A standard way to challenge convergence-based accounts of in ductive 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 s ome 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.

\nMichael Ni
elsen (Columbia University).

\n4:10 pm\, Friday\, November 16th\, 201
8

\nFaculty House\, Columbia University

What does it mean that an ev
ent C “actually caused” event E? The problem of defi
ning actual causation goes beyond mere philosophical speculation. For example\, in many legal arguments\, it is precisely wha
t needs to be established in order to determine resp
onsibility. (What exactly wa
s the actual cause of the car accident or the medical problem?)

The seminar is concerned with applying formal methods to fun damental issues\, with an emphasis on probabilistic reasoning\, decision t heory and games. In this context “logic” is broadly interpreted as coverin g applications that involve formal representations. The topics of interest have been researched within a very broad spectrum of different discipline s\, including philosophy (logic and epistemology)\, statistics\, economics \, and computer science. The seminar is intended to bring together scholar s from different fields of research so as to illuminate problems of common interest from different perspectives. Throughout each academic year\, mee tings are regularly presented by the members of the seminar and distinguis hed guest speakers.

\ndetails tba

\n02/08/2019 Faculty House\,
Columbia University

\n4:00 PM

03/22/2019 Faculty House\, Col
umbia University

\n4:00 PM

04/19/2018 Faculty House\, Columbi
a University

\n4:00 PM

There are two approaches to life. The first one\, which we a
re 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 w
ill 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 allo
w 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\, Jela
luddin Rumi\, Kahlil Gibran\, and even perhaps Jesus. It occurs in many c
ontemporary 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 pres entism and futurism. The purpose is to contrast one with the other. We wil l 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 Ki m.)

DTSTART;TZID=America/New_York:20190222T161000 GEO:+40.807536;-73.962573 LOCATION:Faculty House\, Columbia U @ 116th St & Broadway\, New York\, NY 1 0027\, United States SEQUENCE:0 SUMMARY:Buddha versus Popper: Do we live in the present or do we plan for t he future? Rohit Parikh (CUNY) URL:http://www.noahgreenstein.com/wordpress/event/buddha-versus-popper-do-w e-live-in-the-present-or-do-we-plan-for-the-future-rohit-parikh-cuny/ X-COST-TYPE:free X-TAGS;LANGUAGE=en-US:comparative\,decision theory\,formal X-INSTANT-EVENT:1 END:VEVENT BEGIN:VEVENT UID:ai1ec-7123@www.noahgreenstein.com/wordpress DTSTAMP:20210417T172024Z CATEGORIES;LANGUAGE=en-US:Columbia U CONTACT: DESCRIPTION:Two proof-systems P and P* are said to be complementary when one proves exactly the non-theorems of the other. Complementary systems c ome 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 c omplementing 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 fac ts will be highlighted: 1) for any given provable sequent\, complementary cut-elimination always returns one of its simplest proofs\, and 2) provabl e LK* sequents turn out to be “deductively polarized” by the empty sequent . In the second part\, I will observe how an alternative complementary seq uent system can be obtained by slightly modifying the Gentzen-Schütte syst em G3. I will finally show how this move could pave the way for a novel ap proach to multi-valuedness and proof-theoretic semantics for classical log ic.

DTSTART;TZID=America/New_York:20190308T120000 GEO:+40.807536;-73.962573 LOCATION:Columbia U Philosophy Dept. 716 @ 116th St & Broadway\, New York\, NY 10027\, United States SEQUENCE:0 SUMMARY:Gabriele Pulcini (New University of Lisbon): From Complementary Log ic to Proof-Theoretic Semantics URL:http://www.noahgreenstein.com/wordpress/event/gabriele-pulcini-new-univ ersity-of-lisbon-from-complementary-logic-to-proof-theoretic-semantics/ X-COST-TYPE:free X-TAGS;LANGUAGE=en-US:logic X-INSTANT-EVENT:1 END:VEVENT BEGIN:VEVENT UID:ai1ec-7137@www.noahgreenstein.com/wordpress DTSTAMP:20210417T172024Z CATEGORIES;LANGUAGE=en-US:Columbia U CONTACT:https://fphil.org/2019/03/21/bjorndahl-the-epistemology-of-nondeter minism/ DESCRIPTION:Propositional dynamic logic (PDL) is a framework for reasoni
ng about nondeterministic program executions (or\, more generally\, nondet
erministic actions). In this setting\, nondeterminism is taken as a primit
ive: a program is nondeterministic iff it has multiple possible outcomes.
But what is the sense of “possibility” at play here? This talk explores an
epistemic interpretation: working in an enriched logical setting\, we rep
resent nondeterminism as a relationship between a program and an agent der
iving from the agent’s (in)ability to adequately measure the dynamics of t
he program execution. More precisely\, using topology to capture the obser
vational powers of an agent\, we define the nondeterministic outcomes of a
given program execution to be those outcomes that the agent is unable to
rule out in advance. In this framework\, determinism coincides exactly wit
h *continuity:* that is\, determinism is continuity in the observatio
n topology. This allows us to embed PDL into (dynamic) topological (subset
space) logic\, laying the groundwork for a deeper investigation into the
epistemology (and topology) of nondeterminism.

The seminar is conc erned with applying formal methods to fundamental issues\, with an emphasi s on probabilistic reasoning\, decision theory and games. In this context “logic” is broadly interpreted as covering applications that involve forma l representations. The topics of interest have been researched within a ve ry broad spectrum of different disciplines\, including philosophy (logic a nd epistemology)\, statistics\, economics\, and computer science. The semi nar is intended to bring together scholars from different fields of resear ch so as to illuminate problems of common interest from different perspect ives. Throughout each academic year\, meetings are regularly presented by the members of the seminar and distinguished guest speakers.

\ndetai ls tba

\n02/08/2019 Faculty House\, Columbia University

\n4:00
PM

03/29/2019 Faculty House\, Columbia University

\n4:00 PM\n

04/19/2018 Faculty House\, Columbia University

\n4:00 PM

Convergence to the truth is viewed with some ambivalence in philosophy of science. On the one hand\, methods of inquiry that lead to t he truth in the limit are prized as marks of scientific rationality. But a n agent who\, by using some method\, expects to always converge to the tru th seems to fail a minimum standard of epistemic modesty. This point was r ecently brought home by Gordon Belot in his critique of Bayesian epistemol ogy. In this paper I will study convergence to the truth theorems within t he framework of Edward Nelson’s radically elementary probability theory. T his theory provides an enriched conceptual framework for investigating con vergence and gives rise to an appropriately modest from of Bayesianism.

\nThe seminar is concerned with applying formal methods to fundamental issues\, with an emphasis on probabilistic reasoning\, decision theory an d games. In this context “logic” is broadly interpreted as covering applic ations that involve formal representations. The topics of interest have be en researched within a very broad spectrum of different disciplines\, incl uding philosophy (logic and epistemology)\, statistics\, economics\, and c omputer science. The seminar is intended to bring together scholars from d ifferent fields of research so as to illuminate problems of common interes t from different perspectives. Throughout each academic year\, meetings ar e regularly presented by the members of the seminar and distinguished gues t speakers.

\ndetails tba

\n02/08/2019 Faculty House\, Columbi
a University

\n4:00 PM

03/22/2019 Faculty House\, Columbia Un
iversity

\n4:00 PM

04/19/2018 Faculty House\, Columbia Univer
sity

\n4:00 PM