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Published online by Cambridge University Press: 28 February 2022
Philosophers working in the logical empiricist tradition, such as Rudolf Carnap and Carl Hempel, have held that theoretical terms get their meanings from their connections with observational terms in the postulates of scientific theories. They have tried to explain exactly how this happens, in the sense of giving a logical reconstruction of it. For various reasons, to be discussed below, the belief arose that it is impossible in general to give explicit definitions of theoretical terms. Attention thus shifted to showing how correspondence rules relating theoretical and observational terms give ‘partial interpretations’ to the theoretical terms.
Three objections can be raised against the way in which this enterprise was conceived and carried out. These objections involve what will here be called (1) ‘The Problem of the Theoretical-Observational Dichotomy', (2) ‘The Meaning-Magic Problem', and (3) ‘The Problem of Unwanted Interpretations'. The purpose of this article is to set forth the second and third of these objections and develop a solution to them.
* Such as the system which interprets addition and subtraction in terms of augmentation and diminution of intensive quantities.
See Appendix.
1 For such charges see, for example, Hilary Putnam's ‘What Theories Are Not', in Nagel, E., Suppes, P., and Tarski, A. (eds.), in Logic, Methodology and Philosophy of Science, Stanford 1962; and Peter Achinstein's Concepts of Science, Johns Hopkins Press, 1968.Google Scholar
2 For a fairly recent account along these lines, see the late Carnap's, Rudolf eminently readable Philosophical Foundations of Physics, Basic Books, Inc., New York and London, 1966, p. 267.Google Scholar
3 In constructing a three-valued logic we should keep in mind that in two-valued logic conjunction and alternation are intimately connected with one another, in that they are mutually distributive and are De Morgan transforms of one another. By speaking of an operator analogous to the ɛ of two-valued logic, I mean a binary connective which is associative and commutative; whose truth-table coincides with the two-valued truth-table for ɛ in those cases where only the two standard truth-values are assigned to its conjuncts; and which is such that it and the three-valued analogue for ‘ ∨ ’ are mutually distributive and are De Morgan transforms of one another. There are two ways of giving joint truthtable definitions to ɛ and ‘ ∨ ’ in three-valued logic so that as defined they turn out to be associative, commutative, mutually distributive and De Morgan transforms of one another.
4 The difficulty is found though not acknowledged in Carnap's above-mentioned work. Carnap supposes that the theoretical terms (T-terms’) are uninterpreted until they get their empirical meanings via correspondence rules (“C-postulates”). He says: ‘The C-postulates cannot, of course, be taken alone. To obtain the fullest possible interpretation (though still only partial) for the T-terms, it is necessary to take the entire1 theory, with its combined C- and T-postulates” (ibid., p. 267). He refers to that combination as (TC’. The Ramsey sentence formed by existentially quantifying over each of its theoretical predicate letters is called ‘RTC. He then seeks an analytic meaning postulate (A-postulate’) from which all of the analytic meaning relations involving the theoretical terms can be defined. His suggestion is that
… the simplest way to formulate an A-postulate A T for a theory TC is:
It can easily be shown that this sentence is factually empty…. All the factual content is in the Ramsey sentence FT, which is the Ramsey sentence RTC. The sentence AT simply asserts that jf the Ramsey sentence is true, we must then understand the theoretical terms in such a way that the entire theory is true. It is a purely analytic sentence, because its semantic truth is based on the meanings intended for the theoretical terms (ibid., p. 270).
We have a problem here. The sentence AT looks like a sentence in the object language, not the meta-language. And it looks as though it may be neither true nor false, being infected with meaningless predicate letters. That depends partly on the three-valued truth-table which we give to the conditional sign ‘ ⊃ ’, partly on the truth-value of the Ramsey sentence RTC, and partly on the truth-value which our three-valued logic assigns to ‘TC’. There is in any case no question of AT's automatically turning out analytic, independently of which of the possibilities just mentioned are realized. Suppose that the Ramsey sentence RTC is true, but the consequent 7“Cis neuter. If we take the conditional form ‘/»=#’ to be equivalent to'—p v q', then regardless of which strategy we use to define’ v', the conditional AT must be assigned a truth-value neuter, and is thus not analytic (true simply in virtue of the meanings of its terms).
We have a problem here. The sentence AT looks like a sentence in the object language, not the meta-language. And it looks as though it may be neither true nor false, being infected with meaningless predicate letters. That depends partly on the three-valued truth-table which we give to the conditional sign ‘ ⊃ ’, partly on the truth-value of the Ramsey sentence RTC, and partly on the truth-value which our three-valued logic assigns to ‘TC’. There is in any case no question of AT's automatically turning out analytic, independently of which of the possibilities just mentioned are realized. Suppose that the Ramsey sentence RTC is true, but the consequent TC is neuter. If we take the conditional form ‘p⊃’ to be equivalent to'—p∨q', then regardless of which strategy we use to define ‘ ∨’, the conditional AT must be assigned a truth-value neuter, and is thus not analytic (true simply in virtue of the meanings of its terms).
But Carnap also describes AT as though it were a metalinguistic formula which tells us how we must understand TC if RTC is true. Is this metalinguistic formula analytic? Or is it an exhortation; neither true nor false? Or a resolution about how we are going to interpret the schematic letters in TC? How then is the resolution to be carried out? Certainly AT by itself does not carry out the resolution; that is, it does not impart the intended meanings to the dummy predicate letters appearing in the TC part of it. Some of these difficulties were independently pointed out in James K. Derden's doctoral dissertation ‘Analyticity and Scientific Theories with Special Reference to the Work of Rudolf Carnap’ (University of Toronto, 1971, unpublished). I hope to resolve them here.
5 Example: “If a thermodynamic system is brought reversibly from one thermodynamic equilibrium state to another, then, regardless of the path, the change of entropy is given by: ∫ dq/T.” Here the term ‘change of entropy’ has its significance explained in terms of the way in which entropy change is related to observable facts, such as the temperature of the system and increments or decrements of heat energy.
6 Even dispositional terms such as ‘brittle’ had to be construed as only partially interpreted, for well known reasons reviewed on pages 240 and 241 of the text.
7 In ‘How To Define Theoretical Terms’, Journal of Philosophy 68, 13, July, 9, 1970.