The Logic and Metaphysics Workshop will meet on March 9th from 2:00-4:00 in-person at the Graduate Center (Room 5382) for a talk by Chris Steinsvold (CUNY).

Title: A modest internalist semantics for justified belief

Abstract: Interpreting the box of modal logic as justified belief, we consider a principle of Epistemic Modesty (EM), whereby the agent justifiably believes that at least one of their justified beliefs is false. We discuss a simple topological semantics for KD45+EM, and further argue the topological semantics can be interpreted as an internalist semantics. We focus on the mentalist aspect of internalism, whereby whether a belief is justified depends entirely on the mind (as opposed to the external world). Using Cohen and Lehrer’s well-known New Evil Demon Problem, we give a formal definition of mentalism. Generalizing our definition, we show that for a wide variety of formal semantics, if the semantics is mentalist, then EM is valid in the semantics.

The Logic and Metaphysics Workshop will meet on March 2nd from 2:00-4:00 in-person at the Graduate Center (Room 9207) for a talk by James Walsh (NYU).

Title: A Thomistic synthesis of cosmological and ontological proofs

Abstract: The cosmological and ontological arguments face complementary difficulties. In this talk I will present a synthesis of the two arguments that addresses deficiencies of each. This hybrid argument invokes Thomistic principles linking causality and perfection; chief among these is the Principle of Proportionate Causality, according to which the perfections of effects preexist in their causes. In the spirit of Gödel’s ontological argument, this argument is formalized in higher-order modal logic. After presenting the axioms and the proof, I will discuss various refinements thereof.

The Logic and Metaphysics Workshop will meet on February 23rd from 2:00-4:00 in-person at the Graduate Center (Room 9205) over Zoom (details via mailing list) for a talk by Sara Ayhan (Tohoku).

Title: Contradictions without negation and a proof-theoretic, bilateralist account of connexive logics

Abstract: I’ll present the negation-free fragment of the bi-connexive logic 2C and investigate its properties from the perspective of bilateralist proof-theoretic semantics. I’ll argue that eliminating primitive negation has two important conceptual consequences. First, it requires a reconceptualization of contradictory (also called ‘überconsistent’) logics: in a bilateralist framework, contradiction need not be understood in terms of negation inconsistency, but rather as the coexistence of proofs and refutations for certain formulas within a non-trivial system. Second, it challenges the standard definition of connexive logics, which typically rely on negation-based schemata. Instead, a rule-based conception of connexivity, grounded in bilateralist proof-theoretic semantics, is proposed. This reconception avoids dependence on the validation of specific formula schemata and thereby also dependence on negation.