The final meeting of the logic and metaphysics workshop this semester will be tomorrow, 5/14. Please see the previous post for details.
The Logic and Metaphysics Workshop will meet on May 14th from 4:15-6:15 in room 3309 of the CUNY Graduate Center for a talk by Rohit Parikh (CUNY).
Title: To What Extent is a Group an Individual?
Abstract: Dennett in his Darwin’s Dangerous Idea (1995) and Kinds of Minds (1996) discusses an evolutionary hierarchy of intellectual progress. He calls the hierarchy the ‘Tower of Generate-and-Test,’ where there are five kinds of creatures. These range from ‘Darwinian creatures,’ organisms which are blindly generated and field-tested, to Popperian creatures which can make plans, to creatures like human beings who use ‘language’ to communicate with others like them. One could ask, “at what level, if any, do groups belong” if indeed we can regard them as individuals or as intentional beings? Since they do use language, one would think, they are creatures of this last level. But difficulties arise in thinking of groups as even Popperian. In order for a group to have a real identity, it needs coherence in its “views” and in its actions. To think of it as a game theoretic opponent (or partner) one needs a certain amount of predictability. Such predictablility is not always absent. We know quite well how “Russia,” thought of as an agent, will respond in case of a nuclear attack. But “the Republican party” or “Republicans in Congress” might be less predictable in their response to say the election of Conor Lamb. Two kinds of theoretical issues thus arise. One is epistemic coherence which can exist only if the group possesses mechanisms for intra-group communication. An army preparing to wage a battle needs scouts to gather information and to transmit it to troops. A university needs an internal email system. The other is exhibiting coherence of views where issues like the Arrow theorem or the judgment aggregation paradox may arise. A group where power is more concentrated, at the extreme in one individual, is likely to be more predictable and more consistent in its response. It applies less to a more diverse group like the Democratic party. So a better question to ask than “do groups exist?” is “to what extent is a given set of individuals (with a name) an individual, and on what issues?” In other words we suggest an algorithmic and game theoretic alternative to the ontological question. We will offer some answers while avoiding a surfeit of mathematics.
The Logic and Metaphysics Workshop will meet on May 7th from 4:15-6:15 in room 3309 of the CUNY Graduate Center for a talk by Andreas Ditter (NYU).
Title: The Reduction of Necessity to Essence
Abstract: In ‘Essence and Modality’, Kit Fine proposes that for a proposition to be metaphysically necessary is for it to be true in virtue of the nature of all objects whatsoever. Call this view ‘Fine’s Thesis’. On its intended interpretation, the view takes for granted a notion of essence that is not analyzable in terms of metaphysical necessity. It can thus be understood as an analysis of metaphysical necessity in terms of an independently understood notion of essence. In this talk, I examine Fine’s Thesis in the context of Fine’s logic of essence (LE). I consider different ways in which the view might be developed, investigate their philosophical tenability and make precise how the plausibility of the thesis is dependent on general essentialist principles. I argue that Fine’s own development of the view, which rests on the assumption that metaphysical necessity obeys the modal logic S5, is incompatible with an independently plausible essentialist principle. I show that we can still retain S5 for metaphysical necessity by adopting a theory that is slightly weaker than Fine’s. I will conclude, however, that the most promising defense of Fine’s Thesis in the context of LE involves the adoption of a theory in which the logic of metaphysical necessity is exactly S4, not S5.
The Logic and Metaphysics Workshop will meet on April 30th from 4:15-6:15 in room 3309 of the CUNY Graduate Center for a talk by Sungil Han (Seoul National University).
Title: World-Relative Truth and Pre-Worldly Truth
Abstract: The problem of contingent existence – the problem of how an actual individual, say Socrates, could have not existed – has been a thorny problem in actualist theorists of modality. To solve the problem, Robert Adams divides world-relative truth into truth-in-a-world and truth-at-a-world and proposes that Socrates’s nonexistence is possible in the sense that his nonexistence is true at some possible world, not in some possible world. Adams’s solution relies on a semantic principle by which to determine what are true at a world, but, as he noted himself, the semantic principle leads to implausible consequences. My aim in this talk is to offer a solution along the line of Adams’s proposal without relying on his semantic principle. The fundamental limitation of Adams’s proposal is that his semantic principle is intended to determine what propositions are true at a world, but he provides no proper account of what it means to say that a proposition is true at a world. I offer an account of the notion of truth-at-a-world: to say that a proposition p is true at a world w is to say that the supposition of p is a precondition for w to perform its representational function qua a world-story in the sense that we need to suppose that p if we are to take w to be a world-story. Then I argue that propositions of identity, nonidentity and essences about all actual individuals are true at any world, which vindicates the view, notably espoused by Kit Fine, that these ‘pre-worldly’ truths are unqualifiedly necessary truths.
The Logic and Metaphysics Workshop will meet on April 23rd from 4:15-6:15 in room 3309 of the CUNY Graduate Center for a talk by Melvin Fitting (CUNY).
Title: Quantifiers and Modal Logic
Abstract: In classical logic the move from propositional to quantificational is profound but essentially takes one route, following a direction we are all familiar with. In modal logic, such a move shoots off in many directions at once. One can quantify over things or over intensions. Quantifier domains can be the same from possible world to possible world, shrink or grow as one moves from a possible world to an accessible one, or follow no pattern whatsoever. A long time ago, Kripke showed us how shrinking or growing domains related to validity of the Barcan and the converse Barcan formulas, bringing some semantic order into the situation. But when it comes to proof theory things get somewhat strange. Nested sequents for shrinking or growing domains, or for constant domains or completely varying domains, are relatively straightforward. But axiomatically some oddities are quickly apparent. A simple combination of propositional modal axioms and rules with standard quantificational axioms and rules proves the converse Barcan formula, making it impossible to investigate its absence. Kripke showed how one could avoid this, at the cost of using a somewhat unusual axiomatization of the quantifiers. But things can be complicated and even here an error crept into Kripke’s work that wasn’t pointed out until 20 years later, by Fine. Justification logic was started by Artemov with a system related to propositional S4, called LP. This was extended to a quantified version by Artemov and Yavorskaya, for which a semantics was supplied by Fitting. Recently Artemov and Yavorskaya introduced what they called bounding modalities, by transferring ideas back from quantified LP to S4. In this paper we continue the investigation of bounding modalities, but for axiomatic K since modal details aren’t that important for what I’m interested in. We wind up with axiomatic systems allowing for a monotonic domain condition, an anti-monotonic one, neither, or both. We provide corresponding semantics and give direct soundness and completeness proofs. Unlike in Kripke’s treatment, the heavy lifting is done through generalization of the modal operator, instead of restriction on quantification. (This talk continues one given earlier in the semester in Artemov’s seminar. There are differences, but if you happened to hear that talk, you could easily skip this one since the differences are not great.)
The Logic and Metaphysics Workshop will meet on April 16th from 4:15-6:15 in room 3309 of the CUNY Graduate Center for a talk by Daniel Nolan (Notre Dame).
Title: Metaphysics Beyond Grounding
Abstract: Thinking about metaphysical problems in terms of grounding has its uses, but those uses are limited. I am not a sceptic either about grounding or our ability to make progress on some metaphysical puzzles by invoking it, but I will argue it only has a partial role to play in our metaphysical theories. I will discuss how grounding relates to necessity, to explanation and to parsimony in theory choice. Finally, I will discuss the connection between grounding and the proper aim, or rather aims, of metaphysics.
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.
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.