Conventionalism about Space and Time

Conventionalism about Space and Time Richard Swinburne The British Journal for the Philosophy of Science, Vol. 31, No. 3. (Sep., 1980), pp. 255-272. Stable URL: http://links.jstor.org/sici?sici=0007-0882%28198009%2931%3A3%3C255%3ACASAT%3E2.0.CO%3B2-0 The British Journal for the Philosophy of Science is currently published by Oxford University Press.

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Brit. J. Phil. Sci. 31 (1980),255-272 Printed in Great Britain

Conventionalism About Space and Time * by R I C H A R D S W I N B U R N E I n recent years philosophical writing about space and time has been permeated with a distinction between matters of fact and matters of convention. This distinction was due to Riemann and PoincarC but was developed and popularised by Reichenbach and Griinbaum. Certain claims of science are said to be truly factual and others to be merely conventional. Similar kinds of distinction are of course to be found in philosophical writing about many other issues. I n general philosophy of science there is the distinction between observable entities and properties, and theoretical entities and properties; and nowadays in philosophical writing about language some writers wish to distinguish sharply between such factual matters as which noises a subject uttered at a certain time and such matters of theory as what he meant by what he said. My main concern here is with space and time, but we need to be aware of the wider background. A matter is factual if it is expressed by a factual statement. A factual statement is one which, if true, would state a fact. Something is a fact, I suppose, for these writers, if it truly or really holds, if it is an objective feature of the world. If a factual statement is true, its negation is false; and conversely. By contrast, something is a matter of convention, in the terminology of these writers, if the statement which expresses it is not factual; and so if it is as near to the truth as its apparent negation (i.e. the statement which by its verbal form is the negation of the original statement, and would be its negation if the original statement were factual. If a statement is not factual and so not really making a claim, it cannot properly have a negation.) Let us call such a statement a conventional statement. A conventional statement may form a useful part of science but it does not have a truth-value on its 0wn.l I n conjunction with some other statement it may form a statement with a truth-value-indeed the same *An earlier version of this paper was read at a meeting of the British Society for the Philosophy of Science in May 1979.I am most grateful to those who produced valuable criticisms of it on that occasion and on similar occasions. Thus Reichenbach ([1958],p. 19)claims that in deciding on the criteria for congruence, we are making 'an arbitrary decision that is neither true nor false'.

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truth-value as the conjunction, of its negation with a different statement. The two provide alternative ways of representing the same facts. The above seems to me the central claim which the writers cited wish to make about the statements about space and time which I shall shortly list, normally by calling them 'matters of convention'. Sometimes the writers say that alternative theories on these matters are 'co-legitimate alternatives', or 'factually co-legitimate', or, with respect to different measures of spatial and temporal intervals, that they can be adopted 'with equal factual legitimacy', i.e. that in this sense space or time are 'alternatively metrizable'.' I n his later writings Adolf Grunbaum has developed more specialised senses of 'conventional' and etymologically similar terms-e.g. he wants to say that measurements of congruence are 'convention-laden' if and only if there is no intrinsic metric to space (i.e. if there are no spatial atoms of finite volume). But as Grunbaum also seems to use the other phrases quoted above and similar phrases to make the points which the other writers make, we can list him as holding that the claims which I shall discuss are matters of convention in their sense. A very simple example will illustrate the distinction which the conventionalist has in mind. 'There are four men in this room' is a factual statement: but 'there are x men in this room' is only a conventional statement. By itself the latter has no more truth to it than 'there are 2x men in this room'. But the former constitutes a factual statement when conjoined to 'and x = 4', indeed the same factual statement as the statement made when the latter is conjoined to 'and x = 2'. (In formal logic the conjoining would involve the variable of the second statement being governed by the quantifier of the first statement.) I do not dispute the utility of this distinction. My concern in this paper is with the statements which the writers concerned claim to be conventional and with the criteria which they are using in order to classify them. I list six issues, central in the philosophy of space and time, which the writers concerned have claimed to be matters of convention: (I) Whether a body, such as the Earth, is really in motion (as opposed to, e.g. whether it is moving relative to the Sun, which is a matter of fact). (2) What is the metrical geometry of a region of space-e.g. whether the interior angles of a rectilinear triangle in physical space sum to 180". (3) Whether the distance between two points A and B is or is not the same distance as that between two different points C and D (when C and D do not both lie between A and B); i.e. whether AB is congruent with CD. For these phrases see (e.g.) Griinbaum [1970],p. 580.

Conventionalism About Space and Time 257 (4) Whether the temporal interval between two instants of time t, and t, is the same as that between two instants t , and t , (when t , and t , do not both lie between t, and t,). ( 5 ) What is the topology of space-e.g. whether a certain line in space returns to its starting point or only to a point which looks like its starting point; and so whether or not space is finite. (6) Whether two events E, and E * at different places are simultaneous (when E, and E* are not in fact connectible by a signal-viz. when you cannot send a signal from the place of E, at the time of E, to arrive at the place of E" before or at the same time as the occurrence of E*, or conversely). The grounds which the conventionalists give for holding ( I ) . . . (6) to be matters of convention are of course very loosely, that no one can actually observe whether things are as ( I ) . . . (6) claim; that so long as one is prepared to make alternative hypotheses about other unobservable matters (which one can do without the danger of being shown mistaken by observations) one can maintain which position one likes on the issues; and that there is no unknown factual truth here, because the only such truths are those which are 'in principle' checkable. The conventionalist is thus a verificationist who holds that a statement is a factual statement only if it is in some way verifiable or falsifiable by observation. What I wish to do in this paper is, first, to point out that there are different verificationist theses which have different consequences from each other about which of ( I ) . . . (6) are matters of convention; secondly, to show that only the stronger verificationist theses prove any of them to be matters of convention; and thirdly to comment briefly that the stronger verificationist theses are intuitively not nearly as plausible as the weaker ones. Although conventionalists put forward verificationist arguments for their positions, they seldom distinguish clearly between different possible verificationist theses. Out of many different verificationist theses which could be maintained, I select four typical ones in decreasing order of strength (a thesis being stronger in so far as it pronounces fewer statements to be factual, i.e. rules out more statements from being factual):

[A] A statement is factual if and only if it entails claims which it is physically possible to observe to hold. [B] A statement is factual if and only if it entails claims which it is logically possible to observe to hold. [C] A statement is factual if and only if it could be confirmed or disconfirmed by claims which it is physically possible to observe to hold.

Richard Swinburne [Dl A statement is factual if and only if it could be confirmed or disconfirmed by claims which it is logically possible to observe to hold. 258

As in all these theses a statement's being a 'factual' statement is tied to the notion of something being 'observable', there will be a continuum of statements from clearly factual statements to clearly non-factual statements. This is because there is a whole continuum of entities and properties from the clearly observable to the clearly non-observable-according to whether 'observing', 'in a microscope', 'in an electron-microscope', 'in a cloud chamber' etc. are recognised as observing. However, the kind of contrast which the writers cited wish to make seems to remain whether or not 'observing' via these various devices counts as observing. T h e different verificationist theses suggest different criteria for logical equivalence : [A] Two statements are logically equivalent if and only if they entail the same claims which it is physically possible to observe to hold. (They are then logically equivalent to the conjunction of these claims.) [B] Two statements are logically equivalent if and only if they entail the same claims about what it is logically possible to observe to hold. (They are then logically equivalent to the conjunction of these claims.) [C] Two statements are logically equivalent if and only if they would be equally well confirmed or disconfirmed by all claims, which it is physically possible to observe to hold. [Dl Two statements are logically equivalent if and only if they would be equally well confirmed or disconfirmed by all claims which it is logically possible to observe to hold. Let me bring out the differences between these different verificationist criteria. Let S entail that in circumstances C,, F,; and that in circumstances C,, F,. Let Sf entail that in circumstances C,, F,; and that in circumstances C,, Fi. Suppose that these are all the claims which it is logically possible to observe to hold; that F2and Fi are incompatible; that C, are circumstances which it is physically possible should occur; and that C, are circumstances which it is not physically possible should occur. Then according to [A] S and S' are logically equivalent to each other and t o the claim that in circumstances C,, F,. According to [B] S and S' are not logically equivalent because they make different claims about what would be observed in circumstances which it is not physically possible t o realise. [C], like [A], holds that the only observational evidence relevant to determining the factual content of a statement is evidence which it is physically possible to observe to hold. But an advocate of [C] may hold

Conventionalism About Space and Time 259 that while two statements S and Sf entail exactly the same observational consequences which it is physically possible to observe to hold-that in circumstances C,,E,--(and that no other evidence of observation is relevant), that evidence may nevertheless confirm one statement more than the other. This may be because one statement is simpler than the other (in postulating fewer entities, forces etc., interacting in a mathematically simple way), and thus provides a simpler explanation of the evidence; and simplicity is evidence of truth. In that case [C] holds that S a n d S' are not logically equivalent. [Dl holds that even if the only observational evidence relevant to determining the logical relations of the statements were the same, e.g. if F, and F; were the same, the two statements would still not be logically equivalent if there were any observable evidence (including evidence which it is not physically possible to obtain) which if it were obtained would confirm one statement rather than the other-e.g. on grounds of simplicity. Put loosely, [Dl says-two statements are logically equivalent if and only if there are no conceivable circumstances in which there could be any grounds for asserting the one rather than the other. Clearly [A], is a stronger criterion for logical equivalence than is [B], and also stronger than is [C], and both [B] and [C] are stronger than [Dl; a criterion being stronger in so far as it pronounces more pairs of statements to be logically equivalent to each other. His criterion of logical equivalence gives the conventionalist an easy method of proving a statement to be merely conventional. If one statement S is a conjunction of two statements T and Q, and a statement S', logically equivalent to S, is a conjunction of two statements T' and Q' when T is by its verbal form an apparent contrary of T' and Q of Q', then it is a matter of convention whether T or T' (Q or Q'). This is because if S is 'true', so is S', and conversely, and so then are both T and T'. If the 'truth' of T or T' were an objective fact, then it would rule out the 'truth' of the other. Hence the 'truth' of T must be such as not to rule out the 'truth' of TI, i.e. must be a matter of convention. Put another way T and T' must be incomplete statements, not statements which can be true by themselves. In the earlier example 'there are 2x men in this room' is an apparent contrary of 'there are x men in this room'. But in fact both statements are incomplete, and this is revealed by the fact that when another statement is added to each, the two conjunctions are logically equivalent. The conventionalist then claims that any statement concerned with ( I ) . . . (6) can always be combined with some other statement so as to get a conjunction logically equivalent to another conjunction including an apparent contrary of the original statement; from which it follows that the latter must be a matter of convention.

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Let us now see how this works in practice by considering how conventionalists argue for the conventionality of (6). They adduce the apparent facts, enshrined in the Special Theory of Relativity that light has a certain finite two-way velocity c (about 300,000 km/sec) relative to all inertial frames, and that no signal can travel faster than light. Now consider two points pl and p, on an inertial frame F. A light signal is sent from pl at time t, to p, where it arrives at t*, and is immediately reflected back to p, at which it arrives at t,. Let El be the event of its emission, E* of its reflection, and E, of it arriving back at p,. Since no signal can travel faster than light, E2 and E* are not connectible by a signal. Hence the argument goes, the hypothesis that E * occurs after E,, the

hypothesis that E* is simultaneous with E,, and the hypothesis that EX occurs before E, are all compatible with the observable facts. The first hypothesis combined with the hypothesis that the one-way velocity of light from p1 to p, is < c (and > c in the opposite direction); and the second hypothesis combined with the hypothesis that the one-way velocity in both directions is c both make the same prediction about when the signal will arrive back at p,. And a similar point applies to the third hypothesis. Further observable consequences-e.g. about readings on clocks moved from pl to p,-follow if we add hypotheses about how clocks are affected by transport (e.g. in having their rate speeded up or retarded). With different additional hypotheses added to each we can get all the same consequences which it is physically possible to observe from each of the original hypotheses. Hence, by verificationist principle [A], the alternative conjunctions are logically equivalent, since they hold in the same physically possible worlds. However, the component hypotheses about the temporal relations of E, and E* such as that E, is simultaneous with E*, are apparently contrary to one another. But they have no consequences which are physically possible to observe, by themselves. They are therefore mere matters of convention. Not merely this; but it may plausibly be urged, the alternative conjunctions of hypotheses would be equally well confirmed or disconfirmed by all factual claims which it is physically possible to observe to hold.

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It might seem that the hypothesis that E, is simultaneous with E" plus the hypothesis that light has the same one-way velocity in both directions, is simpler than its rivals, for it alone of the conjunctions of hypotheses which predict the observable facts postulates that light has the same one-way velocity in both directions. It might be urged that this simpler conjunction is, qua simpler, better confirmed by the evidence which it predicts, than its apparent rivals. If we said that E X was earlier than E,, we would have to say that the velocity of light varied with its direction, and that is a more complicated supposition. However, all these velocities are velocities relative to F. Light has the same two-way velocity relative to all inertial frames. And if we say that EXis earlier than E,, then although the velocity of light from p, to p, will then be different in the two directions relative to F, there will be an inertial frame moving with some uniform velocity relative to F relative to which light will have the same one-way velocity in both directions. So, generally any hypothesis about how (within the limits set by signal-connectibility) E" is simultaneous with, later than, or earlier than E, can be conjoined with a hypothesis of equal velocities in both directions relative to some inertial frame, to predict the observed evidence which I have set out. And, the argument goes on, there are no considerations of simplicity which lead us to prefer one inertial frame to any other, by which to measure velocities, for all inertial frames are on a par-for when velocities are measured relative to any inertial frame the laws of nature take their same simplest form. So each total conjunction is equally well confirmed by the stated evidence, and it is not physically possible to obtain more evidence to enable a choice to be made between them. Similar arguments would show that given the predictions of The Special Theory of Relativity, each total conjunction would be equally well confirmed or disconfirmed by other evidence. Hence by criterion [C], as well as by criterion [A], the component hypotheses about the temporal relations of E, and E" are mere matters of convention. This was the kind of consideration underlying Einstein's affirmation of the 'relativity of simultaneity' : So we see that we cannot attach any absolute signification to the concept of simultaneity, but that two events which, viewed from a system of coordinates, are simultaneous, can no longer be looked upon as simultaneous events when envisaged from a system which is in motion relatively to that system.l And so Einstein and the textbooks of Special Relativity suggest that we should think of E, and E X as 'simultaneous in F' and 'not simultaneous in F1,and 'absolutely' neither 'simultaneous', nor 'non-simultaneous'. Einstein [1905],p. 42 f. S

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So given that there are no more relevant observable facts than those predicted by the Special Theory of Relativity, the various claims about simultaneity turn out to be matters of convention by criterion [C] also. However, our universe is not one in which Special Relativity holds in a pure form on the cosmological scale; and cosmology may provide good scientific grounds for preferring one inertial frame of reference to another relative to which to measure velocities (i.e. the laws of cosmology may take a simpler form relative to one inertial frame than relative to others). I have myself argued elsewhere1 that there are such grounds; and that the frame by which velocities ought to be measured is the frame which has the mean motion of the galactic cluster in its neighbourhood. Yet if we ignore this point, we can admit that criterion [C] as well as criterion [A] makes (6) a matter of convention. Clearly however, there are always facts which it is logically possible to observe which would refute any of the alternative hypotheses about the temporal relations of E, and E". For it is at best a physical truth, enshrined in Special Relativity, that no signal can travel faster than light; and it is logically possible that one might be discovered which could so travel. It might then prove possible to refute the hypothesis that E* was earlier than E, by finding a signal which left p, at the time of E, and arrived at p, at the time of E*. And similarly for the other rival hypotheses. So [B], and a fortiori [Dl, do not declare ( 5 ) to be a matter of convention. Why should we adopt [A] or [C]? Why should not we say instead that there is a truth there-that E, is simultaneous with E*, or that it is later than E", or that it is earlier than E"; and although (probably) it is not physically possible to discover what the truth is, or to have any evidence favouring one of the rival hypotheses over others, it is no matter of convention what the truth is. Salmon claims that Reichenbach held that 'statements have the same meaning if it is physically impossible to get evidence to discriminate between them-i.e. to confirm the one and disconfirm the other'., Salmon follows him in suggesting that we should judge a convention to be 'non-trivial' if it arises out of a physical rather than a logical impossibility of verification. But why should the physical impossibility of obtaining evidence to choose between two hypotheses show that they are not really See Swinburne [1968], chapter I I . Salmon [1969], p. 61. For Reichenbach's most developed view on this matter see Reichenbach [1g53]. While indeed he here (p. 97) "advocates a definition of meaning in terms of the physical possibility of verification", he makes the odd claim that "meaning is a matter of definition" and so that alternative (but in his view less useful) definitions of meaning, e.g. in terms of the logical possibility of verification, can be given. This has the strange consequence that it is a matter of convention whether something is a matter of convention or a matter of fact.

Conventionalism About Space and Time 263 in conflict. The grounds which the old-style logical positivist (outside the philosophy of science context) gave for tying meaning to possibility of verification concerned meaning being concerned with what we could conceive ourselves observing, i.e. the logical possibility of observing. The stronger criteria have the consequence that physics in showing what is physically impossible, shows that statements which looked as if they were not logically equivalent, really are. But how can a physical discovery show that sentences do or do not have some meaning or logical relation? Surely it is a linguistic, not a physical matter (not something to be discovered by connecting two wires in a laboratory), what a sentence means or what its logical relations are. If we do go along with the stronger criteria in this case, we have to say the kind of thing which Einstein said in the quotation given above; and if we adopt criterion [A] we have also to say that the factual meaning of a total conjunction of hypotheses of this kind just is the conjunction of its observable consequences, e.g. it is a statement about signal connecability and so forth. But intuitively statements about simultaneity are statements which may or may not be established by sending signals, but they concern something else. I t seems to be very central in our thought about time that if t, is between t, and t, and E* occurred between t, and t,, then either E* occurred before t, or it occurred after t, or it occured at t,. There seems no good reason for not sticking by this way of thinking and saying that all that Special Relativity shows is that nature contains more secrets (viz. about simultaneity) than man can ever discover. I turn now to (2), (3) and (4). I shall discuss only (3), but it will readily appear that exactly the same points can be made with respect to (2) and (4). (2) and (3) are closely connected. If (2) is a matter of convention, so is (3) (for a different metrical geometry entails different measurements of distance, although the converse does not hold). (4) is concerned with the claim about time analogous to that made by (3) about space. Now it looks as if not merely criterion [A], but criterion [B] as well, declare these to be matters of convention. For consider two geometrical theories of congruence (such as (3) is concerned with), one that CD is congruent with A B (i.e. CD = AB) and the other that CD is congruent with 2AB. I find a wooden rod, one end of which coincides with A when the other coincides with B. I then move one end to C, and holding it there, make the other end coincide with D. Both theories remain compatible with the facts. For we can add to each a further theoretical component-to theory one, that the rod and all other measuring devices are unaffected by transport, and to theory two that the rod and all other measuring devices are doubled in size by transport. Only from such total (geometrical plus physical)

264 Richard Swinburne

theories do predictions arise. Any geometrical theory G about congruence between different distances (subject to the restriction in (3)) can be combined with a physical theory P so as to yield all the same consequences which it is logically ~ossible to observe, as an apparently contrary geometrical theory G' with an apparently contrary physical theory P'. Hence by [A] and [B] (G plus P ) is logically equivalent to (GI plus P'); and so G by itself and G' by itself are matters of convention. T h e first difficulty here is that one of the (geometrical plus physical) theories may be not merely incompatible with observations but internally incoherent. For Griinbaum the meaning of 'congruent' (i.e. 'of the same length') is simply that of a 'spatial equality . . . predicate' determined by 'the axioms of congruence' (i.e. axioms which state the logical relations which hold between different statements about length)'; and also by the constraint that two rods which coincide at a place are congruent at that place.2 However, it seems plausible to suppose that as they are ordinarily used the meaning of such terms is fixed not merely by their logical relations and the rules for applying them to coincident bodies but also by other standard cases of their correct application, e.g. that a wooden ruler moved from one side of my room to the other, which preserves congruence relations with other standard measuring rods (and so is not distorted by differential influences, i.e. influences such as heat which expand rods of different material to different degrees) is said to remain approximately 'of the same length'. I n general, one may say, making a similar point about (4), the meaning of talk about the 'length' of temporal and spatial 'intervals' is given in part by these standard cases of correct application of such talk. And if that is so, claims that ordinary mundane objects which preserve congruence relations among themselves suddenly double in length when moved short distances seem incoherent; since they seem to violate the criteria for correct application of such terms.3 Hence any physical theory which embodied such claims would be internally incoherent. If that is right, the fact that all standard measuring devices which coincide with A B coincide with CD would entail the fact that AB is approximately congruent with CD (and so AB # 2CD). In reply Griinbaum may claim that he is using 'congruent' in the 'modern scientific sense' in which the logical relations (plus rules for applying them to coincident bodies) alone determine meaning. But then we may reply that the initially interesting conventionalist claim (3) is no longer as interesting

' Griinbaum [1964], p. 27. 3

This constraint is implicit in all his writing, although he does not spell it out explicitly in the cited passage. I argue this in my [1968], pp. 95 ff., and also in my [1970].

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as it at first seemed to be. Alternatively a conventionalist may reply that his claim concerns large distances in space, where paradigm cases do not dictate correct answers. Let us so understand him, and let us sec what more can be said about his claim in response to this defence. Criteria [ A ] and [B] both pronounce the two conjunctions of geometrical and physical theories logically equivalent. Whatever observable the one conjunction entails, the other entails; and this is not merely a physical but a logical truth. I t is not merely physically impossible but logically impossible to check by conclusive observations whether all rods and other measuring devices moved to some distant region double in size. But criteria [C] and [Dl give no clear answer as to whether the two theories are logically equivalent. I t might seem quite obvious to the anticonventionalist that the two theories differ in simplicity (the universal expansion theory being highly ad hoc and so complex)'; and that as simplicity is evidence of truth, the simpler theory is better confirmed by evidence. But even granted that in this kind of case, simplicity is evidence of truth, the argument begs the question by assuming that there are here two different theories which differ in simplicity. Maybe the difference of simplicity is only a difference in respect of two formulations of the same theory and if so, simplicity would not be evidence of truth. (If Heisenberg's matrix mechanics is just another way of formulating Quantum Theory to Schrodinger's wave mechanics, then even if Heisenberg's mechanics is more complex than Schrodinger's that does not show that it is less likely to be true.) The conventionalist who uses either of criteria [C] and [Dl to justify his position typically also begs the question. He admits that often when the same set of observations is predicted by two rival theories, the observations may make one theory more probable than the other. If they both predict the observations with equal accuracy, one may be simpler than the other and for that reason more likely to be true. Compatible with any finite number of data, there will be an infinite number of theories agreeing in their predictions of the data so far, but differing in their predictions for the future. Of these we judge the simpler theory and its predictions more likely to be true. This well worn point2 was admitted in a limited way even by Reichenbach. But Reichenbach distinguished between 'inductive' and 'descriptive' simplicity. He admitted simplicity as a criterion of choice between theories which agreed in their predictions

' I assume here that there is no background physical theory with which the hypothesis of universal expansion fits better than does its rival. If there was a relevant background physical theory, it is the simplicity of it plus any new hypothesis which is relevant, not the simplicity of a new hypothesis on its own. "ee (e.g.) Jeffreys [1g73], pp. 61-4.

266 Richard Swinburne of observations made so far but differed in their predictions of subsequent observations (e.g. different theories about the paths on which a planet was moving, equally compatible with the positions so far observed). This kind of simplicity he called 'inductive simplicity'. But when there was no difference between two theories in the observations which they predicted, yet one was simpler (in the observable entities, properties, relations etc. which it postulated) the difference between them was, he said, a matter of 'descriptive simplicity'. (z), (3) and (4) are certainly on that definition cases of difference of descriptive simplicity. Then, Reichenbach claimed, inductive simplicity is, descriptive simplicity is not, evidence of truth. But why suppose that? Reichenbach did suppose that because he held that being equivalent in respect of observable facts was the same as being equivalent in respects of all facts1 But that is an assumption which begs all the questions; it is in fact criterion [B] (or perhaps [A]). So, if we appeal to weaker verificationist criteria, we do not seem to be able to solve the issue of whether (z), (3) and (4) are matters of convention. Criteria [A] and [B] will solve the issue. We have seen no good grounds for adopting criterion [A]. What of criterion [B]? [B] has a simple doctrine-a theory is logically equivalent to the conjunction of its consequences which it is logically possible to observe. This does not seem at first sight very plausible. (a) 'all swans are white' seems not to be logically equivalent to (a') 'all swans so far observed and to be observed in future are white'. (b) 'material bodies continue to exist . . when unobserved', seems to be saying something contrary to (b') 'material bodies exist only when observed', even if we add to each such auxiliary hypotheses that their observable consequences are the same. Likewise (c) 'a volume of carbon dioxide consists at all times of a large finite number of molecules, each of which consists of one atom of carbon and two atoms of oxygen', seems to be saying something contrary to (c') 'However small a quantity of carbon dioxide you distinguish, it consists of qualitatively identical matter, but it changes its nature when it enters into chemical interaction or interaction with some measuring apparatus', even when appropriate auxiliary hypotheses are added. I conclude that the stronger verificationist criteria are not at first sight very plausible, and that the weaker ones will not allow us to settle whether (2)' (3) and (4) are matters of convention. ( 5 ) is in just the same situation as (2)' (3) and (4). Reichenbach illustrates his claim that ( 5 ) is a matter 'See Reichenbach [1g38]. He writes (p. 374), 'There are cases in which the simplicity of a theory is nothing but a matter of taste or of economy. These are cases in which the theories compared are logically equivalent, i.e. correspond in all observable facts'.

Conventionalism About Space and Time 267 of convention by his famous story of the spheres.' He imagines a world in which a man finds himself on a huge spherical surface, on which is situated his study. Having explored it all over, he finds a trapdoor in it and discovers another sphere below it, completely enclosed by thc first sphere. He explores this second sphere thoroughly, and then penetrates it to find a third sphere. Eventually he comes to a fifth sphere which measurements with his rod reveal to be of the same size as the first sphere and on which he finds the geography in all respects qualitatively similar to that of the first sphere. He even finds a room qualitatively similar to the study which he left behind. T o ascertain whether this room is his study, he writes a message, locks it in a drawer, passes back through the spheres to the first sphere and finds a qualitatively similar message in his study drawer. Are the two studies and so the two spheres numerically identical or merely qualitatively similar? If they are numerically identical, then space has a non-Euclidean topology. But if they are different, space may be Euclidean; and in that case there is causal action at a distance and all goings-on on sphere I are replicated on sphere 5 (and sphere 9, 13, and so on ad injinitum). According to Reichenbach, N (the claim that space has a certain non-Euclidean topology) plus P (some claim about the behaviour of bodies, including the claim that to some extent bodies preserve their appearance and that goings-on are not replicated) is logically equivalent to E (the claim that space has a Euclidean topology) plus G (some claim about the behaviour of bodies, including the claim that goings-on are replicated). Hence N by itself or E by itself are mere matters of convention. Reichenbach's story is meant to illustrate the general thesis that you can make any claim you like about the topology of physical space, so long as you are prepared also to make claims about strange physical forces complicating effects. Now, as with congruence claims, it does seem not merely physically, but logically impossible to make observations entailed by one of such conjunctions of geometrical and physical theories and not by the other. So not merely criterion [A] but criterion [B] declares (N and P ) to be logically equivalent to ( E and G), and so N and E by themselves to be matters of convention. However, the hypothesis of replication looks complex, and it is natural to urge that, qua simpler, ( N and P ) is more likely to be true than ( E and G); and so that the evidence of observation which both conjunctions entail confirms the former more than the latter, and so the criterion [C] declares them not to be logically equivalent. More generally, it may seem that there will always be physically possible

' Op. cit. section 1 2 .

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observations such that if you are to save some geometrical hypothesis in the face of them, you need so to complicate your physics that it becomes implausible. It looks as if criterion [C], and so a fortiori criterion [Dl, declare (5) not to be a matter of convention. But an opponent may always urge that this is begging the question by assuming that conjunctions such as (N and P) and (E and G) are different theories; for simplicity is only a criterion of choice between theories which are not logically equivalent. The implausibility of criteria [A] and [B] as criteria of logical equivalence, and the fact that criterion [C], and a fortiori criterion [Dl are of little use, suggests that verificationist criteria are of no use for settling whether statements are logically equivalent, and so settling whether (z), (3), (4) and (5) are matters of convention. I do not know of any other general principle which will settle the issues quickly.' All that can be done, I suggest, is to spell out in detail how a Universe in which one conjunction of theories held would differ from a Universe in which an alternative conjunction of theories held; and thereby show that really the two Universes are the same or that really they are different. Thus, one example of a Universe in which one conjunction of theories of type (3) held would be a Universe in which the distances between galaxies at a given cosmic time increase as you get further away from the Earth but there are physical forces at work which expand rods to a similar amount, and increase all two-way signal velocities also so that this is not noticed. One can continue spelling out the nature of these forces, and how actual distance differs from measured distance. By contrast a Universe in which the other conjunction of theories holds would be a Universe in which the distances between galaxies are at a given cosmic time approximately the same, measuring rods are not subject to expanding forces etc. As the Quine [1975] has suggested a test of a non-verificationist kind for determining whether two theories which predict the same observations are logically equivalent. T h e test, roughly, is that two theories are logically equivalent if we can get the one from the other by substituting predicates throughout. T h u s our present theory of physics and chemistry is logically equivalent to one obtained from that theory by replacing all occurrences in it of 'electron' by 'molecule', and all occurrences of 'molecule' by 'electron'. However, as Quine states, this test is concerned only with predicates which (p. 319) 'do not figure essentially in any observation sentences'. But theories normally contain a large number of terms which do occur in observation sentences-e.g. 'contains', 'is composed of', 'particle', 'wave' and in our examples 'distance', 'length', 'moves' and 'at rest'. Whether these terms occur 'essentially' raises a host of difficulties which are no easier to solve than our original difficulties. Quine has no doubt provided a sufficient condition for logical equivalence, but it is in no way obvious that he has provided a useful test, let alone that he has provided a necessary condition for logical equivalence. He admits that in practice there are great difficulties in applying his test. T h e real difficulty is that theories use terms with extra-theoretical meaning (as they must, if they are to be informative) and it is far from clear to what the use of these terms commits a speaker.

Conventionalism About Space and Time 269 spelling-out goes on, it may clearly click that the Universes differ or that they are the same. That may seem feeble, but is not all argument an attempt to settle something questionable by appealing to something more obvious? This is merely a case of that. It might be thought that the logical equivalence of the two Universes (and so the conventionality of (3)) could be proved by showing that the affirmation of existence of a Universe of one kind and the denial of the existence of any Universe of the other kind generated a contradiction. And indeed so it could. But I cannot see how to prove that there is a contradiction until you have proved by some other method (e.g. my feeble spelling out) that there is no difference between the two Universes. For myself, I can only find that this attempt to spell nut a difference between alternative theories in this field fails, and that I cannot make any sense of the supposed distinction between distance and what would be measured by actual rods. (5) on the other hand I find different. There does seem to me to be a clear difference between a non-Euclidean universe (N,) and a Universe with Euclidean geometry in which all effects are replicated (El). I can try to make this clear to someone who does not see the difference by spelling out what is involved in the latter. I ask him to consider another Euclidean universe of nested spheres (E,) in which effects on Sphere I are replicated in almost every detail in Spheres 5, 9, 13 etc., but not quite. Such a universe would be entirely different in character from the non-Euclidean universe Nl in which you reach Sphere I again by passing from Sphere I through spheres 2, 3 and 4. But the universe El in which effects were perfectly replicated would only be very slightly different from E,. So El could not be the same as Nl. In this way I try to draw a contrast between Euclidean and non-Euclidean universes. Others may not accept that I have succeeded in making a contrast, but in that case all that can be done is to go on drawing out the differences and similarities until it does click that the universes are the same or different. Whether or not there are real distinctions to be made between different kinds of relevant Universe, and so whether ( z ) , (3), (4) and (5) are matters of convention is something which can only be shown by detailed spelling-out of what the alternatives amount to-and the process may not immediately lead everyone to the right conclusion. The arguments here may be correct without being immediately persuasive. (I) is in a different position from (z), (3), (4) and (5) in that not merely can criteria [A] and [B] be deployed to show it to be a matter of convention, but criterion [C]clearly can as well. For it follows from the Special Theory of Relativity, as from Newtonian mechanics, that there will be no observable phenomena which are more plausibly explained by supposing

270 Richard Swinburne that a body is at rest relative to an absolute rest frame than by supposing that it is in uniform motion relative to that frame. This is because Special Theory plus the theory that a body B is in motion relative to an absolute rest frame predicts exactly the same consequences as Special Theory plus the theory that B is at rest relative to that frame, and neither conjunction of theories is simpler than the other. Hence, even if we can talk of an absolute rest frame and so of absolute rest and motion, the two theories that B is in absolute motion and that B is at rest absolutely will be equally well confirmed or disconfirmed by all factual claims which it is physically possible to observe to hold,l and hence by criterion [C] they are the same theory. However, it is logically possible that there be observable phenomena incompatible with Special Theory which are most plausibly explained by It could be that M plus the theory that B was in a rival physics absolute uniform motion yielded different observable consequences from the consequences predicted by M plus the theory that B was at rest absolutely; that these latter consequences were observed, and that the only way to save the theory that B was in absolute motion was by making M into a more complex theory M'. (M plus the theory that B was absolutely at rest) might predict all the observations which it was logically possible to make, as did (M' plus the theory that B was in absolute motion). Yet because M was simpler than M', one might claim that the observations confirmed the former conjunction more than the latter, and so that these were not logically equivalent (and so that ( I ) was not a matter of convention). But this argument already assumes what it seeks to prove-that the conjunctions of theories are different-for otherwise no evidence would confirm one against the other. We are back with the same difficulty as with (2), (3), (4) and ( 5 ) . It remains the case that there is no knockdown proof that the rival theories are the same, even if you adopt the weakest verificationist criterion. Again the only way to settle things is to spell out in detail what it would be like for each of the conjunctions to hold, and see if they obviously describe different states of affairs. For myself I now find it difficult to see that they do-whatever the M or M', for I cannot make scnse of the suggested contrast between the alternatives 'B is at rest absolutely' and 'B is in uniform absolute motion', unless these are added to physical theories which give content to the 'absolute'. I cannot understand what is meant by saying that something is moving, unless it is implied or stated relative to what it is ' A similar conclusion also holds if we consider not Special Theory, but the modern cosmology of the Robertson-Walker line element. See Swinburne [1968], p. 59 f. See Swinburne [rg68], p. 65 f. for a development of such a physics.

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moving. Certainly there may be a substance such as the aether filling all space, and thus a difference between bodies which move relative to the aether and bodies which do not. But the moment such a substance is given as the relatum of motion, the question can be asked whether it is moving absolutely or not; and its absolute motion cannot be just motion relative to something in space. (For if it were, we could raise the question about the motion of that something.) And even if space itself is a substance in some sense, I just cannot understand the differences between a body which moves relative to it and a body which does not. But this may be simply the result of a lack of philosophical insight on my part, and maybe more detailed spelling out of the hypothesis would reveal to me the difference. I do not wish to deny that there is a difference between uniform motion relative to an inertial frame, and acceleration relative to an inertial frame. Nor that (if the laws of nature were different) there could be, for all F and F' when F' is in motion relative to F, an observable difference between the laws governing the behaviour of bodies when in motion relative to F and the laws governing their behaviour when in motion relative to F'. I am merely denying that an explanation of this difference in terms of F being at rest 'absolutely' describes a state of affairs intelligible without a physical theory about 'absolute motion' to give meaning to this otherwise empty notion. The main point of this paper was not however to solve the problems of whether ( I ) , (z), (3), (4), ( 5 ) and (6) are matters of convention. It was rather to point out that if you attempt to solve them as conventionalists always have done by an appeal to verficationist criteria you would need some implausibly strong criteria to show any of them to be matters of convention; that weaker verificationist criteria show (6) not to be a matter of convention, but do not settle matters for (I), (z), (3), (4) and ( 5 ) ; and that the only way to settle the status of these is by the non-verificationist method of careful spelling-out of alternatives, which does not allow things to be settled by quick knock-down arguments. University of Keele REFERENCES

A. [19oj]: 'On the Electrodynamics of Moving Bodies', in H. A. Lorentz EINSTEIN, et al. (ed.) The Principle of Relativity: London, Methuen and Co., 1923. A. [1964]: Philosophical Problems of Space and Time. London: Routledge GRCNBAUM, and Kegan Paul Ltd. GRUNBAUM, A. [1970] : 'Space, Time and Falsifiability, Part 1', Philosophy of Science, 37, 469-588. JEFFREYS,H. [1973]: Scientific Injerence, Third edition. Cambridge: Cambridge University Press.

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QUINE, W. V. 0. [197j]: 'On Empirically Equivalent Systems of the World', Erkenntnis, 9, 3 13-28. REICHENBACH, H. [1938]: Experience alzd Prediction. Chicago: University of Chicago Press. REICHENBACH, H. [19j3]: 'The Verifiability Theory of Meaning', in H. Feigl and M. Brodbeck (eds.), Readings in the Philosophy of Science. New York: AppletonCentury-Crofts. (Republished from Proceedings of the American Academy of Arts and Science, 195I, 80.) REICHENBACH, H. [1958]: The Philosophy of Space and Time. New York: Dover Publications. SALMON, W. C. [1969] : 'The Conventionality of Simultaneity', Philosophy of Science, 36, 44-63. R. [1968]: Space and Time. London: Macmillan and Co. SWINBURNE, SWINBURNE, R. [1970]: Review of A. Griinbaum, Geometry and Chronometry in Philosophical Perspective, British Journal for the Philosophy of Science, 21, 308-1 I.