The Logic and Metaphysics Workshop will meet on May 4th from 2:00-4:00 in-person at the Graduate Center (Room 9205) for a talk by Marian Călborean (Bucharest).

Title: The minimal ontology of time: A unified axiomatization for A- and B-theories

Abstract: How little ontology is needed to accommodate the major logical and metaphysical theories of time? I present a first-order framework whose primitive structure consists of moments, events, a temporal order, start and end functions, tense traces, and minimal change and reality flags. Optional geometric schemas are available for Newtonian, branching, relativistic, and fragmentary time. I argue that the axioms are independently motivated and systematically variable and that canonical positions in temporal metaphysics (presentism, growing-block theory, moving-spotlight theory, eternalism, and fragmentalism) can be recovered as parameter settings or schema extensions of the neutral core. I then prove a representation theorem for Prior’s PF and indicate extensions to metric and interval temporal logics. The framework thereby compares the metaphysical costs of temporal ontologies. Conditional on preserving global reality and substantial temporal passage, growing-block theory emerges as the most parsimonious A-theoretic ontology, while Fine-style fragmentalism divides into two non-equivalent variants, depending on whether fragments are understood as tense-coherent histories or as spacetime regions.

The Logic and Metaphysics Workshop will meet on April 27th from 2:00-4:00 in-person at the Graduate Center (Room 9205) for a talk by Mel Fitting (CUNY).

Title: A few intuitionist logics

Abstract: Intuitionistic logic was designed in the 1930’s by Heyting to embody the reasoning of a constructivist mathematician.  In the 1960’s Kripke introduced possible world semantics for it, capturing ideas embodied in intuitionistic reasoning, though it requires classical mathematics to show that it works.  A constructivist doesn’t reason only about mathematics.  The real world is of some interest too.  But there may be gaps in our knowledge, or contradictory information, gluts.  There are relatives of classical logic aimed at this: logic of paradox LP, for gluts; Kleene’s strong three-valued logic K3, for gaps, first-degree entailment FDE, for both.  These don’t take constructivist motivations into account, but there are intuitionistic analogs that do; we call them ILP, IK3, and IFDE.  These are what I will discuss.  These have a Kripke-style semantics, natural tableau proof systems, and share many fundamental properties of Heyting’s calculus.  But much is still unknown, and this is all rather new.  This work has appeared in Notre Dame Journal of Formal Logic, Simple tableaus for simple logics last year and Simple tableaus for simple intuitionistic logics this year.

The Logic and Metaphysics Workshop will meet on April 20th from 2:00-4:00 in-person at the Graduate Center (Room 9205) for a talk by Jacopo Giraldo (Padua).

Title: The Grounding Structure of Location

Abstract: How is the location of a material object metaphysically determined? Is it where it is because of its parts or the bigger wholes it is part of? In this essay, we open an inquiry into this problem by introducing and contrasting two radical principles. The Bottom-Up Grounding-Locative (BUGL) principle holds that the location of a composite object is grounded by the locations of its components and mereological relations between objects and spatiotemporal regions. In contrast, the Top-Down Grounding-Locative (TDGL) principle claims that an object’s location is grounded by the locations of the larger wholes it helps compose, the spatiotemporal relations it bears with the other components, and its own shape and size. Unlike BUGL, TDGL remains metaphysically neutral regarding the ultimate structure of reality, particularly in the context of classical mereology. We show that TDGL exhibits a gradual character: the way in which an object’s location is grounded depends on the scale or size of the system within which the object is located. Ultimately, we discuss the role of the universe and the impact of its peculiar location on the interpretation of TDGL. 

The Logic and Metaphysics Workshop will host a logic workshop on Friday, April 17th, from 1:00 to 6:30 at the Graduate Center (Room 8400 4419). Details here.