Contradictions without negation and a proof-theoretic, bilateralist account of connexive logics (Sara Ayhan)

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. 


Published
Categorized as Spring 2026

Petr Vopěnka’s new infinitary mathematics (Roman Kossak)

The Logic and Metaphysics Workshop will meet on February 9th from 2:00-4:00 in-person at the Graduate Center (Room 9205) for a talk by Roman Kossak (CUNY).

Title: Petr Vopěnka’s new infinitary mathematics

Abstract: Petr Vopěnka (1935–2015) was an influential mathematician and deep and original thinker. In the 1970s, he developed  an axiomatic system of a non-Cantorial set theory, he called Alternative Set Theory (AST). I will present the  axioms of AST and the new concept of natural infinity on which they are based. I will also talk about how Vopěnka’s radical thoughts on the foundations of  mathematics evolved since the 1970s, as presented in his posthumously published book “New Infinitary Mathematics”.

Why gaps and gluts don’t like De Morgan’s (Xander MacSwan)

The Logic and Metaphysics Workshop will meet on February 2nd from 2:00-4:00 in-person at the Graduate Center (Room 9205) for a talk by Xander MacSwan (CUNY).

Title: Why gaps and gluts don’t like De Morgans

Abstract: This paper explores the space of FDE sublogics which lack some combination of De Morgan Laws. A particular method is proposed for generating the sixteen logics, one for each combination of laws, by systematically applying what I will call modular alterations to standard FDE. Each alteration eliminates a particular De Morgan law from FDE both semantically, by making use of nondeterminism in the matrices, and proof theoretically, using rules that are derivable in FDE and are illustrative of contexts in which classical reasoning can be recaptured. The alterations are modular in that they are designed to be freely combinable, where each combination of alterations generates a unique member of the family of logics. After giving some independent philosophical motivation for the semantic and proof theoretic alterations, I will introduce each alteration in turn and prove soundness and completeness for the resulting logics. Finally, I will discuss the prospects of extending the same strategy to K3 and LP, for the definition of a material conditional, and of alternative methods for generating equivalent logics.

Wittgenstein’s response to Kripke’s Wittgenstein (Claudine Verheggen)

The Logic and Metaphysics Workshop will meet on December 8th from 2:00-4:00 in-person at the Graduate Center (Room 8203) for a talk by Claudine Verheggen (York University, Toronto).

Title: Wittgenstein’s response to Kripke’s Wittgenstein

Abstract: In response to the skeptical problem he found in the writings of Ludwig Wittgenstein, Saul Kripke argued that the only possible rejoinder was a skeptical solution. He did not consider what I take to be Wittgenstein’s way out, which is to dissolve the problem, showing that the skeptic’s conception of what it is for words to have meaning is misguided and therefore the skeptical problem unmotivated. Both skeptical solution and dissolution are committed to semantic nonreductionism. But I do not think that both are committed to semantic quietism. I argue that, whereas the skeptical solution can only lead to quietism, as it concedes that the foundational challenge the skeptic has raised cannot be met and thus only descriptive remarks about meaning are forthcoming, the dissolution of the skeptical problem opens up an alternative way of thinking about meaning, a way which generates its own problem, the resolution of which may result in constructive, albeit still non-reductionist, remarks about meaning.

Published
Categorized as Fall 2025

Do the chances update by conditionalization? (Melissa Fusco)

The Logic and Metaphysics Workshop will meet on December 1st from 2:00-4:00 in-person at the Graduate Center (Room 8203) for a talk by Melissa Fusco (Columbia).

Title: Do the chances update by conditionalization?

Abstract: In “Subjectivist’s Guide to Objective Chance”, David Lewis proposes a chance-credence norm he calls the “Principal Principle” (PP). Lewis also writes, in Sec. 11, that a later chance distribution comes from an earlier one by conditionalization. In this talk, I use an accuracy framework to explore temporalist alternatives to PP. Rather than concerning how an agent’s ur-priors defer to the ur-chances, these temporalist alternatives hold that a rational agent defers to the chances that are current for her. I then sketch how a non-conditionalizing update rule can maximize chance’s own expected accuracy over a language capable of expressing this temporalist norm. This update rule is based on Goldstein (2020)’s conditionalization-with-normalization. 

Published
Categorized as Fall 2025

A novel defense of legal gluts (Brad Armour-Garb)

The Logic and Metaphysics Workshop will meet on November 3rd from 2:00-4:00 in-person at the Graduate Center (Room 8203) for a talk by Brad Armour-Garb (SUNY-Albany).

Title: A novel defense of legal gluts

Abstract: While Graham Priest is best known for taking dialetheia—true contradictions (that is, true statements whose negations are also true)—to emerge from the semantic paradoxes, he (1987/2006) has long maintained that the strongest case for dialetheism emerges from the possibility of legal gluts—dialetheia that incorporate some aspect of law. This contrasts with a point made by JC Beall—that the only dialetheia arise from the semantic paradoxes. Priest argues for the possibility of legal gluts, rather than arguing for their actuality, by relying on hypothetical cases and arguing for their plausibility. Beall disputes Priest’s argument for their possibility and argues that they are in fact impossible. In my talk, after setting out assumptions that serve as “common ground” for the current debate, and briefly summarizing arguments for and against their possibility, I show that Beall’s argument against Priest does not work. I then develop a novel argument for their possibility and, time permitting, go further than Priest by making a case for the actuality of legal gluts.

Published
Categorized as Fall 2025

The probability and logical representation of suppositional conditionals (Giuliano Rosella)

The Logic and Metaphysics Workshop will meet on November 17th from 2:00-4:00 in-person at the Graduate Center (Room 8203) for a talk by Giuliano Rosella (Turin).

Title: The probability and logical representation of suppositional conditionals

Abstract: We present new results concerning the probability and logical representation of suppositional conditionals—conditionals whose truth depends on the consequent holding in appropriately selected worlds where the antecedent is true (e.g., Stalnaker conditionals and Lewis counterfactuals). We show that the probability of such conditionals can be precisely captured by an updated Belief function within the framework of Dempster–Shafer Theory of Evidence (DST). A key consequence of this result is that the probability of suppositional conditionals is bounded by standard imaging-updated probabilities. This finding generalizes Lewis’s earlier characterization of Stalnaker conditionals in terms of Imaging and addresses an open problem concerning the characterization of the probability of counterfactuals. Our approach formally bridges DST with conditional logic and employs a logical reconstruction of Lewis’s counterfactuals as a form of necessitated Stalnaker conditionals, leveraging a notable correspondence between modal operators and Belief functions.

Note: This is joint work with Tommaso Flaminio (IIIA-CSIC, Barcelona), Lluis Godo (IIIA-CSIC, Barcelona), and Jan Sprenger (Turin).

Published
Categorized as Fall 2025

Akrasia, explanation, and a rationalist Trojan horse (Michael Della Rocca)

The Logic and Metaphysics Workshop will meet on October 27th from 2:00-4:00 in-person at the Graduate Center (Room 8203) for a talk by Michael Della Rocca (Yale).

Title: Akrasia, explanation, and a rationalist Trojan horse

Abstract: In this talk, I will explore whether weakness of will or, as I think it is better called, akrasia is possible. I will argue that all accounts that accept the possibility of akrasia sever the link between evaluation of an action as best and one’s motivating desires. Such severing is, I will argue on largely rationalist grounds, unintelligible. I will then go out of my way to be generous: I will offer my opponent a powerful and seemingly promising response in the spirit of rationalism to my argument against the possibility of akrasia. However, this “gift” to my opponents surprisingly turns out to be something of a Trojan horse because, far from shoring up the possibility of akrasia, this response to my argument only threatens to cast into doubt or worse not only akrasia, but also the possibility of reasons for action in general and the coherence of the notion of normativity. The talk ends with some observations as to what this new understanding of action without reasons for action and without normativity might look like.

Published
Categorized as Fall 2025

All counterpossibles are false (Eno Agolli)

The Logic and Metaphysics Workshop will meet on October 20th from 2:00-4:00 in-person at the Graduate Center (Room 8203) for a talk by Eno Agolli (CUNY).

Title: All counterpossibles are false

Abstract: Counterpossibles are conditionals with impossible antecedents. All analyses of conditionals today agree that some counterpossibles are true. In this paper, I advance — to my knowledge for the first time — absurdism, the view that all counterpossibles are false. I do that in two steps. First, I show that there exists indeed an alternative analysis of conditionals which entails absurdism and which is well-motivated. The alternative analysis construes conditionals as plural definite descriptions of possible worlds and it is motivated by an impressively thoroughgoing parallelism between conditionals and definite plurals. Second, I show that absurdism itself is independently motivated, as it provides desirable logical results, a better rationale for positing pragmatic repair for counterpossibles, and ties in with a contemporary current of general skepticism toward counterfactuals.

Published
Categorized as Fall 2025

How first order is first order logic? (Juliette Kennedy)

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?

Abstract: Fundamental to the practice of logic is the dogma regarding the first order/second order logic distinction, namely that it is ironclad. Was it always so? The emergence of the set theoretic paradigm is an interesting test case. Early workers in foundations generally used higher order systems in the form of type theory; but then higher order systems were gradually abandoned in favour of first order set theory—a transition that was completed, more or less, by the 1930s. In this talk I will look at first order logic from various points of view, arguing that the distinction between first order and higher order logics, such as second order logic, is somewhat context dependent. From the philosophical or foundational point of view this complicates the picture of first order logic as a canonical logic.
Note: This is joint work with Jouko Väänänen (Helsinki).
Published
Categorized as Fall 2025