Source
Mind and Language 26 (2011) 540–573
(with Phil Serchuk and Ian Hargreaves)
Publications
The development of mathematical logic from Russell to Tarski: 1900-1935
Source
Leila Haaparanta, ed., The History of Modern Logic. New York and Oxford: Oxford University Press, 2009, pp. 318-471 (with Paolo Mancosu and Calixto Badesa)
Reprinted in Paolo Mancosu, The Adventure of Reason. Interplay Between Philosophy of Mathematics and Mathematical Logic, 1900-1940. Oxford: Oxford University press, 2010
Effective finite-valued approximations of general propositional logics
Source
Avron, Arnon; Dershowitz, Nachum; Rabinovich, Alexander (Eds.). Pillars of Computer Science: Essays Dedicated to Boris (Boaz) Trakhtenbrot on the Occasion of His 85th Birthday. Lecture Notes in Computer Science 4800. Berlin: Springer, 2008. 107-129
(with Matthias Baaz)
First-order Gödel logics
Source
Annals of Pure and Applied Logic 147 (2007) 23-47 (with Matthias Baaz and Norbert Preining)
Gödel’s first incompleteness theorem and mathematical instrumentalism
WORK IN PROGRESS! Comments welcome! Preprint
Hilbert’s program then and now
Source
Dale Jacquette, ed., Philosophy of Logic. Handbook of the Philosophy of Science, vol. 5. (Elsevier, Amsterdam, 2006), 411-447.
Kurt Gödel and computability theory
Source
Logical Approaches to Computational Barriers Second Conference on Computability in Europe, CiE 2006, Swansea. Proceedings. LNCS 3988 (Springer, Berlin, 2006) 575-583
The epsilon calculus and Herbrand complexity
Source
Studia Logica 82 (2006) 133-155
(with Georg Moser)
Critical study of Michael Potter’s Reason’s Nearest Kin
Source
Notre Dame Journal of Formal Logic 46 (2005) 503-513/
Reviewed Work:
Michael Potter, Reason's Nearest Kin. Philosophies of Arithmetic from Kant to Carnap. Oxford University Press, Oxford, 2000. x + 305 pages
Download from Project Euclid
Kurt Gödel, paper on the incompleteness theorems (1931)
Source
Ivor Grattan-Guinness, ed., Landmark Writings in Mathematics (North-Holland, Amsterdam, 2004), 917–925
Abstract
This entry for the Landmark Writings in Mathematics collection discusses Kurt Gödel's 1931 paper on the incompleteness theorems, with a special emphasis on the historical and philosophical context.
Decidability of quantified propositional intuitionistic logic and S4 on trees of height and arity ≤ ω
Source
Journal of Philosophical Logic 33 (2004) 155–164.
Hilbert’s “Verunglückter Beweis,” the first epsilon theorem, and consistency proofs
Source
History and Philosophy of Logic 25 (2004) 79–94.
The practice of finitism: Epsilon calculus and consistency proofs in Hilbert’s Program
Source
Synthese 137 (2003) 211-259.
Characterization of the axiomatizable prenex fragments of first-order Gödel logics
In: 33rd International Symposium on Multiple-valued Logic. Proceedings. Tokyo, May 16-19, 2003 (IEEE Computer Society Press, 2003) 175-180 (with Matthias Baaz and Norbert Preining)
Abstract: The prenex fragments of first-order infinite-valued Gödel logics are classified. It is shown that the prenex Gödel logics characterized by finite and by uncountable subsets of [0, 1] are axiomatizable, and that the prenex fragments of all countably infinite Gödel logics are not axiomatizable.
Download from IEEE Xplore:
Hilbert’s Finitism: Historical, Philosophical, and Metamathematical Perspectives
Source
Dissertation, University of California, Berkeley, Spring 2001
Abstract
In the 1920s, David Hilbert proposed a research program with the aim of providing mathematics with a secure foundation. This was to be accomplished by first formalizing logic and mathematics in their entirety, and then showing—using only so-called finitistic principles—that these formalizations are free of contradictions.
Tableaux for reasoning about atomic updates
Source
Logic for Programming, Artificial Intelligence, and Reasoning. 8th International Conference, LPAR 2001. Proceedings, LNAI 2250. (Springer, Berlin, 2001) 639-653
(with Christian G. Fermüller and Georg Moser)
Quantified propositional Gödel logics
Source
Voronkov, Andrei, and Michel Parigot (eds.) Logic for Programming and Automated Reasoning. 7th International Conference, LPAR 2000. Proceedings, LNAI 1955 (Springer, Berlin, 2000) 240-256
(with Matthias Baaz and Agata Ciabattoni)
Hypersequents and the proof theory of intuitionistic fuzzy logic
Source
Clote, Peter G., and Helmut Schwichtenberg (eds.), Computer Science Logic. 14th International Workshop, CSL 2000. Fischbachau, Germany, August 21-26, 2000. Proceedings.
(Springer, Berlin, 2000) 187-201
(with Matthias Baaz)
Completeness before Post: Bernays, Hilbert, and the development of propositional logic
Source
Bulletin of Symbolic Logic 5 (1999) 331–366.
Note on generalizing theorems in algebraically closed fields
Source
Archive for Mathematical Logic 37 (1998) 297–307
(with Matthias Baaz)