his judgement that Jones owns a Ford is justified, and he therefore knows the disjunction, as soon as he made the inference step. Whether we, who attribute knowledge or mere belief to the subject, consider Smith’s judgement to be justified, depends on our point of view, and all the extra information we have obtained about Smith, Jones and Brown. Given that we know that Jones does not own a Ford, we do not count Smith’s ‘evidence’ for the judgement that Jones owns a Ford as giving him a justification for his judgement. Smith has therefore no justification for the disjunctive judgement, and thus has no knowledge, from the perspective of an attributor who has all the background information. The only thing we can say is that not both the subject and the knowledge attributor can be right. In order to formulate a Gettier case one has to shift, in the same story, from the perspective of the subject, in order to call his belief ‘justified’, to that of the attributor, who knows that the subject’s belief is true, for a completely different, accidental reason. Essential to the thesis that knowledge is what counts as knowledge from a first-person perspective, is that we always make our claims from a certain perspective, and that one cannot adopt two perspectives at the same time. Given that knowledge is essentially first-person, that is, that knowledge is perspectival, Gettier cases cannot be formulated. The intuition that underlies the Gettier problem is the constructivist point that even though a judgement is evident, it is fallible: the cognitive act on which the evidence of the judgement depends, might not be a ‘real’ cognitive act.

8 Conclusion The notion of cognitive act is of importance for an epistemology that is apt for constructive type theory, and for epistemology in general. Linguistic philosophers, such as Zeno Vendler, have pointed out that there are certain uses of the verb ‘to know’ that indicate that we have such a concept. It is argued here that an epistemology for

123

Synthese (2011) 180:391–417

415

constructive type theory needs to explain its epistemic concepts in terms of the primitive notion of cognitive act. Instead of taking knowledge attributions as the primary use of the verb ‘to know’ that needs to be given an account of, and understanding a first-person knowledge claim as a special case of knowledge attribution, the account of knowledge that is given here understands first-person knowledge claims as the primary use of the verb ‘to know’. Knowledge attributions are understood as a complex and derived phenomenon. It is for this reason that one may call the concept of knowledge explained in this paper a phenomenological concept of knowledge. There are also important differences between the notion of knowledge introduced here and that of the early phenomenologists: an epistemology for constructive type theory is not in need of a separate act of intuition, besides the cognitive act, in the elucidation of the different moments that are presupposed by the cognitive act. The notion of judgemental evidence as it is introduced here also differs from the notion of evidence used by the early phenomenologists: evidence as it is understood in this paper is fallible, because the evidence of a judgement is the result of a cognitive act, that is, an act that counts as cognitive for the person who makes the judgement. This means that the problem of evidence formulated by Nelson can be answered: evidence is to be understood as a phenomenological characteristic of our judgements, not as a characteristic that transcends the judging person. A judgement is evident if it is the result of a cognitive act that counts as cognitive for the judging person. This means that being evident is being evident-for-me, and because epistemic truth, or judgemental correctness, is explained in terms of evidence, this seems to imply a relativism with respect to truth, and it thus seems that there is a form of error that cannot be explained by the theory. It is for this reason that another notion of truth is introduced, truth as reality. The order of explanation of the epistemic concepts in this paper is different from the explanatory order in modern analytic epistemology, where knowledge is explained in terms of belief, and this makes the theory sometimes difficult to understand. The cognitive act is understood here as a primitive notion, and the act of judgement is explained in terms of the cognitive act. A mere act of judgement, judging without a ground, is understood as a modification of the cognitive act. The way such concepts as modification and etiolation are used in this paper, and the idea that we need to explain first-person knowledge claims prior to giving an explanation of knowledge attributions are part of a method that may be called linguistic phenomenology. If one takes seriously the idea that knowledge is primarily knowledge from a firstperson perspective, Gettier cases cannot consistently be formulated. Gettier cases can only be formulated if one shifts within the same story from the perspective of the knowing subject, from which perspective the judgement counts as justified and correct, and thus as knowledge, to the perspective of the person who is to attribute knowledge to the subject, from whose perspective the ‘justification’ and ‘truth’ of the judgement are the result of pure luck, which means that the subject is not considered to have knowledge. It thus seems to be possible to use the concept of knowledge introduced in this paper to elucidate certain problems in modern epistemology. Acknowledgements I thank Per Martin-Löf and Göran Sundholm for extensive comments on a former version of this paper. I thank Mark van Atten for the stimulating discussions on intuitionism and

123

416

Synthese (2011) 180:391–417

phenomenology during my sabbatical leave in Paris (IHPST, fall 2005), and my colleague Eric Schliesser for his comments on a former version of this paper. Parts of this paper were presented at Groningen, Paris (IHPST), Leuven and Aberdeen; I thank the organizers and participants. Open Access This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

References Adler, J. E. (2002). Belief’s own ethics. Cambridge, MA: MIT Press. Almeder, R. (1974). Truth and evidence. The Philosophical Quarterly, 24, 365–368. Austin, J. L. (1946). Other minds. In J. L. Austin (Ed.), Philosophical papers (2nd ed., pp. 76–116). Oxford: Oxford University Press. (Reprinted in 1970) Austin, L. J. (1962). Sense and sensibilia. Oxford: Oxford University Press. Bernet, R., Kern, I., & Marbach, E. (1989). Edmund Husserl: Darstellung seines Denkens. Hamburg: Felix Meiner Verlag. Brentano, F. (1930). Wahrheit und Evidenz. Hamburg: Felix Meiner Verlag. Brentano, F. (1956). Die Lehre vom richtigen Urteil. Bern: Francke Verlag. DeRose, K. (2002). Assertion, knowledge, and context. The Philosophical Review, 111, 167–203. Gettier, E. (1963). Is justified true belief knowledge?. Analysis, 23, 121–123. Goldman, A. (1976). Discrimination and perceptual knowledge. The Journal of Philosophy, 73, 771–791. Hamlyn, D. W. (1968). Aristotle De Anima. Translated with Introduction and Notes by D. W. Hamlyn. Oxford: Clarendon Press. (Reprinted in 1993) Heyting, A. (1931). Die intuitionistische Grundlegung der Mathematik. Erkenntnis, 2, 106–115. Husserl, E. (1901). Logische Untersuchungen, Hua XVIII, E. Holenstein (Ed.). (The Hague: Martinus Nijhoff, 1975); and Hua XIX, U. Panzer (Ed.). (The Hague: Martinus Nijhoff, 1984). Husserl, E. (1929). Formale und transzendentale Logik; Versuch einer Kritik der logischen Vernunft. Halle: Max Niemeyer Verlag. Husserl, E. (1939). Erfahrung und Urteil. Hamburg: Felix Meiner Verlag. (Reprinted in 1985) Lewis, D. (1996). Elusive knowledge. Australasian Journal of Philosophy, 74, 549–567. Locke, J. (1689). In P. H. Nidditch (Ed.), An essay concerning human understanding (based on the fourth edition). Oxford: Clarendon Press. (Reprinted in 1975) Martin-Löf, P. (1985). On the meanings of the logical constants and the justification of the logical laws. Nordic Journal of Philosophical Logic, 1, 11–61. http://www.hf.uio.no/filosofi/njpl. (Reprinted in 1996) Martin-Löf, P. (1987). Truth of a proposition, evidence of a judgement validity of a proof. Synthese, 73, 407–420. Martin-Löf, P. (1991). A path from logic to metaphysics. In Atti del Congresso Nuovi problemi della logica e della filosofia della scienza (Vol. II, pp. 141–149). Bologna: CLUEB. Martin-Löf, P. (1995). Verificationism then and now. In W. Schlimanovich, E. de Pauli, & F. Stadler (Eds.), The foundational debate (pp. 187–196). Dordrecht: Kluwer. Martin-Löf, P. (1998). Truth and knowability: On the principles C and K of Michael Dummett. In H. G. Dales & G. Oliveri (Eds.), Truth in mathematics (pp. 105–114). Oxford: Clarendon Press. Moser, P. K. (1989). Knowledge and evidence. Cambridge: Cambridge University Press. Nelson, L. (1908). Über das sogenannte Erkenntnisproblem. In Paul Bernays, a.o. (Eds.), Leonard Nelson Gesammelte Schriften II. Hamburg: Felix Meiner. (Reprinted in 1973) Parsons, C. (2004). Brentano on judgment and truth. In D. Jacquette (Ed.), The Cambridge companian to Brentano (pp. 168–196). Cambridge: Cambridge University Press. Peirce, C. (1878). How to make our ideas clear. In N. Houser & C. Kloesel (Eds.), The essential Peirce (Vol. 1, pp. 124–141). Bloomington: Indiana University Press. Ranta, A. (1994). Type-theoretical grammar. Oxford: Clarendon Press. Ryle, G. (1949). The concept of mind. London: Hutchinson. Sundholm, G. (1983). Constructions, proofs and the meaning of logical constants. Journal of Philosophical Logic, 12, 151–172.

123

Synthese (2011) 180:391–417

417

Sundholm, G. (1994). Existence, proof and truth-making: A perspective on the intuitionistic conception of truth. Topoi, 13, 117–126. Sundholm, G. (1997). Implicit epistemic aspects of constructive logic. Journal of Logic, Language, and Information, 6, 191–212. Sundholm, G. (1998). Inference, consequence, implication: A constructivist’s perspective. Philosophia Mathematica, 6, 178–194. Sundholm, G. (2002). A century of inference: 1847–1936. In P. Gärdenfors, J. Wolenski, & K. Kijania-Placek (Eds.), In the scope of logic methodology and philosophy of science (Vol. II, pp. 565–580). Dordrecht: Kluwer. Sundholm, G. (2004). Antirealism and the roles of truth. In I. Niniluoto, M. Sintonen, & J. Wolenski (Eds.), Handbook of epistemology (pp. 437–466). Dordrecht: Kluwer. Tugendhat, E. (1970). Der Wahrheitsbegriff bei Husserl und Heidegger. Berlin: de Gruyter. van der Schaar, M. (1999). Brentano on truth and the law of excluded middle. In T. Childers (Ed.), The LOGICA yearbook 1998 (pp. 110–120). Prague: Filosofia. van der Schaar, M. (2003). Brentano on logic, truth and evidence. Brentano Studien, 10, 119–150. van der Schaar, M. (2006). On the ambiguities of the term Judgement. An evaluation of Twardowski’s distinction betweeen action and product. In A. Chrudzimski & D. Lukasiewicz (Eds.), Actions products and things; Brentano and Polish philosophy (pp. 35–53). Frankfurt: Ontos Verlag. van der Schaar, M. (2007). The assertion-candidate and the meaning of mood. Synthese, 159, 61–82. van der Schaar, M. (2009). Judgement, belief and accepance. In G. Primiero & S. Rahman (Eds.), Acts of knowledge: History, philosophy and logic; essays dedicated to Göran Sundholm (pp. 267– 286). London: College Publications. Vendler, Z. (1967). Linguistics in philosophy. Ithaca: Cornell University Press. von Kutschera, F. (1981). Grundfragen der Erkenntnistheorie. Berlin: de Gruyter. Williams, B. (2002). Truth and truthfulness. Princeton: Princeton University Press. Williamson, T. (2000). Knowledge and its limits. Oxford: Clarendon Press.

123

This page intentionally left blank z

Synthese (2011) 180:419–442 DOI 10.1007/s11229-009-9709-3

On the distinction between Peirce’s abduction and Lipton’s Inference to the best explanation Daniel G. Campos

Received: 3 February 2009 / Accepted: 30 October 2009 / Published online: 15 December 2009 © Springer Science+Business Media B.V. 2009

Abstract I argue against the tendency in the philosophy of science literature to link abduction to the inference to the best explanation (IBE), and in particular, to claim that Peircean abduction is a conceptual predecessor to IBE. This is not to discount either abduction or IBE. Rather the purpose of this paper is to clarify the relation between Peircean abduction and IBE in accounting for ampliative inference in science. This paper aims at a proper classification—not justification—of types of scientific reasoning. In particular, I claim that Peircean abduction is an in-depth account of the process of generating explanatory hypotheses, while IBE, at least in Peter Lipton’s thorough treatment, is a more encompassing account of the processes both of generating and of evaluating scientific hypotheses. There is then a two-fold problem with the claim that abduction is IBE. On the one hand, it conflates abduction and induction, which are two distinct forms of logical inference, with two distinct aims, as shown by Charles S. Peirce; on the other hand it lacks a clear sense of the full scope of IBE as an account of scientific inference. Keywords Hypothesis · Abduction · Inference to the best explanation · Scientific reasoning · Peirce

There is a tendency in the philosophy of science literature to link abduction to the inference to the best explanation (IBE), and in particular, to claim that Peircean abduction is a conceptual predecessor to IBE. For instance, Peter Lipton, like Gilbert Harman before him (1965, pp. 88–89), simply cites, without argument, Peircean abduction as one of the antecedent, and apparently insufficiently developed, accounts of inductive

D. G. Campos (B) Brooklyn College, City University of New York, New York, USA e-mail: [email protected]

123

420

Synthese (2011) 180:419–442

IBE (Lipton 1991, p. 58). I think this is inaccurate, as it is not based on any systematic comparison of these concepts. One consequence is the tendency to dismiss or disregard, without studying it carefully, Peircean abduction as an account of ampliative inference that may be of interest today, in its own right, especially for those who see in explanationism an important contemporary avenue to account for ampliative reasoning in scientific inquiry. Another consequence, I will argue, is that some important distinctions about the nature of scientific reasoning are lost when we blur the distinction between abduction and IBE, and so our own philosophical understanding of such reasoning is impoverished. This is not to discount either abduction or IBE. Rather the purpose of this paper is to clarify the relation between Peircean abduction and the IBE in accounting for ampliative inference in science. In that sense, this paper aims at a proper classification—not justification—of types of scientific reasoning. I will explicitly adopt a Peircean perspective, so as to clarify how the matter stands from that view point; however, I do not mean to discount other perspectives, but to promote philosophical dialogue. In particular, I will claim that Peircean abduction is an in-depth account of the process of generating explanatory hypotheses, while IBE, at least in Lipton’s thorough treatment, is a more encompassing account of the processes both of generating and of evaluating scientific hypotheses. There is then a two-fold problem with the claim that abduction is IBE. On the one hand, it conflates abduction and induction, which are two distinct forms of logical inference, with two distinct aims, as shown by Charles S. Peirce; on the other hand it lacks a clear sense of the full scope of IBE as an account of scientific inference. Some recent articles that otherwise advance in important ways our understanding of IBE, on the one hand, and abduction, on the other, still conflate the two concepts without argument. For instance, Barnes (1995) examines Lipton’s account of inference to the loveliest explanation in detail. His article begins, however, with the assumption that abduction and IBE are the same: C. S. Peirce’s discussion of ‘abduction’ is typically cited as the first attempt to argue that our willingness to infer that a hypothesis H is true is based on the judgment that H qualifies as a good explanation of the data which support it. Gilbert Harman advocated this approach to inference by arguing in his (1965) that enumerative induction is valid only when applied as a special case of a more fundamental mode of inference he called ‘inference to the best explanation’. (Barnes 1995, p. 251) However, this very description of abduction, in so far as it speaks of data as supporting a hypothesis, is already more along the lines of Bayesian inductive, rather than Peircean abductive, inference as we will see. Schurz (2008), in turn, has recently made an important contribution towards our understanding of abduction by providing a classification of different patterns of abduction and suggesting criteria to evaluate hypotheses resulting from each pattern. However, Schurz asserts that abductions are special patterns of IBE (2008, pp. 201–202), even though he recognizes a distinction between inductive and abductive inference along Peircean lines (2008, p. 202). In recent literature, nonetheless, there are some important exceptions to the conflation between Peircean abduction and IBE. Three notable ones are Hintikka (1998), Minnameier (2004), and Paavola (2006). Hintikka (1998) convincingly argues that

123

Synthese (2011) 180:419–442

421

Peircean abduction comprehends more ways of creating scientific hypotheses than just IBE. However, his dismissal of IBE does not do justice to well-articulated views such as Lipton’s. Minnameier (2004) argues that abduction ought to be distinguished from IBE. His reclassification of IBE as a form of Peircean induction, however, is different from the reclassification that I will suggest based on a thorough review of Lipton’s version of IBE. Also, Minnameier’s aim is an overall exposition and defense of Peirce’s triadic theory of scientific inquiry—in which abductive, deductive, and inductive inferences form part of a dynamical, rational process—and he discusses its implications for contemporary epistemological problems regarding notions such as realism, truth, coherence, and unification, whereas my aims are more focused on a Peircean classification of types of inference in scientific inquiry. Paavola (2006), on the other hand distinguishes between two varieties of abduction, Harmanian—of which Lipton’s IBE is a development and which is usually concerned with issues surrounding scientific realism—and Hansonian—which is a development of Peirce’s abduction and concerns more directly the logic of discovery—whereas I will argue that Harmanian-Liptonian IBE should not be labeled abduction as it involves more than the creative generation of explanatory hypotheses. Overall, I consider my article to be complementary to theirs, and I will note agreements and disagreements wherever suitable throughout my essay. My hope is that this article contributes a detailed account of Peirce’s concept of abduction as different from induction that helps to clarify its place and continued importance in an overall classification of forms of scientific inference, even as researchers continue to develop more detailed accounts of abduction along Peircean lines that can be clearly distinguished from accounts of IBE.1 To achieve my classificatory aims, this paper is divided in three sections. The first section treats of Peirce’s concept of abduction. I sketch its historical development as part of a triad of types of inference that also includes induction and deduction. Then I concentrate on expounding Peirce’s mature view of abduction in contradistinction to induction. Section 2 discusses IBE as a viable account of non-deductive inference. Here I briefly discuss Harman (1965), as the first account of IBE that brought the issue to center of philosophical interest in recent history. But instead of reviewing all the various accounts of IBE, I discuss Lipton’s account of IBE in depth, as I think it is the most thoroughly developed one. Section 3 compares Peirce’s account of abduction with Lipton’s account of IBE in order to display their similarities and, especially, their important differences for a philosophical account of ampliative reasoning in science. 1 Charles Peirce’s concept of abduction Much of the confusion and controversy over Charles Peirce’s own understanding of abduction is due to three reasons. The first is lack of scholarly attention, on the part of philosophers of science, to the historical development of his thought, so that 1 This is why I admittedly do not review in its entirety the literature on abduction and IBE but rather concentrate on distinguishing between Peirce’s original account of abduction and Lipton’s account of IBE. My aim is to reclassify without evaluating or denying the importance of recent developments and criticisms of abduction, on the one hand, and IBE, on the other.

123

422

Synthese (2011) 180:419–442

passages from different periods of his thought and from texts with different purposes are cited together and held to be inconsistent or puzzling. Second, Peirce’s thought was thoroughly systematic, structured by logical categories and a distinct epistemology in the way of Aristotle or Kant, but discussions of Peircean abduction in philosophy of science often sever this concept completely from the system. Third, the concept “abduction” has been developed in further ways that are non-Peircean—e.g. Bayesian abduction—so that it is sometimes difficult to pinpoint what is meant by “abduction” in different contexts. A thorough historical review of Peirce’s evolving account of abduction and of subsequent philosophical off-shoots is not possible here. Instead, after a historical sketch I will offer an interpretation of Peirce’s mature, systematic account of abduction, especially as distinguished from induction. In a seminal 1867 paper entitled “On the Natural Classification of Arguments,” Peirce classifies arguments into a triad.2 His aim in that paper—an aim which will also guide my discussion here—is to provide a classification of the various kinds of arguments, without undertaking yet to discuss their justification or validity. Under the influence of his sustained study of Kant, Peirce classifies arguments as either analytic or synthetic. Analytic arguments are deductive, and synthetic arguments are classified as either induction or hypothesis. Although his conception of the different kinds of argument, and especially of induction and hypothesis (later abduction or retroduction), evolved over the course of his research in logic, Peirce always maintained a triadic classification.3 For Peirce the classification of arguments really corresponds to, or reflects, the various basic kinds of reasoning that we might require in order to confront various situations in the course of our inquiries. As Peirce would put it in 1898, the three forms of argument are but the “scaffolding” that reveals the structure of the three basic kinds of inferential reasoning (RLT, p. 141).4 Until about 1900 Peirce usually addressed the classification of arguments and the corresponding classification of kinds of reasoning by showing that there are three basic figures of syllogism that correspond, in turn, to three basic kinds of reasoning. In other words, he typically addressed the triad in reasoning by showing, first, that there is a formal distinction between three kinds of argument and, second, that this formal distinction corresponds to an actual distinction between three kinds of inferential reasoning,5 where by inference Peirce means the “controlled adoption of a belief as a

2 See “On the Natural Classification of Arguments,” Proceedings of the American Academy of Arts and Sciences, April 9, 1867. Reprinted in W 2, pp. 23–48. Note that following standard practice in Peirce scholarship, I will abbreviate Peirce (1982–2000) as W, followed by volume and page number. 3 I cannot offer here a discussion of the development of Peirce’s views on the three kinds of argument. For an account of this development, see Santaella (1998). 4 Following standard practice in Peirce scholarship, I will abbreviate Peirce (1992) as RLT. 5 Peirce’s argument can be found in “On the Natural Classification of Arguments” (W 2, pp. 23–48). A

partial version of the argument is also found in “Types of Reasoning” (RLT, pp. 123–142). See Hilary Putnam’s “Comments” on this last text (in RLT, pp. 59–67). The reader may notice that, strictly speaking, there are four basic figures of the syllogism. To the corresponding fourth kind of reasoning, analogy, Peirce ascribes a “mathematical provenance” and he considers it to be of a “mixed character” in relation to the three basic kinds (RLT, p. 141).

123

Synthese (2011) 180:419–442

423

consequence of other knowledge” (CP 2.442; 1893?).6 This is also the strategy that he deployed in his 1898 Cambridge Conferences lecture entitled “Types of Reasoning.”7 The key to the argument is that, according to Peirce, “demonstrative inference is the limiting case of probable inference. Certainty pro is probability 1. Certainty con is probability 0” (RLT, p. 136). This is reflected in the first figure of the syllogism. Peirce presents the probable syllogism as follows: The proportion r of the Ms possess π as a haphazard character; These Ss are drawn at random from the Ms; Therefore, probably and approximately, the proportion r of the Ss possess π . If the proportion r = 1 in the limiting case, and if we take π to be the quality P, that is, if all the Ms possess some quality P, then this probable inference becomes a valid demonstrative syllogism in the first figure: All M are P All S are M All S are P. Similarly, if the proportion r = 0, the probable inference also becomes a valid demonstrative syllogism in the first figure: No M are P All S are M No S are P. In general, then, valid demonstrative syllogisms are limiting cases of probable inferences in the first figure. In Peirce’s words, the first figure of probable reasoning embraces “all necessary reasoning as a special case under it. It is in fact Deduction” (RLT, p. 138). Given Peirce’s description, deductive reasoning consists in drawing an inference about a specific character of the objects or events in a sample on the basis of our knowledge of the character of the objects in the population from which we know the sample to be drawn at random. In deductive reasoning we proceed from our knowledge of the character of a population and of the method of sampling to a conclusion about the character of the sample. 6 In defining inference, Peirce alternatively writes: “When it happens that a new belief comes to one as consciously generated from a previous belief—an event which can only occur in consequence of some third belief (stored away in some dark closet of the mind, as a habit of thought) being in a suitable relation to that second one—I call the event an inference, or a reasoning” (EP2, p. 463; 1913). It is important to highlight also that Gerhard Minnameier directly addresses objections to Peirce’s abduction being considered a form of inference (Minnameier 2004, pp. 86–90). Note that following standard practice in Peirce scholarship, I will abbreviate Peirce (1932) as CP followed by volume and paragraph number, and I will abbreviate Peirce (1998) as EP2. 7 See RLT, pp. 123–142.

123

424

Synthese (2011) 180:419–442

Turning to a second kind of reasoning, Peirce argues that a valid syllogism in the third figure is the limiting case of inductive reasoning. The third figure of probable reasoning is the following: These Ss are drawn at random from the Ms; Of these Ss, the proportion ζ possess the haphazard character π; Therefore, probably and approximately, the proportion ζ of the Ms possess π . For Peirce, this is the formula of induction (RLT, p. 139). The form of the argument reflects the structure of inductive reasoning—from the character of a sample of objects drawn at random from a population we infer the character of the population. Induction, then, is usually for Peirce the form of reasoning that leads to knowledge of the probability of general rules or laws. For Peirce our knowledge of general rules or laws of nature comes from our experience, where “experience” consists in everything that our “reactions” or “clashes” with outward reality force our minds to acknowledge. When we reason inductively, we infer the probable prevalence of general laws on the basis of our sample of experience. However, as Peirce himself emphasizes, while inductive reasoning can lead to knowledge of the probability that attaches to general rules, it “can never make a first suggestion” (RLT, p. 139). That is, induction itself can never suggest for investigation the possible laws, rules, regularities, or uniformities that may prevail in a population of phenomena. It can only infer the ratio in which the character π already chosen for study is present in the population; this ratio gives us a probable and approximate general rule. Induction can only confirm or deny, with a given degree of approximation, the prevalence of conjectured laws, rules, or regularities in the population. In short, inductive reasoning only serves to test a conjecture regarding the general character of a population; it can never suggest a conjecture for inductive testing. Accordingly, Peirce places great emphasis on the ampliative force of a third kind of reasoning, different from both deduction and induction—a form of reasoning that results in what Peirce calls “first suggestions” or conjectures of all kinds, including suggestions regarding general laws or regularities. The third kind of reasoning is abduction or retroduction. The form of abductive argument corresponds to the second figure of the probable syllogism: Anything of the nature of M would have the character π , taken haphazard; S has the character π ; Provisionally, we may suppose S to be of the nature of M. Peirce restates this in conditional form as: If μ were true, then π , π  , π  would follow as miscellaneous consequences; But π , π  , π  are in fact true; Provisionally, we may suppose that μ is true.

123

Synthese (2011) 180:419–442

425

He observes that this “kind of reasoning is very often called adopting a hypothesis for the sake of its explanation of known facts” where the resulting explanation is the modus ponens: If μ is true, then π , π  , π  are true; μ is true; Therefore, π , π  , π  are true. (RLT, p. 140) In short, for Peirce abductive reasoning is inference to an explanatory hypothesis, and this form of reasoning is to be distinguished from induction, in which we have already adopted a hypothesis and are only testing its consequences. When in our inquiries we are confronted with new, often puzzling, facts that we seek to explain, we are in a situation that requires us to make a conjecture that would explain the facts, and to adopt the conjecture provisionally as a hypothesis that we may test. Experiential sampling is also crucial in this situation. It is the course of experience, whether in everyday life or in methodical inquiry, that often presents us with unexplained phenomena. In this situation, then, the sample of facts is given to us by the course of experience. So long as this is the case, we may consider the sample to be taken haphazard. The abductive suggestion consists in the conjecture that a general rule, say the general character of a certain type of event, explains the facts under investigation. We may note at this point that there are at least two species of abductive reasoning. Under one species, which we might term “habitual abduction,” the inquirer already knows a general rule or law, and the reasoning consists in grasping that the known general rule, when applied to the facts under investigation, provides an explanation for those facts. So the inquirer provisionally hypothesizes that the general rule is at work in the production of the facts. In short, the abductive suggestion is the hypothesis that the observed facts result from the known rule or law. Habitual abduction, then, usually takes the form of the conjectural classification of facts by way of laws for the purpose of explaining those facts. However, under the second species, which we might term “creative abduction,” the general rule itself is not known in advance of the inquiry into the observed facts and their explanation. The inquirer is confronted with puzzling facts, but she does not know of a general rule, law, or nature that may readily explain them. She must conceive the explanation itself. In terms of the preceding formula of abductive argument, the difference between habitual and creative abduction is that in habitual abduction the inquirer already knows the general rule stated in the first premise and her reasoning consists in associating the rule with the observed phenomena, while in creative abduction she must conceive the general rule itself, and state it in the major premise of the argument. As I have already noted, Peirce’s triadic classification of arguments and forms of reasoning evolved throughout the course of his logical investigations. The progressive and evolving distinction between induction and hypothesis, which in his mature work becomes a thoroughgoing distinction between induction and abduction, is a crucial part of the development of his triadic classification. Peirce recounts his evolving views

123

426

Synthese (2011) 180:419–442

on the distinction at various junctures.8 Only gradually did Peirce come to view abduction as a distinct form of reasoning, not to be classified as a species of induction but as a separate kind of reasoning altogether. Moreover, he came to see the syllogistic form as too narrow to account for all ampliative scientific reasoning, thus placing more emphasis on a methodological account of reasoning kinds. Douglas Anderson argues that Peirce’s concept of abduction evolved markedly as he developed his philosophy: Peirce began by viewing abduction as an ‘evidencing process’ and later switched to treating it as the stage of scientific inquiry which leads us to hypotheses. As an evidencing process abduction was, just as induction, a way to decide for or against given hypotheses–it was one logical form of deciding probability. However, even at this early stage Peirce acknowledged the other aspect of abduction: its function as a source of new hypotheses. Therefore the shift is not simply from evidencing process to source of new ideas, but a shift from a conflation of these two ideas to a particular emphasis on the latter. (1986, p. 148)9 This distinction between induction and abduction is one of the most original aspects of Peirce’s logical classifications, and it will be worthwhile to expound briefly his reasons for making the distinction. We have already seen that the formal structure of both forms of argument is different, corresponding to two different reasoning situations that an inquirer might confront. Thus, we should take the forthcoming comments to be an elaboration of the distinctions already laid out implicitly in the preceding triadic classification. Above all, we will pay attention to the distinction as related to the different aims of inferential reasoning at different stages of scientific inquiry. In the 1898 Lectures Peirce provides the distinct structural forms of inductive and abductive argument. Now, their structural form reveals a remarkable distinction— inductive reasoning relies upon abductive assumptions. Hilary Putnam writes: [B]y requiring that ‘induction’ include a premise to the effect that the sampling method is random, Peirce was telling us that all induction requires prior knowledge of lawlike statements. For the statement that a method of sampling is random…requires knowledge of the equality of certain future frequencies, and is thus a species of lawlike knowledge, knowledge of generals. (“Comment” in RLT, p. 67) Induction, on the Peircean model, presupposes that any object from the population would be sampled with equal frequency in the course of sampling in the infinite longrun. This presupposition of randomness in sampling amounts to a presupposition of a lawlike process. And it is an abductive presupposition; a conjecture regarding the nature of the sampling process. Induction must rely upon hypotheses and abductive conjectures to get off the ground as a form of reasoning.10 The economy of research requires this and there is no way around it in actual scientific practice. 8 See for instance RLT, p. 141. 9 See also Burks (1946, p. 303) and Fann (1970, p. 32). 10 I must emphasize that this is different from claiming that induction is reducible to abduction—a claim rejected by Anderson (1986) and Schurz (2008, p. 202). The claim here is that induction relies upon, but is not reducible to, abduction. See also Putnam (“Comment” in RLT, p. 67) and Minnameier (2004, p. 82).

123

Synthese (2011) 180:419–442

427

Accordingly, Peirce evaluates the merit or warrant of scientific forms of reasoning on the basis of whether they achieve their ends to facilitate the progress of scientific inquiry. The key question for Peirce is not whether abduction or induction can ever attain the level of formal justification that deductive reasoning has, but whether as methods of reasoning they fulfill their respective function within the economy of scientific research.11 Regarding ends, in 1898 Peirce argues that while induction serves to test claims regarding the general character of phenomena, it can never suggest the conjectures that are to be tested inductively. Abductive reasoning responds to the need, arising from the economy of research, that at a given stage of an inquiry into the principles and causes of observed phenomena we must come up with conjectures, no matter how tentative they may be or how unlikely it may seem at the outset that they will turn out to be true. Peirce offers the example of scientific inquiry into cuneiform writing. In order to take the first steps towards reading cuneiform inscriptions, inquirers had to make some guesses regarding their meaning, and had to hold these guesses provisionally as hypotheses for inductive testing (RLT, p. 142). The testing could consist in ascertaining whether the hypothesized interpretation of the inscriptions would lead to probably and approximately true readings of other, perhaps undiscovered, writings. Inductive reasoning responds to the need dictated by the economy of research that we must test our plausible conjectures in order for scientific inquiry to progress. Peirce further develops abductive logic in his mature work. In the 1903 Harvard Lectures on Pragmatism, Peirce provides one of his fullest and clearest expressions of the logic of abduction. He describes abduction as the logical process of forming an explanatory hypothesis and again classifies it as a logical form of inference distinct both from deduction and from induction. He shows that even though abduction only asserts its conclusion “problematically or conjecturally,” as an inference it has a definite logical form, namely: “The surprising fact, C, is observed; But if A were true, C would be a matter of course. Hence, there is reason to suspect that A is true” (EP2, p. 231). “Thus,” Peirce continues, “A cannot be abductively inferred, or if you prefer the expression, cannot be abductively conjectured, until its entire contents is already present in the premiss, ‘If A were true, C would be a matter of course”’ (EP2, p. 231). This premise amounts to stating that A would explain C, so Peirce is arguing that we cannot infer A unless our inference be to an explanatory hypothesis. In short, a condition for the admissibility of a hypothesis is that the hypothesis would account for the facts, and on those explanatory grounds we hold the hypothesis to be plausible. The result of abductive reasoning, then, is the suggestion of what may plausibly be the case or fact that explains an observed phenomenon. This is different from the deductive conclusion that something must necessarily be the case under given hypothetical 11 Hintikka defends this view based on the distinction between definitory and strategic rules of inference— abduction responds mainly to strategic rules (1998, pp. 512–515). Schurz in turn defends this view by adopting a distinction between justificatory and strategic functions of different types of inference (2008, pp. 203–205). Abductions serve the strategic or discovery function of “finding a most promising conjecture (conclusion) which is set out to further empirical test operations” (2008, p. 203).

123

428

Synthese (2011) 180:419–442

or axiomatic conditions and from the inductive conclusion that something probably will be the case, in a calculable proportion of cases, upon the fulfillment of some particular conditions in nature (EP2, pp. 215–216). According to Peirce, in the whole process of scientific inquiry, abductive hypotheses are mere plausible suggestions that we then take up for inductive experimental testing. But these “mere abductive suggestions” are the only source of scientific discovery, while inductive conclusions are a matter of experimental verification. Again, herein we find the key distinction between the reasoning situations that call for abduction or induction. The question of abduction is the question of explanation of observed facts, while the question of induction is the question of the degree of agreement between observed and predicted facts. Creative abductive inferences are the site of novel conception, as the entities involved in the causes, principles, or laws that plausibly explain the observed phenomena are often of a different nature than the observed phenomena. That is, when we propose a hypothetical explanation for an observed fact, we often conceive causes, principles, or laws that involve entities essentially different from the observed fact. In creative abduction, we begin with an observed particular phenomenon, we suppose a general explanation—a cause, a law, or a principle—that involves entities that are of a different nature than the observed particular phenomenon, and we provisionally conclude that the supposition is plausible. There is no such need for innovative conception in induction, where we assess the probable and approximate degree to which we may generalize a rule or theory. Admittedly, there are two tasks involved in a complete philosophical account of abductive reasoning. One is to describe its logical form and to account for the rules that make it a rational process—in Peirce’s terms, a self-controlled thinking activity in which we can describe and criticize the principles of reasoning that we employ. Another task is to explain how the abductive suggestions or conjectures arise in the first place. The later task concerns the origin of creative abduction. That is, it concerns the epistemic source of the supposition “if A were true, C would be explained.” Thus, while my most important aim here is to introduce Peirce’s triadic classification of reasoning and to explain his reasons for distinguishing between induction and abduction as two distinct forms of reasoning, it is necessary to make some observations on Peirce’s account of how the reasoning process of abduction works.12 Peirce attributes the origin of first explanatory suggestions to our “Abductive Insight”—a faculty of reasoning, akin to instinct, that continuously transforms our “perceptual judgments,” which are not subject to rational self-control, into “abductive conjectures” subject to logical criticism via the logic of abduction (EP2, pp. 217–218). One of Peirce’s “cotary” propositions to sharpen his account the logic of abduction is that “abductive inference shades into perceptual judgment without any sharp line of demarcation between them; or in other words our first premises, the perceptual judgments, are to be regarded as an extreme case of abductive inferences, from which they differ in being absolutely beyond criticism,” that is, beyond any rules or maxims for critiquing or assessing the logical merit of abductive hypotheses (EP2, p. 227). Furthermore, Peirce continues: 12 For one of Peirce’s fullest expositions, see his 1903 Harvard Lecture “Pragmatism as the Logic of Abduction” (EP2, pp. 226–241).

123

Synthese (2011) 180:419–442

429

The abductive suggestion comes to us like a flash. It is an act of insight, although of extremely fallible insight. It is true that the different elements of the hypothesis were in our minds before; but it is the idea of putting together what we had never before dreamed of putting together which flashes the new suggestion before our contemplation. (EP2, p. 227) Conceiving an original explanatory hypothesis, I propose, involves for Peirce both the work of perception and imagination. Peirce’s analysis of perception is itself quite complex. I will merely sketch some aspects of it that will be helpful to understand its relation to creative abduction.13 Very roughly, a percept (object) imposes its presence upon a perceptual awareness, and a perceptual judgment—a sign that purports to represent the percept—is formed as a result of the interaction between percept and perceiver. This perceptual judgment in the perceiver’s mind is itself an uncontrollable hypothesis so as to the contents of the percept, and must itself be logically scrutinized, in the course of experience, for us to learn whether it does accurately represent the percept. According to Sandra Rosenthal, for Peirce “[a]ll knowledge begins with perception, but perception is not the having of brute givens. Rather, there is a creative element in perceptual awareness, an interpretive creativity brought by the perceiver” (p. 193). Sometimes the perceptual judgment may contradict the perceiver’s expectations or experimental predictions, presenting her with a problem in need of explanation. Here the explicit work of the imagination is crucial. For Peirce, perception and imagination are indeed continuous with and shade into each other. According to him, in relation to knowledge and belief—that is, as a matter for logic—it is not valuable “to draw a hard and fast line of demarcation between perception and imagination,” even if as a matter of physiological psychology the distinction may be justified (CP 7.646, 1903). For our purposes, this is because the semiotic outcomes of both perceiving and imagining are signs—signs that flow in the course of continuous, ongoing reasoning processes. The imagination consists in “the power of distinctly picturing to ourselves intricate configurations” (MS 252, n.d.).14 That is, the imagination is a semiotic ability to create, recreate, and transform signs. When a perceptual judgment disrupts our expectations and presents us with a problem, the imagination works to form schemata or diagrams of the situation, searching for explanations. In the case of abduction, explanatory hypotheses are signs—diagrams that rearrange the relations among facts so as to explain them.15 Sometimes new elements (explanatory facts) are introduced into the diagrammatic hypothesis to explain the perceived, unexpected facts. “Diagrams” or explanatory schemata may include formalized theories, equations, statistical models, figures, representations of atomic or molecular structures, and so on. The abductive insight consists in associating or relating explanatory and perceived facts in a novel way or, as Peirce puts it, in “the idea of putting together what we had never before dreamed of putting together.” In this 13 See a 1903 account of perception in CP 7.619–636. A good article to start exploring interpretations of Peirce on perception is Rosenthal (2004). 14 References to Peirce’s manuscripts are abbreviated as MS followed by their Robin Catalogue (1967)

number. 15 For accounts of the importance of Peirce’s logical concept of “diagram” in his philosophy see Kent

(1997) and Stjernfelt (2000).

123

430

Synthese (2011) 180:419–442

process, the semiotic imagination is guided by the character of observed facts, existing knowledge, previous experience, problem-context, and maxims of good abductive reasoning. This is why abduction, as Douglas Anderson argues, is the “basis for scientific creativity as both insight and inference” (1986, p. 145). He thus defends Peirce’s account of abduction against a common objection which generally reduces to the claim that Peirce’s view is fundamentally paradoxical in holding that abduction is both an insight and an inference. One version of the objection is that the logical form of abduction, as presented in the 1903 Harvard Lectures, precludes originality in hypothesis formation because the hypothesis itself is included in the premises, so the hypothesis must have been invented before drawing the conclusion, while the conclusion is that there is evidence for the hypothesis (Frankfurt 1958). Anderson replies that the form as stated should not be taken too literally or rigidly and out of context. That the concluded hypothesis must be a possible explanation of the observed problematic fact is a formal constraint on the conclusion, not a material element of it. The conclusion should be read as “probably A” and not as the inductive conclusion that there is evidence for A— the context rules the latter out. So the conclusion is a hypothesis and not the outcome of an evidencing process.16 Moreover, the objection conflates logical and temporal priority. The premise “If A then C” is logically but not necessarily temporally prior to the conclusion “Probably A” (Anderson 1986, pp. 156–157). Anderson concludes: “On Peirce’s view it is possible for the hypothesis and its abductive application to occur together. Therefore, abductions may be insightful and originative and still have logical form” (p. 157). Another version of the objection is that Peirce’s descriptions of abduction establish it as an intuitionistic theory which must also preclude logical form” (Anderson 1986, p. 155). However, Anderson replies, Peirce explicitly rejects intuitionism; indeed, “[f]or Peirce, any insight must be mediated by its context” (Anderson 1986, p. 160). More specifically, Peirce’s abduction is fallible and possibilistic, unlike infallible intuitions. Moreover, intuitions are unmediated, but abductions are thoroughly mediated— they take place in media res, in the context of problem-solving, and are influenced by previous thoughts, experience, and overall context (1986, pp. 160–161). Other commentators have elaborated specific accounts on how this contextual problem-solving may proceed. Hintikka (1998), for instance, describes abductive reasoning as a Socratic 16 Note that this once again highlights the distinction between abduction and induction. It emphasizes that hypothesis creation for the sake of explanation and hypothesis selection on the basis of inductive experimental evidence are different for Peirce. Although Peirce occasionally writes of abduction as the process of selecting or choosing a hypothesis (CP 6.525, n.d.; CP 7.219, 1901), in those contexts he means that among several explanatory hypotheses one may be selected for inductive testing on the basis of abductive considerations including explanatory merit, but not experimental testing or probabilistic weighing of evidence. At one point, Peirce is quite explicit about this, claiming that abductive inference may involve “a preference for any one hypothesis over others which would equally explain the facts as long as this preference is not based upon any previous knowledge bearing upon the truth of the hypotheses, nor on any testing of any of the hypotheses, after having admitted them on probation” (CP 6.525, n.d.). It is only in this very limited sense that abduction may be not only hypothesis creation but also selection. As I will argue, this is very different from selecting a hypothesis inductively as the best. Thus Fann’s contention that Peirce does not clearly distinguish between hypothesis construction and selection is too strong (1970, pp. 41–44). On this point, see also Hintikka (1998, p. 511).

123

Synthese (2011) 180:419–442

431

process that consists in asking strategic why-questions and seeking rational answers akin to making a series of strategic moves in game-theoretic contexts (“games of inquiry”).17 Regarding the (procedural) logic of abduction, Peirce himself argues that it requires that an abductive hypothesis be (i) explanatory and (ii) capable of experimental verification, if the hypothesis is to be adopted (see EP2, pp. 226–241). Experimental verification, however, is not reducible to narrow formulas—such as August Comte’s positivist formula that in order to be verifiable a hypothesis must predict phenomena that are directly observable (EP2, p. 225)—but rather involves the entire logic of induction—itself a related, complex matter of logical investigation for Peirce. Elsewhere, Peirce provides other rules for the logic of abduction, that is, for the process of adopting explanatory hypotheses for testing. Hookway (1985, pp. 225–226) provides a concise summary of other elements of the logic of abduction, including Peirce’s recommendations that we should (iii) favor hypotheses that seem simple, natural, and plausible to us (CP 6.447), (iv) prefer theories that explain a wide range of phenomena to those more narrow in scope (CP 7.221); (v) be mindful of successful theories in other areas and choose hypotheses that employ similar kinds of explanations, that is, be mindful of analogies; and (vi) keep always present the question of economy of money, time, thought, and energy, which for Peirce is the “leading consideration in Abduction” (CP 5.600). (vii) Peirce also warns against giving undue preference to hypotheses on the basis of their “antecedent likelihoods” (CP 5.599), emphasizing therefore that the question of the plausibility of an abductive hypothesis is different from the question of its antecedent probability or likelihood. A conjecture might be highly improbable and yet it may seem plausible to us and therefore worthwhile adopting for further inquiry. As we will see, this anticipates a major difference between Peircean abduction and Peter Lipton’s account of IBE, insofar as Lipton associates the generation of explanatory hypotheses to considerations of the prior probability of hypotheses as described by Bayesianism. Let us turn, then, to an assessment of IBE. 2 Inference to the best explanation In order to prepare the way for a comparison with Peircean abduction, let us turn to an exposition of the IBE. Harman (1965) provided the first exposition of IBE in the recent spur of philosophical interest that IBE has generated over the last forty-five years. Harman proposes it as the fundamental form of non-deductive inference—a form that is often warranted in cases where, for example, simple enumerative induction is not and that, moreover, includes enumerative induction as one of its special cases. He writes that in an IBE “one infers, from the premise that a given hypothesis would provide a ‘better’ explanation for the evidence than would any other hypothesis, to the conclusion that the given hypothesis is true” (Harman 1965, p. 89). This characterization points to at least three relevant features of the inference to hypotheses. First, in science, when we have some given empirical data, we formulate several alternative hypotheses that are compatible with it; we do not simply formulate one such hypothesis 17 For a recent thorough account of abduction, see Aliseda (2006).

123

432

Synthese (2011) 180:419–442

and stop there. Second, the hypotheses that we infer are explanatory. There may be several, even infinitely many, hypotheses that are compatible with some observation, but not all of these alternative hypotheses will be explanatory. This of course raises the question of what is an explanatory hypothesis, or more simply, what is an explanation. Harman does not undertake to answer this question, very extensive in itself, but he points out, third, that we infer hypotheses that explain the evidence better than any of the alternatives. This opens up the possibility of arguing that although we may not be able to determine absolutely what an explanation is, we can at least make relative judgments regarding better or worse explanations. That is, when confronted with two or more alternative explanatory hypotheses for the data, we can make judgments about their relative merit on the basis of some relevant criteria. Harman briefly points to some such criteria when he asks under what conditions we can make, for example, a warranted enumerative inductive inference. He answers: “Whenever the hypothesis that all A’s are B’s is (in the light of all the evidence) a better, simpler, more plausible (and so forth) hypothesis than is the hypothesis, say, that someone is biasing the observed sample in order to make us think that all A’s are B’s” (Harman 1965, p. 91). Moreover, Harman argues that one of the crucial features of the IBE is that it reveals the role that “lemmas” play in inferring explanatory hypotheses. Articulating, exposing and evaluating such lemmas is an important aspect of the analysis of knowledge that results from inference since, according to Harman, there is a wide agreement among epistemologists that if we are to know, our belief must be both true and warranted. That is, a necessary condition of knowledge is not only that our final belief be true, but also that the lemmas, or intermediate propositions between premises and conclusion, be true. Otherwise, if the intermediate propositions “are warranted but false, then [we] cannot be correctly described as knowing the conclusion” (Harman 1965, p. 92). Harman calls this necessary condition for knowledge the “condition that the lemmas be true” (p. 92). These often implicit lemmas are an intrinsic part of the inference from evidence to best explanatory hypotheses.18 In sum, Harman’s model of IBE reveals that the scientist formulates several alternative explanatory hypotheses for the evidence and infers the best one by appealing to some relevant criteria for judging the relative merit of explanations and to some implicit lemmas. Moreover, the model attempts to account for the fact that ampliative inferences are not of the form of enumerative induction since ampliative hypotheses often appeal to concepts that are not part of the evidence. In formal terms, that is, ampliative hypotheses involve terms that do not appear in the statements of the evidence. However, Harman’s model of IBE has some problems in accounting for the ampliative inference to explanatory hypotheses. First, the model does not explain how the explanatory hypotheses arise. The model takes the alternative explanatory hypotheses as given and reveals that we infer the best one, but it does not analyze the reasoning process through which the scientist conceives such hypotheses. This is mainly because Harman treats explanatory inference abstractly and not as an actual scientific practice. Second, it does not make a sufficiently sharp distinction between two reasoning 18 Note that Harman treats the IBE as if it were deductive by subjecting it to the standards of justification of deductively certain knowledge.

123

Synthese (2011) 180:419–442

433

processes involved in inferring explanatory hypotheses—namely, the process of formulating several plausible explanatory hypotheses and the process of inferring the best one. And third, because the model fails to make the distinction between formulating plausible hypotheses and inferring the best one, it hastily describes the inference to an explanatory hypothesis as the inference to the truth, and not to the plausibility, of the hypothesis. Peter Lipton develops an improved model of the IBE in some important ways, especially with respect to the second and third problems above. Lipton proposes that his model describes situations in which “it is not simply that the phenomena to be explained provide reasons for inferring the explanations: we infer the explanations precisely because they would, if true, explain the phenomena” (Lipton 1991, p. 57). As we will see, for Lipton this inference is inductive, even if it is not an inference in which the evidence provides probabilistic support for the conclusion, but one in which we infer a hypothesis because it explains the evidence. So he writes that IBE is “a new model of induction, one that binds inference in a new and exciting way. According to [it], our inferential practices are governed by explanatory considerations” (Lipton 1991, p. 58). Lipton describes the form of this inference as follows: Given our data and our background beliefs, we infer what would, if true, provide the best of the competing explanations we can generate for those data (so long as the best is good enough for us to make any inference at all). (Lipton 1991, p. 58) In the following assessment of his model, I advance Lipton’s apt emphasis on the role of explanatory considerations as guides to hypothetical inference, while I point out some difficulties that arise from his classification of IBE as inductive. Lipton makes two important distinctions regarding the sorts of explanations that we seek when we infer explanatory hypotheses. First, he distinguishes between actual and potential explanations. For his model, Lipton assumes “inferential and explanatory realism,” that is, (a) that a goal of inference is truth, (b) that our actual inferential practices generally take us toward the goal of truth, and (c) that for something to be an actual explanation, it must be at least approximately true (Lipton 1991, p. 59). So the actual explanation of a phenomenon is its true, or at least approximately true, explanation, in reality. A model of inference to the best actual explanation fails to describe our inferential practices since it portrays all of our inferences to be true, when our “inductive practice is fallible: we sometimes reasonably infer falsehoods” (Lipton 1991, p. 59). It also fails to account for the role of competing explanations in inference and mischaracterizes our inferential process as we can only decide whether a hypothesis is an actual explanation after we have inferred it. Consequently, Lipton proposes a model of inference in which we first consider potential explanations and then infer the best one. Potential explanations need not be true explanations of the empirical evidence; they need only be plausible explanations that accord with our system of beliefs and that would provide some way to understand the observed phenomenon. The plausibility of potential explanatory hypotheses acts as an “epistemic filter”: in our inferential process we do not consider all possible explanations—for example we do not consider arbitrary ones—but only the potential explanations, that

123

434

Synthese (2011) 180:419–442

is, the plausible ones that are “live options” to become the actual explanation (Lipton 1991, pp. 60–61). The upshot of the foregoing distinction is to characterize IBE as a process consisting of two “epistemic filters.” According to Lipton, in our reasoning we deploy the first filter to select a group of plausible explanations for an observed phenomenon from a vast pool of possible explanations. Then we use a second filter to select the best explanation from the group of competing plausible explanations. In this way, Lipton’s account improves on the second and third problems with Harman’s model. That is, Lipton distinguishes between the process of generating explanatory hypotheses and that of selecting the best one, and he accounts for the fact that in generating hypotheses our foremost consideration is the plausibility, not yet the actual truth, of the explanation. Lipton distinguishes, second, between the likeliest and loveliest explanations. Given the empirical evidence, the likeliest explanation is “the explanation that is most warranted,” while the loveliest explanation is “the one which would, if correct, be the most explanatory or provide the most understanding” (Lipton 1991, p. 61). He writes, “[l]ikeliness speaks of truth; loveliness of potential understanding” (Lipton 1991, p. 61). For Lipton, one way to understand this distinction is to see that we evaluate likeliness, but not loveliness, with respect to the total available evidence. For example, he observes that Newtonian mechanics is one of the loveliest explanations in science and, at one time, it also was one of the likeliest of the then available data. As the theory of special relativity arose along with the new data that supports it, Newtonian mechanics became a less likely explanation of all of the data, but it remains a lovely explanation of the old data, that is, it still helps us to understand clearly the physical phenomena that it explains well. By this example Lipton also tries to illustrate that likely and lovely explanations are differently affected by new competing explanations, as a new explanation may make the current one less likely but not necessarily less lovely (Lipton 1991, p. 62). From a Peircean perspective, the crucial distinction that Lipton is drawing implicitly is that we evaluate the likeliness of a hypothesis by way of inductive probability, while we evaluate its loveliness by way of explanatory plausibility. In evaluating inductive probability, we weigh the relative support that all of the empirical data provide for one or the other hypothesis; while in evaluating explanatory plausibility, we judge how well an explanation coheres with our current system of beliefs, that is, with our background theoretical knowledge, and with what we perceive or think to be possible. I think the reason that Lipton does not distinguish between inductive probability and explanatory plausibility explicitly, even when he makes all the other aforementioned distinctions, is that he considers the IBE to be an inductive inference, while at the same time he argues that it is an inference to the loveliest explanation. The inference is clearly non-deductive but, like Harman, Lipton does not consider the possibility that IBE may be non-inductive. If Lipton were to associate the inference to the likeliest explanation explicitly with the inductive estimation of the probability of a hypothesis given the evidence, he would have to at least discuss explicitly the possibility that inference to the loveliest explanation is non-inductive. He would have to consider whether the inference to the loveliest explanation is a third form of inference, for instance, abductive. Recalling that, on Peircean grounds, induction and abduction are

123

Synthese (2011) 180:419–442

435

different forms of inference with different aims, and that induction is an evaluation of probability while abduction is a suggestion of plausibility, we now can see that the inference to the loveliest explanation, as it has been described so far and if it is a viable form of inference, must be abductive and not inductive. For now, let us continue a discussion of Lipton’s model of inference to the loveliest explanation, as I consider it to be a viable model of inference that is misscategorized. Lipton rejects a description of IBE as inference to the likeliest explanation because it begs the questions of what are the marks of likeliness, what principles we use to judge one inference more likely than another one, and what features of an argument lead us to say that the premises make the conclusion likely (Lipton 1991, p. 62). In other words, since IBE should describe strong inductive arguments in which “the premises make the conclusion likely,” we beg the question when we simply say that to infer a hypothesis is to infer the likeliest explanation (Lipton 1991, p. 62). In contrast, describing the inference to the loveliest explanation elucidates how explanatory considerations guide our inference to a hypothesis. Lipton spells out some of these guidelines. First, he points out that, in order to choose the loveliest explanation, we may perform experiments to narrow the field of candidate plausible hypotheses resulting from the first filter. Second, the lovely explanations that we infer tend to fulfill our preferences for explanations that (a) specify a causal mechanism,19 (b) are precise, and (c) unify our understanding and our explanatory scheme (Lipton 1991, pp. 56–68).20 In sum, Lipton’s characterization of IBE as the inference to the loveliest potential explanation aptly elucidates that, when we infer explanatory hypotheses, (i) we initially generate relevant candidate hypotheses that are plausible explanations of the empirical evidence, and (ii) then we choose, for testing, the hypothesis that yields the deepest potential understanding of the observed empirical phenomena. I find this description of explanatory inference to be appealing and generally compatible with abduction. However, in the context of the same discussion, we can locate the beginning of a conflation between considerations of loveliness and likeliness that loses sight of the different inquiring aims that guide the processes of generating hypotheses, on the one hand, and evaluating them, on the other. From a Peircean perspective, this loss of clear focus eventually leads to a conflation between abduction and induction. For Lipton, the model of the inference to the loveliest potential explanation claims that the explanation that would, if true, provide the deepest understanding, is the explanation that is likeliest to be true. Such an explanation suggests a really lovely explanation of our inferential practice itself, one that links the

19 According to Lipton, our search for rational explanations of phenomena is often best understood as a search for the unknown causes of observed effects. Lipton recognizes that the logical form of IBE does not necessarily presuppose a causal theory of explanation and that the philosophical question of what is an explanation is complex and unsettled, so he hopes that other possibly correct theories of explanation may turn out to be compatible with his account of the inference. I would emphasize strongly also that the term “mechanism” here should not be narrowly associated with a mechanistic, necessitarian, absolutely deterministic theory of the universe. 20 For an evaluation of these and other criteria suggested by Lipton, see Barnes (1995).

123

436

Synthese (2011) 180:419–442

search for truth and the search for understanding in a fundamental way. (Lipton 1991, p. 63)21 Lipton suggests that the hypothesis that leads to the profoundest understanding may also be the likeliest to be true. In his more recently revised exposition of IBE, Lipton develops this idea further in order to argue that Bayesianism and explanationism are not only compatible, but also complementary, accounts of non-deductive inference (Lipton 2004, pp. 103–120). Bayesianism is compatible with IBE because Bayes’ theorem regards constraints on permissible combinations of degrees of belief, while explanatory consideration may still guide inference without breaking probabilistic rules (Lipton 2004, p. 106). Moreover, Bayes’ theorem and explanationism are actually complementary since “explanatory considerations provide a central heuristic we use to follow the process of conditionalization [of the probability of a hypothesis given the evidence], a heuristic we need because we are not very good at making the probabilistic calculations directly” (Lipton 2004, p. 107). Lipton suggests four ways in which explanatory considerations act as a heuristic surrogate for estimating probabilities and moving from prior to posterior probabilities in Bayesian inference, where p(H/E) = p(E/H) [p(H)/p(E)]. First, explanatory considerations help inquirers to estimate likelihoods—that is, the antecedent probability of observing the evidence given the hypothesis, p(E/H). This is because it might be that “one way we judge how likely E is on H is by considering how well H would explain E” (Lipton 2004, p. 114). Second, explanatory considerations may help to determine the prior probabilities, p(H) and p(E) (Lipton 2004, pp. 115–116). Third, explanatory considerations help in the determination of relevant evidence, E, since we may chose an epistemically relevant datum on the consideration that the hypothesis would explain it (Lipton 2004, p. 116). Thus far Lipton links explanatory considerations to the (Bayesian) inductive practice of evaluating the probability of a hypothesis given the evidence and even of choosing evidence relevant to evaluating the hypothesis. But as he points out, Bayesianism is silent regarding the context of discovery, that is, the conceptual origin or generation of explanatory hypotheses.22 Fourth, then, Lipton suggests that IBE complements Bayesianism in accounting for the generation of hypotheses, since “asking what would explain the available evidence is an aid to hypothesis construction” (Lipton 2004, p. 116). Explanatory considerations help hypothesis construction because (a) the aims of scientific inquiry are often explanatory themselves, (b) scientists wish to generate hypotheses that have a reasonably high prior probability, and (c) scientists often prefer to entertain fertile hypotheses with high content, that is, that may help to explain a wide variety of phenomena (Lipton 2004, p. 116).

21 For other accounts of discovery as a logical process involving the search for explanation, see Schaffner (1993), especially Chap. 2, and Hanson (1965). 22 This is why I think that the process of updating the probabilities of hypotheses based on evidence should not be called “abduction.” Here, in fact, is what the Peircean might say about Bayesian abduction: “In the first place, drop the label abduction. There is no abduction described here! As Lipton observes, this says nothing about the context of discovery: where do hypotheses come from? By what reasoning processes and methods are they invented? That’s the question of abduction. Second, the Bayesian model only provides one possible (normative) logic of induction: how to evaluate the admissibility of hypotheses based on evidence.” This is not, again, to discount Bayesian inference but to distinguish it from abduction.

123

Synthese (2011) 180:419–442

437

From a Peircean standpoint, in the process of generating candidate hypotheses for scientific scrutiny, we are in the realm of abductive inference. Our aim at this stage of inquiry is to create hypotheses that may explain observed phenomena. The considerations of explanatory scope and fertility, of overall loveliness, are abductive considerations. However, in this account, they are again conflated with inductive considerations of likeliness and probability. Lipton’s account seems to lead to some ambiguity when considerations of loveliness and likeliness may lead to contradictory conclusions regarding the tenability of a hypothesis. From a Peircean perspective, in the context of discovery we may generate and tentatively uphold for further scrutiny lovely or fertile hypotheses, even if they may seem unlikely or a priori improbable. In an unfinished 1913 essay, Peirce made a distinction between “security” and “uberty” in inferential reasoning.23 The security of an inference is its degree of certainty; the uberty of an inference—especially the inference to a plausible hypothesis—is its potential to lead to undiscovered truth. The uberty of an abductive hypothesis is different from its a priori likeliness and even from its immediate fruitfulness in solving a problem: “I can hardly be supposed to have selected the unusual word ‘uberty’ instead of ‘fruitfulness’ merely because it is spelled in half as many letters” (EP2, p. 472). He makes a distinction between, say, the fruitfulness of scientific observation and the uberty of a scientific hypothesis: “Observations may be as fruitful as you will, but they cannot be said to be gravid with young truth in the sense in which reasoning may be” (EP2, p. 472). Modern science needs the uberty of abductive hypotheses for making progress. However, there tends to be a tension between security and uberty intrinsic to scientific reasoning: secure reasonings—such as deductions and well-tested inductions—do not open new, but risky and a priori unlikely, paths of investigation that may nonetheless be “gravid” with potential truth. Peirce goes so far as to claim that the main impediment to the progress of modern science is not so much the occasionally false deductions or inductions that scientists make, but the neglect to pursue systematically those abductive hypotheses rich in uberty: [E]ven the most admirable of modern reasoners, and in those kinds of reasoning in which they are at their very best, occasionally draw inferences that [are] utterly unfounded, but which more or less tinge all their subsequent teachings. Yet considering modern science as a whole, I believe its positively wrong conclusions are of small moment compared with its neglect systematically to consider possibilities among which there are likely to be keys to undiscovered treasuries of truth. (EP2, p. 466)24 23 See “An Essay Toward Improving our Reasoning in Security and in Uberty” (EP2, pp. 463–474). In

this regard, consider also the following passage by Peirce: “Nothing has caused so much waste of time and means, in all sorts of researches, as inquirers becoming so wedded to certain likelihoods as to forget all the other factors of the economy of research; so that, unless it be very solidly grounded, likelihood is far better disregarded, or nearly so” (CP 7.220, 1901; quoted in Minnameier 2004, p. 84). 24 This suggests a possible comparison between Peirce’s and Kuhn’s (1964) philosophies of scientific inquiry. In Kuhnian terms, Peirce seems to think that the practice of “normal science” is conservative and, by seeking secure reasoning, mainly extends the theories involved in the reigning paradigm; however, Peirce warns that this conservatism may block, as much as aid, the progress of science. Scientific practice ought not to wait for crises in order to systematically pursue rich abductive hypotheses. Pursuing this possible comparison in depth is, however, beyond the immediate aims of this paper.

123

438

Synthese (2011) 180:419–442

The upshot of the foregoing Peircean distinction, for our purposes, is that in conflating the scientific generation of lovely hypotheses with an evaluation of their likeliness, we would neglect the need, in scientific practice, of generating, pondering, and pursuing hypotheses rich in their possibility to lead to undiscovered truth and deeper understanding, even if they are a priori improbable. In the abductive stage of inquiry, then, we may seek to originate lovely hypotheses. Evaluation of likeliness or probability is a subsequent, inductive stage of inquiry. The conflation in Lipton’s account is partly due his to losing sight of different inferential aims. For instance, in arguing for the importance of explanatory considerations in generating hypotheses, Lipton writes that scientists’ “interest in scope and fertility is a promising area in which explanationist considerations may operate, since scientists may judge theoretical fertility or promise by assessing the explanatory potential of the hypotheses they are evaluating” (Lipton 2004, pp. 116–117). Here explanatory potential at once serves as a guide to generate and to evaluate hypotheses. For the Peircean, however, in order to understand scientific reasoning it is important to keep in sharp focus the distinction between two different goal-directed activities, namely, seeking to invent fertile explanatory hypotheses and evaluating the tenability of those proposed hypotheses.

3 Comparative assessment of two accounts of ampliative inference On the whole, how does the Peircean account of abductive reasoning compare with Lipton’s account of IBE? I think there are several compatible elements between the accounts. The most important common feature is that both views emphasize that scientists are guided by explanatory considerations in the process of hypothesis generation. This process involves both the invention of plausible explanations and a consideration of their explanatory merits. Moreover, the criteria, under both models, for judging the relative plausibility of hypothetical explanations are compatible and even complementary. The Peircean conditions that hypotheses admissible for further scientific inquiry be explanatory and yield conceivable testable predictions are compatible with Lipton’s view that we deem to be more plausible those explanatory hypotheses that are precise, unify our understanding and our explanatory scheme, and specify a causal mechanism. First, it is reasonable to say that hypotheses that are capable of experimental verification—in Peirce’s broad sense of having conceivable practical consequences that can be put to the test of experiment or experience—must be sufficiently precise so as to suggest how the consequences might follow from the hypothesis under specific conditions. The preference for precision is, in Peircean terms, the condition that admissible abductive hypotheses contain only clear and distinct conceptions, that is, conceptions for which we can conceive possible, relevant practical bearings. This is what Peirce calls the maxim of pragmatism, namely: “Consider what effects that might conceivably have practical bearings we conceive the object of our conception to have: then, our conception of those effects is the whole of our conceptions of the object” (EP2, p. 135). For Peirce, this is a maxim of logic, and more specifically, the maxim of the logic of abduction, which ought to perform two services: “[I]t ought, in the first

123

Synthese (2011) 180:419–442

439

place, to give us expeditious riddance of all ideas essentially unclear. In the second place, it ought to lend support [to], and help render distinct, ideas essentially clear but more or less difficult of apprehension” (EP2, p. 239). So abductive hypotheses, in order to be admissible, must be sufficiently clear so as to be capable of rendering testable experimental or experiential consequences, and this is akin to our preference for precise explanations. Second, the practical consequences of an abductive hypothesis are conceivable on the basis of our entire system of beliefs and so also on the basis of everything that is part of our explanatory scheme. In order to follow the pragmatic maxim, our reasoning about the concepts involved in a hypothesis must involve all relevant elements from our system of knowledge so as to identify the ways in which a proposed hypothesis coheres or does not cohere with our existing beliefs. That is, we do not reason on the basis of isolated terms and propositions; we reason on the basis of a whole understanding that helps us to elucidate the concepts and consequences of the explanatory hypotheses that we formulate when confronted with an unexplained phenomenon. How well our hypotheses cohere with our overall scientific beliefs serves as a guideline in the initial assessment of the tenability of a hypothesis, and this is an important reason why she infers it either as a lovely explanation or as a plausible abductive explanation, depending on the respective inferential models that we have deployed to interpret her reasoning. Along these lines, moreover, Minnameier argues that abductive inference tends to unify scientific knowledge and to initiate a triadic process of inquiry—consisting of abduction, deduction, and induction—that leads toward improved coherence in knowledge (Minnameier 2004, pp. 94–97). Unification here is “a form of explanation” while coherence is the “overall organization of knowledge” (Minnameier 2004, p. 94). Put in terms that I have used in this article, abductive inference unifies knowledge by plausibly explaining unexpected facts as the would-be consequences of general principles or causes. Minnameier observes that this notion of unification is different from the one suggested by Kitcher (1981) which consists in the search for generalized patterns of explanation that can be applied deductively or inductively in a wide range of scientific domains (Minnameier 2004, p. 95). As he puts it, “Whereas Kitcher intends to provide a common basis for as many diverse phenomena as possible, abductive approaches work the other way round by starting from local incoherencies which are then tried to reintegrate in a more complex structure” (Minnameier 2004, p. 95). The process of inquiry that ensues after an abductive suggestion is deemed plausible for further scrutiny may then lead to improved local and global coherence (Minnameier 2004, pp. 95–97). That is, it may lead to an improved organization of knowledge in particular fields of science and in our overall system of knowledge. Again put in terms I have used, habitual abductions may improve local coherence by explaining initially surprising facts via previously known principles or laws, while creative abductions may improve global coherence by discovering entirely novel principles or laws. Admittedly, these claims require further inquiry,25 but I present them here to strengthen the view that

25 See Minnameier (2004) for a full discussion and further references.

123

440

Synthese (2011) 180:419–442

both Lipton’s account of IBE and Peirce’s account of abduction incorporate a scientific preference for explanatory hypotheses that unify knowledge and understanding. The third issue—namely, that of abductive hypotheses fulfilling our preference for explanations that specify a causal mechanism—is more complicated, but I think the Peircean model of abduction can accommodate it.26 Lipton admits that the question of a philosophical theory of explanation is not settled, but his hope is that, whatever the true theory of explanation may turn out to be, it will be compatible with his logical description of IBE. I agree with Lipton that it is not within the scope of an account of the logic of ampliative inference to solve the question of a true theory of explanation. Nonetheless, Lipton does think that whatever a good explanation may be, one of the characteristics we prefer is that it specify some causal mechanism by way of which the observed phenomenon occurs. This is compatible with Peirce’s logic of abduction which may admit various types of causal explanations of phenomena and is quite open-ended in this regard. For instance, Lipton favors a causal model of explanation (1991, Chap. 3) while Hanson favors a model of explanation that appeals to physical laws and principles, including causal laws (1965, Chap. 3), and I think both approaches are compatible with Peirce’s account of abduction as the process of generating explanatory hypotheses.27 In sum, I think it is reasonable to claim that Lipton’s criteria for preferable hypotheses are largely compatible with the Peircean conditions for the admissibility of hypotheses, and therefore, with the abductive model of inference. However, it is important to emphasize again that at the end of our ampliative reasoning we conclude that a hypothesis is plausible, not probable. This is an indication that the reasoning is abductive, not inductive. It is precisely here where I think Lipton misclassifies his model of IBE as inductive. Were he to advocate a model of inference to the likeliest potential explanation, the classification of the inference as straightforwardly inductive would be understandable because the question of likeliness, in Lipton’s terms, is a question of inductive probability in Peircean terms. Likeliness is a measure—quantitative or qualitative—of the degree to which a general hypothesis agrees with all the evidence, so it is a measure of the inductive probability of the hypothesis. But Lipton mainly advocates a model of inference to the loveliest potential explanation, that is, to the explanation that provides the deepest understanding of the phenomenon, and this is an abductive inference. Let me then put forth my assessment as follows. The discussion in the preceding section has prepared the way to argue that the inference to the loveliest explanation is a form of abduction that Lipton misclassifies as a form of induction and that this misclassification amounts to a conflation of two distinct forms of inference. The conflation blurs an important distinction between the tentative, exploratory inference that first 26 This is so long as the word “mechanism” does not imply any absolute mechanistic determinism. From a Peircean standpoint, the vague term “causal process” might be better in order to prevent the mechanistic connotations. 27 Here I find some reason for minor disagreement with Sami Paavola’s recent distinction between what he labels as Lipton’s “Harmanian abduction” and the Peirce-based “Hansonian abduction” (Paavola 2006). I rather think that Peircean abduction can be linked to, but clearly distinguished from, Lipton’s IBE, while also holding, as Paavola has recently argued, that “Hansonian [i.e. Peircean] abduction is not connected with any specific model of explanation” (Paavola 2006, p. 97).

123

Synthese (2011) 180:419–442

441

suggests a plausible explanatory hypothesis and the probabilistic inductive inference that admits or rejects a hypothesis as scientifically tenable. Precisely in this regard, Paavola has convincingly argued that loveliness is a better conceptual criterion of explanatory plausibility when associated to abduction in the tradition of Peirce than when linked to a full account of IBE: Loveliness is difficult for IBE because the criteria for loveliness, which are at the same time criteria for the best explanation, should be, if not a guarantee, at least a strong indication of the truth of an explanation (Lipton 2004, pp. 60–61). The dilemma for IBE, then, seems to be the need to emphasize loveliness along with the special character of IBE. But doing so undermines IBE’s credibility as a plausible form of inference to truth. Abduction fares better in these respects because it is, from the start, a weaker form of inference than IBE, and it separates the generation and justification of hypotheses more clearly. Loveliness is no guarantee of finding the best explanation, but it can be an ancillary criterion when searching for promising candidates or ideas. It can be an indication of a good, potential hypothesis, although the hypothesis must then be tested with other means. (Paavola 2006, p. 100) Meanwhile, inference to the best explanation, in so far as it moves beyond considerations of loveliness to the assessment of likeliness of a hypothesis, whether through further explanatory considerations standing as heuristic surrogates for probabilities or through the direct assessment of probabilities—Bayesian or classical—is a combination of abduction and induction. To the extent that IBE is an account of the processes both of generating and of evaluating scientific hypotheses, where explanatory considerations are guides both to generating lovely hypotheses and to evaluating their likeliness, then it is a mixture of two distinct forms of inference with two different aims. Conceptual confusion arises when these two distinct inferential forms and aims are conflated. However, when they are distinguished properly, Lipton’s account of IBE provides a more comprehensive picture of scientific reasoning than only accounting for the abductive suggestion of explanatory hypotheses. By comparing both accounts of scientific reasoning, I do not want to reject the important perspective that IBE has to offer. I do want to suggest, however, that a reclassification of Lipton’s model of the inference to the best explanation as a mixed form of abductive and inductive inference, along with a thorough description of Peircean abduction, better elucidate in their full scope the various kinds of inference involved at various stages of scientific inquiry. What is lost, overall, in blurring the distinction between abduction and induction by claiming that Peircean abduction is IBE? Beyond the formal distinction between two forms of inference, we lose clear sight of the different aims of scientific reasoning— conjecturing versus evaluating—at different stages of inquiry. As a result, we also lose focus on providing a deeper account of hypothesis formation alone, apart from questions of the scientific assessment and evaluation of those hypotheses, once they have been proposed. We lose emphasis on thoroughly describing the mark of abduction—the act of bringing relevant, often innovative, concepts to bear in creative ways on the plausible explanation of previously unexplained phenomena.

123

442

Synthese (2011) 180:419–442

Acknowledgements I would like to express respectfully my gratitude to the late Professor Peter Lipton who had graciously engaged me in correspondence when I was beginning to draft this article. His commentaries and observations on the main ideas improved the article substantially, and his overall encouragement was especially valuable to me, as it was, no doubt, to many other scholars.

References Aliseda, A. (2006). Abductive reasoning: Logical investigations into discovery and explanation. Dordrecht: Springer. Anderson, D. (1986). The evolution of Peirce’s concept of abduction. Transactions of the Charles S. Peirce Society, 22, 145–164. Barnes, E. (1995). Inference to the loveliest explanation. Synthese, 103, 252–277. Burks, A. (1946). Peirce’s theory of abduction. Philosophy of Science, 13, 301–306. Fann, K. T. (1970). Peirce’s theory of abduction. The Hague: Martinus Nijhoff. Frankfurt, H. G. (1958). Peirce’s notion of abduction. The Journal of Philosophy, 55, 593–596. Hanson, N. R. (1965). Patterns of discovery: An inquiry into the conceptual foundations of science. Cambridge, UK: Cambridge University Press. Harman, G. H. (1965). The inference to the best explanation. The Philosophical Review, 74, 88–95. Hintikka, J. (1998). What is abduction? The fundamental problem of contemporary epistemology. Transactions of the Charles S. Peirce Society, 34(3), 503–533. Hookway, C. (1985). Peirce. London: Routledge. Kent, B. (1997). The interconnectedness of Peirce’s diagrammatic thought. In N. Houser, D. Roberts, & J. Van Evra (Eds.), Studies in the logic of Charles Sanders Peirce (pp. 445–459). Indianapolis: Indiana University Press. Kitcher, P. (1981). Explanatory unification. Philosophy of Science, 48, 507–531. Kuhn, T. (1964). The structure of scientific revolutions. Chicago: University of Chicago Press. Lipton, P. (1991). Inference to the best explanation. New York: Routledge. Lipton, P. (2004). Inference to the best explanation: Second edition. New York: Routledge. Minnameier, G. (2004). Peirce-suit of Truth—Why inference to the best explanation and abduction ought not to be confused. Erkenntnis: An International Journal of Analytic Philosophy, 60(1), 75–105. Paavola, S. (2006). Hansonian and Harmanian abduction as models of discovery. International Studies in the Philosophy of Science, 20(1), 93–108. Peirce, C. S. (1932–1958). Collected papers of Charles Sanders Peirce, Vols. 1–8. In P. Weiss, C. Hartshorne, & A. W. Burk (Eds.). Cambridge, MA: Harvard University Press. (Abbreviated CP.) Peirce, C. S. (1982–2000). Writings of Charles S. Peirce: A chronological edition. Bloomington: Indiana University Press. (Abbreviated W.) Peirce, C. S. (1992). Reasoning and the logic of things. Cambridge, MA: Harvard University Press. (Abbreviated RLT.) Peirce, C. S. (1998). The essential Peirce: Selected philosophical writings 2. Indianapolis: Indiana University Press. (Abbreviated EP2.) Robin, R. S. (1967). The annotated catalogue of the papers of Charles S. Peirce. Amherst: University of Massachusetts Press. Rosenthal, S. (2004). Peirce’s pragmatic account of perception: Issues and implications. In C. Misak (Ed.), The Cambridge companion to Peirce (pp. 193–213). Cambridge, UK: Cambridge University Press. Santaella, L. (1998). La evolución de los tres tipos de argumento: Abducción, inducción y deducción. Analogía Filosófica, 12(1), 9–20. Schaffner, K. F. (1993). Discovery and explanation in biology and medicine. Chicago: The Chicago University Press. Schurz, G. (2008). Patterns of abduction. Synthese, 164, 201–234. Stjernfelt, F. (2000). Diagrams as centerpiece of a Peircean epistemology. Transactions of the Charles S. Peirce Society, 36(3), 357–392.

123

Synthese (2011) 180:443–463 DOI 10.1007/s11229-010-9712-8

Supervenience and neuroscience Pete Mandik

Received: 5 June 2008 / Accepted: 7 January 2010 / Published online: 27 January 2010 © Springer Science+Business Media B.V. 2010

Abstract The philosophical technical term “supervenience” is frequently used in the philosophy of mind as a concise way of characterizing the core idea of physicalism in a manner that is neutral with respect to debates between reductive physicalists and nonreductive physicalists. I argue against this alleged neutrality and side with reductive physicalists. I am especially interested here in debates between psychoneural reductionists and nonreductive functionalist physicalists. Central to my arguments will be considerations concerning how best to articulate the spirit of the idea of supervenience. I argue for a version of supervenience, “fine-grained supervenience,” which is the claim that if, at a given time, a single entity instantiates two distinct mental properties, it must do so in virtue of instantiating two distinct physical properties. I argue further that despite initial appearances to the contrary, such a construal of supervenience can be embraced only by reductive physicalists. Keywords

Supervenience · Physicalism · Neuroscience · Reductionism

1 Introducing fine-grained supervenience The philosophical technical term “supervenience” is frequently used in the philosophy of mind as a concise way of capturing a, if not the, core idea of physicalism, which, if stated as a slogan, is the idea that there are no mental differences without physical differences.1 Since most physicalists aren’t physicalists just about the mind, the slogan really is that there are no differences without physical differences. One 1 For an excellent review of key notions and applications of supervenience, see McLaughlin and Bennett (2006). See Wilson (2005) for criticisms of the adequacy of supervenience for formulating physicalism.

P. Mandik (B) William Paterson University, Wayne, NJ, USA e-mail: [email protected]

123

444

Synthese (2011) 180:443–463

feature of supervenience that explains much of its appeal is that it seems to offer a way of spelling out physicalism that is neutral with respect to reductive and nonreductive varieties of physicalism. It is a major goal of this paper to offer novel arguments against this alleged neutrality. I will be arguing for reductive physicalism. Further, I’ll be taking sides in the version of the debate between reductive and nonreductive materialists as that debate is played out between psychoneural reductionists or type-identity theorists on the one hand and nonreductively inclined functionalists motivated by multiple-realization considerations on the other. Given this, then, I will have little, if anything, to say that explicitly addresses versions of the debate that hinge on other motivations for nonreductionism—motivations such as those concerning the alleged normativity of mental-state ascriptions. It is my intention, then, to argue for the reduction of the mental to the neural and against the functionalist multiple realizability of the mental by the physical. Central to my arguments will be considerations concerning how best to articulate the spirit of the idea of supervenience. The most explicit early statement directly relevant to the philosophy of mind of what supervenience consists in is due to Davidson (1970, p. 88). Davidson relayed the idea of saying that the mental supervenes on the physical in a way that may be paraphrased as the following pair of propositions: (1) No two entities can differ at a time with respect to their mental properties without differing at that time with respect to their physical properties. (2) No single entity can change with respect to its mental properties without changing with respect to its physical properties. As formulated, (1) and (2) do not make sufficiently explicit the idea that, more than being correlated with certain physical properties, mental properties are had in virtue of having certain physical properties. That Davidson had such a determination thesis in mind is made clear in a later work wherein he explicates the mental being supervenient on the physical by writing that “the physical characteristics of an event (or object or state determine the psychological characteristics” (Davidson 1973, pp. 716–717, emphasis in original).2 It is better, then, to formulate Davidsonian supervenience as this pair of propositions: (1) If, at a given time, two entities instantiate two distinct mental properties, they must do so in virtue of instantiating two distinct physical properties. (2) If, at two distinct times, a given entity instantiates two distinct mental properties, it must do so in virtue of instantiating two distinct physical properties at those times.3 2 I will have relatively little to say about how “in virtue of” should be spelled out, but it will suffice for

the present discussion to think of “in virtue of” as signaling a kind of noncausal determination of ψ by φ that is consistent with, but does not entail, that ψ and φ are one and the same. 3 It is perhaps worth stressing here that what is relevant about Davidson to the current project is not the

particular considerations that motivated the nonreductive portion of his nonreductive physicalism (considerations having to do with the alleged normativity of the mental, etc.). What is relevant is his influential supervenience-based explication of the physicalist portion of his nonreductive physicalism. Such an explication of physicalism has been embraced as consistent with a variety of motivations for nonreductivism, varieties such as functionalist multiple realizability considerations.

123

Synthese (2011) 180:443–463

445

Subsequent writers offered formulations of supervenience that varied either in terms of their modal force (e.g., logical, nomological, etc.) or in terms of what entities were under consideration (e.g., persons, space-time regions, entire worlds, etc.).4 Such variations are of little interest here. What is of interest is a formulation of the core idea of physicalism—the “no differences…” slogan—overlooked by Davidson and subsequent authors: (3) If, at a given time, a single entity instantiates two distinct mental properties, it must do so in virtue of instantiating two distinct physical properties.5 Since this formulation will be the focus of the current paper, I prefer a more informative label and will use “fine-grained supervenience” or FGS for short. In case it has gone unnoticed, the key difference between FGS on the one hand and (1) and (2) on the other is that where (1) concerns multiple entities at a single time and (2) concerns a single entity at multiple times, FGS concerns a single entity at a single time. I think it should be fairly obvious that FGS is a distinct yet reasonable way of cashing out the “no differences …” slogan, but I will spell this out further anyway.6 One thing that isn’t obvious, but will be a major aim of this paper to argue for, is that FGS leads to reductive physicalism. Sections 2–4 are dedicated to spelling out arguments from FGS to reductive physicalism. Sections 2 and 3 articulate thought experiments concerning how certain functionalist nonreductive considerations give rise to highly counterintuitive scenarios of what I shall call “mental–mental supervenience”—scenarios that physicalists will want to rule out and will need to embrace reductive physicalism to do so. Where the line of argument developed in Sects. 2 and 3 specifically targets functionalist varieties of nonreductivism, the argument in Sect. 4 4 For a recent and brief review of these variations, see Lynch and Glasgow (2003, p. 202). Variations concerning modal force are perhaps more directly relevant to clarifying the “in virtue of” locution than variations concerning the relata of the supervenience relation. While I’m largely bypassing such issues, I will note that my interest in insisting on focusing on Davidson’s 1973 “determination” formulation instead of the 1970 formulation, is that a formulation of fine-grained supervenience that follows the pattern of the 1970 wording seems like a relatively uninteresting thesis. It would be the thesis that a thing that has two mental properties at a time must have two physical properties at that time. Few things have fewer than two physical properties. Especially any things complicated enough to have any mental properties. It seems on the face of it a more interesting claim that a thing that has two mental properties at a time must have two different physical properties in virtue of which the two mental properties are had. 5 Hereafter, reference to properties in this paper is limited to determinate properties as opposed to merely

determinable properties. Arguably, without such a restriction, a determinable property and one of its determinates can share a supervenience base and thus constitute a counterexample to this formulation. 6 Note how different this is from older formulations such as those discussed by Hofweber (2005, pp. 6–7) or this formulation of “strong” supervenience discussed by Wilson (2005, p. 433), wherein it is

formulated as holding between families of properties A and B, elements of which are co-instantiated in individuals in a domain D: A strongly supervenes on B iff  (∀x ∈ D)(∀a ∈ A)(x has a → (∃b ∈ B)(x has b∧  (∀y ∈ D)(y has b → y has a))). FGS is not entailed by formulations such as strong supervenience. Instead, strong supervenience is compatible with the falsity of FGS. We might state this compatibility in the following way: Whereas strong supervenience is compatible with multiple realizability insofar as there might be a physical property, b*, other than b that suffices for a, strong supervenience is compatible with the falsity of FGS insofar as there might be some mental property, a*, other than a that b suffices for.

123

446

Synthese (2011) 180:443–463

develops a regress argument that targets all versions of nonreductive physicalism. After Sect. 4, I turn from spelling out the entailments of FGS to consider, in Sects. 5 and 6, reasons for embracing FGS. Finally, in Sect. 7, I will address why, if one is convinced of reductive physicalism, one should believe in the reduction of the mental to the neural.

2 Some things qualia cannot do Regardless of whether one is a reductive or a nonreductive physicalist, there are certain things about qualia that one must regard as impossible. If you have qualia, and someone else is your physical doppelgänger, then it is impossible for them to have any of the following: (a) inverted qualia, (b) absent qualia, (c) fading qualia, and (d) dancing qualia.7 While readers will likely already be familiar with these impossibilities, I’ll spell them out a bit more and also spell out what is supposed to make them impossible. This will help convey the gist of how supervenience is useful in formulating physicalist attitudes about what can and cannot happen with qualia. This will also be useful for setting the stage for the arguments for FGS to come.

2.1 Inverted qualia Seeing red things involves having a certain kind of qualia. Let’s call them “red qualia” for short and remain neutral on whether red qualia are so called due to their literal redness or their relations to literal redness. Literal redness is literally the opposite of literal greenness. If we arranged hues in such a way that adjacency reflects similarity, we’d wind up with a circle and a 180◦ rotation—an inversion—of that circle would put red where green was and vice versa. We could presumably do the same thing with your physical doppelgänger’s qualia and, so to speak, put her red qualia where your green qualia are and vice versa. However, we could do this only if physicalism was false. If physicalism is true, then we can’t. And here supervenience articulates the reason why: (1) says that no two entities can differ mentally without differing physically. This rules out (a) because it involves two entities differing mentally without differing physically.

2.2 Absent qualia If physicalism were false, then your physical doppelgänger could be utterly devoid of qualia—it could be a philosopher’s zombie—in spite of being just like you with respect to how many and what kind of particles it is made of and how those particles are arranged and move through space and time. But physicalists do not tolerate absent qualia for the same reason they do not tolerate inverted qualia: version (1) of 7 See Chalmers (1996, pp. 247–275) for an extended discussion of the sorts of things, such as dancing,

that physicalists forbid qualia to do.

123

Synthese (2011) 180:443–463

447

supervenience prohibits entities differing in a mental respect without differing in a physical respect. 2.3 Fading qualia Fading qualia are like absent qualia, but it takes a different time, not a different person, to get them. If you were to remain the same physically but you gradually changed from having qualia to not having qualia, then you would have fading qualia. Such a possibility is excluded by physicalism, and here the exclusion is due to clause (2) of supervenience. Since an entity cannot change mentally without changing physically, and “fading qualia” is shorthand for situations where qualia change without physical changes, fading qualia are impossible. 2.4 Dancing qualia Dancing qualia are rapid intrasubjective qualia inversions and reversions. Like inverted qualia, there is a 180◦ re-mapping. Like fading qualia, the difference is across times, not persons. Like fading qualia, the impossibility of dancing qualia is entailed by clause (2) of supervenience. 3 More things qualia cannot do and trouble for functionalism We have not yet begun to consider arguments against nonreductive physicalism. Nor have we put FGS to work. Let us change all that. To get this change rolling, let us consider a new thing that may be impossible for qualia: doubled qualia. Doubled qualia occur when two minds, one whose qualia are inverted with respect to the other—a “green mind” and a “red mind,” respectively—share a supervenience base. What it means to share a supervenience base is that there are no physical differences in virtue of which the red mind and the green mind differ. Davidsonian supervenience, the conjunction of (1) and (2), does not rule out doubled qualia. To appreciate this failure of Davidsonian supervenience, it will help to attempt to imagine doubled qualia. To imagine doubled qualia, begin by imagining someone other than you, call him or her “Person X”, who is not your physical doppelgänger. Let us stipulate that there is some physical difference between you and Person X. That is, there are two minds inside of Person X—a red mind and a green mind—whereas you only have the standard-issue red mind. Suppose further that all and only the physical properties that give rise to X’s red mind are the same physical properties that give rise to X’s green mind. Suppose, as well, that the physical properties that give rise to X’s red mind are different from the physical properties that give rise to your red mind. If you are having a hard time imagining this, it is likely due to your tacit or explicit acceptance of FGS. Your acceptance of (1) and (2) can’t explain this. In particular, the difference between you and X—the fact that you have only a red mind whereas X has a green one as well as a red one—is fully consistent with (1), since we have stipulated that there is a physical difference between you and Person X.

123

448

Synthese (2011) 180:443–463

Those physicalists who find doubled qualia to be weird are likely to find the following intolerably bizarre: intermittently doubled qualia. To get warmed up for intermittently doubled qualia, stop to appreciate the following stipulation about Person X: the red mind and the green mind need not have any awareness of each other whatsoever. What this means, then, is that for all you know, your qualia are doubled right now. For all you know, there’s someone else “in there” with you right now and what it’s like to be them is just like what it is like to be you except for the inversion-of-the-color-qualia bit. Now, imagine further that you undergo the following recurring physical change: The set of physical properties P1, which suffice to instantiate just the red mind are replaced by a set of distinct physical properties P2, which suffice for both a red mind and a green mind. So, according to the intermittently doubled qualia thought experiment, you change from P1 to P2 and back again, which changes you from undoubled qualia to doubled qualia and back again. And all of this happens without you—the red mind—even noticing. Perhaps you think that intermittently doubled qualia are impossible. You may be right. But here’s one thing that will not rule them out: clause (2) of supervenience. Clause (2) prohibits you from changing mentally without changing physically, but the intermittently doubled qualia thought experiment stipulated that there were physical changes accompanying the change to a doubled state. Physicalists should agree that doubled qualia are absurd. They should likewise agree on the absurdity of intermittently doubled qualia. (Hereafter I will use “doubled qualia” as shorthand for both the intermittent and nonintermittent varieties.) If you call yourself a “physicalist” but you believe in a theory that entails the possibility of doubled qualia, then you have some serious problems. To sum up the section so far: Davidsonian supervenience rules out only some of the obvious impossibilities concerning qualia. Clause (1) rules out (a) inverted and (b) absent qualia. Clause (2) rules out (c) fading qualia and (d) dancing qualia. Neither (1) nor (2) rules out doubled qualia. And I am betting physicalists would very much like to rule out doubled qualia. If so, then physicalists should explicitly embrace FGS. They probably implicitly already have, but more on this in Sects. 5 and 6. One thing that one might say about doubled qualia is that no one really needs to worry about them since, even though no theory rules them out, no theory entails them. However, I think maybe there are theories that entail the possibility of doubled qualia. I think perhaps functionalism does. This is interesting because many, if not most, nonreductive physicalists are functionalists. Suppose physicalism, P, just is (1)&(2)&FGS. Suppose also that functionalism, F, entails doubled qualia. Doubled qualia contradict P, especially the FGS part of P. Physicalist functionalists adhere to the conjunction F&P. If F entails doubled qualia, then that would be a reductio of F&P. In the face of such a reductio, one must consider either giving up F or giving up P. Before getting into the account of how functionalism leads to doubled qualia, some brief comments are in order about what functionalism is supposed to be.8 Functionalism has a positive part and a negative part. The positive part is what makes a mental

8 Classic formulations are to be found, of course, in Putnam (1967) and Fodor (1974).

123

Synthese (2011) 180:443–463

449

state the mental state that it is. The negative part is what doesn’t matter to making a mental state the mental state that it is. The positive part says that essential to the instantiation of some mental state are the causal relations that state bears to other states. (Different varieties differ on further requirements for those causal interactions, e.g., whether they must include interactions to states outside of the body or whether they must be describable as implementing computations, but little hinges on these variations here.) The negative part is an insistence upon the psychological irrelevance of certain lower-levels of physical organization. (Different varieties differ on how low one must go to find the irrelevant level—e.g., cells or chemicals—but little hinges on these variations for now.) One distinctive and widely known feature of functionalism is its commitment to multiple realizability, the idea that two entities can differ in their low-level physical properties while those distinct low-level physical properties suffice for—that is, realize—instances of the same mental property. It’s the negative part of functionalism that leads to multiple realizability, and it is multiple realizability that makes functionalism fit so well with nonreductivism. If Jones and Smith can have a mental property in common while having no physical properties in common, then that mental property cannot reduce to—that is, cannot be identical to—either of those physical properties. It is also the negative part of functionalism that leads to doubled qualia. Multiple realizability may be construed as allowing for mental realizers as well as mental realizeds. I turn now to spell out further how functionalism leads to either doubled qualia or something very close to doubled qualia that I will call “mental–mental supervenience.” There is a familiar class of alleged counterexamples to functionalism, instances of which are Searle (1980) Chinese Room and Block (1978) Chinese Nation. The way such counterexamples are supposed to work is by coming up with hypothetical instances in which the functionalist causal-relational criteria for mentality are satisfied by a system that nonetheless does not instantiate mentality. Functionalists correctly challenged whether these were obvious counterexamples instead of just obvious instances of begging the question against functionalism. I don’t think extant fans of the counterexamples gave compelling defenses of them. I think, however, that their status as counterexamples is defensible. First, let’s spell out in further detail the counterexamples in question, starting with Searle’s Chinese Room. Imagine that functionalists have codified the causal interactions between system states alleged to suffice for that system to count as understanding Chinese. Such a codification can be expressed as a program or set of instructions that, if running on a computer, would enable it to thereby implement an artificial intelligence capable of understanding Chinese. A person can follow these instructions, or instructions isomorphic to them. A person, then, can execute the program. In Searle’s Chinese Room thought experiment, we are to imagine this program being written in English and executed by a non-Chinese-speaking English speaker. Searle offers that we imagine him playing this role, sitting in a room in which Chinese queries written on cards come in through the “in” slot and appropriate Chinese responses go out the “out” slot. Crucially, Searle claims that he can follow the English instructions that would result in appropriate Chinese responses to Chinese queries without understanding Chinese himself. Searle’s argument, in brief, against functionalism is that running the program—implementing the causal interactions specified by the program—cannot

123

450

Synthese (2011) 180:443–463

suffice for understanding Chinese, since Searle can run the program without understanding Chinese. One functionalist response—the “systems response”—is that while Searle may not understand Chinese, Searle alone is not instantiating the requisite causal interactions. Instead, the causal interactions that suffice for understanding Chinese include more than those inside of Searle. They also include the causal interactions with the cards coming in and out the slots as well as with the instruction manual wherein the program is written. In short, the objection is that Searle comprises only a part of the total system responsible for implementing understanding of Chinese. Searle counters that the cards and manual are inessential and that the crucial features of the thought experiment can be preserved in a version wherein Searle memorizes the instructions. Chinese queries are put to him verbally and he utters appropriate responses all without actually understanding Chinese. At this point in the dialectic we have something very close to doubled qualia—an instance of what I call “mental–mental supervenience.” Consider what bullet-biting functionalists must say to Searle at this point: They must say that Searle’s mental activities, which do not themselves constitute understanding of Chinese, nonetheless give rise to a second mind that does understand Chinese. In other words, the Chinese-understanding mind supervenes on Searle’s monolingual English-understanding mind, which in turn supervenes on Searle’s brain. I want to emphasize here that the scenario that I am describing as an instance of mental–mental supervenience and thus a violation of FGS is not the scenario as initially described in the systems reply—call this “the whole-room scenario.” It is instead the scenario described by Searle in response to the systems reply—call this “the internalized-room scenario.” The whole-room scenario looks to be easily described as consistent with FGS and thus not an instance of mental–mental supervenience. The whole-room scenario may plausibly be described as providing two different physical supervenience bases for the Chinese-understanding mind and Searle’s monolingual English mind. The Chinese-understanding mind supervenes on a larger physical system than does Searle’s—a physical system that includes various contents of the room, the cards, and Searle himself. In contrast, Searle’s own mind plausibly supervenes on only a proper part of that larger physical system, a proper part likely restricted to just Searle’s own brain. (For simplicity’s sake I here assume a kind of internalism about Searle’s mind.) Turning from the whole-room scenario to the internalized-room scenario, it looks like there is nothing external to Searle’s brain to figure in a distinct physical supervenience base for the Chinese-understanding mind. Searle has here memorized the rules and manipulates the symbols involved for following the program in his mind. The Chinese-understanding mental states supervene on Searle’s rule-following mental states, which in turn supervene on Searle’s brain states. Thus does the internalized-room scenario count as an example of mental–mental supervenience and a violation of FGS. Bullet-biting functionalists simply accept the possibility of the internalized-room scenario. To make the example even closer to doubled qualia, we can note that there is nothing essential to the “understanding Chinese” stuff—we could have had the program be a simulation of seeing red and Searle be color-blind.

123

Synthese (2011) 180:443–463

451

Let’s turn to look at Block’s Chinese Nation counterexample to functionalism. As in Searle’s thought experiment, imagine that functionalists have codified a specification of the causal roles alleged to suffice for instantiating a mental state. Instead of imagining Searle himself following the rules, imagine the populous nation of China put to the task. Perhaps we imagine each individual Chinese citizen playing the role of a neuron (which would require it being very populous) and interneural communication replaced with intercitizen communication via walkie-talkie. Like Searle, this collection of individuals is imagined to implement a program. Like Searle, Block claims that the functionalists are mistaken in supposing that running the program suffices for mentality. Block alleges that no mental states are implemented aside from the mental states of the individual citizens. Supposing that the program was an English-understanding program, the claim is that non-English-speaking Chinese-speaking citizens could run the program without the individual citizens or any emergent “group-mind” thereby understanding English. Changing the example to be about qualia, we can stipulate that the program in question is a “seeing red” program and that the Chinese are all color-blind. The example—seeing red as opposed to understanding language—matters little for this paper. What does matter is what certain functionalists say to such examples. They bite the bullet and affirm that the activity of the citizens suffices for the instantiation of a separate “group” mind—that a distinct solitary übermind arises out of the collective action of these individual unterminds.9 Does such a bullet-biting-functionalist response to the Chinese Nation constitute an affirmation of mental–mental-supervenience? Not yet, but with minor modifications it will. Before saying what the modifications are, let’s first say why they are needed. Why they are needed is because the situation as described so far does not have the übermind and the collection of unterminds sharing a supervenience base. The unterminds, let us suppose, supervene on the brains of the citizens. The übermind, in contrast, supervenes on the brains plus the walkie-talkies. The addition of the walkie-talkies suffices to distinguish the übermind’s supervenience base from the untermind-collection’s supervenience base. There are two ways of changing the example, though, to make it a genuine case of mental–mental supervenience. The first way is that we can, à la the Clark and Chalmers (1998) extended-mind thesis, stipulate that conditions are satisfied allowing that each citizen’s mind “extends” beyond their skull to supervene on the walkie-talkies and much else besides. The second way is that we can get rid of the walkie-talkies and implement direct mind-to-mind (or brain-to-brain) communication between the citizens. On either option the color-blind untermind collective, which contains no red qualia, supervenes on exactly the same set of physical properties that the red-qualiacontaining übermind supervenes on. And thus we have another case of mental–mental supervenience provided by the bullet-biting functionalist. At this point a functionalist who sees where this is all going may attempt the following objection:

9 See, for example, Lycan (1987, pp. 33–34) and Braddon-Mitchell and Jackson (1996, p. 106).

123

452

Synthese (2011) 180:443–463

The kinds of mental–mental supervenience that arise in the bullet-biting responses to Searle and Block arise only in those responses and, instead of biting bullets, we wish simply to dismiss such “counterexamples” as silly. In response to the imagined objection I say the following: I don’t think that functionalists can easily dismiss mental–mental supervenience as arising only in these outlandish scenarios. At least some functionalists are explicitly aware of how functionalist considerations lead to the view that group minds are a common occurrence. And one version of functionalist embrace of the widespread occurrence of group minds is the view—homuncular functionalism—that holds that each individual human mind is itself a group mind. Homuncular functionalism (aka homunctionalism) as advocated by Lycan (1987) and Dennett (1978), also involves mental–mental supervenience. According to the homunctionalists, a human mind taken at the personal level is decomposable into a handful of subpersonal homunculi, each of which is decomposable into further homunculi. At each level of decomposition the units at that level have genuinely mental properties, but of a stupider, simpler sort than those found at the levels above. The recursive decomposition bottoms out with units so simple and stupid as to succumb to wholly mechanistic and nonpsychological explanations. But any two adjacent levels above the “bottom-out” level offer examples of mental–mental supervenience. Consider the personal level and the first subpersonal level of homuncular decomposition right below it. The personal level, which contains one mind, supervenes on the next level down, which consists of many interacting homuncular minds. The homuncular functionalist view of the mind is analogous to the bullet-biting functionalist construal of Block’s Chinese Nation insofar as both hold that a high-level “group” mind can supervene on a multitude of lower-level minds. Thus, mental–mental supervenience is not restricted to bullet-biting functionalism. If homunctionalism is true, then it happens all of the time. It is worth spelling out exactly how these functionalists got into this position and what a problematic place this is to be. The possibility of mental–mental supervenience follows from functionalism. According to functionalism, all that matters to the instantiation of a mental event is that certain causal relations obtain between parts of the realizing system. Functionalism allows, then, that (i) the parts of the realizing system can have their own mental properties and (ii) the causal relations between parts of that system can be instances of mental causation. The possibility of mental–mental supervenience, however, poses a serious threat to theorists who subscribe to the conjunction of physicalism and functionalism, because the possibility of mental–mental supervenience leads to a reductio ad absurdum of that conjunction. The key to the reductio is the fact that the possibility of mental–mental supervenience contradicts physicalism, since the possibility of mental–mental supervenience is the possibility of mental differences obtaining without physical differences obtaining. As mentioned previously, functionalism is just one kind of nonreductive physicalism. Perhaps nonreductive physicalists who are functionalists will react to the mental– mental supervenience arguments by abandoning functionalism in favor of some other nonreductive physicalism. The following argument seals off all escape routes. It is not

123

Synthese (2011) 180:443–463

453

simply a reductio of physicalism and functionalism. It is a reductio of physicalism and nonreductionism. 4 The regress argument Nonreductive physicalism about mental properties is nonreductive because it holds that no mental property is identical to any physical property. Call this the nonidentity thesis. It is physicalist because it holds that there can be no mental differences that obtain without obtaining in virtue of physical differences. Call this the supervenience thesis. In the present section I will work with a generalized supervenience thesis, a thesis that consists in a conjunction of the generalizations of (1), (2), and FGS. The generalized versions—I’ll call them “(1*),” “(2*),” and FGS*—are generalized because they concern properties in general instead of a restricted focus on mental properties. They are as follows: (1*) If, at a given time, two entities instantiate two distinct properties, they must do so in virtue of instantiating two distinct physical properties. (2*) If, at two distinct times, a given entity instantiates two distinct properties, it must do so in virtue of instantiating two distinct physical properties at those times. (FGS*) If, at a given time, a single entity instantiates two distinct properties, it must do so in virtue of instantiating two distinct physical properties. In case anyone is wondering why physicalists should accept generalized versions of (1), (2), and FGS—versions that aren’t just about mental properties, but about all properties—we can perhaps gesture toward considerations along the lines considered in connection with qualia in Sects. 2 and 3. If doubled qualia and intermittently doubled qualia strike physicalists as sufficiently repugnant to embrace FGS, then we might invite them to consider analogous situations involving, instead of the doubling of qualia, the doubling of moral, political, economic, or aesthetic properties. For example, contemplate how obviously inconsistent with physicalism would be a scenario of intermittently doubled morality whereby a single situation or agent switched from having one set of moral properties to two sets of disparate moral properties in concert with a minute physical change, such as the firing of a single neuron. I will not spell this out further here, but I hope it suffices to suggest that what makes doubled qualia repugnant to physicalists is the doubling and not anything peculiar to qualia.10 I turn now to the construction of the regress. Given (1*), (2*), and FGS*, if a and b differ with respect to the mental properties M1 and M2 that they instantiate, they must do so in virtue of instantiating some distinct physical properties P1 and P2 . Here’s where problems arise. The demands of supervenience don’t require only that mental differences give rise to physical differences. All differences must give rise to physical differences. (That’s what “no difference without a physical difference” means.) It 10 An anonymous referee has made a suggestion about these doubling arguments, a suggestion that I want

to here note as a welcome one. The suggestion is that these considerations depend for their intuitive force on realism about properties and qualia. A physicalist who also embraces such realisms is highly unlikely to want to embrace doubling.

123

454

Synthese (2011) 180:443–463

follows, then, that if the thesis of nonidentity holds, there is sense to be made of the question of in what consists the difference between M1 and P1 . If they are distinct, there must be some physical difference in virtue of which they differ. Call that physical difference P3 . P3 also must differ from M1 , otherwise nonidentity is violated. P3 must further differ from P1 , otherwise there would be no physical difference in virtue of which M1 and P1 differ. So the difference between M1 and P1 demands the positing of a distinct property, P3 . Since P3 is distinct from M1 , the question again arises of in what consists the distinction, and the answer will involve P4 , which by similar chains of reasoning will lead to P5 and P6 and so on. This is a bad thing. If we think of the relations between the supervenient and subvenient properties in terms of explanation, then where the regress is infinite the target never gets explained. Fans of nonidentity should give up on physicalism altogether. Fans of physicalism should embrace identity theory.11 It is worth spelling out that the construction of the regress does not depend on reifying “being different” as a property unto itself. The relevant notion of difference can be unequivocally spelled out in terms of distinctness—that is, failure of identity. Thus, the argument may be stated as follows: Physicalism requires that no properties can be nonidentical without being instantiated in virtue of nonidentical physical properties. In the case of nonidentical mental properties M1 and M2 , they are instantiated in virtue of P1 and P2 . The thesis of the nonidentity of the mental to the physical that is essential to nonreductive physicalism requires that M1 be identical to no physical property and thus be not identical to P1 . An application of physicalism (the conjunction of (1*), (2*), and FGS* that we can summarize with the “no properties can be nonidentical without…” slogan) to M1 and P1 requires the instantiation of P3 , which is itself nonidentical to P1 and M1 . Note here that I am not assuming the existence of P3 to get the argument rolling. That would indeed be an assumption that reifies difference as a property unto itself. Instead I am showing how the unwelcome P3 arises as a consequence of the conjunction of physicalism and nonreductivism. Continuing, then, we see that just as the unwelcome P3 , arises, so does its unwelcome brethren P4 through P∞ . This is because an application of physicalism to M1 and P3 requires, for the sorts of reasons already stated, the instantiation of P4 . It should be clear at this point how M1 and P4 require P5 and so on to P∞ . At this point the nonreductive physicalist may wish to resist the argument by resisting the reading offered here of all differences requiring physical differences. This would be to protect nonreductive physicalism by rejecting physicalism as I’ve characterized it here. However, a serious question arises, then, as to what’s physicalistic about nonreductive physicalism. To appreciate the problem, consider the following: Reductive physicalism and nonreductive physicalism are going to have to give different answers to questions such as 11 Lynch and Glasgow (2003) run a similar regress argument concerning supervenience, but the target

of their argument is “superdupervenience,” a brand of nonreductive physicalism that affirms the physical explicability of the supervenience relation. The conclusion of their regress argument is that superdupervenience is impossible. What Lynch and Glasgow do not attempt is to argue as I have against generalized nonreductive physicalism.

123

Synthese (2011) 180:443–463

455

“in virtue of what are two properties different?” The reductive physicalist will always be able to give the same answer regardless of the properties in question. However, depending on the properties, the nonreductivist will have to give different answers. The different answers will depend on whether the properties in question are (i) two different mental properties, (ii) two different physical properties, or (iii) a mental property and a physical property. Spelling this out further yields the following: (i) In the mental–mental case, the two mental properties are nonidentical in virtue of being instantiated by physical properties that are nonidentical. (ii) In the physical–physical case, the difference is due simply to the two physical properties being nonidentical. (iii) In the mental–physical case, the difference is due simply to the mental property and the physical property being nonidentical. If we ask the nonreductivist what’s physicalistic about (i)–(iii), which is to ask what merits considering the differences in question to be physical differences, we only get satisfying answers for (i) and (ii). For (ii), what makes the difference in question a physical difference is that there are two properties that are nonidentical and both physical. For (i), what makes the difference in question a physical difference is parasitic on (ii). For (iii), the difference is simply that the properties are nonidentical. But since one of the properties in question is nonphysical, there seem to be no grounds for regarding the difference in question as a physical difference (since neither (i) nor (ii) can supply the grounds). Further, there seem to be no grounds for considering the position in question a version of physicalism. It is dualism. It is time now to consider arguments for FGS. Perhaps we have pretty much already seen one, and it goes pretty much like the following: If FGS was not a part of physicalism, then doubled qualia would be compatible with physicalism. But doubled qualia are not compatible with physicalism. Therefore, FGS is a part of physicalism. This argument has the virtue of validity, but perhaps the second premise can be questioned. At least, no argument has been given for the second premise. I assume most physicalists will like the second premise, and perhaps this is argument enough. More can be said, of course. As I will discuss in Sect. 5, I think, for instance, that current practice in cognitive neuroscience is shot through with what looks like empirical support for and/or tacit acceptance of FGS. I also think that there are projects outside of cognitive neuroscience that are similarly FGS-friendly, a point I will discuss further in Sect. 6.

5 Reflections on neuroscience and a defense of fine-grained supervenience On several occasions when I’ve talked to people about mental–mental supervenience and how it should be ruled out by physicalism, I’ve been confronted by something like the following response: Insofar as cognitive functions are not localized to specific regions of the brain, mental–mental supervenience happens all of the time and should be embraced by physicalists, not ruled out by the postulation of FGS.

123

456

Synthese (2011) 180:443–463

I think this response is exactly wrong, although it will take some explaining to get the point across. The explaining will require a review of some cognitive neuroscience, with an emphasis on evidence for and models of two different ideas on how cognitive functions are related to the brain. These two different ideas often appear in the relevant literature under the headings of “localizationism” and “holism.”12 In brief, localizationism involves locating the neural bases for distinct cognitive functions in distinct regions of the brain. Holism allows that distinct cognitive functions can share brain regions. Localizationism is obviously consistent with FGS, since brain-region differences are obviously physical differences. However, as I’ll argue in a bit, all of the evidence for holism is fully consistent with FGS as well. My interest here is primarily in models of holism, for I will be keen on seeing whether evidence for holism constitutes evidence against FGS. Perhaps the most fruitful and popular way of modeling how distinct mental properties may share brain regions comes from connectionism. My interest here will be in a review of the main relevant ideas of connectionism to show that holism does not provide counterexamples to FGS. Connectionism involves modeling cognition in terms of neural networks. A neural network is a set of units (the neurons) and the connections between them. Let us consider a relatively simple connectionist model. Each neuron can be in one of several states of activation. We might think of these as real-numbered values ranging from 0 to 1. What state of activation a neuron will be in at a given time can be influenced by the state of activations of other neurons that are connected to it. Values called “weights” may be assigned to the connections, determining how much influence the other neuron may have via that connection. What state of activation a neuron goes into at a given time is determined by that neuron’s transition function, which takes into consideration the states of activation and weights of adjacent neurons. Thus, for example, a neuron’s activation may be a sigmoidal function of the weighted sum of the states of activation of the neurons connected to it. One typical kind of neural network—a three-layer feed-forward network—has input neurons, output neurons, interneurons (hidden units), and connections that allow for a flow of information in a single direction from input units to hidden units and hidden units to outputs. In a “massively connected” three-layer feed-forward net, every input unit is connected to every hidden unit and every hidden unit is connected to every output unit. The topology of the network—the number of units and connections between them—is set by hand. The weights, however, are set instead by an automatic procedure—a learning rule that optimizes the set of weights to allow the network to perform some particular task. One such example comes from a network constructed by Garrison Cottrell and his colleagues, as described by Churchland (1995). The network has 4,096 input neurons configured as a 64 × 64 unit retina, with each retinal unit’s activation coding increments of brightness. The hidden layer has 80 units. The output layer has 8 units: 1 unit codes for face vs. non-face, 1 for male, 1for female, and 5 units encode “names” for faces. The network was trained with a set of photographs of 11 different faces. Training involves starting with the network’s weights

12 For discussions of localizationism and holism, see Anderson (2007) and Mundale (2002).

123

Synthese (2011) 180:443–463

457

initially set to random values. Initial performance is, as expected, quite poor. Application of the back-propagation learning rule involves measuring differences between the right answer and the actual given answer and then making small changes to the weights based on a measurement of degree of error. After thousands of trials that involve exposing the retinal units to bit-mapped photographs of faces, the network can be tested to see how well it recognizes stimuli as being faces, being female or male, etc. When tested on faces from the training set, performance is 100%. When tested on a test set of novel faces, the network performed about 10–15% less well than on the faces from the training set. Such performance is comparable to the performance of human subjects. Let us turn now to consider what it might mean to attribute mental states to such a neural network.13 There are two general kinds of mental states to consider: occurrent states and abeyant states. Occurrent states, like percepts, are events of relatively short duration. Abeyant states, in contrast, are relatively more long-term, such as long-term memory or stored knowledge. When we attribute such states to networks, occurrent states are implemented by patterns of activation and abeyant states are implemented by the connection weights (Churchland and Sejnowski 1992, p. 165; Haugeland 1991, p. 84). If connectionist networks constitute counterexamples to FGS, then they will do so either in virtue of occurrent states or abeyant states. And it is relatively easy to see that occurrent psychological states implemented in connectionist networks will not pose any special problems for FGS. Distinct occurrent mental states are implemented by distinct patterns of neural activation. For example, the pattern of activations that constitutes the identification of a face as female is clearly distinct from the one for a male. If there is to be a problem for FGS, it will be posed by abeyant states. If we look to the facial-recognition network, we can see how the problem might arise. The network’s knowledge of male faces is distributed across the connection weights, likely the very same weights across which the knowledge of female faces is distributed. Is this, then, a counterexample to FGS? Are distinct mental states instantiated in virtue of all and only the same physical states? To see that we don’t have a counterexample to FGS, we need to appreciate that the distinct physical properties that give rise to the distinct abeyant states are physical dispositional properties of the network. In the case of the knowledge of male faces, this is implemented in virtue of the physical disposition to activate the “male” output unit in response to male faces. The distinct abeyant state of knowledge of female faces is implemented by the distinct physical disposition to activate the “female” output unit in response to female faces. There is nothing problematic or even unusual about distinct physical dispositions being distributed across the same spatial regions. Consider, for example, the distribution of a sugar cube’s solubility and fragility throughout its volume. For another example, consider the gravitational and magnetic properties of a chunk of iron. Both are distributed throughout the chunk, yet both are distinct physical properties and both 13 Of course, some people will be loath to attribute any mental states to such neural networks. However, such people are of little interest here, since my interest here is in considering possible counterexamples to FGS construed in terms of the instantiation of mental states by such neural networks.

123

458

Synthese (2011) 180:443–463

may be regarded as dispositions—the disposition to behave one way in a magnetic field and the disposition to behave another way in a gravitational field. Now, it is one thing for the bases of distinct dispositions to be equally spatially distributed and another thing for distinct dispositions to share a supervenience base, for the first thing, but not the second, is consistent with fine-grained supervenience. If two allegedly distinct dispositions turn out to share a supervenience base, then the allegation of their distinctness turns out to be false. Such a view is consistent with a Quinean view of dispositions that identifies dispositions such as solubility or fragility of, for example, a sugar cube with the microphysical structure of the sugar cube (Quine 1960, pp. 222–225). If the sugar cube’s solubility and fragility are to be identified with one and the same microstructure, then, by the transitivity of identity, these allegedly distinct dispositions are not distinct after all. Applying a Quinean attitude toward dispositions to the cases of allegedly distinct pieces of knowledge construed as abeyant states of the neural network involves treating the allegations of distinctness as false. If all and only the same connection weights constitute the network’s knowledge of what male faces look like and its knowledge of what female faces look like, then the correct view is that these attempted knowledge attributions fail to attribute distinct mental states to the network. Whatever knowledge the network has, it is one and the same piece of knowledge that constitutes its ability to recognize male faces and its ability to recognize female faces. Turning to questions of qualia, we see that qualia can be attributed to neural networks but the main proposals view them as occurrent not abeyant representations and as such whatever was said above about consistency with FGS applies as well to qualia. As I spell this out briefly in Mandik (2007, p. 427): When Churchland discusses color qualia, he articulates a reductive account of them in terms of Land’s theory that human perceptual discrimination of reflectance is due to the sensory reception of three kinds of electromagnetic wavelengths by three different kinds of cones in the retina (Land 1964). In keeping with the kinds of state-space interpretations of neural activity that Churchland is fond of, he explicates color qualia in terms of points in three dimensional spaces, the three dimensions of which correspond to the three kinds of cells responsive to electromagnetic wavelengths. Each color sensation is identical to a neural representation of a color (a neural representation of a spectral reflectance). Each sensation can thus be construed as a point in this 3-D activation space and the perceived similarity between colors and the subjective similarities between corresponding color qualia are definable in terms of proximity between points within the 3-D activation space. On such a neural network model of qualia, distinct qualia will be implemented in ways fully consistent with FGS. Lest anyone think current cognitive neuroscience is wholly holistic, it is worth pausing to appreciate just how much is actually quite localizationist. Examples of mental processes localized to specific cortical regions include the visual perception of color and motion (Mandik 2007). Other aspects of vision with distinct localizations include visual recognition of object identity and the visual perception of an object’s spatial

123

Synthese (2011) 180:443–463

459

location (Mishkin et al. 1983). Further examples include the localization distinct kinds of linguistic competence to Broca’s and Wernicke’s areas (Bechtel 2001). Koch (2004) has even found evidence of neurons that fire specifically in response to Bill Clinton. Evidence for localism is evidence for FGS. However, it is worth emphasizing that FGS does not require localism. Holism can be consistent with FGS. Holistic implementations of multiple cognitive functions by a single neural system is consistent with FGS as long as the different functions arise in virtue of physical differences in the neural system.

6 FGS outside of neuroscience One need not look only to cognitive neuroscience to detect commitments to FGS. We can find tacit, if not explicit, allegiance to FGS in various lines of research in the philosophy of mind that are quite removed from any explicit appeal to cognitive neuroscience. Below I briefly review two: Fodor’s (1975) Language of Thought theory of cognition and Rosenthal’s (2005) Higher Order Thought theory of consciousness. There is something especially interesting about finding FGS lurking in Fodor’s theory, since Fodor is such a high-profile critic of reductive physicalism. In brief, the language-of-thought hypothesis (LOT) holds that having distinct thoughts not only involves having distinct physical states, but also that these states are composed of distinct re-combinable physical components. So, for example, if a person thinks the distinct thoughts birds fly and insects fly, this involves having distinct physical representational states—in these cases a state that represents birds, a state that represents insects, and a state that represents flying. Thinking that birds fly involves a relation of a person to two distinct inner physical items, the bird-representation and the flight-representation. Thinking the distinct thought that insects fly involves a relation to a distinct set of inner physical items, in this case the insect-representation and the flight-representation. The crucial case to consider to see exemplification of FGS concerns when a single individual at a given time instantiates distinct mental properties. Here, LOT supplies distinct physical properties. If one thinks, at a given time, both that birds fly and that insects fly, distinct physical representations—representations of birds and representations of insects—account for the distinctness of the thoughts. (Additionally, distinct tokenings of the flight-representation may be involved.) Since much of the discussion in this paper concerns consciousness, it will be useful to briefly consider a philosophical account of consciousness. Rosenthal identifies conscious states with mental states that one has a thought about. Higher-order mental states are mental states that are about other mental states. Conscious states are plausibly states one is conscious of and Rosenthal explains what it means to be conscious of a mental state in terms of thinking of a mental state. Rosenthal is no dualist, so the states in question—both lower- and higher-order—are supposed to be distinct physical states. There are several ways in which we can come up with exemplifications of FGS consistent with HOT. One would involve a subject undergoing two distinct states, one of which is conscious and the other of which is not. The two states would be physically distinct states, and the conscious one would be further distinguished by a third state, the higher-order thought about it.

123

460

Synthese (2011) 180:443–463

Further work of Rosenthal’s (2005) that provides exemplifications of FGS is his homomorphism account of sensory qualities. Sensory qualities are properties of sensory states in virtue of which the states resemble and differ from one another. States of persons, being states, do not bear first-order resemblances to objects. However, the set of resemblances and differences between the sensory states is homomorphic to the set of resemblances and differences between the objects in the external world that we perceive with our senses. Just as a specific color may be identified in virtue of a set of relations to other colors, a sensory quality may be identified in virtue of a set of relations to other sensory qualities. Again, since Rosenthal is no dualist, these states, qualities, and relations are supposed to be physical. The homomorphism theory can be used to construct an exemplification of FGS as follows: A perception of, say, the Japanese flag involves several sensory qualities. To name a few: one corresponding to redness, another to whiteness, and still others for the circularity of the red spot and the rectangularity of the flag itself. The homomorphism theory entails that the distinct mental properties—in this case, the distinct sensory qualities—are instantiated by a given individual at a given time in virtue of distinct physical properties.14 LOT and HOT are not unique. Exemplifications of FGS similar to those in connection with LOT can be constructed instead in terms of Evans’s Generality Constraint (Davies 1991; Evans 1982). In the domain of philosophical accounts of consciousness, exemplifications of FGS can be spelled out in theories other than HOT. First-order representationalist theories such as Tye (1995) and Dretske (1995) would do just as well. I will not take the time here to spell out further details. Pointing out the widespread tacit commitment to FGS serves two purposes. The first is to drive home the point that FGS is not to be given up lightly. The second is that, in some cases at least, there are deep tensions in these theories insofar as, like Fodor’s, they involve commitments to nonreductive physicalism. For, as it has been a major goal of this paper to show, FGS and nonreductivism constitute an untenable pairing. Given the first point, the second point leads us to see that if one member of the pair is to be given up, it should be nonreductivism.

7 Concluding remarks: what’s the big deal about brains? The point of discussing commitments to FGS by people not explicitly committed to neural reductionism is to show that FGS is not simply something held by people with a prior conviction that everything mental will turn out to be neural. However, I very much want to urge the point that everything mental will turn out to be neural and it is now time to consider the question “Why the brain?” Perhaps the relevant question is better put this way: Assuming that the considerations concerning mental–mental supervenience, doubled qualia, and the regress argument conclusively prove that all mental 14 While the main features of Rosenthal’s accounts of consciousness and sensory qualities may perhaps be adopted by dualists, Rosenthal’s own allegiance to physicalism and intention that the accounts be consistent with physicalism are clear. See in particular Rosenthal 2005, p. 195.

123

Synthese (2011) 180:443–463

461

properties must reduce to physical properties, why think that the physical properties that they reduce to will be neural properties? Why, indeed? It seems to be an open question whether distinctively neural properties are essential to the instantiation of mental properties. One can buy into reductive physicalism and reject neural reduction bases in favor of chemical or thermodynamic reduction bases, just to name a few. Perhaps, then, systems that have no distinctively neural properties—nonetheless have certain chemical or thermodynamic profiles that suffice for mentality. Perhaps. But I doubt it. I hope that I may be forgiven for being so brief about this, but I think there are three reasons (at least) for thinking that the physical reduction of the mental should be a neural reduction. The first reason for believing in neural reduction is that no uncontroversial examples of entities that implement consciousness or cognition exist without brains, or at least, neural networks. It is uncontroversial that alert human adults have mental states. It is also uncontroversial that they have brains. Things are much more contested for the brainless. A brain is a part of a body and so a ghost, being disembodied, would presumably constitute a brainless realization of mentality. I think it safe to say that there is no non-controversial evidence for ghosts. Sometimes philosophers discussing multiple realizability suppose it possible for there to be aliens or artifacts that instantiate mentality brainlessly with heads instead full of goo or microchips. However, such thought experiments do not sufficiently grapple with the question of how to be sure when we have an instance of brainlessness on our hands. A head full of goo or microchips is not necessarily a head without a brain unless brains are necessarily made out of neither goo nor chips. But if the possibility remains that there could be goo-brains or chip-brains, imagining implementations of mentality realized in different kinds of stuff is not necessarily imagining brainless implementations. Thus even if goo-heads or chip-heads were discovered to implement mentality (which, so far, has not yet happened) they still would not count as uncontroversial confirmations of the mind-endowed lacking brains. The second reason for believing in neural reduction is that there is no reason to doubt that it is in virtue of their brains (or their brains plus something else) that creatures like us implement consciousness or cognition. Let us entertain briefly how unpromising non-neurocentric theories have been. Mental properties are had by an organism either in virtue of the whole organism or one of its proper parts. Further, it is easy to accumulate evidence against the first disjunct. For example, traumatic amputations do not necessarily rob amputees of their mentality. Further evidence along these lines may be obtained by comparing the relative effects on mentality of lobotomies and appendectomies. That the seat of our soul is some proper part of us is old news, but the appendix never had a chance and the Aristotelian coronary hypothesis was rejected long ago. What we know about where drugs need to go to go to work and what brain injuries impair what mental functions has tipped the scales pretty clearly in favor of neurocentrism. Now, these sorts of considerations, while they lead to the view that the brain is important for mentality, they leave open the question of whether the implementation of mentality is exhaustively neural. In opposition to what we might call the neural

123

462

Synthese (2011) 180:443–463

exhaustion thesis (the thesis that the mental is exhaustively neural), we have various embodied, embedded, and externalist proposals for including the body and even chunks of the environment of the organism as part of the supervenience base of the organism’s mental properties. While it is far beyond the scope of this paper to refute the theses of the embodied and extended mind, the third point in favor of neural reductionism is relevant to these issues. The third reason for believing in neural reduction is that no reductive research program has been as productive as neural ones. There have been, in recent decades, three major proposals that have been physicalistic without reducing mentality, à la behaviorism, to the behavior of whole organisms: classic computationalism, connectionism, and (certain versions of) dynamic-systems theory (see Eliasmith 2003 for a review of these three positions). Classicism got wedded, in many people’s minds, to nonreductive physicalism, largely due to the influence of Fodor (1974) and Putnam (1967). Dynamic-systems theory included proposals of a specifically neural character, (Freeman 1991) while others looked like warmed-over behaviorism (van Gelder 1995). Either way, dynamic systems theory was confronted with some devastating objections (Eliasmith 2001; Glymour 1997; Grush 1997). The main point here, though, is not any knock-down refutations of non-neurocentric research programs. The point here is that neurocentric research programs have been massively productive both in theory and in application. To summarize: (i) no uncontroversial examples of brainless mentality exist, (ii) organisms that have mentality and brains have mentality in virtue of their brains, and (iii) neurocentric reductionist research programs have been massively more productive than non-neurocentric reductionist research programs. So, if mental properties are going to reduce to physical properties, then (i)–(iii) give reason to believe that the physical properties in question are going to be neural. And why should we think that mental properties are going to reduce to physical properties? The answer is that, if we are going to be physicalists at all, contemplation of doubled qualia and related scenarios leads us to embrace formulations of physicalism that include fine-grained supervenience. Further, once fine-grained supervenience is included in the definition of physicalism, the only way to avoid a nasty regress is to embrace a formulation of physicalism that is reductive. Acknowledgements For helpful remarks on earlier versions, I thank Murat Aydede, William Bechtel, Lawrence Davis, Anthony Dardis, Chris Eliasmith, Rick Grush, Bryce Huebner, Brian Keeley, Adam Pautz, Tom Polger, John Post, Jesse Prinz, David Rosenthal, Peter Ross, Eric Thomson, Anders Weinstein, Chase Wrenn, Jeffrey Yoshimi, Tad Zawidzki, and two anonymous referees. For keeping my “that” and my “which” nonidentical I thank Rachelle Mandik.

References Anderson, M. (2007). The massive redeployment hypothesis and the functional topography of the brain. Philosophical Psychology, 21(2), 143–174. Bechtel, W. (2001). Linking cognition and brain: The cognitive neuroscience of language. In W. Bechtel, P. Mandik, J. Mundale, & R. S. Stufflebeam (Eds.), Philosophy and the neurosciences: A reader. Oxford: Basil Blackwell. Block, N. (1978). Troubles with functionalism. Minnesota Studies in the Philosophy of Science, 9, 261–325.

123

Synthese (2011) 180:443–463

463

Braddon-Mitchell, D., & Jackson, F. (1996). Philosophy of mind and cognition. Oxford: Blackwell. Chalmers, D. (1996). The conscious mind: In search of a fundamental theory. New York: Oxford University Press. Churchland, P., & Sejnowski, T. (1992). The computational brain. Cambridge, MA: MIT Press. Churchland, P. M. (1995). The engine of reason, the seat of the soul: A philosophical journey into the brain. Cambridge, MA: MIT Press. Clark, A., & Chalmers, D. J. (1998). The extended mind. Analysis, 58, 7–19. Davidson, D. (1970). Mental events. In L. Foster & J. Swanson (Eds.), Experience and theory (pp. 79– 101). Amherst, MA: University of Massachusetts Press. Davidson, D. (1973). The material mind. In P. Suppes, L. Henkin, A. Joja, & G. C. Moisil (Eds.), Logic, methodology and the philosophy of science (pp. 709–722). Amsterdam: North-Holland Publishing Company. Davies, M. (1991). Concepts, connectionism, and the language of thought. In W. Ramsey, S. Stich, & D. Rumelhart (Eds.), Philosophy and connectionist theory (pp. 229–257). Hillsdale, NJ: Lawrence Erlbaum. Dennett, D. C. (1978). Brainstorms. Cambridge, MA: MIT Press. Dretske, F. (1995). Naturalizing the mind. Cambridge, MA: MIT Press. Eliasmith, C. (2001). Attractive and in-discrete: A critique of two putative virtues of the dynamicist theory of mind. Minds and Machines, 11, 417–442. Eliasmith, C. (2003). Moving beyond metaphors: Understanding the mind for what it is. Journal of Philosophy, 100, 493–520. Evans, G. (1982). The varieties of reference. Oxford: Oxford University Press. Fodor, J. A. (1974). Special sciences, or the disunity of science as a working hypothesis. Synthese, 28, 97–115. Fodor, J. A. (1975). The language of thought. Cambridge, MA: Harvard University Press. Freeman, W. J. (1991). The physiology of perception. Scientific American, 264(2), 78–85. Glymour, C. (1997). Goethe to van gelder: Comments on ‘dynamical systems’ models of cognition (Electronic version). Department of History and Philosophy of Science, University of Pittsburgh PhilSci Archive. Retrieved June 5, 2008, from http://philsci-archive.pitt.edu/archive/00000139/. Grush, R. (1997). Review of port and van gelder’s mind as motion. Philosophical Psychology, 10(2), 233–242. Haugeland, J. (1991). Representational genera. In W. Ramsey, S. P. Stich, & D. E. Rumelhart (Eds.), Philosophy and connectionist theory (pp. 61–89). Hillsdale, NJ: Lawrence Erlbaum. Hofweber, T. (2005). Supervenience and object dependent properties. The Journal of Philosophy, CII(1), 5–32. Koch, C. (2004). The quest for consciousness. Englewood, CO: Roberts & Company. Land, E. H. (1964). The retinex. Scientific American, 52, 247–264. Lycan, W. (1987). Consciousness. Cambridge, MA: MIT Press. Lynch, M., & Glasgow, J. (2003). The impossibility of superdupervenience. Philosophical Studies, 113, 201–221. Mandik, P. (2007). The neurophilosophy of consciousness. In M. Velmans & S. Schneider (Eds.), The Blackwell companion to consciousness (pp. 418–430). Oxford: Basil Blackwell. McLaughlin, B., & Bennett, K. (2006). Supervenience. The Stanford encyclopedia of philosophy (Electronic version, Fall 2006 ed.). Retrieved June 5, 2008, from http://plato.stanford.edu/archives/ fall2006/entries/supervenience/. Mishkin, M., Ungerleider, L. G., & Macko, K. A. (1983). Object vision and spatial vision: Two cortical pathways. Trends in Neurosciences, 6, 414–417. Mundale, J. (2002). Concepts of localization: Balkanization in the brain. Brain and Mind, 3, 313–330. Putnam, H. (1967). The nature of mental states. In W. H. Capitan & D. D. Merrill (Eds.), Art, mind, and religion. Pittsburgh University Press. Quine, W. V. (1960). Word and object. Cambridge, MA: MIT Press. Rosenthal, D. (2005). Consciousness and mind. Oxford: Clarendon Press. Searle, J. R. (1980). Minds, brains, and programs. Behavioral and Brain Sciences, 3, 417–457. Tye, M. (1995). Ten problems of consciousness. Cambridge, MA: MIT Press. van Gelder, T. (1995). What might cognition be if not computation?. Journal of Philosophy, 92, 345–381. Wilson, J. M. (2005). Supervenience-based formulations of physicalism. Nous, 39(3), 426–459.

123