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Bisemilattice Semantics for Intuitionistic and Relevant Modal Logics (Yale Weiss)

The Logic and Metaphysics Workshop will meet on October 4th from 4:15-6:15 (NY time) via Zoom for a talk by Yale Weiss (CUNY GC).

Title: Bisemilattice Semantics for Intuitionistic and Relevant Modal Logics

Abstract: In this talk, I consider modal logics extending J (intuitionistic logic) and RMO (sometimes called ‘constructive mingle’). Adapting previous work of Humberstone, all of these systems are given a purely operational bisemilattice semantics and soundness and completeness results are proved. I consider a way of exactly translating each intuitionistic modal system into a relevant modal companion and discuss what, if any, light this sheds on the interpretation of the relevant companions. Various applications are examined (e.g., to developing constructive theories of entailment) and results germane to those applications are proved. I also discuss connections between the present semantic framework and related frameworks, including Fine’s hybrid operational-partial order semantics, inquisitive semantics, and Urquhart’s semilattice semantics.

A Recipe for Paradox: A Better Schema than the Inclosure Schema (Rashed Ahmad)

The Logic and Metaphysics Workshop will meet on September 27th from 4:15-6:15 (NY time) via Zoom for a talk by Rashed Ahmad (University of Connecticut).

Title: A Recipe for Paradox (A Better Schema than the Inclosure Schema)

Abstract: In this talk, we provide a recipe that not only captures the common structure between semantic paradoxes but it also captures our intuitions regarding the relations between these paradoxes. Before we unveil our recipe, we first talk about a popular schema introduced by Graham Priest, namely, the inclosure schema. Without rehashing previous arguments against the inclosure schema, we contribute different arguments for the same concern that the inclosure schema bundles the wrong paradoxes together. That is, we will provide alternative arguments on why the inclosure schema is both too broad for including the Sorites paradox, and too narrow for excluding Curry’s paradox. We then spell out our recipe. Our recipe consists of three ingredients: (1) a predicate that has two specific rules, (2) a simple method to find a partial negative modality, and (3) a diagonal lemma that would allow us to let sentences be their partial negative modalities. The recipe shows that all of the following paradoxes share the same structure: The liar, Curry’s paradox, Validity Curry, Provability Liar, a paradox leading to Löb’s theorem, Knower’s paradox, Knower’s Curry, Grelling-Nelson’s paradox, Russell’s paradox in terms of extensions, alternative liar and alternative Curry, and other unexplored paradoxes. We conclude the talk by stating the lessons that we can learn from the recipe, and what kind of solutions does the recipe suggest if we want to adhere to the Principle of Uniform Solution.

Carnap is not a Pluralist (Teresa Kouri Kissel)

The Logic and Metaphysics Workshop will meet on September 20th from 4:15-6:15 (NY time) via Zoom for a talk by Teresa Kouri Kissel (Old Dominion University).

Title: Carnap is not a Pluralist

Abstract: Rudolf Carnap is often thought to be a prototype of a logical pluralist. That is, Carnap is thought to hold that more than one logic is correct. I will show in this paper that he cannot be a logical pluralist. I will also show that he cannot be a logical monist or nihilist. In effect, depending on how and where we ask “is logical pluralism true?”, or “how many logics are correct?”, we will find that the answer differs. Thus, he cannot be said to hold that only one of those theories is correct.