Relevant logics as topical logics (Andrew Tedder)

The Logic and Metaphysics Workshop will meet on April 1st from 4:15-6:15 in-person at the Graduate Center (Room 7395) for a talk by Andrew Tedder (Vienna).

Title: Relevant logics as topical logics

Abstract: There is a simple way of reading a structure of topics into the matrix models of a given logic, namely by taking the topics of a given matrix model to be represented by subalgebras of the algebra reduct of the matrix, and then considering assignments of subalgebras to formulas. The resulting topic-enriched matrix models bear suggestive similarities to the two-component frame models developed by Berto et. al. in Topics of Thought. In this talk I’ll show how this reading of topics can be applied to the relevant logic R, and its algebraic characterisation in terms of De Morgan monoids, and indicate how we can, using this machinery and the fact that R satisfies the variable sharing property, read R as a topic-sensitive logic. I’ll then suggest how this approach to modeling topics can be applied to a broader range of logics/classes of matrices, and gesture at some avenues of research.

Modal quantifiers, potential infinity, and Yablo sequences (Michał Godziszewski)

The Logic and Metaphysics Workshop will meet on March 18th from 4:15-6:15 in-person at the Graduate Center (Room 7395) for a talk by Michał Godziszewski (Warsaw).

Title: Modal quantifiers, potential infinity, and Yablo sequences

Abstract: When properly arithmetized, Yablo’s paradox results in a set of formulas which (with local disquotation in the background) turns out to be consistent, but omega-inconsistent. Adding either uniform disquotation or the omega-rule results in  inconsistency. Since the paradox involves an infinite sequence of sentences, one might think that it doesn’t arise in finitary contexts. We study whether it does. It turns out that the issue depends on how the finitistic approach is formalized. On one of them, proposed by Marcin Mostowski, all the paradoxical sentences simply fail to hold. This happens at a price: the underlying finitistic arithmetic itself is omega-inconsistent. Finally, when studied in the context of a finitistic approach which preserves the truth of standard arithmetic, the paradox strikes back — it does so with double force, for now the inconsistency can be obtained without the use of uniform disquotation or the omega-rule.

Note: This is joint work with Rafał Urbaniak (Gdańsk).

A moderate theory of overall resemblance (Dan Marshall)

The Logic and Metaphysics Workshop will meet on March 25th from 4:15-6:15 in-person at the Graduate Center (Room 7395) for a talk by Dan Marshall (Lingnan).

Title: A moderate theory of overall resemblance

Abstract: This paper defends the moderate theory of overall resemblance stated by: A) y is at least as similar to x as z is iff: i) every resemblance property shared by x and z is also shared by x and y, and ii) for any resemblance family of properties F, y is at least as similar to x as z is with respect to F. In this account, a resemblance property is a property that corresponds to a genuine respect in which two things can resemble each other, whereas a resemblance family is a set of properties with respect to which things can be more or less similar to each other. An example of a resemblance property is being cubical, an example of a non-resemblance property is being either a gold cube or a silver sphere, and an example of a resemblance family is the set of specific mass properties.

Dispensing with the grounds of logical necessity (Otávio Bueno)

The Logic and Metaphysics Workshop will meet on March 11th from 4:15-6:15 in-person at the Graduate Center (Room 7395) for a talk by Otávio Bueno (Miami).

Title: Dispensing with the grounds of logical necessity

Abstract: Logical laws are typically conceived as being necessary. But in virtue of what is this the case? That is, what are the grounds of logical necessity? In this paper, I examine four different answers to this question in terms of: truth-conditions, invariance of truth-values under different interpretations, possible worlds, and brute facts. I ultimately find all of them wanting. I conclude that an alternative conception of logic that dispenses altogether with grounds of logical necessity provides a less troublesome alternative. I then indicate some of the central features of this conception.

Declaring no dependence (Elise Crull)

The Logic and Metaphysics Workshop will meet on March 4th from 4:15-6:15 in-person at the Graduate Center (Room 7395) for a talk by Elise Crull (CUNY).

Title: Declaring no dependence

Abstract: Viable fundamental ontologies require at least one suitably stable, generic-yet-toothy metaphysical dependence relation to establish fundamentality. In this talk I argue that recent experiments in quantum physics using Page-Wootters devices to model global vs. local dynamics cast serious doubt on the existence of such metaphysical dependence relations when – and arguably, inevitably within any ontological framework – physical systems serve as the relata.

Semantic paradoxes as collective tragedies (Matteo Plebani)

The Logic and Metaphysics Workshop will meet on February 26th from 4:15-6:15 in-person at the Graduate Center (Room 7395) for a talk by Matteo Plebani (Turin).

Title: Semantic paradoxes as collective tragedies

Abstract: What does it mean to solve a paradox? A common assumption is that to solve a paradox we need to find the wrong step in a certain piece of reasoning. In this talk, I will argue while in the case of some paradoxes such an assumption might be correct, in the case of paradoxes such as the liar and Curry’s paradox it can be questioned.

Some model theory for axiomatic theories of truth (Roman Kossak)

The Logic and Metaphysics Workshop will meet on February 5th from 4:15-6:15 in-person at the Graduate Center (Room 7395) for a talk by Roman Kossak (CUNY).

Title: Some model theory for axiomatic theories of truth

Abstract: Tarski’s arithmetic is the complete theory of (N,+,x,Tr), where (N,+,x) is the standard model of arithmetic and Tr is the set of Gödel numbers of all true arithmetic sentences. An axiomatic theory of truth is an axiomatic subtheory of Tarski’s arithmetic. If (M,+,x,T) is a model of an axiomatic theory of truth, then we call T a truth class. In 1981, Kotlarski, Krajewski, and Lachlan proved that every completion of Peano’s arithmetic has a model that is expandable to a model  with a truth class T that satisfies all biconditionals in Tarski’s definition of truth formalized in PA. If T is such a truth class, it assigns truth values to all sentences in the sense of M, standard and nonstandard. The proof showed  that such truth classes can be quite pathological. For example, they may declare true some infinite disjunctions of the single sentence (0=1). In 2018, Enayat and Visser gave  a much simplified model-theoretic proof, which opened the door for further investigations of nonstandard truths, and many interesting new results by many authors appeared. I will survey some of them, concentrating on their model-theoretic content.

Spring 2024 Schedule

The Logic and Metaphysics Workshop will be meeting on Mondays from 4:15 to 6:15 unless otherwise indicated. Talks will be in-person only at the CUNY Graduate Center (Room 7395). The provisional schedule is as follows:

Feb 5. Roman Kossak (CUNY)

Feb 12. NO MEETING

Feb 19. NO MEETING

Feb 26. Matteo Plebani (Turin)

Mar 4. Elise Crull (CUNY)

Mar 11. Otávio Bueno (Miami)

Mar 18. Michał Godziszewski (Warsaw)

Mar 25. Dan Marshall (Lingnan)

Apr 1. Andrew Tedder (Vienna)

Apr 8. Asya Passinsky (CEU)

Apr 15. Jessica Collins (Columbia)

Apr 22. NO MEETING

Apr 29. Anandi Hattiangadi (Stockholm)

May 6. Lorenzo Rossi (Turin)