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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

“Is Truth Dead?” asked Time Magazine last year. Since people clearly care about the truth, at least in mundane matters, truth is alive. If an airline agent tells you the flight to Dallas is leaving from Gate B16, you expect the flight to Dallas to be leaving from Gate B16, and complain sorely if it’s not.

But if the truth does still matter, why do we elect people who don’t seem to care what the truth is?

The answer to this question, argues philosopher Louise Antony, has partly to do with the structure of human knowledge, and partly to do with the structure of our society. We can’t do anything about the first matter, but we can do plenty about the second.

Louise Antony is Professor of Philosophy at the University of Massachusetts-Amherst. She is the author of numerous essays on the philosophy of mind, epistemology, and feminist theory. She is also a past president of the Eastern Division of the American Philosophical Association.

https://www.facebook.com/events/577253882608942/

Contrary to Damien Keown (2001), who worries that metaphysical and epistemological inquiry may distract from ethical investigation, Bronwyn Finnigan and Koji Tanaka (2008) argue such questions may provide grounding for practical application of a Buddhist ethical path. I follow this line of inquiry into Buddhist theories of truth in order to better understand right speech as conceived in the Early Buddhist Suttas. I focus on what the Abhaya Sutta explicitly instructs and what it leaves out regarding the types of words the Tathagata does not say or has a sense of the proper time for saying them. K. N. Jayatilleke (1963) and Mark Siderits (1979) provide convincing evidence that contrary to popular characterizations of the

 Buddhist theory of truth as pragmatic, Early Buddhist Suttas rest on some form of correspondence theory of truth. Siderits shows that at the very least, there is an uneasy tension between correspondence and pragmatic theories. I contrast their position with Francisca Cho and Richard K. Squier’s (2016) argument describing the Buddhist theory of truth as pragmatic based on the use of language and lies. I supplement Cho and Squier with Jonathan Silk’s (2008) work on truth and lies in Buddhist texts in order to argue that there may be an impasse on adjudicating Buddhist theories of truth.

With a response from:

Mark Siderits (Emeritus, Illinois State University)

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)

Randomized acts play a marginal role in traditional Bayesian decision theory, essentially only one of tie-breaking. Meanwhile, rationales for randomized decisions have been offered in a number of areas, including game theory, experimental design, and machine learning. A common and plausible way of accommodating some (but not all) of these ideas from a Bayesian perspective is by appeal to a decision maker’s bounded computational resources. Making this suggestion both precise and compelling is surprisingly difficult. We propose a distinction between interesting and uninteresting cases where randomization can help a decision maker, with the eventual aim of achieving a unified story about the rational role of randomization. The interesting cases, we claim, all arise from constraints on memory.

UNIVERSITY SEMINAR ON LOGIC, PROBABILITY, AND GAMES
On the Rational Role of Randomization
Thomas Icard (Stanford)

A standard way to challenge convergence-based accounts of inductive success is to claim that they are too weak to constrain inductive inferences in the short run. We respond to such a challenge by answering some questions raised by Juhl (1994). When it comes to predicting limiting relative frequencies in the framework of Reichenbach, we show that speed-optimal convergence—a long-run success condition—induces dynamic coherence in the short run. This is joint work with Eric Wofsey.

Michael Nielsen (Columbia University).
4:10 pm, Friday, November 16th, 2018
Faculty House, Columbia University

What does it mean that an event C “actually caused” event E? The problem of defining actual causation goes beyond mere philosophical speculation.  For example, in many legal arguments, it is precisely what needs to be established in order to determine responsibility.   (What exactly was the actual cause of the car accident or the medical problem?) The philosophy literature has been struggling with the problem of defining causality since the days of Hume, in the 1700s. Many of the definitions have been couched in terms of counterfactuals. (C is a cause of E if, had C not happened, then E would not have happened.) In 2001, Judea Pearl and I introduced a new definition of actual cause, using Pearl’s notion of structural equations to model counterfactuals.  The definition has been revised twice since then, extended to deal with notions like “responsibility” and “blame”, and applied in databases and program verification.  I survey the last 15 years of work here, including joint work with Judea Pearl, Hana Chockler, and Chris Hitchcock. The talk will be completely self-contained.

The seminar is concerned with applying formal methods to fundamental issues, with an emphasis on probabilistic reasoning, decision theory and games. In this context “logic” is broadly interpreted as covering applications that involve formal representations. The topics of interest have been researched within a very broad spectrum of different disciplines, including philosophy (logic and epistemology), statistics, economics, and computer science. The seminar is intended to bring together scholars from different fields of research so as to illuminate problems of common interest from different perspectives. Throughout each academic year, meetings are regularly presented by the members of the seminar and distinguished guest speakers.

details tba

02/08/2019 Faculty House, Columbia University
4:00 PM

03/22/2019 Faculty House, Columbia University
4:00 PM

04/19/2018 Faculty House, Columbia University
4:00 PM

There are two approaches to life. The first one, which we are identifying with Sir Karl Popper, is to think before we act and to let our hypotheses die in our stead when the overall outcome is likely to be negative. We act now for a better future, and we think now which action will bring the best future. Both decision theory and backward induction are technical versions of this train of thought.  The second approach, which we will identify with the Buddha, is to live in the present and not allow the future to pull us away from living in the ever present  Now. The Buddha’s approach is echoed in many others who came after him, Jelaluddin Rumi, Kahlil Gibran, and even perhaps Jesus.  It occurs in many contemporary teachers like Eckhart Tolle and Thich Nhat Hanh.  We may call Popper’s approach “futurism” and the Buddha’s approach “presentism.”

In this talk, we will discuss various aspects of the discourse on presentism and futurism. The purpose is to contrast one with the other. We will not attempt to side with one against the other, and instead leave it as a future project to find a prescriptive action-guiding choice between the two. We merely conjecture that a better optimal choice between these two positions may be somewhere in between. (This is joint work with Jongjin Kim.)