2026 Fall

• Mel Fitting (CUNY), “A Few Intuitionistic Logics”, 11/20, 1–3pm, Room 5409,

  • Intuitionistic logic was formulated in the 1930’s by Arend Heyting, and was designed to embody the reasoning of an intuitionistic mathematician (HPC, for “Heyting Predicate Calculus”). A rough equivalent to “intuitionist” here is “constructivist”. HPC has been much studied ever since for a surprisingly broad range of reasons, but that does not concern us here. In the 1960’s Saul Kripke introduced the now standard possible world semantics for intuitionistic logic, formally capturing the ideas embodied in intuitionistic reasoning, though it requires classical mathematics to show it is Heyting’s calculus that it captures.

As a matter of fact, a person with constructivist motivations does not exclusively reason about mathematics. The real world is doubtless a subject of interest too. But concerning the real world, we may have gaps in our knowledge. Or we may have contradictory information to work with, often called gluts. Relatives of classical logic have been introduced for such reasoning. Perhaps the most common are the logic of paradox, LP, for gluts; Kleene’s strong three-valued logic, K3, for gaps, and first-degree entailment, FDE, for both. But these do not take constructivist motivations into account.

It turns out there are intuitionistic analogs of the logics just mentioned, LP, K3, and FDE. These are what I will discuss. Intuitionistic versions have a Kripke-style semantics, natural tableau proof systems, and share many of their fundamental properties with Heyting’s calculus. But much is still unknown, since this is all rather new.

For background, Heyting’s own explanation is still good reading: Intuitionism: An Introduction, North-Holland Publishing Co, 1956, revised edition 1971. Kripke’s paper on intuitionistic semantics is of historical importance, but a more friendly discussion can be found in Wikipedia’s article, Kripke Semantics. My own work has now appeared. A background paper appeared in Notre Dame Journal of Formal Logic , followed by Simple tableaus for simple logics. There is a third paper in the sequence, but it wanders from the topics I will be discussing, so skip it for now.

(This talk is a revised version of a talk I gave in Peru a year ago.)

• Jayme Koszyn (Student Talk, NYU Gallatin), “No Time Like the Present: The Barcan Formula and its Relationship to the Contradiction of the ‘Now. ”, 12/11, 1–3pm, Room 5409,

  • The "now" appears as it disappears, disappears as it appears: it is a contradiction. My talk extends this claim to features of the Barcan Formula (BF). Axiom 11 of Barcan’s quantified modal logic system, as outlined in her 1946 “A Functional Calculus of First Order Based on Strict Implication” which quantifies Lewis and Langford’s 1932 propositional logic system S2—and to which axiom Prior gave the BF its name—inspired key philosophical concepts, including within temporal logic. I position my intuitions about the “now” with a proof that is as volatile in form as is the “now” itself against the background of the BF’s metaphysical exuberance, thereby inviting a debate about how we perceive and reason about the “now,” and i) show that the “now” is a contradiction, as well as ii) introduce semantic values that may change within a proof that is in itself dynamic. Questions include: Can an animated proof that has its own dimensions of “nowness” help us understand the “now” in a deeper sense, in ways related to the BF’s mining of new connections between quantified modal logic and metaphysics? Can a new kind of proof (that still retains rigor) help us to understand the mysteries of abstract ideas other than time, such as knowledge, morality, and even God? Asking these questions build on and honors—during its 80th anniversary—the metaphysical powers of the BF, a formula which provided thinkers including Prior and Williamson with iterative motivation and inspiration. 

• Melissa Fusco (Columbia), “Must the Chances Update by Conditionalization? ”, 10/30, 1–3pm, Room 5409,

  • This paper presents a case study in the relationship between formal semantics and epistemic utility theory. I show how a non-conditionalizing update rule, based on Goldstein (2020)’s conditionalization-with-normalization, can maximize expected accuracy over a modal language with a two-parameter domain semantics (Yalcin, 2007, a.o.). The two-parameter architecture is important, because it gives the language the capacity to express chance-deference norms. My treatment is motivated by Caie (2015)’s “Temporal Principle”—roughly, the claim that rational agents defer to the current actual chances. 

SPRING 2O26