William Demopoulos

On the Rational Reconstruction of Our Theoretical Knowledge

This paper concerns the rational reconstruction of physical theories initially advanced by F. P. Ramsey and later elaborated by Rudolf Carnap. The Carnap–Ramsey reconstruction of theoretical knowledge is a natural development of classical empiricist ideas, one that is informed by Russells philosophical logic and his theories of propositional understanding and knowledge of matter; as such, it is not merely a schematic representation of the notion of an empirical theory, but the backbone of a general account of our knowledge of the physical world. Carnap–Ramsey is an illuminating approach to epistemological problems that remain with us, one whose difficulties are shared by accounts that have sought to replace it. 1Introduction 2Russells theory of propositional understanding 3Ramseys primary and secondary systems 4Carnaps reconstruction of the language of science and an observation of Newman 5Extension of the foregoing to constructive empiricism 6Putnams model‐theoretic argument and the semantic view of theories 7The problem clarified and resolved

Learnability and linguistic theory

Introduction: Learnability and Linguistic Theory.- Learning Theory and Natural Language.- The Plausibility of Rationalism.- On Applying Learnability Theory to the Rationalism-Empiricism Controversy.- On Certain Substitutes for Negative Data.- Markedness and Language Development.- Learning the Periphery.- Some Problems in the Parametric Analysis of Learnability.- From Cognition to Thematic Roles: The Projection Principle as an Acquisition Mechanism.- List of Contributors.- Index of Names.- Index of Subjects.

Frege, hilbert, and the conceptual structure of model theory

This paper attempts to confine the preconceptions that prevented Frege from appreciating Hilbert’s Grundlagen der Geometrie to two: (i) Frege’s reliance on what, following Wilfrid Hodges, I call a Frege‐Peano language, and (ii) Frege’s view that the sense of an expression wholly determines its reference.I argue that these two preconceptions prevented Frege from achieving the conceptual structure of model theory, whereas Hilbert, at least in his practice, was quite close to the model‐theoretic point of view.Moreover, the issues that divided Frege and Hilbert did not revolve around whether one or the other allowed metalogical notions.Frege, e.g., succeeded in formulating the notion of logical consequence, at least to the extent that Bolzano did; the point is rather that even though Frege had certain semantic concepts, he did not articulate them model‐theoretically, whereas, in some limited sense, Hilbert did

Frege and the rigorization of analysis

This paper has three goals: (i) to show that the foundational program begun in theBegriffsschrift, and carried forward in theGrundlagen, represented Freges attempt to establish the autonomy of arithmetic from geometry and kinematics; the cogency and coherence of‘intuitive’ reasoning were not in question. (ii) To place Freges logicism in the context of the nineteenth century tradition in mathematical analysis, and, in particular, to show how the modern concept of a function made it possible for Frege to pursue the goal of autonomy within the framework of the system of second-order logic of theBegriffsschrift. (iii) To address certain criticisms of Frege by Parsons and Boolos, and thereby to clarify what was and was not achieved by the development, in Part III of theBegriffsschrift, of a fragment of the theory of relations.

On some fundamental distinctions of computationalism

The following paper presents a characterization of three distinctions fundamental to computationalism, viz., the distinction between analog and digital machines, representation and nonrepresentation-using systems, and direct and indirect perceptual processes. Each distinction is shown to rest on nothing more than the methodological principles which justify the explanatory framework of the special sciences.

Three Views of Theoretical Knowledge

Of the three views of theoretical knowledge which form the focus of this article, the first has its source in the work of Russell, the second in Ramsey, and the third in Carnap. Although very different, all three views subscribe to a principle I formulate as ‘the structuralist thesis’; they are also naturally expressed using the concept of a Ramsey sentence. I distinguish the framework of assumptions which give rise to the structuralist thesis from an unproblematic emphasis on the importance of ‘structural’ differences for the analysis and interpretation of theories belonging to the exact sciences, and I review a number of logical properties of Ramsey sentences using very simple arithmetical theories and their models. I then develop a reconstruction of the views of Russell, Ramsey, and Carnap that clarifies the interrelationships among them by appealing to aspects of the arithmetical examples that inform my discussion of Ramsey sentences. I conclude with an account of the philosophical basis of the structuralist thesis and the fundamental difficulty to which it leads. 1 Introduction 2 Ramsey Sentences and Craig Transcriptions 3 Ramsey Sentences and the Applications of a Theory 4 Extensions and Expansions of Models and Russell’s Structuralism 5 Ramsey on Theories 6 Carnap’s Synthesis 7 The Structuralist Thesis 1 Introduction 2 Ramsey Sentences and Craig Transcriptions 3 Ramsey Sentences and the Applications of a Theory 4 Extensions and Expansions of Models and Russell’s Structuralism 5 Ramsey on Theories 6 Carnap’s Synthesis 7 The Structuralist Thesis

Some remarks on the bearing of model theory on the theory of theories

The present paper offers some remarks on the significance of first order model theory for our understanding of theories, and more generally, for our understanding of the “structuralist” accounts of the nature of theoretical knowledge that we associate with Russell, Ramsey and Carnap. What is unique about the presentation is the prominence it assigns to Craig’s Interpolation Lemma, some of its corollaries, and the manner of their demonstration. They form the underlying logical basis of the analysis.

The Possibility Structure of Physical Systems

This paper develops the logical interpretation of non-relativistic quantum mechanics initially proposed by Hilary Putnam [11]. (See also [1] and [2].) The main features of this interpretation are briefly summarized in this introduction.

Effects and Propositions

The quantum logical and quantum information-theoretic traditions have exerted an especially powerful influence on Bub’s thinking about the conceptual foundations of quantum mechanics. This paper discusses both the quantum logical and information-theoretic traditions from the point of view of their representational frameworks. I argue that it is at this level—at the level of its framework—that the quantum logical tradition has retained its centrality to Bub’s thought. It is further argued that there is implicit in the quantum information-theoretic tradition a set of ideas that mark a genuinely new alternative to the framework of quantum logic. These ideas are of considerable interest for the philosophy of quantum mechanics, a claim which I defend with an extended discussion of their application to our understanding of the philosophical significance of the no hidden variable theorem of Kochen and Specker.

Completeness and Realism in Quantum Mechanics

Kochen and Specker ([5], Theorem 1) have shown that a finite partial Boolean algebra Dof quantum mechanics has no two-valued homomorphisms. In my view, this theorem bears on the completeness of quantum mechanics insofar as this is related to the problem of hidden variables and the probabilistic character of the theory: the quantum theory is complete but indeterministic in the sense that the maximal amount of information regarding a system may be significantly probabilistic. It should be noted that this interpretation of the theorem requires a modification of Kochen and Specker’s analysis of statistical theories — basically, it requires treating the algebraic structure of physical magnitudes as theoretically primitive. These matters are discussed in some detail in [1].