Qua, per se, and other topic-transformative operators (Thomas M. Ferguson)

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).

Published
Categorized as Fall 2024

The logic of sequences (Cian Dorr and Matt Mandelkern)

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.

Published
Categorized as Fall 2024

The disjunction property for operational relevance logics (Daniel West)

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).

Published
Categorized as Fall 2024

Value and freedom (Rohit Parikh)

The Logic and Metaphysics Workshop will meet on September 23rd from 4:15-6:15 in-person at the Graduate Center (Room 4419) for a talk by Rohit Parikh (CUNY).

Title: Value and freedom

Abstract: In order to decide how good a society is, we need some measure of goodness. And the goodness of a society is typically obtained by somehow summing up the well beings of its members. Various approaches include Utilitarianism and Rawlsianism as well as the Leximin approach suggested by Amartya Sen. But Sen and Nussbaum have suggested that the Capability of an individual, what the individual can do, should be the real measure of well being. Another issue is that of freedom. My freedom can be diminished by some restrictive laws. But it can also be diminished by some handicap, or by certain social methods not being available. How to measure the amount of freedom I have? Is it simply the number of options I have, or does the value of the options also matter? And what is the mathematics of freedom?

Note: An extended abstract is available here.

Published
Categorized as Fall 2024