In this talk I will defend a view according to which certain mathematical facts depend counterfactually on certain historical facts. Specifically, I will sketch an alternative possible history for us in which (I claim) the proposition ordinarily expressed by the English sentence “there is a universal set” is true, despite its falsity in the actual world.
Logic & Metaphysics Workshop
Feb 26 Martin Pleitz, Muenster
Mar 5 Vera Flocke, NYU
Mar 12 Roy Sorensen, WUSTL
Mar 19 Alex Citkin, Private Researcher
Mar 26 Chris Scambler, NYU
Apr 2 SPRING RECESS. NO MEETING
Apr 9 Greg Restall, Melbourne
Apr 16 Daniel Nolan, Notre Dame
Apr 23 Mel Fitting, CUNY
Apr 30 Sungil Han, Seoul National
May 7 Andreas Ditter, NYU
May14 Rohit Parikh
From basic arithmetic to the calculation of rocket trajectories, mathematics provides an elegant means of systematically understanding and quantifying the world around us. Beyond its computational functions, however, mathematics serves an even more vital purpose: It illuminates the most fundamental knowledge of our universe, furnishing the tools that classical physics, quantum mechanics, and astronomy use to develop and build upon their findings.
But why should mathematics be so effective in explaining our universe, as first noted by Nobel laureate physicist Eugene Wigner? Why have fundamental laws discovered through pure mathematics turned out to describe the behavior of our physical world with such remarkable precision, from the fundamental law of gravitation to Maxwell’s electromagnetic equations? Given that our physical universe is comprised of mathematical properties, some have posited that mathematics is the language of the universe, whose laws reveal what appears to be a hidden order in the natural world. But are there also limits to what mathematics can reveal about the mystery of our universe?
Theoretical physicist S. James Gates Jr. and science writer Margaret Wertheim join Steve Paulson to explore the mystery of our universe and the uncanny potential of mathematics to reveal the laws of nature.
*Reception to follow
This event is part of the Conversations on the Nature of Reality series.
Moderated by journalist Steve Paulson, Executive Producer of Wisconsin Public Radio’s To the Best of Our Knowledge, this three-part series at the New York Academy of Sciences brings together leading scientists and thinkers to explore the fundamental nature of reality through the lens of personal experience and scientific inquiry.
To learn more about each lecture and to purchase tickets, click on the links below.
- The Mystery of Our Mathematical Universe, Wednesday, October 10, 2018
- Human Cognition and the AI Revolution, Thursday, December 6, 2018
- Reality is Not As it Seems, Thursday, February 7, 2019
n his seminal work Counterfactuals, David Lewis presents a family of systems of conditional logic—his V-family—which includes both his preferred logic of counterfactuals (VC/C1) and Stalnaker’s conditional logic (VCS/C2). Graham Priest posed the problem of finding systems of (labeled) tableaux for logics from Lewis’s V-family in his Introduction to Non-Classical Logic (2008, p. 93). In this talk, I present a solution to this problem: sound and complete (labeled) tableaux for Lewis’s V-logics. Errors and shortcomings in recent work on this problem are identified and corrected (especially close attention is given to a recent paper by Negri and Sbardolini, whose approach anticipates my own). While most of the systems I present are analytic, the tableaux I give for Stalnaker’s VCS and its extensions make use of a version of the Cut rule and, consequently, are non-analytic. I conjecture that Cut is eliminable from these tableaux and discuss problems encountered in trying to prove this.
The Logic and Metaphysics Workshop will be meeting on Mondays from 4:15 to 6:15 in room 6494 of the Graduate Center, CUNY (365 5th Avenue). The (provisional) schedule is as follows:
Sep 17. Sander Breckers, Utrecht
Sep 24. Hanoch Ben-Yami, CEU
Oct 1. Otavio Bueno, Miami
Oct 8. GC CLOSED. NO MEETING
Oct 15. Alfredo Freire, Campinas
Oct 22. Yale Weiss, GC
Oct 29. Boris Kment, Princeton
Nov 5. Melissa Fusco, Columbia
Nov 12. Amy Seymour, Fordham
Nov 19. Andrew Tedder, UConn
Nov 26. Justin Bledin, Johns Hopkins
Dec 3. Suki Finn, Southampton
Dec 10. Byong Yi, Toronto
Daniel King (BS, Lafayette College. MS, PhD, University of Virginia) is a mathematics scholar with special interests in mathematics education, game theory, history and philosophy of mathematics, and the outreach of mathematics to the social sciences and the humanities. He currently teaches an undergraduate course, Game Theory: The Study of Strategy and Conflict.
In this talk, King will focus on two particularly intriguing “games:” Newcomb’s Problem and the Prisoners’ Dilemma. The analysis of both games leads us to a curious paradox of sorts. Fascinating and perplexing, these games and the paradoxes they unleash serve to challenge some of our most cherished beliefs and philosophical viewpoints. No prior knowledge of game theory (or advanced-level mathematics) is required in order to enjoy and fully engage with the ideas we explore in this talk.
This event is sponsored by Friends of Sarah Lawrence College and is open to the public.
To register for this event, or for more information on the Friends of Sarah Lawrence College, please e-mail friends@sarahlawrence.edu or call 914.323.6154.
Well-known ties between arithmetical proof and intuitionistic logic make it natural to think of provability in terms of intuitionistic logic and hence absolute provability in terms of one of its extensions. For this reason, we propose Intuitionistic Tense Logic, or tINT, to study absolute provability. We delineate tINT models and a Hilbert-style system, and then prove soundness and completeness. We then use the tINT framework to discuss and compare ideas of absolute provability of authors in the literature.
The Saul Kripke Center is pleased to announce that Vincent A. Peluce (PhD student, Philosophy, CUNY Graduate Center) will deliver the fourth Saul Kripke Center Young Scholars Series talk on Thursday, December 5, 2019, from 2:00 to 4:00 in room 9206 of the CUNY Graduate Center.
The workshop is funded by the National Science Foundation (SES-1921688) and is aimed at bringing together academics who study the notion of mathematical explanation from philosophical and from educational/psychological perspectives. The idea is to bring together philosophers of mathematics, epistemologists, psychologists, and mathematics educators, to discuss how developments in their own fields could meaningfully contribute to the work on mathematical explanation where their fields intersect. In particular, we want to explore the ways in which mathematical explanation engenders understanding, by focusing on (1) the relationship between different types of philosophical accounts of mathematical explanation, (2) educational approaches to the characterization of effective explanations in the mathematics classroom, and (3) work at the intersection of these two perspectives.
All speakers:
Mark Colyvan
University of Sydney
Matthew Inglis
Loughborough University
Marc Lange
University of North Carolina, Chapel Hill
Tania Lombrozo
Princeton University
Alexander Renkl
University of Freiburg
Keith Weber
Rutgers University – New Brunswick
Orit Zaslavsky
New York University