The significance of the Curry-Howard isomorphism

Zach, Richard. 2019. “The Significance of the Curry-Howard Isomorphism.” In Philosophy of Logic and Mathematics. Proceedings of the 41st International Ludwig Wittgenstein Symposium, edited by Gabriele M. Mras, Paul Weingartner, and Bernhard Ritter, 313–25. Publications of the Austrian Ludwig Wittgenstein Society, New Series 26. Berlin: De Gruyter. https://doi.org/10.1515/9783110657883-018. The Curry-Howard isomorphism is a proof-theoretic result … Continue reading The significance of the Curry-Howard isomorphism

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Sets, Logic, Computation: An Open Introduction to Metalogic

Sets, Logic, Computation is an introductory textbook on metalogic. It covers naive set theory, first-order logic, sequent calculus and natural deduction, the completeness, compactness, and Löwenheim-Skolem theorems, Turing machines, and the undecidability of the halting problem and of first-order logic. The audience is undergraduate students with some background in formal logic, e.g., what is covered … Continue reading Sets, Logic, Computation: An Open Introduction to Metalogic

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forall x: Calgary. An Introduction to Formal Logic

forall x: Calgary is a full-featured textbook on formal logic. It covers key notions of logic such as consequence and validity of arguments, the syntax of truth-functional propositional logic TFL and truth-table semantics, the syntax of first-order (predicate) logic FOL with identity (first-order interpretations), translating (formalizing) English in TFL and FOL, and Fitch-style natural deduction … Continue reading forall x: Calgary. An Introduction to Formal Logic

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Rudolf Carnap: Early Writings

The Collected Works of Rudolf Carnap, Volume 1 Edited by A.W. Carus, Michael Friedman, Wolfgang Kienzler, Alan Richardson, and Sven Schlotter. With editorial assistance by Steve Awodey, Dirk Schlimm, and Richard Zach. Oxford: Oxford University Press, 2019. Publisher linkGoogle Books

Non-analytic tableaux for Chellas’s conditional logic CK and Lewis’s logic of counterfactuals VC

Zach, Richard. 2018. “Non-Analytic Tableaux for Chellas’s Conditional Logic CK and Lewis’s Logic of Counterfactuals VC.” Australasian Journal of Logic 15 (3): 609–28. https://doi.org/10.26686/ajl.v15i3.4780. Priest has provided a simple tableau calculus for Chellas's conditional logic Ck. We provide rules which, when added to Priest's system, result in tableau calculi for Chellas's CK and Lewis's VC. … Continue reading Non-analytic tableaux for Chellas’s conditional logic CK and Lewis’s logic of counterfactuals VC

PhD, Postdoc with Rosalie Iemhoff

Postdoc position in Logic at Utrecht University, the Netherlands. The postdoc is embedded in the research project “Optimal Proofs” funded by the Netherlands Organization for Scientific Research led by Dr. Rosalie Iemhoff, Department of Philosophy and Religious Studies, Utrecht University. The project in mathematical and philosophical logic is concerned with formalization in general and proof … Continue reading PhD, Postdoc with Rosalie Iemhoff

Raymond Smullyan

Proof by legerdemain

Peli Grietzer shared a blog post by David Auerbach on Twitter yesterday containing the following lovely quote about Smullyan and Carnap: I particularly delighted in playing tricks on the philosopher Rudolf Carnap; he was the perfect audience! (Most scientists and mathematicians are; they are so honest themselves 'that they have great difficulty in seeing through … Continue reading Proof by legerdemain

Rumfitt on truth-grounds, negation, and vagueness

Zach, Richard. 2018. “Rumfitt on Truth-Grounds, Negation, and Vagueness.” Philosophical Studies 175 (8): 2079–89. https://doi.org/10.1007/s11098-018-1114-7. In The Boundary Stones of Thought (2015), Rumfitt defends classical logic against challenges from intuitionistic mathematics and vagueness, using a semantics of pre-topologies on possibilities, and a topological semantics on predicates, respectively. These semantics are suggestive but the characterizations of … Continue reading Rumfitt on truth-grounds, negation, and vagueness

Why φ?

Yesterday, @gravbeast asked on Twitter, Does anyone know why we traditionally use Greek phi and psi for metasyntactic variables representing arbitrary logic formulas? Is it just because 'formula' begins with an 'f' sound? And chi was being used for other things? Although Whitehead and Russell already used φ and ψ for propositional functions, the convention … Continue reading Why φ?

Logic Colloquium, Udine

The European Summer Meeting of the Association of Symbolic Logic will be in Udine, just north of Venice, July 23-28. Abstracts for contributed talks are due on April 27. Student members of the ASL are eligible for travel grants! lc18.uniud.it