The Logic and Metaphysics Workshop will meet on December 2nd from 4:15-6:15 in-person at the Graduate Center (Room 4419) for a talk by Sam Burns (Columbia).

Title: Formalizability and mathematical rigor

Abstract: Mathematicians do not generally prove theorems via formal derivations. Given that formal derivations are the contemporary ideal of mathematical rigor, this raises questions as to how informal proofs can be rigorous. Responding to this worry, derivationists claim that an informal proof is rigorous if it can be routinely translated into a formal derivation. In this talk I raise some concerns about derivationism as a universal claim about mathematical rigor. I break the derivationist thesis into two parts: a claim about the formalizability of the theorems themselves, and a claim about the formalizability of mathematical inferences. I then discuss some case studies that call into question the plausibility of each part of the derivationist thesis. Based on these case studies, I suggest that a contextualist account of mathematical rigor best coheres with mathematical practice, thereby rejecting the claim that (complete) formalizability is a desideratum in all mathematical contexts.

The Logic and Metaphysics Workshop will meet on December 9th from 4:15-6:15 in-person at the Graduate Center (Room 4419) for a talk by Justin Clarke-Doane (Columbia).

Title: Intuition and observation

Abstract: The motivating question of this talk is: ‘How are our beliefs in the theorems of mathematics justified?’ This is distinguished from the question ‘How are our mathematical beliefs reliably true?’ We examine an influential answer, outlined by Russell, championed by Gödel, and developed by those searching for new axioms to settle undecidables, that our mathematical beliefs are justified by ‘intuitions’, as our scientific beliefs are justified by observations. On this view, axioms are analogous to laws of nature. They are postulated to best systematize the data to be explained. We argue that there is a decisive difference between the cases. There is agreement on the data to be systematized in the scientific case that has no analog in the mathematical one. There is virtual consensus over observations, but conspicuous dispute over intuitions. In this respect, mathematics more closely resembles philosophy. We conclude by distinguishing two ideas that have long been associated — realism (the idea that there is an independent reality) and objectivity (the idea that in a disagreement, only one of us can be right). We argue that, while realism is true of mathematics and philosophy, these domains fail to be objective. One upshot of the discussion is that even questions of fundamental physics may fail to be objective insofar as the mathematical, logical, and evaluative hypotheses that they presuppose fail to be.  Another is pragmatism.  Factual questions in mathematics, modality, logic, and evaluative areas go proxy for non-factual practical ones.

Note: This is joint work with Avner Ash (Boston College).

The Logic and Metaphysics Workshop will meet on November 18th from 4:15-6:15 in-person at the Graduate Center (Room 4419) for a talk by Claudio Calosi (Venice) and Damiano Costa (Lugano).

Title: Pluralisms in gunky worlds

Abstract: The possibility of gunk, namely the possibility that an entity possesses an infinitely descending chain of smaller and smaller parts, has famously been used by Schaffer (2010) to argue in favour of priority monism, namely the view that the whole universe is the fundamental concrete entity on which any of its parts depends. In this paper, we present and explore different principled ways of being a priority pluralist in gunky worlds, thus deflecting the gunk argument. Some of these ways turn out to be examples of middleism, i.e. the view that the fundamental level is that of middle-sized and mereologically intermediate objects. Hence, they don’t only effectively deflect the gunk threat to pluralism, but they also catalyse any argument in favour of the middleist position.

The Logic and Metaphysics Workshop will meet on November 11th from 4:15-6:15 in-person at the Graduate Center (Room 4419) for a talk by Friederike Moltmann (CNRS).

Title: On the ontology and semantics of absence

Abstract: This talk proposes a new semantic analysis of verbs of absence such as ‘lack’ and ‘be missing’. The semantics is based on the notion of a conceptual whole and its (conceptual) parts, which generates both variable embodiments (of the whole and its structural parts) and modal objects of the sort of a ‘lack’. It involves an extension of truthmaker semantics (applied to modal objects) where truthmakers (satisfiers) now include parts of wholes. The talk rehabilitates entities of the sort of ‘lacks’ often subject to ridicule, most notoriously by Chomsky.

The Logic and Metaphysics Workshop will meet on November 4th from 4:15-6:15 in-person at the Graduate Center (Room 4419) for a talk by Elena Ficara (Paderborn).

Title: Logic and discrimination

Abstract: My talk is about the connection between logic and discrimination, with special focus on Plumwood’s ideas in her groundbreaking article ‘The Politics of Reason. Towards a Feminist Logic’ (1993). Although Plumwood’s paper is not focused on the notion of discrimination, what she writes is useful for illuminating some basic mechanisms of thought that are at the basis of discriminatory practices. After an introductory section about the concepts of logic and discrimination at the basis of my analysis, I present Plumwood’s ideas in 1993 with a special focus on their relevance for understanding the nature of discrimination. More specifically, I use examples of discriminatory practices that make the connection between logical operations and oppression envisaged by Plumwood clear. I focus especially on two questions: Can logic produce discrimination? Can logic contribute to the fight against discrimination? If so, how?

The Logic and Metaphysics Workshop will meet on November 25th from 4:15-6:15 in-person at the Graduate Center (Room 4419) for a talk by Damian Szmuc (Buenos Aires).

Title: More semantics for Angell’s logic of Analytic Containment

Abstract: This presentation aims to explore new semantics for Angell’s logic of Analytic Containment through the discussion of the topic-transformativeness of negation. For this purpose, we review some new developments by Song, Omori, Arenhart, and Tojo on two-address valuations for topic-transparent logics related to content inclusion, and extend their techniques for Angell’s logic of Analytic Containment. In particular, we present a 4-valued non-deterministic and a 16-valued deterministic semantics, both obtained through direct products of De Morgan lattices and involutive semilattices.

The Logic and Metaphysics Workshop will meet on October 28th from 4:15-6:15 in-person at the Graduate Center (Room 4419) to celebrate its 10th Anniversary. For this special occasion, there will be a panel discussing (inter alia) currents trends in, and the future of, Logic and Metaphysics.

Topic: The present and future of logic and metaphysics

Panelists: Hartry Field (NYU), Mel Fitting (CUNY), Noah Greenstein (Independent Scholar), Graham Priest (CUNY), and Achille Varzi (Columbia)

The Logic and Metaphysics Workshop will meet on October 21st from 4:15-6:15 in-person at the Graduate Center (Room 4419) for a talk by Thomas M. Ferguson (Rensselaer).

Title: Qua, per se, and other topic-transformative operators

Abstract: Recent work challenging principles of topic transparency in topic-sensitive logics has relied on providing accounts of connectives that are topic-transformative, that is, which non-trivially influence the overall topic assigned to a complex. This leads naturally to the question of what operators in natural language might also act as topic-transformative functions. This talk reviews work in progress studying “qua”, “per se”, and other topic-transformative operators. After discussing ways to analyze these operators, we will emphasize how such analyses are likely to assist in a parallel project of updating Richard Sylvan’s work on relevant containment logic.

Note: This is joint work with Pietro Vigiani (Pisa) and Jitka Kadlečková (Rensselaer).

The Logic and Metaphysics Workshop will meet on October 7th from 4:15-6:15 in-person at the Graduate Center (Room 4419) for a talk by Cian Dorr (NYU) and Matt Mandelkern (NYU).

Title: The logic of sequences

Abstract: In the course of proving a tenability result about the probabilities of conditionals, van Fraassen (1976) introduced a semantics for conditionals based on ω-sequences of worlds, which amounts to a particularly simple special case of ordering semantics for conditionals. On that semantics, ‘If p, then q’ is true at an ω-sequence just in case q is true at the first tail of the sequence where p is true (if such a tail exists). This approach has become increasingly popular in recent years. However, its logic has never been explored. We axiomatize the logic of ω-sequence semantics, showing that it is the result of adding two new axioms to Stalnaker’s logic C2: one, Flattening, which is prima facie attractive, and a second, Sequentiality, which is complex and difficult to assess. We also show that when sequence semantics is generalized to arbitrary (transfinite) ordinal sequences, the result is the logic that adds only Flattening to C2. We also explore the logics of a few other interesting restrictions of ordinal sequence semantics, and explore whether sequence semantics is motivated by probabilistic considerations, answering, pace van Fraassen, in the negative.

The Logic and Metaphysics Workshop will meet on September 30th from 4:15-6:15 in-person at the Graduate Center (Room 4419) for a talk by Daniel West (CUNY).

Title: The disjunction property for operational relevance logics

Abstract: A logic has the disjunction property just in case whenever a disjunction is valid, at least one of its disjuncts is valid. The disjunction property is important to constructivists and is a well-known feature of intuitionistic logic. In this talk I present joint work with Yale Weiss in which we use model-theoretic techniques to show that the disjunction property also holds in Urquhart’s operational relevance logics. This is a known result in the case of the positive semilattice logic, but the proof is quite different, being proof-theoretic rather than semantic. These results suggest that operational relevance logics merit further attention from a constructivist perspective. Along the way, we also provide a novel proof that the disjunction property holds in intuitionistic logic.

Note: This is joint work with Yale Weiss (CUNY).