Calendar

SHIGENORI NAGATOMO (Temple University)

With responses from:

GRAHAM PRIEST (CUNY Graduate Center)

Please join us at Columbia University’s Religion Department on FRIDAY, APRIL 8th at 5:30PM for his lecture entitled:

“The Logic of Not: An Invitation to an Holistic Mode of Thinking”

This presentation extends an invitation to an holistic mode of understanding to those who are concerned with current global situations. It thematically deals with the logic that appears in the sutra called the Diamond Sutra which belongs to the prajñāpāaramitā literature of Mahayana Buddhism. This logic is called “logic of not” because a negation appears in the formulation of the idea of identity as is expressed in the following: “A is not A, therefore it is A.” This logic cuts against the grain of the assumptions which the mode of thinking predominant in the Western philosophical tradition accepts as its modus operandi, namely the conceptual paradigm of the “either-or ego-logical dualistic standpoint.” This presentation argues that this paradigm generates a problem of fragmentation, which we take to be the root of many of the problems we face today, by analyzing the phrases such as “either-or,” “dualistic” and “ego-logical.” It then turns to an analysis of “the logic of not” by showing how it differs from Aristotle’s logic, while providing the philosophical reasons why the Diamond Sutra formulates its understanding of reality in terms of “the logic of not.” With this clarification, the presentation discusses how a transparency of mind and the idea of interdependency are necessary for achieving an holistic perspective, i.e., to understand things holistically.  This mode of thinking will be effective to correct the problem of fragmentation, for example, in dealing with such topics as I knowing myself, the I-thou relationship, and environmental concerns.

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April 29: Sara McClintock (Emory University)

We will provide more information regarding the topic of each speaker’s
presentation as the semester progresses. We hope to see you all at what
promises to be a semester of discussion and engagement.

Heart of DARCness
Huw Price (University of Cambridge)
4:10 pm, Thursday, October 13th, 2016
Faculty House, Columbia University

Abstract. Alan Hajek has recently criticised the thesis that Deliberation Crowds Out Prediction (renaming it the DARC thesis, for ‘Deliberation Annihilates Reflective Credence’). Hajek’s paper has reinforced my sense that proponents and opponents of this thesis often talk past one other. To avoid confusions of this kind we need to dissect our way to the heart of DARCness, and to distinguish it from various claims for which it is liable to be mistaken. In this talk, based on joint work with Yang Liu, I do some of this anatomical work. Properly understood, I argue, the heart is in good shape, and untouched by Hajek’s jabs at surrounding tissue. Moreover, a feature that Hajek takes to be problem for the DARC thesis – that it commits us to widespread ‘credal gaps’ – turns out to be a common and benign feature of a broad class of cases, of which deliberation is easily seen to be one.

Rationalizability, originally proposed by Bernheim and Pearce, generalizes the notion of Nash equilibrium. Nash equilibrium requires common knowledge of strategies. Rationalizability only requires common knowledge of rationality. However, their original notion assumes that the payoffs are common knowledge. I.e. agents do know what world they are in, but may be ignorant of what other agents are playing.

We generalize the original notion of rationalizability to consider situations where agents do not know what world they are in, or where some know but others do not know. Agents who know something about the world can take advantage of their superior knowledge. It may also happen that both Ann and Bob know about the world but Ann does not know that Bob knows. How might they act?

We will show how a notion of rationalizability in the context of partial knowledge, represented by a Kripke structure, can be developed.

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

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.​

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

The circa 9th century CE poet-saint Saraha enjoys a close association with spontaneity in both his reported actions and recorded works. This association leads him to be popularly read and remembered as a freewheeling antinomian sacred figure opposed to institutions, rituals, and even social norms. His appears to be a call to joyful chaos. But many of his verses invite readers towards a different kind of chaos, towards mental/perceptual chaos as the path towards correct conventional perception.

What does it mean to correctly perceive an object? Many Buddhist sources describe how perception functions, and theorize the differences between correct and incorrect perception. A related important distinction is made between conventional and ultimate truth in the discussion of the reality of phenomena even when correctly perceived. But this arguably epistemic distinction may also be understood as the difference between an ordinary person’s correct perception and a Buddha’s perception. I am not here exploring ultimate truth. I am interested in conventional truth, in what makes it true. Broadly, correct conventional perception is associated with the product of a rational mind processing sense perceptions fed to it by functioning sense organs, and conventional truth then is the experience of that reality. Correct conventional perception can be contrasted with incorrect conventional perception, which would be perception based on an irrational or deluded mind, or an experience based on damaged or non-functioning sense organs.

Saraha, however, sings a different tune. His work tells us that the very process of identifying and recognizing objects – what most of us would associate with the basic skills necessary to get around in the world – is itself deluded, its objects adventitious. He calls this kind of perception drenpa (dran pa; usually translated as mindfulness, memory, or recollection). In other words, he claims that our very perception of objects – no matter how carefully or clearly experienced – is evidence of our being deluded. In contrast, correct conventional perception is the undoing of that object-making, what he refers to as drenmé (dran med). Drenmé is an uncommon term the contexts of the two truths and meditation. Usually denoting a swoon or a coma, here it refers to a reversal or undoing of drenpa. What does it mean – if it means anything – to describe our perception of objects itself as evidence of our delusion? Can perception as object-making ever produce truth?

The Columbia Society for Comparative Philosophy (CSCP) is a University Seminar dedicated to the advancement of projects that draw on both western and non-western philosophy. The CSCP meets monthly on the campus of Columbia University and occasionally hosts conferences.

Please save the following dates for our upcoming talks:

March 30: Kin Cheung (Moravian College)

April 13: Lara Braitstein (McGill University)

May 11: David Cummiskey (Bates College)

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.