On Physicalistic Models of Non-Physical Terms Gustav Bergmann Philosophy of Science, Vol. 7, No. 2. (Apr., 1940), pp. 151-158. Stable URL: http://links.jstor.org/sici?sici=0031-8248%28194004%297%3A2%3C151%3AOPMONT%3E2.0.CO%3B2-T Philosophy of Science is currently published by The University of Chicago Press.
Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/about/terms.html. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://www.jstor.org/journals/ucpress.html. Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission.
JSTOR is an independent not-for-profit organization dedicated to and preserving a digital archive of scholarly journals. For more information regarding JSTOR, please contact
[email protected].
http://www.jstor.org Fri May 18 08:18:56 2007
O n Physicalistic Models of NonPhysical T e r m s BY
GUSTAV BERGMANN
OME of the objections most frequently raised against the thesis of physicalism can be summarized as follows: (V) The notions of the biological and social sciences, as e. g. organic whole and Gestalt, means and ends, leadership and hierarchical order, the entire structure and meaning of these scientific systems, are of a type essentially different from those of physics. Consequently they can not be expressed by means of the mathematical language used by physics, and it is "logically impossible" to reduce these sciences to physics. To analyze the scientific meaning of this statement, let us first restate the thesis of physicalism: (P) Any observable process is describable in terms of physics. In this context "physics" means the scientific system language, the most general rules of which are at present given by relativity and quantum theory, and by virtue of the latter it includes, a t least in principle, what is usually known as chemistry. "Describable in terms of physics" however has two possible meanings, viz: ( I ) physical description of the syndromes or symptoms necessarily coordinated (directly or indirectly) to any meaningful construct in any science, (e.g. psychology) without the 151
1.52
On Physicalistic Models
possibility of reducing the laws of the science in question (e. g. the laws of psychology) to those of physics; or (2) the possibility of deriving the laws of any science from the laws of physics. According to this analysis, two possible meanings, P ( I ) and P(2) of (P) have to be distinguished. I t has been repeatedly pointed out, especially and most clearly by Feigl, that P ( I ) is equivalent to the thesis of empiricism; therefore a recent suggestion also made by Feigl in a still unpublished paper,* to restrict the use of the term physicalism to P(z) seems amply justified. In this paper the meaning given to (P) is always P(2). At the present state of affairs, P(2), as well as its negation, obviously is a prognosis. I t should be realized, however, that (V)also can be interpreted as a meaningful prognosis as to the formal character of still undiscovered "physical" laws, thus somewhat specifying the meaning of the negation of P(2). This has been most lucidly shown by Carnap in his analysis of the possible meaning of vitalism. In his above-mentioned paper, Feigl has elabcrated and supplemented this study by an analysis of the related problem of emergence. So far the discussion seems closed, in spite of the fact, that as far as empirical prognosis is concerned, our ideas are largely determined by the same emotional forces which rule our attitude towards their more "philosophical" representatives. I n this context only one remark should be made: Suppose that psychotherapy and "brain physics," both equally advanced, will be able to achieve certain therapeutic effects, each by its own means, the one by verbal treatments, the other by the application of electro-magnetic fields or the administration of certain drugs. In this case, the belief that the physico-therapeutic treatment will be a prior; preferable, would belong to the emotional background of the physicalistic thesis and not to its scientific content. But physics being what it is a t present, logical analysis might still be able to make a contribution by pointing out one more * To appear in the Journalfor
Unified Sciencc.
G. Bergmann
I53
possible meaning of (V). P u t on the linguistic level, (V) implies : (V') Within the (mathematical) system language of (theoretical) physics, one can not define terms corresponding to the terms of the non-physical sciences (in short: nonphysical terms). In this statement "correspondence" means: isomorphism as to the syntactical rules. The mathematical form of the physical system language is apparently of great importance for this interpretation. Therefore it might be of some interest to give at least one mathematical modelfor a non-physicalterm. Such a model might be enormously simplified and only partially cover the meaning of the term it is intended to represent. Yet it could still furnish some indication as to the type of mathematical relations which correspond to the non-physical terms. Below an attempt is made to construct such a model and a suggestion as to the type of mathematical structures corresponding to the terms in question is derived from it. But let me first make a few more general remarks. As it goes with outsiders in any science the non-mathematician's knowledge of mathematics is necessarily limited, but in mathematics this restriction is much more marked than in any other field. (Given for instance an equation system, "mathematics" means for almost everybody the series of transformations leading to the "solution" of the given system.) Actually, however, the bulk of mathematical theorems deals with more "general" problems, as, e.g. : which relationships within the solving system can be deduced from certain relationships within the given system; how is the solving system affected by a certain class of transformations, if operated upon the given system; and so forth. And it seems to be this latter type of "structural" properties of the describing systems which corresponds to the non-physical terms. If this holds true, one might also be able to locate the origin of that feeling of "higher dignity," of "specific meaning" so often claimed for the biological and social sciences. For propositions about relations between properties of equation systems are linguistically on a different level than the transformations leading
On Physicalistic Models
to the "solution" of such systems, and the laws of the non-physical sciences would not be anything else but relations between such properties of the equation systems occurring in the description given by theoretical physics. On the other hand the "meaning" of a non-physical term A could be interpreted as the class of properties and relations derivable from the corresponding mathematical property A' for the most general type of systems to which the property A' can be attributed. This is but an obvious application of Carnap's definition of "content."' Finally it should be emphasized that the line of thought followed in this paper is a straightforward application of Koehler's concept of isomorphism on the level of language analysis. Let us now consider the motor of a car. A pressure on the accelerator produces a change in speed, but if such a change in speed is brought about by some processes inside the motor, it is not followed by a corresponding change in the position of the accelerator. The accelerator and the man who operates it control the machine but the machine does not control the man. This one-wayness is held to be essential for the extra-physical, social aspect of the machine as a tool, and this very one-waydirectedness is also supposed to be at least one characteristic trait of any means-end relation, or, to put it still more psychologically and anthropomorphically, of any purposive or hierarchic order. According to (V'), it should therefore elude any attempt a t expression, if one limits oneself strictly to the language of the equations describing the functioning of the "machine." I t might be helpful to consider a simpler apparatus, the elaboration of an idea once used by Zilsel2 in a similar context. The apparatus consists of three parts: I . An oversaturated solution of a salt, 2. A device subjecting the temperature of the solution to slow periodical changes. As the temperature goes up and down It might be that this interpretation covers also a possible meaning of "conceptual properties of constructs", a term frequently used by Lewin in his works on theoretical psychology. E. Zilsel, Die Naturwissenschaften, 15, 1927, p. 280f.
G . Bergmann
I55
the concentration of the oversaturated solution changes, and so does its density. 3. A densimeter vertically suspended in the fluid and an apparatus pressing it down vertically in certain time intervals. Otherwise the densimeter is free; therefore, if no pressure is exerted upon it, it shows the "true density" of the solution. When immersed by the mechanism, however, the "scale density" shown differs from the "true density" of the solution. The pressing mechanism can be thought of as a part of the densimeter, for instance as a gas volume of changing pressure with the densimeter proper as a piston. The whole system has the following properties: parts I and 2 (corresponding to the accelerator in our previous example) control part 3 (corresponding to the motor), but the pressing mechanism inside part 3 has no effect upon the other parts, only the "scale density7' becomes "wrong," while it works. Thus we have also a model of the type of connection between a recording instrument and what it measures, between the sign and the designated. Let now be
the system of m independent equations with n variables that is the physical description of our apparatus. Simplification is pushed so far, that there is no distinction made for the timevariable, and the fact that one has most frequently to deal with differential equations is likewise disregarded. Let x, be the "true density" xl the "scale density." Let us furthermore assume that those rather general mathematical conditions, under which the following well-known theorem (Th) holds, are fulfilled within the range of the variables necessary for the description of the apparatus. (Th) If one selects arbitrarily any n-m variables, e.g. x,+~, . . ., xn out of the series of n variables XI, xz, . . ., x,, the
On Physicalistic Models remaining m variables, e.g., XI, . . . xmcan be represented as functions of the n-m variables arbitrarily chosen:
and the system (2) is equivalent to (I). Without further assumptions, the "dependent variables" on the left side of (2) depend really upon all the "independent variables" on the right, i.e. any change of any independent variable affects each dependent variable, and this holds true for any of the
(i) possible choices of independent variables.
It i s
a property of system (I), if a choice, for which this is not the case, exists. Let us assume that for system (I) xl, x2 . . ., xn-, is such a choice, and that in (2') xn depends only upon the variables X2,
. . . Xn-m:
I t is likewise a property of ( I ) if the inverse relation between XI and x, does not exist, i.e. if there is no representation (2"), where XI on the left would not actually depend upon x, on the right. But with the meaning given above to xl and x,, it is easy to see that these two "structural" properties of (I) together correspond to the controlling-controlled relation between the parts of the apparatus. The very simple device to get this result was, besides a mathematical truism, the inclusion of the "man on the wheel" in the model. I t is obvious and therefore hardly worth mentioning, that the above used properties of ( I ) can also be interpreted as a mathematical model of Gestalt within the described physical system. Here the ambiguous term Gestalt (see its analysis by Grelling and Oppenheim, Erkenntnis, 7 , 1938, p. 211) is to be understood in its second meaning as "Wirkungssystem" (system of inter-
G . Bergmann
I57
action). If, for instance, in a large system ( I ) the variables can be separated in several sub-groups, so that the variables of any sub-group depend only upon each other, we deal actually with several independent systems, with a "sum of wholes." Within one such Gestalt, various degrees and types of interconnectedness may correspond to properties of the model like that formulated in (2'). Again, the following structure of (2')
suggests itself as a model of the partial interdependence of Gestalten. Let us finally mention another problem, the difference between proximal and distal determination, or, as it is sometimes formulated, between teleology, the allegedly exclusive realm of nonphysical conceptualisation, and "mechanical" causality, the field of physics and its mathematical language. For psychology, the issue has been thoroughly discussed in a recent paper by Heider.8 As a matter of fact, one could hardly think of a better way to explain its meaning than by closely following the solution of a differential equation, for instance the computation of the movement of an elastic string with both ends fixed. Neither the fact that the ends are immovable nor their distance, the length of the cord, intervene in the formulation of the differential equation. Only the locally acting force and the density of the material, both "proximal determinants," appear in this step. This equation, however, has an infinite manifold of solutions. Hence, to determine those solutions which satisfy the boundary conditions, one has to introduce the length of the string as a "distal determination." Thus one gets the frequencies as a function of both, the local and the distal constants. As far as teleology proper is concerned, the time element has again been disregarded in this a F.
Heider, Psychological Reuiew, 46, 1939,p. 383-410.
On Physicalistic Models
well-known and uncomplicated example. But this does not affect the only essential trait of the mathematical model, viz. the fact, that both proximal constants, e.g. the coefficients of a differential equation, and distal constants, the "boundary conditions," e.g., the state of the system a t a given (future) time, determine the solution of even the simplest differential equation. So there seems to be an abundance of mathematical properties exhibiting the same pattern as the terms of the biological and social sciences, and which, therefore, if attributed to the describing equations of physics and properly identified, may yield a "translation" of the terms and laws of these sciences. At least there is no reason why what is conceivable in a model could not also be realized in fact.
State University of Iowa.
