The Logic and Metaphysics Workshop will meet on October 6th from 2:00-4:00 in-person at the Graduate Center (Room 8203) for a talk by Juliette Kennedy (Helsinki).

Title: How first order is first order logic?

The Logic and Metaphysics Workshop will meet on Friday, October 3rd, from 9:30-5:30 in-person at the Graduate Center (Room 8203) for a workshop on relevance logic. The program is available here.

The Logic and Metaphysics Workshop will meet on Friday, September 26th, from 11:00-5:00 in-person at the Graduate Center (Room 7113.08) for a workshop on Paraconsistent Computing. The program is available here.

The Logic and Metaphysics Workshop will meet on September 29th from 2:00-4:00 in-person at the Graduate Center (Room 8203) for a talk by Will Nava (NYU).

Title: Horizontal Fregeanism

Abstract: Fregeanism is the view that primitive expressive roles correspond to metaphysically distinct kinds. For example: singular terms refer to objects whereas predicates ascribe properties, and properties are not objects. Fregeanism is typically paired with the assumption that properties cannot apply to properties of the same ‘rank’, thereby generating a hierarchical space of metaphysical kinds (and corresponding expressive roles). I propose an alternative horizontal Fregeanism, on which properties can self-apply, so no hierarchy is introduced. The metaphysical kinds are just objects, n-place properties (for each n), and propositions. In this talk, I’ll defend horizontal Fregeanism over the hierarchical alternative. I’ll also argue that the view calls for a novel syntax; one that allows direct self-application (i.e. sentences of the form FF), while still respecting the distinction between objects, properties, and propositions. I will present this syntax, along with an attractive logic formulated in it.

The Logic and Metaphysics Workshop will meet on September 22nd from 2:00-4:00 in-person at the Graduate Center (Room 8203) for a talk by Fernando Cano-Jorge (Otago).

Title: The heresies project

Abstract: In the late 90’s, Richard Sylvan and Jack Copeland advanced the idea that computability is logic relative and that the Church-Turing thesis is false. Sylvan called this The Heresies Project and at its core is the idea that couching computability theory on a paraconsistent logic can take us beyond the classically computable. In the first part of this talk, I provide a brief introduction to paraconsistent computability theory, distinguishing non-revisionary approaches vs. Sylvan and Copeland’s more radical proposal. In the second part of this talk, I discuss what is required to pursue The Heresies Project. I will focus on Robinson arithmetic based on Sylvan’s preferred logic, DK, and its ability to both represent all recursive functions and prove Gödel’s first incompleteness theorem. I conclude that one of the keys to The Heresies Project, i.e. using an inconsistent metatheory, seems to clash with the arithmetic’s capacity to capture all recursive functions.