EDWARD N. ZALTA
C-FORS is glad to announce two guest lectures by
Professor Edward N. Zalta (Stanford University)
- LECTURE 1: 04 June 2025, 03.00 PM – 04.30 PM (GMH 652)
- LECTURE 2: 05 June 2025, 10.15 AM – 12.00 PM (GMH 652)
LECTURE 1: The Metaphysics of Possibility Semantics
Works by Humberstone (1981, 2011), van Benthem (1981, 2016), Holliday (2014, 2025), and Ding & Holliday (2020) attempt to develop a semantics of modal logic in terms of “possibilities”, i.e., “less determinate entities than possible worlds” (Edgington 1985). These works take possibilities as semantically primitive entities, stipulate a number of semantic principles that govern these entities (namely, Ordering, Persistence, Refinement, Cofinality, Negation, and Conjunction), and then interpret a modal language via this semantic structure. In this paper, we *define* possibilities in object theory (OT), and *derive*, as theorems, the semantic principles stipulated in the works cited. We then raise a concern for the semantic investigation of possibilities without a primitive modal operator, and show that no such concerns apply to the metaphysics of possibilities as developed in OT.
Authors: Edward N. Zalta and Uri Nodelman
LECTURE 2: Number Theory Without Mathematics: Some Observations
In our paper “Number Theory and Infinity Without Mathematics” (Journal of Philosophical Logic, 53 (2024): 1161-1197, doi:10.1007/s10992-024-09762-7), Uri Nodelman and I answer the questions: (1) Which set or number existence axioms are needed to prove the theorems of “ordinary” mathematics? (2) How should Frege’s theory of numbers be adapted to a modal setting, so that the fact that equivalence classes of equinumerous properties vary from world to world won’t give rise to different numbers at different worlds? (3) Can one reconstruct Frege’s theory of numbers in a non-modal setting *without* mathematical primitives such as “the number of Fs” (#F) or mathematical axioms such as Hume’s Principle? In this talk, I’ll review the technical developments and our answers (surprisingly, our answer to (1) is “none”) and then draw a number of observations how our results preserve Frege’s attempt to provide logical and epistemological foundations for arithmetic.
Authors: Edward N. Zalta and Uri Nodelman
ORGANIZER: Øystein Linnebo