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The Reduction of Necessity to Essence (Andreas Ditter)

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.

World-Relative Truth and Pre-Worldly Truth (Sungil Han)

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.

Quantifiers and Modal Logic (Melvin Fitting)

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.)

Metaphysics Beyond Grounding (Daniel Nolan)

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.