In the following article I intend to examine the problem of the unity of the proposition in Russell, Frege, and Wittgenstein. My chief aim will be to draw attention to the distinction between Russell’s conception of propositional constituents, on the one hand, with Frege and Wittgenstein’s on the other. My focus will be on Russell’s view of terms as independent, propositions being built up out of these building blocks, compared with Frege and Wittgenstein’s ‘top down’ approach. Furthermore, I will argue (...) that, contra certain other commentators, Frege’s metaphor of saturation and unsaturation does not serve as a solution to the problem of unity, and that the extension of this metaphorical language to Wittgenstein is, therefore, inappropriate. (shrink)

Rudolf Carnap’s mature work on the logical reconstruction of scientific theories consists of two components. The first is the elimination of the theoretical vocabulary of a theory in terms of its Ramsification. The second is the reintroduction of the theoretical terms through explicit definitions in a language containing an epsilon operator. This paper investigates Carnap’s epsilon-reconstruction of theories in the context of pure mathematics. The main objective here is twofold: first, to specify the epsilon logic underlying his suggested definition of (...) theoretical terms and a suitable choice semantics for it. Second, to analyze whether Carnap’s approach is compatible with a structuralist conception of mathematics. (shrink)

In 1907 Einstein had the insight that bodies in free fall do not “feel” their own weight. This has been formalized in what is called “the principle of equivalence.” The principle motivated a critical analysis of the Newtonian and special-relativistic concepts of inertia, and it was indispensable to Einstein’s development of his theory of gravitation. A great deal has been written about the principle. Nearly all of this work has focused on the content of the principle and whether it has (...) any content in Einsteinian gravitation, but more remains to be said about its methodological role in the development of the theory. I argue that the principle should be understood as a kind of foundational principle known as a criterion of identity. This work extends and substantiates a recent account of the notion of a criterion of identity by William Demopoulos. Demopoulos argues that the notion can be employed more widely than in the foundations of arithmetic and that we see this in the development of physical theories, in particular space–time theories. This new account forms the basis of a general framework for applying a number of mathematical theories and for distinguishing between applied mathematical theories that are and are not empirically constrained. (shrink)

This essay examines Friedman's recent approach to the analysis of physical theories. Friedman argues against Quine that the identification of certain principles as ‘constitutive’ is essential to a satisfactory methodological analysis of physics. I explicate Friedman's characterization of a constitutive principle, and I evaluate his account of the constitutive principles that Newtonian and Einsteinian gravitation presuppose for their formulation. I argue that something close to Friedman's thesis is defensible.

Carnap's conception of linguistic frameworks is widespread; however, it is not entirely clear nor consensual to pinpoint what is the influence of his stance within the traditional realist/anti-realist debate. In this paper, we place Carnap as a proponent of a scientific realist stance, by presenting what he called “linguistic realism”. Some possible criticisms are considered, and a case study is offered with wave function realism, a popular position in the philosophy of quantum mechanics.

Scientific inquiry has led to immense explanatory and technological successes, partly as a result of the pervasiveness of scientific theories. Relativity theory, evolutionary theory, and plate tectonics were, and continue to be, wildly successful families of theories within physics, biology, and geology. Other powerful theory clusters inhabit comparatively recent disciplines such as cognitive science, climate science, molecular biology, microeconomics, and Geographic Information Science (GIS). Effective scientific theories magnify understanding, help supply legitimate explanations, and assist in formulating predictions. Moving from their (...) knowledge-producing representational functions to their interventional roles (Hacking 1983), theories are integral to building technologies used within consumer, industrial, and scientific milieus. -/- This entry explores the structure of scientific theories from the perspective of the Syntactic, Semantic, and Pragmatic Views. Each of these views answers questions such as the following in unique ways. What is the best characterization of the composition and function of scientific theory? How is theory linked with world? Which philosophical tools can and should be employed in describing and reconstructing scientific theory? Is an understanding of practice and application necessary for a comprehension of the core structure of a scientific theory? How are these three views ultimately related? (shrink)

This dissertation makes two primary contributions. The first three chapters develop an interpretation of Carnap's Meta-Philosophical Program which places stress upon his methodological analysis of the sciences over and above the Principle of Tolerance. Most importantly, I suggest, is that Carnap sees philosophy as contiguous with science—as a part of the scientific enterprise—so utilizing the very same methods and subject to the same limitations. I argue that the methodological reforms he suggests for philosophy amount to philosophy as the explication of (...) the concepts of science through the construction and use of suitably robust meta-logical languages. My primary interpretive claim is that Carnap's understanding of logic and mathematics as a set of formal auxiliaries is premised upon this prior analysis of the character of logico-mathematical knowledge, his understanding of its role in the language of science, and the methods used by practicing mathematicians. Thus the Principle of Tolerance, and so Carnap's logical pluralism, is licensed and justified by these methodological insights. This interpretation of Carnap's program contrasts with the popular Deflationary reading as proposed in Goldfarb & Ricketts. The leading idea they attribute to Carnap is a Logocentrism: That philosophical assertions are always made relative to some particular language, and that our choice of syntactical rules for a language are constitutive of its inferential structure and methods of possible justification. Consequently Tolerance is considered the foundation of Carnap's entire program. My third chapter argues that this reading makes Carnap's program philosophically inert, and I present significant evidence that such a reading is misguided. The final chapter attempts to extend the methodological ideals of Carnap's program to the analysis of the ongoing debate between category- and set-theoretic foundations for mathematics. Recent criticism of category theory as a foundation charges that it is neither autonomous from set theory, nor offers a suitable ontological grounding for mathematics. I argue that an analysis of concepts can be foundationally informative without requiring the construction of those concepts from first principles, and that ontological worries can be seen as methodologically unfruitful. (shrink)

Every physical theory has two different forms of mathematical equations to represent its target systems: the dynamical and the kinematical. Kinematical constraints are differentiated from equations of motion by the fact that their particular form is fixed once and for all, irrespective of the interactions the system enters into. By contrast, the particular form of a system's equations of motion depends essentially on the particular interaction the system enters into. All contemporary accounts of the structure and semantics of physical theory (...) treat dynamics, i.e., the equations of motion, as the most important feature of a theory for the purposes of its philosophical analysis. I argue to the contrary that it is the kinematical constraints that determine the structure and empirical content of a physical theory in the most important ways: they function as necessary preconditions for the appropriate application of the theory; they differentiate types of physical systems; they are necessary for the equations of motion to be well posed or even just cogent; and they guide the experimentalist in the design of tools for measurement and observation. It is thus satisfaction of the kinematical constraints that renders meaning to those terms representing a system's physical quantities in the first place, even before one can ask whether or not the system satisfies the theory's equations of motion. (shrink)

In the early 1970s it is was realized that there is a striking formal analogy between the Laws of black-hole mechanics and the Laws of classical thermodynamics. Before the discovery of Hawking radiation, however, it was generally thought that the analogy was only formal, and did not reflect a deep connection between gravitational and thermodynamical phenomena. It is still commonly held that the surface gravity of a stationary black hole can be construed as a true physical temperature and its area (...) as a true entropy only when quantum effects are taken into account; in the context of classical general relativity alone, one cannot cogently construe them so. Does the use of quantum field theory in curved spacetime offer the only hope for taking the analogy seriously? I think the answer is 'no'. To attempt to justify that answer, I shall begin by arguing that the standard argument to the contrary is not physically well founded, and in any event begs the question. Looking at the various ways that the ideas of "temperature" and "entropy" enter classical thermodynamics then will suggest arguments that, I claim, show the analogy between classical black-hole mechanics and classical thermodynamics should be taken more seriously, without the need to rely on or invoke quantum mechanics. In particular, I construct an analogue of a Carnot cycle in which a black hole "couples" with an ordinary thermodynamical system in such a way that its surface gravity plays the role of temperature and its area that of entropy. Thus, the connection between classical general relativity and classical thermodynamics on their own is already deep and physically significant, independent of quantum mechanics. (shrink)