Gödel’s disjunction asserts that either “the mind cannot be mechanized” or “there are absolutely undecidable statements.” Arguments are examined for and against each disjunct in the context of precise frameworks governing the notions of absolute provability and truth. The focus is on Penrose’s new argument, which interestingly involves type-free truth. In order to reconstruct Penrose’s argument, a system, DKT, is devised for absolute provability and type-free truth. It turns out that in this setting there are actually two versions of the disjunction and its disjuncts. The first, fully general versions end up being (provably) indeterminate. The second, restricted versions end up being (provably) determinate, and so, in this case there is at least an initial prospect of success. However, in this case it will be seen that although the disjunction itself is provable, neither disjunct is provable nor refutable in the framework.
UNIVERSITY SEMINAR ON LOGIC, PROBABILITY, AND GAMES
Gödel’s Disjunction
Peter Koellner (Harvard University)
5:00 pm, Friday, April 7th, 2017
716 Philosophy Hall, Columbia University
Nietzsche Circle Presents: An Evening with Music and Philosophy
Speakers:
- Michael Teinmann
- Yunus Tuncel
Pianist:
- Aysegul Durakoglu
RSVP required!
Refreshments will be served. If you like to attend, Please RSVP by sending email to Luke Trusso at trussol@nietzschecircle.com
The umwelt is a notion invented by the Baltic-German biologist Jakob von Uexküll. It represents how a creature, an animal, a child or even an adult “sees” the world and is a precursor to the Wumpus world in contemporary AI literature. A fly is caught in a spider’s web because its vision is too coarse to see the fine threads of the web. Thus though the web is part of the world, it is not a part of the fly’s umwelt. Similarly a tick will suck not only on blood but also on any warm liquid covered by a membrane. In the tick’s umwelt, the blood and the warm liquid are “the same”.
We represent an umwelt as a homomorphic image of the real world in which the creature, whatever it might be, has some perceptions, some powers, and some preferences (utilities for convenience). Thus we can calculate the average utility of an umwelt and also the utilities of two creatures combining their umwelts into a symbiosis.
A creature may also have a “theory” which is a map from sets of atomic sentences to sets of atomic sentences. Atomic sentences which are observed may allow the creature to infer other atomic sentences not observed. This weak but useful notion of theory bypasses some of Davidson’s objections to animals having beliefs.
Russell, Stuart J., and Peter Norvig. “Artificial intelligence: a modern approach (International Edition).” (2002).
Von Uexküll, J., von Uexküll, M., & O’Neil, J. D. (2010). A foray into the worlds of animals and humans: With a theory of meaning. U of Minnesota Press.
It has been said that there are not different “types” or categories of music, only good music and bad music. How can we know the difference between good and bad music however? Well, on some accounts, there are indeed different types (‘low’ vs ‘high’ art), some of which are by definition bad, others good. Yet, on other accounts, music is music – there are no essential differences in kind, and it is simply each listener’s favorable or unfavorable reaction to any given song or piece of music that decides its quality. In very broad strokes, these two contrasting orientations represent attitudes common in modernist and postmodernist theories, respectively. In the former, Western classical music was privileged (unjustly, in some respects) above all other kinds. However, the latter orientation, which is currently in fashion, seems to reduce all musical meaning and appraisal to little more than our own mental projections. In this presentation, a third, alternative way to identify musical “types” is proposed, one that seeks to illuminate meaningful musical distinctions in the natures and functions of three musical kinds (folk, mass, and art music), with some surprising results. A brief piano performance will precede the talk.
Monday, December 11, 2017 at 6pm. This event is part of the Philosophy Series at The Cornelia Street Café, located at 29 Cornelia Street, New York, NY 10014 (near Sixth Avenue and West 4th St.). Admission is $10, which includes the price of one drink. Reservations are recommended (212. 989.9319)
Jason Cutmore is a concert pianist, teacher, and the founder and director of the Canadian music festival, Alberta Pianofest. He has performed solo piano and collaborative recitals across much of North America, Europe, and India, and has published articles in peer review journals and trade magazines. Mr Cutmore lives in New York City, and is currently completing a Master’s degree in Philosophy at the CUNY Graduate Center.
We examine general decision problems with loss functions that are bounded below. We allow the loss function to assume the value ∞. No other assumptions are made about the action space, the types of data available, the types of non-randomized decision rules allowed, or the parameter space. By allowing prior distributions and the randomizations in randomized rules to be finitely-additive, we find very general complete class and minimax theorems. Specifically, under the sole assumption that the loss function is bounded below, every decision problem has a minimal complete class and all admissible rules are Bayes rules. Also, every decision problem has a minimax rule and a least-favorable distribution and every minimax rule is Bayes with respect to the least-favorable distribution. Some special care is required to deal properly with infinite-valued risk functions and integrals taking infinite values. This talk will focus on some examples and the major differences between finitely-additive and countably-additive decision theory. This is joint work with Teddy Seidenfeld, Jay Kadane, and Rafael Stern.
UNIVERSITY SEMINAR ON LOGIC, PROBABILITY, AND GAMES
Finitely-Additive Decision Theory
Mark Schervish (Carnegie Mellon)
4:10 pm, Friday, February 16th, 2018
Faculty House, Columbia University
Alfred Hitchcock’s Vertigo is a brilliant, suspenseful mystery exploring the often dangerous intimacy between love, compulsion, and death. It is also a profound meditation on the power of art. While it invites us to go on seeing art as a mimesis – a “representation,” or “imitation” of life – it also cryptically asks whether art objects might do more than merely represent life, even whether they might exercise power over death. James Stewart’s Scotty has been compared to Orpheus in quest of Eurydice; I suggest that he’s worth comparing to Admetus, who wished he could be Orpheus, and who imagines clinging to a statue to recapture his lost wife. The spell cast by Hitchcock in Vertigo shows us just how bewitching art can be when it has us under its sway.
Monday, March 19, 2018 at 6pm. This event is part of the Philosophy Series at The Cornelia Street Café, located at 29 Cornelia Street, New York, NY 10014 (near Sixth Avenue and West 4th St.). Admission is $10, which includes the price of one drink. Reservations are recommended (212. 989.9319)
Nickolas Pappas is Professor of Philosophy at City College and the Graduate Center, CUNY, where he has taught since 1993. He is the author of several books and around 40 articles, mostly on topics in ancient philosophy. His books include the Routledge Philosophical Guidebook to Plato’s Republic, now in its third edition; and most recently The Philosopher’s New Clothes (Routledge, 2016).
Elliot Paul, assistant professor of philosophy, and Joan Snitzer, cochair and director of visual arts in the Department of Art History, come together to discuss the relationship between creative expression and appreciation in this installment of From the Faculty Lounge. Paul and Snitzer will explore creativity’s role in our happiness and moral choices, and how an artist’s ownership of their creativity compares to an audience’s influence.
Moderated by Provost Linda Bell
Space is limited and available on a first-come, first-served basis. Please arrive early as this event will be filmed and doors will close promptly at 6:30 PM.
From the Faculty Lounge
What is Creativity?
Thursday, May 3, 2018
6:30 PM
Sulzberger Parlor, 3rd Floor Barnard Hall
For more information, visit barnard.edu/events. View previously recorded conversations here.
You probably know the Lucas Brothers from their Netflix comedy special On Drugs or their appearances in TV shows and movies like Lady Dynamite and 22 Jump Street. You might not know that they are serious students of philosophy. Join us on Wednesday, November 28th at 7:30 PM in the Strand Bookstore’s 2nd Floor Art Department as Kenny and Keith Lucas join Michael Brownstein (Associate Professor of Philosophy at John Jay College and author of The Implicit Mind) to discuss how philosophy shapes their comedy, how comedy works, the weirdly popular idea that comedians are today’s philosophers, and more.
The price of admission is a $5 gift certificate to the Strand. (You were probably going to spend $5 at the Strand some time soon, anyway.) Please purchase tickets here and share the Facebook event. I will take all the help I can get in spreading the word.
Stay tuned for more info about Kwame Anthony Appiah’s December 4th talk about identity at Philosophy in the Library!
Two proof-systems P and P* are said to be complementary when one proves exactly the non-theorems of the other. Complementary systems come as a particular kind of refutation calculi whose patterns of inference always work by inferring unprovable conclusions form unprovable premises. In the first part of my talk, I will focus on LK*, the sequent system complementing Gentzen’s system LK for classical logic. I will show, then, how to enrich LK* with two admissible (unary) cut rules, which allow for a simple and efficient cut-elimination algorithm. In particular, two facts will be highlighted: 1) for any given provable sequent, complementary cut-elimination always returns one of its simplest proofs, and 2) provable LK* sequents turn out to be “deductively polarized” by the empty sequent. In the second part, I will observe how an alternative complementary sequent system can be obtained by slightly modifying the Gentzen-Schütte system G3. I will finally show how this move could pave the way for a novel approach to multi-valuedness and proof-theoretic semantics for classical logic.
Professor Barbara Gail Montero is the director of (and a performer in) the upcoming multimedia, interdisciplinary event Curved Spacetimes: Where Friedrich Nietzsche Meets Virginia Woolf. Prof. Nickolas Pappas will also perform (reading spoken word as Friedrich Nietzsche), and Prof. Jonathan Gilmore is a member of the team that brought the project to fruition.
According to the American Society for Aesthetics (who partially funded this project with a $7,000 grant), Curved Spacetimes is “multisensory event focused on the Physics, Aesthetics, and Metaphysics of Time. . . .[T]he evening will commence with a Nietzsche-Woolf-curved-spacetime-inspired reception that will allow you to test your knowledge of our central figures. Following the reception, you will experience Nietzsche, Woolf and curved spacetime coming to life on the stage (through dance, live music and the spoken word), and then listen to a panel discussion that will take you more deeply into the ideas guiding the performance.”
When: Sunday, March 17, 2019: 6-9 pm
Where: The Tank, 312 W. 36th St. 1st floor, New York City.
Schedule of Events
- 6 PM: Pre-performance catered reception—pass the Woolf/Nietzsche pre-test for a free drink!
- 7 PM: Performance
- 8 PM: Panel discussion on the physics, aesthetics, and metaphysics of time
Choreography: Logos Dance Collective (Barbara Gail Montero, Theresa Duhon, Patra Jongjitirat, and Gregory Kollarus)
Performers: Elise Crull, Theresa Duhon, Maxine Flasher-Duzgunes, Patra Jongjitirat, Gregory Kollarus, Barbara Gail Montero, and Nickolas Pappas
Music: Selections from Bach’s Cello Suites, performed live by cellist Ivan Luza
Text: excerpts from Thus Spoke Zarathustra, The Gay Science, Mrs. Dalloway, and The Diary of Virginia Woolf
Panelists for the after-performance discussion:
- Jeff Friedman, Associate Professor of Dance Rutgers University
- Kathleen Higgins, Professor of Philosophy, University of Texas at Austin
- Timothy Maudlin, Professor of Philosophy, New York University
- Heather Whitney, JD, Harvard Law School & PhD Candidate, New York University
Moderator: Rebecca Ariel Porte, Writer and member of the Core Faculty at the Brooklyn Institute for Social Research.
Free tickets for students in philosophy, literature, dance and physics are supported by the ASA grant and are available from bmontero@gc.cuny.edu
For all others, tickets are on sale now on-line at The Tank
Project Team:
- Barbara Gail Montero (Project Director), Professor of Philosophy, CUNY and Founder and member of the Logos Dance Collective
- Jonathan Gilmore, Professor of Philosophy, CUNY
- Maxine Flasher-Duzgunes, BFA student in Dance at NYU’s Tisch School of the Arts and member of the Logos Dance Collective
- Cliff Mak, Assistant Professor of English, Queens College, CUNY