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.
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.
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.
The Logic and Metaphysics Workshop will meet on March 5th from 4:15-6:15 in room 3309 of the CUNY Graduate Center for a talk by Vera Flocke (NYU).
Title: The Metasemantics of Indefinite Extensibility
Abstract: Indefinite extensibility is the thesis that any domain of quantification can always be expanded. But how is the possibility of expanding domains of quantification reflected in the semantics of quantified sentences? This paper discusses the relevant meta-semantic options within a framework that distinguishes between semantic values and assertoric contents. This choice of a framework is independently motivated, helps received accounts of indefinite extensibility to escape weighty objections and adds to the available metasemantic options. I then argue for a hitherto overlooked view according to which quantified sentences express stable semantic values but variable assertoric contents. Specifically, the semantic value of quantified sentences are sets of possible worlds that are structured by two equivalence relations, one of which models counterfactual necessity and the other one of which models objectivity. Assertoric contents however are ordinary possible worlds propositions. The advantage of this view is that it explains succinctly what’s at issue in the debate between generality-absolutists, who think that quantification over absolutely everything is possible, and generality-relativists. If the box expresses objectivity, this disagreement concerns the Barcan formula, which entails that domains do not grow as one moves to objectively-accessible worlds.
The Logic and Metaphysics Workshop will meet on February 26th from 4:15-6:15 in room 3309 of the CUNY Graduate Center for a talk by Martin Pleitz (Muenster).
Title: A Dynamic Solution to the Liar Paradox
Abstract: The Liar paradox arises when we combine the assumption that a sentence can refer to itself with our naïve notion of truth and apply our unrevised logic. Most current approaches to the Liar paradox focus on revising our notion of truth and logic because nowadays almost everyone is convinced that there are self-referential sentences. I will argue against this conviction. My argument starts from observations about the metaphysics of expressions: A meaningful expression is based in a syntactic expression which in turn is based in a non-semiotic object, and these are pairwise distinct. As all objects of this three-fold ontology exist only relative to contexts, we can import ideas from tense logic about how existence and reference can interact in a contextualist metaphysics. Semantico-metaphysical reasoning then shows that in this dynamic setting, an object can be referred to only after it has started to exist. Hence the self-reference needed in the Liar paradox cannot occur, after all. As this solution is contextualist, it evades the expressibility problems of other proposals.
Please note that Roy Sorensen (Washington University in St. Louis) will be replacing Graham Priest (CUNY) as the speaker on March 12.
The Logic and Metaphysics Workshop will be meeting on Mondays from 4:15 to 6:15 in room 3309 of the Graduate Center, CUNY (365 5th Avenue). The following is the schedule:
Feb 12. GC CLOSED. NO MEETING
Feb 19. GC CLOSED NO MEETING
Feb 26. Martin Pleitz, Muenster
Mar 5. Vera Flocke, NYU
Graham Priest, CUNY Roy Sorensen, WUSTL
Mar 19. Alex Citkin, Private Researcher
Mar 26. Chris Scambler, NYU
Apr 2. SPRING RECESS. NO MEETING
Apr 9. Greg Restall, Melbourne
Apr 16. Daniel Nolan, Notre Dame
Apr 23. Mel Fitting, CUNY
Apr 30. Sungil Han, Seoul National
May 7. Andreas Ditter, NYU
May 14. Rohit Parikh, CUNY