Feb 26 Martin Pleitz, Muenster
Mar 5 Vera Flocke, NYU
Mar 12 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
May14 Rohit Parikh
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.
This meeting is open to all who are interested. Please feel free to pass this announcement on, or direct others to our website at logic.commons.gc.cuny.edu.
Logic and Metaphysics Workshop
Spring 2018
Feb 26 Martin Pleitz, Muenster
Mar 5 Vera Flocke, NYU
Mar 12 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
May14 Rohit Parikh
In a famous passage from Outlines of Pyrrhonism, Sextus Empiricus presents four different accounts of the conditional in increasing strength. Contemporary analogues have been identified (subject to various degrees of controversy) for the first three, but the last, which even fails to satisfy A>A, has proved elusive. In this talk, I discuss ways of modeling this heterodox conditional. Taking a cue from Sextus, I regard the characteristic feature of this conditional as one of proper (conceptual) containment and approach it using the framework of containment logic. Different implementations of this approach are discussed and evaluated both for their historical and technical merits. In the course of the talk, I will discuss (among other things) the relationship between Sextus’ third and fourth accounts, how Kripke semantics can be and has been used to deepen our understanding of various ancient conditionals, and how ancient notions of containment might yield interesting new (old) perspectives on contemporary containment logic.
Saul Kripke Center, Young Scholars Series: Yale Weiss, “Sextus Empiricus’ Fourth Conditional and Containment Logic”
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 available for advance reading here.
This meeting is open to all who are interested. Please feel free to pass this announcement on, or direct others to our website at logic.commons.gc.cuny.edu.
Logic & Metaphysics Workshop
Feb 26 Martin Pleitz, Muenster
Mar 5 Vera Flocke, NYU
Mar 12 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
May14 Rohit Parikh
Feb 26 Martin Pleitz, Muenster
Mar 5 Vera Flocke, NYU
Mar 12 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
May14 Rohit Parikh
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.
Logic & Metaphysics Workshop
Feb 26 Martin Pleitz, Muenster
Mar 5 Vera Flocke, NYU
Mar 12 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
May14 Rohit Parikh
Feb 26 Martin Pleitz, Muenster
Mar 5 Vera Flocke, NYU
Mar 12 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
May14 Rohit Parikh
Feb 26 Martin Pleitz, Muenster
Mar 5 Vera Flocke, NYU
Mar 12 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
May14 Rohit Parikh
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.
Logic & Metaphysics Workshop
Feb 26 Martin Pleitz, Muenster
Mar 5 Vera Flocke, NYU
Mar 12 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
May14 Rohit Parikh
In this short talk, I present a new account of the nature of proof, with the aim of explaining how proof could actually play the role in reasoning that it does, and answering some long-standing puzzles about the nature of proof. Along the way, I’ll explain how Kreisel’s Squeezing argument helps us understand the connection between an informal notion of of validity and the notions formalised in our accounts of proofs and models, and the relationship between proof-theoretic and model-theoretic analyses of logical consequence.