CARNAP and the RATIONAL RECONSTRUCTION of the LANGUAGE of PHYSICS William Demopoulos Dedicated to the Memory of Herbert Feigl
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CARNAP AND THE RATIONAL RECONSTRUCTION OF THE LANGUAGE OF PHYSICS William Demopoulos Dedicated to the memory of Herbert Feigl 0 Introduction 1 Logicism, Hilbert and the problem of a priori knowledge 2 Special relativity and the fact/convention dichotomy 3 Theoretical and observational sentences 4 Correspondence rules 5 Ramsey and Carnap sentences and the distinction between the factual and the conventional 6 A Quinean problem and its solution 7 Considerations in favor of Carnap’s reconstruction 8 Is a theory its Ramsey sentence? 9 Empiricism and reconstruction 0 Introduction Carnap’s intellectual development is well-documented in his Autobiography for the Schilpp volume that is devoted to his work. It is, for the purposes of this paper, worth recalling that he was a student of Frege’s during the 1910 Fall semester and the Summer semesters of 1913 and 1914, studying first courses on Frege’s Begriffsschrift and, in 1914, taking the course, Logic in mathematics.1 Shortly after the First War, Carnap wrote Russell asking him where he might purchase a second-hand copy of Principia, post-War inflation in Germany being rampant and the Freiburg library without a copy; Russell responded by copying out by hand 35 pages of its central definitions. From the Autobiography we also learn that Carnap’s interest in philosophy of physics emerged early in his career: as a doctoral student, he formulated the intention of writing a dissertation on the axiomatization of special relativity. The less than enthusiastic reception of this idea by Max Wien, the head of the Institute of Physics at Jena, led him to write on the foundations of geometry instead. The dissertation was completed in 1921 under the title Der Raum, and it was with its composition that he became intimately acquainted with the work of Hilbert. It is no exaggeration to say that the core of Carnap’s philosophy of science consists in his proposals for the rational reconstruction of the language of physics. His Aufbau (1928) was his first extended application of the method of reconstruction to the analysis of empirical knowledge. The approach taken there was gradually transformed and refined in later work. In Logical syntax (1934) §72 Carnap proposed that the logic of science is the proper replacement for traditional philosophy; and in §82 of that work he presented a “logical analysis” of the language of physics. The reconstruction that Carnap articulated in Testability and meaning (1936/37)—his first major publication in English—is the clearest anticipation of the mature view he developed in the 1950s and 60s, the view that forms the focus of our study. My discussion is organized as follows. After briefly reviewing its historical context and philosophical motivation, the exposition begins with Carnap’s final proposal for the rational reconstruction of the language of physics. This proposal has not received the -2- attention it deserves; it is, for example, particularly relevant to the assessment of his long- standing debate with Quine over the possibility of drawing a non-arbitrary fact/convention dichotomy, and it bears importantly as well on the characterization of his reconstruction as “syntactic.” Having expounded Carnap’s mature position on the nature of theoretical knowledge, I turn to consider how various of his earlier views can be located within it. Although the present paper defends Carnap against certain misconceptions, it is also concerned to expose a fundamental limitation in his account of theoretical knowledge. 1 Logicism, Hilbert and the problem of a priori knowledge From the point of view of foundations of mathematics, the principal influences on Carnap’s approach to reconstruction are two. There is first and foremost the influence of modern logic and its deployment by Frege and Russell in their articulation of logicism. Secondly, there is Hilbert’s “first program,” by which I mean his program of axiomatization and the methodology it introduced for understanding the nature of mathematical theories, especially the role this approach assigned to axioms for our understanding of the primitives of a mathematical theory. Logicism’s attempt to account for the aprioricity of mathematics by representing it as an extension of logic foundered, in Frege’s case, on the inconsistency of his system, and in the case of Russell, on the need to assume a posteriori principles.2 Logicism’s legacy was, therefore, mixed: its central development—polyadic logic with multiple generality—proved an indispensable tool for the logical analysis of the language of science. But logicism left unsolved the fundamental problem of responding to the Kantian claim that mathematics represents a counter-example to any theory of knowledge that seeks to minimize the importance of the synthetic a priori. In his Foundations of geometry, Hilbert articulated a view of geometrical axioms that provided the key to Carnap’s emendation of logicism. Hilbert was widely interpreted as having shown that in so far as intuition has a role to play in geometrical knowledge, it is one that can be wholly relegated to psychology.3 In particular, the classical view that the subject matter of geometry is tied to intuition, in the sense that intuition is needed to vindicate the truth of its axioms or the validity of its reasoning, was decisively addressed by Hilbert’s demonstration that Euclidian geometry—or, indeed, any geometrical theory—does not have a fixed subject matter to which its axioms are responsible. The language of geometry is freely interpretable subject only to the constraint that the interpretation must respect the logical category of its vocabulary. The subject matter of the axioms includes any interpretation containing a system of objects which makes them true; the truth of the axioms thus consists in the existence of such a system of objects, and therefore amounts to nothing more than their consistency. The account of the aprioricity of geometry that emerges from Hilbert’s investigations is based on the observation that geometrical axioms—and more generally, the axioms of any mathematical theory—are constitutive of their subject-matter. Carnap perceived that this idea might plausibly be extended to arithmetic as well. The contribution of logicism to the philosophy of pure mathematics would then be seen to lie not in its account of the axioms of arithmetic but in its elucidation of mathematical reasoning as an elaboration of purely logical reasoning.4 The successful extension of Hilbert’s view of geometrical -3- axioms to the rest of mathematics depends on whether the aprioricity attributed to the axioms can be shown to derive from their analyticity. This requires both an explication of analyticity and a demonstration that the explication correctly characterizes the relevant cases. For Carnap, the crucial notion on which the successful explication of analyticity relies is that of factual content. Carnap’s solution to the problem of a priori knowledge is to argue that it lacks factual content and is, in this sense, analytic. Analyticity thus becomes something that can attach to a mathematical theory independently of whether or not it is recoverable from the basic laws of logic. More generally, Carnap’s approach seeks to preserve the fundamentally empiricist intuition that reality is not accessible to reason alone while admitting the presence of a genuinely a priori component to theoretical knowledge. 2 Special relativity and the fact/convention dichotomy Poincaré’s contention that the nature of the true geometry of space is indeterminate, or equivalently, his contention that the question, “What is the geometry of space?,” is not well-formed, lies at the heart of the logical empiricists’ theory of theories and their correct interpretation. But it was Einstein’s 1905 analysis of simultaneity that suggested to the logical empiricists a systematic means of addressing the factual content of physical theories. They held that Einstein’s methodology established that the central task of the epistemological analysis of science is to provide a clear separation of the factual from the conventional components of empirical knowledge in general, and of physical knowledge in particular.5 Einstein had argued that reflection on the criterion of application for the relation of simultaneity shows it to depend on connecting distant events by some means of signaling. According to the logical empiricists, the epistemological content of special relativity consisted in Einstein’s development of this observation into a demonstration that principles which, on the surface, appear to be descriptive of physical events, are in reality prescriptive statements controlling the empirical interpretation of the language of physics. Included among such principles is the equality of the to and fro velocities of light in any determination of distant simultaneity. This appears to be a simple descriptive claim. It is, however, a convention we freely adopt in order to give empirical content to our kinematical statements. Indeed, many apparently descriptive statements—that asserting the isotropy of space, for example—turn out to have a nonfactual and conventional character. By a natural extension, the traditional question of the correct geometry of space is one that is also relative to the adoption of conventions controlling the interpretation of the geometrical primitives; a central task of the philosophy of physical geometry is to uncover these conventions. Einstein’s analysis of simultaneity thus provided a template for extending the method of rational reconstruction to empirical theories, one in which the fact/convention dichotomy is of central importance, and one that highlights the importance of principles of epistemic interpretation for the basic concepts of an empirical theory. Later we will see in some detail how this template came to be reflected in Carnap’s proposals. -4- 3 Theoretical and observational sentences Factual content is expressed in terms of the observational vocabulary of a theory, where, it is important to emphasize, the notions of observational vocabulary item and observational sentence are artifacts of the rational reconstruction.