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Isomorphisms in a Category of Proofs (Greg Restall)

The Logic and Metaphysics Workshop will meet on April 9th from 4:15-6:15 in room 3309 of the CUNY Graduate Center for a talk by Greg Restall (Melbourne).

Title: Isomorphisms in a Category of Proofs

Abstract: In this talk, I show how a category of classical proofs can give rise to three different hyperintensional notions of sameness of content. One of these notions is very fine-grained, going so far as to distinguish p and p∧p, while identifying other distinct pairs of formulas, such as p∧q and q∧p; p and ¬¬p; or ¬(p∧q) and ¬p∨¬q. Another relation is more coarsely grained, and gives the same account of identity of content as equivalence in Angell’s logic of analytic containment. A third notion of sameness of content is defined, which is intermediate between Angell’s and Parry’s logics of analytic containment. Along the way we show how purely classical proof theory gives resources to define hyperintensional distinctions thought to be the domain of properly non-classical logics.

Slides/Handout: for those interested, the slides and handout for this talk will be made available for advance reading here.

Mathematical Truth is Historically Contingent (Chris Scambler)

The Logic and Metaphysics Workshop will meet on March 26th from 4:15-6:15 in room 3309 of the CUNY Graduate Center for a talk by Chris Scambler (NYU).

Title: Mathematical Truth is Historically Contingent

Abstract: In this talk I will defend a view according to which certain mathematical facts depend counterfactually on certain historical facts. Specifically, I will sketch an alternative possible history for us in which (I claim) the proposition ordinarily expressed by the English sentence “there is a universal set” is true, despite its falsity in the actual world.

Admissibility of Multiple-Conclusion Rules of Logics with the Disjunction Property (Alex Citkin)

The Logic and Metaphysics Workshop will meet on March 19th from 4:15-6:15 in room 3309 of the CUNY Graduate Center for a talk by Alex Citkin (Private Researcher).

Title: The Admissibility of Multiple-Conclusion Rules of Logics with the Disjunction Property

Abstract: I study admissible multiple-conclusion rules of logics having the meta-disjunction expressible by a finite set of formulas. I show that in such logics the bases of admissible single- and multiple-conclusion rules can be converted into each other. Since these conversions are constructive and preserve cardinality, it is possible to obtain a simple way of constructing a base of admissible single-conclusion rules, by a given base of admissible multiple-conclusion rules and vice versa. Because the proofs are purely syntactical, these results can be applied to a broad class of logics.

Confessing to a Superfluous Premise (Roy Sorensen)

The Logic and Metaphysics Workshop will meet on March 12th from 4:15-6:15 in room 3309 of the CUNY Graduate Center for a talk by Roy Sorensen (WUSTL).

Title: Confessing to a Superfluous Premise

Abstract: In a hurried letter to beleaguered brethren, Blaise Pascal (1658) confesses to a lapse of concision: “I have made this longer than usual because I have not had time to make it shorter.”  Pascal’s confession was emulated with the same warmth as philosophers now emulate the apology introduced by D. C. Mackinson’s “The Preface Paradox”. Could Pascal’s confession of superfluity be sound? Pascal thinks his letter could be conservatively abridged; the shortened letter would be true and have the exact same content. In contrast to the Preface Paradox, where Mackinson’s author apologizes for false assertions, Pascal apologizes for an excess of true assertions. He believes at least one of his remarks could be deleted in a fashion that leaves all of its consequences entailed by the remaining assertions. Pascal’s confession of superfluity is plausible even if we count the apology as part of the letter (as we should since this is the most famous part of the letter). Yet there is an a priori refutation. Any conservative abridgement must preserve the implication that there is a superfluous assertion. This means any abridged version can itself be abridged. Since the letter is finite, we must eventually run out of conservative abridgements. Any predecessor of an unabridgeable abridgement is itself an unabridgeable.  So the original letter cannot be conservatively abridged.

Manuscript: for those interested, the manuscript has been made available for advance reading here.