I. Published Papers

“Classical and Intuitionistic Models of Arithmetic”, Notre Dame Journal of Formal Logic 37, 1996, 452-461

Discusses the question whether all nodes in a Kripke model of Heyting Arithmetic must be classical models of Peano Arithmetic. Proves, among other things, that this is always the case if the frame of the Kripke model is ordered like the natural numbers.

“Fragments of HA based on Sigma_1-induction”, Archive for Mathematical Logic 37, 1997, 37-49

Investigates certain fragments of Heyting Arithmetic, namely those obtained by restricting the induction schema to (a) Sigma_1 formulae, (b) Pi_1 formulae, and (c) prenex formulae. Proves, among other things, that the theories under (a) and (b) are not (as in the classical case) equivalent, that theory (a) is well-behaved, but theory (b) isn't, and that theory (c) is no stronger proof-theoretically than Heyting Arithmetic with the induction schema restricted to Pi_2 formulae.

“Aspekte der Frege-Hilbert-Korrespondenz”, History and Philosophy of Logic 18, 1997, 201-209

German paper on some aspects of the debate between Frege and Hilbert. Argues that Frege understood Hilbert's axiomatic method way better than Hilbert himself at the time.

“Constructing Kripke Models of Certain Fragments of Heyting’s Arithmetic”, Publications de l'Institut Mathématique n.s. 63 (77), 1998, 1-8

Shows how to build Kripke models of the subtheories of Heyting Arithmetic obtained by restricting the induction schema to Pi_1 and Pi_2 formulae, respectively.

“Consistent Fragments of Grundgesetze and the Existence of Non-Logical Objects”, Synthese 121, 1999 (appeared in print in 2000), 309-328

Proves the consistency of a subtheory of Frege's system in the Grundgesetze obtained by restricting the second-order comprehension schema to Delta^1_1 formulae. Discusses some curious properties of this theory and of Richard Heck's predicative fragment.

with H.-C. Schmidt am Busch: “Auf der Suche nach Freges Nachlaß”, in: Gottfried Gabriel and Uwe Dathe (eds.), Gottlob Frege – Werk und Wirkung, Paderborn: mentis, 2000, 267-281

Recounts the authors' efforts to find out what really happened to Frege's Nachlass. Presents evidence to the effect that the received tale of its destruction during the war is not well supported. Speculates that the Nachlass might still exist. (German. English translation in preparation.)

with Fernando Ferreira: “On the Consistency of the Delta^1_1-CA Fragment of Frege’s Grundgesetze”, Journal of Philosophical Logic 31, 2002, 301-311

Proves the consistency of the Delta^1_1 comprehension fragment of Frege's Grundgesetze system reconstructed in a more standard linguistic setting than was done in the 1999 Synthese paper. The proof is mathematically way more sophisticated, using recursively saturated models.

“World Travelling and Mood Swings”, in: Benedikt Löwe, Thoralf Räsch, Wolfgang Malzkorn (eds.), Foundations of the Formal Sciences II, Kluwer (Trends in Logic), 2003, 257-260

Provides an accessible proof of a certain inexpressibility result in modal predicate logic originally due to Harold Hodes. Plays a role in the two forthcoming papers on mood mentioned below.

 

II. Forthcoming Papers

 

“Russell’s Paradox in Consistent Fragments of Frege’s Grundgesetze”, to appear in: Godehard Link (ed.), One Hundred Years of Russell’s Paradox, de Gruyter 2004

Provides a survey of results on subtheories of Frege's Grundgesetze system obtained by restricting the second-order comprehension schema.

with Peter Schroeder-Heister: “Frege’s Permutation Argument Revisited”, to appear in Synthese, February 2005

Identifies two interpretations of section 10 of Grundgesetze, one metalogical and one mathematical. Shows that Frege's permutation argument is invalid, and his identifiability thesis false, on the metalogical reading, and that the argument is valid and the thesis true on the mathematical interpretation. Argues from textual evidence that the mathematical reading does more justice to Frege.

“Modality, Mood, and Descriptions”, to appear in: Reinhard Kahle (ed.), Intensionality – An Interdisciplinary Discussion, Lecture Notes in Logic, AK Peters

Argues that Kripke's modal argument against description theories of proper names fallaciously fudges important grammatical distinctions of English pertaining to verb mood. Provides a formal apparatus that incorporates indicative and "subjunctive" predicates as an alternative to standard modal predicate logic, and shows that Kripke's argument is invalid when reconstructed in this framework.

“In the Mood”, to appear in the Journal of Philosophical Logic

Updates and refines the previous paper, especially by taking into account the strategy of semantic ascent used by Kripkeans against wide-scopers.

“Wittgensteinian Predicate Logic”, to appear in the Notre Dame Journal of Formal Logic 45 (1), 2004.

Improves on Hintikka's pioneering work on the revisionary logic advocated by Wittgenstein in Tractatus 5.53-5.535 (no identity symbol, expressing identity of object by identity of sign, and difference of objects by difference of signs). Provides a cut-free sequent and a Hilbert style calculus for Wittgensteinian predicate logic and proves soundness and completeness, thus establishing that this logic is not only as expressive, but also as tractable as standard first-order logic with identity.

 

III. Unpublished Work

 

with Hans-Christoph Schmidt am Busch: "Heinrich Scholz and Jan Lukasiewicz"

Recounts the story of a friendship during dark times.

 

 

Kai Frederick Wehmeier

Logic & Philosophy of Science

School of Social Sciences

3151 Social Science Plaza A

University of California, Irvine

Irvine, CA 92697

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email: wehmeier@uci.edu