The Logic and Metaphysics Workshop will meet on March 24th from 2:00-4:00 in-person at the Graduate Center (Room 7395) for a talk by Davide Sutto (Oslo).

Title: The iterative conception of pluralities

Abstract: Georg Cantor informally distinguished between “consistent” and “inconsistent” multiplicities as those many things that, respectively, can and cannot be thought of as one, i.e., as a set. In this talk I propose a framework that clarifies the distinction through a contemporary development of the iterative conception of set. Reshaping Tim Button’s Level Theory by means of plural logic, I define and axiomatize the notion of a plural level. This provides an explanation of Cantor’s consistent multiplicities as level-bound pluralities, namely as those pluralities that appear at some level of the plural cumulative hierarchy of sets. Furthermore, it also yields a development of set theory from plural logic that retains the full power of the comprehension axiom schema. This feature is especially relevant as it enables a parallel understanding of inconsistent multiplicities as those pluralities that are not level-bound, that is, as proper classes.

The Logic and Metaphysics Workshop will meet on March 17th from 4:00-6:00 in-person at the Graduate Center (Room 7395) for a talk by Greg Restall (St Andrews).

Title: Modal logic and contingent existence

Abstract: In this talk, I will defend contingentism, the idea that some things exist contingently. It might be surprising that this needs defence, but natural reasoning principles concerning possibility and necessity on the one hand, and the existential and universal quantifiers on the other, have led some to necessitism, the view that everything that exists, exists necessarily. Almost all recent work on modal semantics makes essential use of possible worlds models. These models have proved useful for analysing the structural properties of modal logics, but it is less clear that they fix the meaning of our modal vocabulary, given that we have no grasp of what counts as a possible world, independent of our grasp of what counts as possible. In this talk, I describe an inferentialist semantics for modal and quantificational vocabulary, not as a rival to possible worlds models, but as an explanation of how the concepts we do employ can be modelled using possible worlds. I then use this inferentialist semantics to clarify the contingentist’s commitments, and offer answers to necessitist objections.

The Logic and Metaphysics Workshop will meet on March 17th from 2:00-4:00 in-person at the Graduate Center (Room 7395) for a talk by Marian Călborean (Bucharest).

Title: Vagueness as dispersion

Abstract: Classical logic (FOL) is thought to be incompatible with the fuzzy cutoffs of vague predicates. I conceptualize vagueness as the dispersion of negative and positive cases of predicates such as “tall” across ranks defined by the preferred ordering—e.g., “having less or equal cm of height”. I distinguish vertical dispersion—both negative and positive cases of the predicate can share the same measurement—and horizontal dispersion—change happens with gradually fewer intercalations of negative and positive cases. Parallel to the non-classical approach of Cobreros et al. (2012), I introduce two classical shorthand modifiers “strictly” and “broadly”. Then, the Sorites paradox is solved by weakening the principle of tolerance to “If a person is strictly tall, anyone one less cm of height is broadly tall”, noted ∀xy.((Lxy ∧ [L]Ty) ⊃ Tx). This notational extension of FOL is conservative and can express higher-order vagueness.

The Logic and Metaphysics Workshop will meet on March 3rd from 2:00-4:00 in-person at the Graduate Center (Room 7395) for a talk by Koji Tanaka (ANU).

Title: What’s so impossible about impossible worlds?

Abstract: Imagine a world where the laws of nature (or physics) are different from those in the actual world. In such a world, Usain Bolt might run faster than the speed of light. Graham Priest argues that such a world would be a physically impossible world. By analogy, a world where the laws of logic are different from those in the actual world is said to be a logically impossible world. But what’s so impossible about such a world? I argue that there is nothing impossible about a world that is merely different from the actual world. I will show that Priest’s position conflates how to evaluate modal statements with how to identify the actual world among all worlds. After rejecting Priest’s position, I will conclude by arguing that what makes a world impossible is not the difference in laws, but the violation of those laws.

The Logic and Metaphysics Workshop will meet on March 10th from 2:00-4:00 in-person at the Graduate Center (Room 7395) for a talk by Rani Rachavelpula (Columbia).

Title: Generating gunk

Abstract: An object is gunky iff all its parts have proper parts. Since Anaxagoras, philosophers have appealed to the existence of gunk to support a range of metaphysical views. These discussions raise questions about the composition of gunk: How is gunk generated? How do we get gunk? Obviously, gunk cannot be composed of atoms. Otherwise, we have admitted objects into our ontology (i.e. atoms) with no proper parts. This has led to the widespread belief that gunk cannot be generated. It must be given. In this talk we prove this claim to be false. Though gunk cannot be generated by atoms, it can nevertheless be generated by some fundamental parts. We apply Weyl’s Equidistribution Theorem to produce a mereological model of a universe which is gunky yet generated by a single element. This dispels other misconceptions about gunk and provides a new perspective on debates about metaphysical fundamentality.

The Logic and Metaphysics Workshop will meet on February 10th from 2:00-4:00 in-person at the Graduate Center (Room 7395) for a talk by Sergei Artemov (CUNY).

Title: Consistency of PA is a serial property, and it is provable in PA

Abstract: We revisit the question of whether the consistency of Peano Arithmetic PA can be established in PA and answer it affirmatively. Since PA-derivations are finite objects, their Gödel codes are standard natural numbers, and PA-consistency is equivalent to the series ConS(PA) of arithmetical formulas “n is not a code of a proof of 0 = 1” for numerals n = 0, 1, 2, … In contrast, in the consistency formula Con(PA) “for all x, x is not a proof of 0 = 1,” the quantifier “for all x” captures standard and nonstandard numbers, Con(PA) is strictly stronger than PA-consistency. Adopting Con(PA) as PA-consistency was a strengthening fallacy: the unprovability of Con(PA) does not yield the unprovability of PA-consistency. A proof of a serial property is a selector proof: prove that each instance has a proof. We selector prove ConS(PA) thus showing that PA-consistency is provable in PA. We discuss other theories and perspectives for Hilbert’s consistency program.

The Logic and Metaphysics Workshop will meet on February 24th from 2:00-4:00 in-person at the Graduate Center (Room 7395) for a talk by Eduardo Fermé (Madeira).

Title: Belief change: An introduction

Abstract: The 1985 paper by Carlos Alchourrón (1931–1996), Peter Gärdenfors, and David Makinson (AGM), “On the Logic of Theory Change: Partial Meet Contraction and Revision Functions” was the starting-point of a large and rapidly growing literature that employs formal models in the investigation of changes in belief states and databases. In this talk, the first 40 years of this development are briefly summarized. The topics covered include equivalent characterizations of AGM operations, extended representations of the belief states, change operators not included in the original framework, iterated change, applications of the model, its connections with other formal frameworks, and criticism of the model.

The Logic and Metaphysics Workshop will meet on February 3rd from 2:00-4:00 in-person at the Graduate Center (Room 7395) for a talk by Noah Greenstein (Independent Scholar).

Title: Existentialism, deontic logic and de dicto – de re

Abstract: I investigate how to logically formalize Existentialist obligations, i.e., obligations we have to ourselves and ourselves alone. It is argued that Standard Deontic Logic cannot distinguish between obligations imposed by an external system, like society or a theory of ethics, and self-imposed Existential obligations. A solution to this ambiguity is proposed by applying the De Dicto – De Re distinction to Deontic Logic in the style of Epistemic Logic: by varying the order of the existential quantifier and the modal operator, we can change the interpretation of the statement to represent Existential or external obligations. This leads to a kind of Formal Existentialism, where formal analysis can be applied to Existentialist claims, and new perspectives on standing problems in Deontic Logic.

The Logic and Metaphysics Workshop will be meeting on Mondays from 2:00 to 4:00 pm unless otherwise indicated. Talks will be in-person only at the CUNY Graduate Center (Room 7395). The provisional schedule is as follows:

Feb 3. Noah Greenstein (Independent Scholar)

Feb. 10. Sergei Artemov (CUNY)

Feb 17. NO MEETING

Feb 24. Eduardo Fermé (Madeira)

Mar 3. Koji Tanaka (ANU)

Mar 10. Rani Rachavelpula (Columbia)

Mar 17. Double Session (2:00 to 6:00 pm): Marian Călborean (Bucharest), Greg Restall (St Andrews)

Mar 24. Davide Sutto (Oslo)

Mar 31. NO MEETING

Apr 7. Allison Aitken (Columbia)

Apr 14. NO MEETING

Apr 21. Jacob McNulty (Yale)

Apr 28. Claudine Verheggen (York, CA)

May 5. Luca Incurvati (ILLC)

May 12. Mircea Dumitru (Bucharest)