"On the Rational Reconstruction of our Theoretical Knowledge"

Compiled by

Eddie Yeghiayan

"On the Relation of Topological to Metrical Structure." In Michael Radner and Stephen Winokur, eds.,

*Analyses of Theories and Methods of Physics and Psychology*, pp. 263-272. Minnesota Studies in the Philosophy of Science, 4. Minneapolis, Minn.: University of Minnesota Press, 1970.

(with Jeffrey Bub.) "The Interpretation of Quantum Mechanics." In Robert S. Cohen and Marx W. Wartofsky, eds.,

*Logical and Epistemological Studies in Contemporary Physics*, pp. 92-122. Boston Studies in the Philosophy of Science, 13. Synthese Library. Dordrecht & Boston: Reidel, 1974.

"Fundamental Statistical Theories." In Patrick Suppes, ed.,

*Logic and Probability in Quantum Mechanics*, pp. 421-431. Synthese Library, 78. Dordrecht & Boston: Reidel, 1976."The Possibility Structure of Physical Systems." In W. L. Harper and C. A. Hooker, eds.,

*Foundations of Probability Theory, Statistical Inference, and Statistical Theories of Science: Proceedings of an International Research Colloquium held at the University of Western Ontario, London, Canada, 10-13 May 1973*, Vol. 3, pp. 55-80. The University of Western Ontario Series in Philosophy of Science, 6. Dordrecht & Boston: Reidel, 1976."Remark on a paper: "Boolean Properties of Observables in Axiomatic Quantum Mechanics."

*Reports on Mathemtical Physics*(1976), 9(2):171-176.

On M.J. Mapolhkcynski's "Boolean Properties of Observables in Axiomatic Quantum Mechanics."*Reports on Mathematical Physics*(1971), 2(2):135-150.Review of C.A. Hooker, ed.,

*Contemporary Research in the Foundations and Philosophy of Quantum Theory: Proceedings of a Conference held at the University of Western Ontario, London, Canada*.*Synthese*(September 1976), 33(2-4):489.(with Jeffrey Bub.) Review of Robert G. Colodny and Arthur Fine, eds.,

*Paradigms & Paradoxes: The Philosophical Challenge of the Quantum Domain*.*Philosophia*(1976), 6(2):333-344."What is the Logical Interpretation of Quantum Mechanics?" In R.S. Cohen, C.A. Hooker, A.C. Michalos, and J.W. van Evra, eds.,

*PSA 1974: Proceedings of the 1974 Bienial Meeting of the Philosophy of Science Association*, pp. 721-728.

"Completeness and Realism in Quantum Mechanics." In Robert E. Butts and Jaakko Hintikka, eds.,

*Foundational Problems in the Special Sciences*, pp. 55-80. Proceedings of the Fifth International Congress of Logic, Methodology, and Philosophy of Science, London, Ontario, Canada, 1975, Part 2. The University of Western Ontario Series in Philosophy of Science, 10. Dordrecht & Boston: Reidel, 1977.

Review of C.A. Hooker, ed.,

*Contemporary Research in the Foundations and Philosophy of Quantum Theory*.*Philosophia*(1978), 7(2):391-395.

"Boolean Representations of Physical Magnitudes and Locality."

*Synthese*(September 1979) 42(1):101-119.Review of William C. Price and Seymour S. Chissick, eds.,

*The Uncertainty Principle and Foundations of Quantum Mechanics: A Fifty Years' Survey*.*Philosophy of Science*(June 1979), 46(2):333-338.(with A. Stairs.) Review of William R. Shea's

*Basic Issues in the Philosophy of Science*.*Dialogue*(1979), 18(3):421-425.

"Locality and Algebraic Structure of Quantum Mechanics." In Patrick Suppes, ed.,

*Studies in the Foundations of Quantum Mechanics*, pp. 119-144. East Lansing. Mich.: Philosophy of Science Association, 1980."A Remark on the Completeness of the Computational Model of Mind."

*Behavioral and Brain Sciences*(March 1980), 3(1):135.

Commentary on Z.W. Pylyshyn's "Computation and Cognition: Issues in the Foundations of Cognitive Science."

Review of Jaakko Hintikka, ed.,

*Bertrand Russell's Early Philosophy Part I*. (*Synthese*(1980), 45(1).)*Russell*(1981), 1(2):163-170.Review of Robert L. Causey's

*Unity of Science*.*Philosophical Review*(January 1981), 90(1):150-153.

"The Rejection of Truth-Conditional Semantics by Putnam and Dummett."

*Philosophical Topics*(1982), 13(1):135-153.

"The aim of this paper is the modest one of reviewing some of the recent work of Putnam and Dummett on realism. I have attempted to clarify what this work takes the issues surrounding realism to be, and I've tried to clarify and evaluate some of the arguments against various forms of realism each has given."Review of Bas C. van Fraasen's

*The Scientific Image*.*Philosophical Review*(October 1982), 91(4):603-607.

(with R.J. Matthews.) "On the Hypothesis that Grammars are Mentally Represented."

*Behavioral and Brain Sciences*(September 1983), 6(3):405-406.

Commentary on E.P. Stabler, Jr.'s "How Are Grammars Represented?"

(with Michael Friedman.) "The Concept of Structure in Russell's

*The Analysis of Matter*.*Philosophy of Science*(December 1985), 52(4):621-639.

Edited (with Ausonio Marras.)

*Language Learning and Concept Acquisition: Foundational Issues*. Norwood, NJ: Ablex, 1986Edited (with Zenon W. Pylyshyn.)

*Meaning and Cognitive Structure: Issues in the Computational Theory of Mind*. Norwood, NJ: Ablex, 1986.

"On Some Fundamental Distinctions of Computationalism."

*Synthese*(January 1987), 70(1):79-96.

"The following paper presents a characterization of three distinctions fundamental to computationalism, viz., the distinction between analog and digital machines, representation and non-representation-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."

Review of Sohan Modgil and Celia Modgil, eds.,

*Noam Chomsky: Consensus and Controversy*.*Interchange*(1988), 19(1):82-83.

(with Michael Friedman.) "The Concept of Structure in

*The Analysis of Matter*." In C. Wade Savage and C. Anthony Anderson, eds.,*Rereading Russell: Essays in Bertrand Russell's Metaphysics and Epistemology*pp, 183-199. Minnesota Studies in the Philosophy of Science, 12. Minneapolis: University of Minnesota Press, 1989.

Reprint of "The Concept of Structure in Russell's*The Analysis of Matter*(1985).Edited (with Robert J. Matthews.)

*Learnability and Linguistic Theory*. Studies in Theoretical Psycholinguistics, 9. Dordrecht & Boston: Kluwer, 1989.

Critical Notice: Hilary Putnam's

*Representation and Reality*.*Philosophy of Science*(June 1990), 57(2):325-333."The Homogeneous Form of Logic Programs with Equality."

*Notre Dame Journal of Formal Logic*(1990), 31(2):291-303.

Critical Notice of Michael Dummett's

*Frege: Philosophy of Mathematics*.*Canadian Journal of Philosophy*(September 1993), 23(3):477-497.

"The aim of this critical notice is to elucidate Dummett's contributions to the issues surrounding Frege's contextual definition of number (the number of Fs equals the number of Gs if the Fs and the Gs are in one-one correspondence) and the interpretation of 'Frege's theorem' -- the theorem that the second order theory consisting of the contextual definition implies the infinity of the natural numbers. To do so, we focus on Dummett's account of the context principle, his discussion of Frege's use of contextual definition, and his treatment of the 'Julius Caesar problem'."(with John L. Bell.) "Frege's Theory of Concepts and Objects and the Interpretation of Second-Order Logic."

*Philosophia Mathematica*(1993), 1(2):139-156.

"This paper casts doubt on a recent criticism of Frege's theory of concepts and extensions by showing that it misses one of Frege's most important contributions: the derivation of the infinity of the natural numbers. We show how this result may be incorporated into the conceptual structure of Zermelo-Fraenkel Set Theory. The paper clarifies the bearing of the development of the notion of a real-valued function on Frege's theory of concepts; it concludes with a brief discussion of the claim that the standard interpretation of second-order logic is necessary for the derivation of the Peano Postulates and the proof of their categoricity."

"The Contemporary Interest of an Old Doctrine."

*Proceedings of the Biennial Meetings of the Philosophy of Science Association*(1994), 2:209-216.

"We call Frege's discovery that, in the context of second-order logic, Hume's principle-- viz., the number of Fs = the number of Gs if, and only if, FaG, where FaG (the Fs and the Gs are in one-to-one correspondence) has its usual, second-order, explicit definition--implies the infinity of the natural numbers, Frege's theorem. We discuss whether this theorem can be marshalled in support of a possibly revised formulation of Frege's logicism.""Frege, Hilbert, and the Conceptual Structure of Model Theory."

*History and Philosophy of Logic*(1994), 15(2):211-225.

"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."

*Journal of Philosophical Logic*(June 1994), 23(3):225-245.

"This paper has three goals: i) to show that the foundational program begun in the*Begriffsschrift*, and carried forward in the*Grundlagen*, represented Frege's 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 Frege's 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 the*Begriffsschrift*. 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 the*Begriffsschrift*, of a fragment of the theory of relations."

(Edited, and with an Introduction.)

*Frege's Philosophy of Mathematics*. Cambridge, Mass.: Harvard University Press, 1995.

"This collection of essays addresses three main developments in recent work on Frege's philosophy of mathematics: the emerging interest in the intellectual background to his logicism; the rediscovery of Frege's theorem; and the reevaluation of the mathematical content of*The Basic Laws of Arithmetic*. Each essay attempts a sympathetic, if not uncritical, reconstruction, evaluation, or extension of a facet of Frege's theory of arithmetic. Together they form an accessible and authoritative introduction to aspects of Frege's thought that have, until now, been largely missed by the philosophical community.""Frege and the Rigorization of Analysis." In William Demopoulos, ed.,

*Frege's Philosophy of Mathematics*, pp. 68-88. Cambridge, Mass.: Harvard University Press, 1995.

(with John L. Bell.) "Elementary Propositions and Independence."

*Notre Dame Journal of Formal Logic*(1996), 37(1):112-124.

"This paper is concerned with Wittgenstein's early doctrine of the independence of elementary propositions. Using the notion of a free generator for a logical calculus-- a concept we claim was anticipated by Wittgenstein--we show precisely why certain difficulties associated with his doctrine cannot be overcome. We then show that Russell's version of logical atomism--with independent particulars instead of elementary propositions--avoids the same difficulties."

"The Centrality of Truth to the Theory of Meaning." In Dunja Jutronic-Tihomirovic, eds,

*The Maribor Papers in Naturalized Semantics*. Maribor: Maribor, 1997.

"In*The Logical Basis of Metaphysics*, Michael Dummett argues that, in what he calls "the weak sense," truth is the central notion of a theory of meaning. To say that truth is central to a meaning theory, is tantamount to saying, in Michael Devitt's phraseology, that "truth is definitional of the semantic task of explaining meaning"--a position Devitt rejects, claiming that to include truth in the definition of the semantic task would be "ad hoc." I explain the broad outlines of Dummett's program and articulate the scope and interest of the idea that truth is its central notion.""In memoriam - Robert E. Butts - 1928-1997."

*Synthese*(July 1997), 112(1):1-2.

"The Philosophical Basis of Our Knowledge of Number."

*Nous*(December 1998), 32(4):481-503.

"After briefly sketching what I take to have been the major intellectual motivation for Frege's logicism, I consider three topics arising from its presentation in*Grundlagen*: (i) Frege's contextual definition of the cardinality operator and his derivation from it of the infinity of the number sequence--what has come to be known as "Frege's theorem"; (ii) Frege's deployment of the context principle as the basic tool in his analysis of the central question of*Grundlagen*, namely, the question: How are numbers given to us if we have neither experience nor intuition of them?; (iii) the degree of success that we may, with hindsight, see Frege to have achieved, both with respect to this question and with respect to other aims of his logicist program."

"On the Theory of Meaning of 'On Denoting'."

*Nous*(September 1999), 33(3):439-458.

"The issue on which I intend to focus is whether there is anything else, anything more than ontological economy, which, in Russell's mature account of the constituents of propositions, is gained by his rejection of denoting concepts. I will argue that in order to answer this question, it is necessary to appreciate that by the time of "On Denoting," Russell was not merely advancing a claim of philosophical logic or a theory of the logical form of the descriptive phrases of English."

Review of Michael D. Potter's

*Reason's Nearest Kin: Philosophies of Arithmetic from Kant to Carnap*.*British Journal for the Philosophy of Science*(September 2001), 52(3):599-612.

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