Metro Area Philosophy of Science Presents:
Elizabeth Miller (Yale),
Title: TBA.
Jonathan Bain (NYU)
What Explains the Spin-Statistics Connection?
The spin-statistics connection plays an essential role in explanations of non-relativistic phenomena associated with both field-theoretic and non-field-theoretic systems (for instance, it explains the electronic structure of solids and the behavior of Einstein-Bose condensates and superconductors). However, it is only derivable within the context of relativistic quantum field theory (RQFT) in the form of the Spin-Statistics Theorem; and moreover, there are multiple, mutually incompatible ways of deriving it. This essay attempts to determine the sense in which the spin-statistics connection can be said to be an essential property in RQFT, and how it is that an essential property of one type of theory can figure into fundamental explanations offered by other, inherently distinct theories.
Abstract. Many philosophers think that mathematics is about ‘structure’. Many philosophers would also explicate this notion of ‘structure’ via model theory. But the Compactness and Löwenheim–Skolem theorems lead to some famously hard questions for this view. They threaten to leave us unable to talk about any particular ‘structure’.
In this talk, I outline how we might explicate ‘structure’ without appealing to model theory, and indeed without invoking any kind of semantic ascent. The approach involves making use of internal categoricity. I will outline the idea of internal categoricity, state some results, and use these results to make sense of Putnam’s beautiful but cryptic claim: “Models are not lost noumenal waifs looking for someone to name them; they are constructions within our theory itself, and they have names from birth.”
Please join us to celebrate the memory of Raymond Smullyan, mathematician, musician, magician, teacher, author, showman, and dear friend. There will be two speakers, Melvin Fitting and Graham Priest, followed by an open mic session.
If you would like an open mic slot or would like to contribute to the slide show of Ray’s life, please indicate that in the RSVP. While this event is open to the public, a photo ID is required to enter the building and an RSVP is appreciated as space is limited.
A dinner will follow the event at a nearby restaurant.
The standard way to show the consistency of a theory, or the independence of a given statement from that theory, is to exhibit a model. But there’s more than one thing that’s been called a “model” as this notion has evolved from its original role in 19th century foundations of geometry to its current role as a universallyapplicable tool in logic. This talk investigates some of the changes that bring us to the modern notion, and asks to what extent various kinds of model do, or don’t, successfully demonstrate various kinds of consistency and independence.
When: Friday October 20, 11:00am-1:00pm (with reception to follow)
Where: NYU Philosophy Department, 5 Washington Place, Room 202
Nina Emery (Mount Holyoke), November 3, The Graduate Center, CUNY
Potentialism is the view in the philosophy of mathematics that one’s mathematical universe, whether in arithmetic or set theory, is never fully completed, but rather unfolds gradually as new parts of it increasingly come into existence or become accessible or known to us. As in the classical dispute between actual versus potential infinity, the potentialist holds that objects in the upper or outer reaches have potential as opposed to actual existence, in the sense that one can imagine forming or discovering always more objects from that realm, as many as desired, but the task is never completed. Recent work has emphasized the modal aspect of potentialism, and in this talk, I shall describe a general model-theoretic account of the modal logic of potentialism, identifying specific modal principles that hold or fail depending on features of the potentialist system under consideration. This work makes use of modal control statements, such as buttons, switches, dials and ratchets and the connection of these kinds of statements with the modal theories S4, S4.2, S4.3 and S5. I shall take the various natural kinds of arithmetic and set-theoretic potentialism as illustrative cases.
This is joint work in separate projects with Øystein Linnebo, Victoria Gitman, Roman Kossak and W. Hugh Woodin. See http://jdh.hamkins.org/the-modal-principles-of-potentialism-logic-and-metaphysics-workshop-cuny-november-2017/ for questions and commentary concerning this talk.
Logic and Metaphysics Workshop Fall 2017:
September 11 Lovett, NYU
September 18 Skiles, NYU
September 25 Jago, Nottingham
October 2 Greenstein, Private Scholar
October 9 GC Closed. No meeting
October 16 Ripley UConn
October 23 Mares, Wellington
October 30 Woods, Bristol
November 6 Hamkins, GC
November 13 Silva, Alagoas
November 20 Yi, Toronto
November 27 Malink, NYU
December 4 Kivatinos, GC
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.