Abstract
Carnap’s treatment of theoretical terms involves, first, his conception of them as being only “partially” interpreted, second, his use of the Ramsey sentence on behalf of this conception. (The latter, in particular, has been insightfully examined recently by Bill Demopoulos.) Carnap’s treatment has not satisfied either instrumentalists (like van Fraassen) or realists (like Stathis Psillos). (It has also not satisfied Demopoulos.) I argue that the place of Carnap’s views on theoretical terms within his general project of Wissenschaftslogik has been misunderstood, and the full force of his uniquely anti-metaphysical conception has not been appreciated.
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- 1.
See Psillos (2000, pp. 153–154). This chapter includes Carnap’s previously unpublished lecture, “Theoretical Concepts in Science,” delivered in Santa Barbara on December 29, 1959
- 2.
Carnap announces the replacement of traditional philosophy by the new discipline of what he calls Wissenschaftslogik (the logic of science) in The Logical Syntax of Language (§72): “Wissenschaftslogik takes the place of the inextricable tangle of problems known as philosophy.”
- 3.
As Martin Gardner explains in his Forward to the second edition (1974, pp. v–vi): “In response to a friendly letter from Grover Maxwell , Carnap agreed (shortly before his death in 1970) that his all-too-brief comments on the conflict between instrumentalism and realism, with respect to the nature of scientific theory, be clarified. With this in mind, he made certain alterations on the two pages [255–256], and added a new footnote referring to a 1950 paper which gives his views in more detail.”
- 4.
- 5.
This point is first emphasized in Demopoulos (2003, § 5).
- 6.
The connection between this remark and contemporary structural realism will become clearer below: see note 23 below, together with the paragraph to which it is appended.
- 7.
For the case of quantum mechanics, in particular, see Carnap (§ 25, 210–211): “If we demand from the modern physicist an answer to the question what he means by the symbol ‘ψ’ of his calculus, and are astonished that he cannot give an answer, we ought to realize that the situation was already essentially the same in classical physics. There the physicist could not tell us what he meant by the symbol ‘E’ in Maxwell’s equations. […] An ‘intuitive understanding’ or a direct translation of ‘E’ into terms referring to observable properties is neither necessary nor possible. The situation of the modern physicist is not essentially different. He knows how to use the symbol ‘ψ’ in the calculus in order to derive predictions which we can test by observations. (If they have the form of probability statements, they are tested by statistical results of observations.) Thus the physicist, although he cannot give us a translation into everyday language, understands the symbol ‘ψ’ and the laws of quantum mechanics. He possesses that kind of understanding which alone is essential in the field of knowledge and science.”
- 8.
- 9.
Demopoulos (2008, note 17, pp. 374–375) points out that Hempel is far from suggesting this explicitly. So perhaps it is better to say that Hempel’s discussion appears to suggest to Carnap that the Ramsey sentence is inductively superior to the Craig re-axiomatization (see the discussion below).
- 10.
Demopoulos (2007) provides an outstanding discussion of the motivations for Carnap’s view of theoretical terms and its relationship, in particular, with the Hilbertian axiomatic method. In the course of his discussion, however, Demopoulos criticizes Carnap’s use of the Ramsey sentence for requiring only the existence of an appropriate mathematical structure—which, as Demopoulos shows, is “almost analytic” in so far as it logically follows from the totality of the observational consequences of the theory together with a cardinality assumption (a version of the Newman problem: see note 4 above). Carnap’s own view, however, is that the synthetic content of a theory does not exceed its empirical content, and he aims to defend this view, moreover, against the metaphysical excesses of both realism and instrumentalism. Demopoulos, from this point of view, appears to be relying on a fundamentally realist intuition about what the (synthetic) content of a scientific theory should be taken to be.
- 11.
Carnap makes this clear in Philosophical Foundations of Physics (1966/1974, pp. 253–254): “Ramsey certainly did not mean—and no one has suggested—that physicists should abandon theoretical terms in their speech and writing. To do so would require enormously complicated statements. For example, it is easy to say in the customary [realistic] language that a certain object has a mass of five grams… . [But] the translation of even this brief sentence into the Ramsey language demands an immensely long sentence, which contains the formulas corresponding to all the theoretical postulates, all the correspondence postulates, and their existential quantifiers… . It is evident that it would be inconvenient to substitute the Ramsey way of speaking for the ordinary discourse of physics in which theoretical terms are used [, … so that] physicists find it vastly more convenient to talk in the shorthand language that includes theoretical terms, such as ‘proton’, ‘electron’, and ‘neutron’.”
- 12.
Demopoulos (2008, § 5) defends Carnap’s attribution of analyticity to the Carnap sentence—making use of Winnie (1970)—by arguing that the Carnap sentence of T (but not in general T itself) can be viewed as an implicit definition of the theoretical terms that is non-creative in the sense of generating no observational consequences not already implied by the Ramsey sentence. My own aim, however, is not to defend this attribution (which is intuitively very plausible in any case), but to investigate what follows from it, on Carnap’s understanding, for the realism/instrumentalism dispute.
- 13.
From this point of view, the theoretical constants are really term-forming operators rather than primitive non-logical constants, and it is precisely this that is then made completely explicit in the ɛ-operator variant. For the ɛ-operator, applied to any open sentence, selects an arbitrary object from the domain that satisfies this open sentence. For details see Carnap (1961), Psillos (2000).
- 14.
However, there are models of the Craig re-axiomatization of a theory in which the Ramsey sentence of the theory is not true. So the truth of the observational consequences alone does not imply the truth of the theory. But if we understand empirical adequacy (as Carnap appears to do) to include both deductive and inductive systematization of the phenomena, then the point in the text holds. For a detailed discussion of the technical issues surrounding this point, and of its history in the logical literature, see Demopoulos (2011).
- 15.
Demopoulos (2003, § 5) makes a closely related point (without referring to Carnap) by arguing that the conjunction of van Fraassen’s constructive empiricism and the semantic view of theories is an unstable philosophical position. My argument is that Carnap’s own position is not at all unstable in this way and, moreover, is thereby stably neutral between realism and instrumentalism.
- 16.
See especially the conclusion of the chapter on the Ramsey sentence in the first edition of Philosophical Foundations of Physics (1966, p. 256): “It is obvious that there is a difference between the meanings of the instrumentalist and the realist ways of speaking. My own view, which I shall not elaborate here, is that the conflict between the two approaches is essentially linguistic. It is a question of which way of speaking is to be preferred under a given set of circumstances. To say that a theory is a reliable instrument—that is, that the predictions of observable events that it yields will be confirmed—is essentially the same as saying that the theory is true and that the theoretical, unobservable entities it speaks about exist. Thus, there is no incompatibility between the thesis of the instrumentalist and that of the realist. At least, there is no incompatibility so long as the former avoids such negative assertions as, ‘… but the theory does not consist of sentences which are either true or false, and the atoms, electrons, and the like do not really exist’.” Van Fraassen’s agnosticism, by contrast, needs to make room for precisely the assertion that the theory is empirically adequate but its postulated theoretical entities do not exist.
- 17.
As we saw in note 7 above, the case of quantum mechanics was an especially important part of Carnap’s motivations for originally proposing the partial interpretation view of theoretical terms in 1939. To see what conceptual problems Carnap might have in mind here (in Philosophical Foundations of Physics), compare Carnap’s earlier discussion of the importance of the analytic/synthetic distinction in modern physics (1966/1974, pp. 257–258): “In my opinion, a sharp analytic-synthetic distinction is of supreme importance for the philosophy of science. The theory of relativity, for example, could not have been developed if Einstein had not realized that the structure of physical space and time cannot be determined without physical tests. He saw clearly the sharp dividing line that must always be kept in mind between pure mathematics, with its many types of logically consistent geometries, and physics, in which only experiment and observation can determine which geometries can be applied most usefully to the physical world. This distinction between analytic truth (which includes logical and mathematical truth) and factual truth is equally important today in quantum theory, as physicists explore the nature of elementary particles and search for a field theory that will bind quantum mechanics to relativity.” So it appears that Carnap may now have particularly in mind the problem of developing a consistent axiomatic approach to relativistic quantum field theory.
- 18.
The illustration, set off in small type, is as follows (ibid.): “First, all mathematical concepts are reducible to those of the theory of relations; four-dimensional tensor or vector fields are structural schemata; the network of world-lines with the relations of coincidence and proper time is a structural schema where only one or two relations are still named—which (relations), moreover, are already uniquely determined by the character of the schema.”
- 19.
The German is “die physikalische Welt,” and Carnap thereby trades on the distinction between “physisch” (corporeal or material as opposed to psychological or mental [“psychisch”]) and “physikalisch” (pertaining to the science of physics).
- 20.
Carnap further characterizes the physical-qualitative coordination as follows (ibid.): “[There] subsists a one-many coordination between qualities and state-magnitudes of such a kind that, if an assignment of physical state-magnitudes from some or another (purely numerical) structure holds at a physical point and its neighborhood, then to the coordinated world-point of the perceptual world the quality coordinated to this structure is always assigned, or at least can always be consistently assigned. But the coordination is not univocal in the converse direction: the assignment of a quality to a world-point of the perceptual world does not determine which particular state-magnitude structure is assigned to the neighborhood of the coordinated physical world-point; only a class is [thereby] determined to which this structure must belong. The physical-qualitative coordination can certainly not be free of the imprecision that attaches to the perceptual world in general.” This lack of determinacy in the coordination from the qualitative to the physical realm reflects the circumstance, already noted, that any inference from the former to the latter (e.g., from the observable behavior of iron filings to the structure of the electromagnetic fields in their neighborhood) is inductive rather than deductive (compare the paragraph to which note 8 above is appended).
- 21.
This process of testing is described in an extremely open-ended way (§ 82): “A sentence of physics, whether it is a P-fundamental sentence [i.e., a physical axiom—MF] or an otherwise valid sentence or an indeterminate assumption (i.e., a premise whose consequences are investigated), is tested, in that consequences are deduced from it on the basis of the transformation rules of the language until one finally arrives at propositions of the form of protocol-sentences. These are compared with the protocol-sentences actually accepted and either confirmed or disconfirmed by then. If a sentence that is an L-consequence of certain P-fundamental sentences contradicts a proposition accepted as a protocol-sentence, then some alteration must be undertaken in the system… . There are no established rules for the kind of alteration that must be made.”
- 22.
The same idea occurs in “Empiricism, Semantics, and Ontology,” in Carnap’s discussion of the linguistic framework described as “The spatio-temporal coordinate system for physics” (1956a, p. 212): “The new entities are the space-time points. Each is an ordered quadruple of four real numbers, called its coordinates, consisting of three spatial and one temporal coordinates. The physical state of a spatio-temporal point or region is described either with the help of qualitative predicates (e.g., ‘hot’) or by ascribing numbers as values of a physical magnitude (e.g., mass, temperature, and the like).” Carnap’s comments on the distinction between internal and external questions relevant to this framework are especially interesting and instructive (213): “Internal questions are here, in general, empirical questions to be answered by empirical investigations. On the other hand, the external questions of the reality of physical space and physical time are pseudo-questions. A question like ‘Are there (really) space-time points?’ is ambiguous. It may be meant as an internal question; then the affirmative answer is, of course, analytic and trivial. Or it may be meant in the external sense: ‘Shall we introduce such and such forms into our language?’; in this case it is not a theoretical but a practical question, a matter of decision rather than assertion, and hence the proposed formulation would be misleading. Or finally, it may be meant in the following sense: ‘Are our experiences such that the use of the linguistic forms in question will be expedient and fruitful?’ This is a theoretical question of a factual, empirical nature. But it concerns a matter of degree; therefore the formulation in the form ‘real or not?’ would be inadequate.”
- 23.
The structural realist conception of theoretical terms was introduced by John Worrall (1989) as a way of preserving referential continuity over time while accommodating such cases as the non-existence of an electromagnetic aether as originally conceived. Such cases are to be accommodated precisely by maintaining that mathematical structure is nonetheless preserved in the transition (for example) between the earlier aether theories of electromagnetism of Green and Stokes and Maxwell’s theory of the electromagnetic field. For discussion, see Psillos (1999, chapters 6 and 7).
- 24.
Carnap makes some interesting—but also tantalizingly brief—remarks on “revolutionary” scientific changes in his reply to Quine in Schilpp (1963, p. 921) .
- 25.
Carnap’s above remarks concerning the ɛ-operator, recorded in (Psillos 2000, p. 171), might be taken to imply that some “indeterminacy” always will (and indeed always should) remain, so that a unique specification of the designation is never possible. It appears to me, however, that a weaker reading is also available, according to which Carnap is only saying that, if we begin with a situation where we do not have a unique specification (as in the example Carnap uses), then the ɛ-operator is exactly what we want—for it can then adequately represent both non-unique and unique specifications. In the Aufbau, Carnap was aiming for “purely structural concepts” in science, defined by “structural definite descriptions” (§ 15), and the illustration from relativistic space-time theory provided in the following section (§ 16; see note 18 above) takes the two primitive relations of the theory to be “already uniquely determined by the [purely formal] character of the [structural] schema.” In the Aufbau, however, Carnap takes the relations over which the variables of the theoretical language range to be explicitly definable from an observational (and indeed autopsychological) basis—which is certainly not the case in the later period now under consideration. This raises delicate logical issues about the general formal possibility of unique specifications for the theoretical terms that are closely related to the Newman problem : for further discussion, see again Demopoulos and Friedman (1985), Demopoulos (2003).
- 26.
Lewis worked closely with Carnap at UCLA and is fully cognizant of (and indeed directly inspired by) Carnap’s work on the Ramsey sentence (1970, note 4, p. 431).
- 27.
Lewis (1970) does not directly consider the logical issues related to the Newman problem concerning the general formal possibility of unique realizations (note 25 above), although he does consider an allied logical problem raised in Winnie (1967). Lewis (1984, note 9, p. 224) does consider the Newman problem (as an anticipation of Hilary Putnam’s “model-theoretic argument”), and he replies by appealing to an “inegalitarian” view of physical properties restricted to those that “carve nature at the joints.” At this point, however, his opposition to Putnam’s “descriptivism” appears far removed from the implicit definition conception of theoretical terms, and, in any case, his emphasis on “objective joints in nature” introduces exactly the kind of metaphysics Carnap is most concerned to avoid. Demopoulos (2003) discusses Carnap on theoretical terms, the Newman problem, Winnie (1967), and Lewis (1970) (as well as Putnam’s argument). Against this background, I hope more fully to discuss, from a Carnapian perspective, the relationship between Lewis (1970) and Lewis (1984) in future work.
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Friedman, M. (2012). Carnap’s Philosophical Neutrality Between Realism and Instrumentalism. In: Frappier, M., Brown, D., DiSalle, R. (eds) Analysis and Interpretation in the Exact Sciences. The Western Ontario Series in Philosophy of Science, vol 78. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-2582-9_6
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