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.
Propositional dynamic logic (PDL) is a framework for reasoning about nondeterministic program executions (or, more generally, nondeterministic actions). In this setting, nondeterminism is taken as a primitive: 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 represent nondeterminism as a relationship between a program and an agent deriving from the agent’s (in)ability to adequately measure the dynamics of the program execution. More precisely, using topology to capture the observational 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 with continuity: that is, determinism is continuity in the observation 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 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
03/29/2019 Faculty House, Columbia University
4:00 PM
04/19/2018 Faculty House, Columbia University
4:00 PM
Neuroprediction, the use of neuroscientific data to predict human behavior, can sound like science fiction. But with the advent of neuroimaging and the continuing rapid development of other non-invasive brain measurements, neuroprediction is increasingly a real-world phenomenon.
Deep philosophical, legal, and neuroscientific questions arise regarding the use of these methods to predict behavior. Like all scientific tools, whether or not these technologies are used responsibly depends on who uses them. For instance, recent research illustrates the potential use of neuroprediction to assess an individual’s risk of (re-)engaging in antisocial conduct in forensic contexts. While the use of brain-based data may add predictive value to existing risk assessment tools, at the same time, the use (or misuse) of neuroprediction in courtrooms may imply violations of individual rights and liberties under the pretext of enhancing public safety. In addition to these legal implications, neuroprediction presents several technological and neuroscientific challenges. The non-invasive measures currently available are only indirect measures of cognitive activity. Understanding the conceptual, ethical, and legal dimensions surrounding the use of neuroprediction technologies helps crystallize the issues at hand and potentially provides moral guidance for those who wish to capitalize on these new tools as their prevalence and specificity continue to advance.
In this seminar, four experts from neuroscience, law, and philosophy will discuss recent findings in neuroprediction research, the predictive power of brain-based evidence compared to behavioral evidence, as well as the ethical and legal concerns emerging from the entrance of neuroprediction in the courts of law.
Speakers:
Arielle Baskin-Sommers, Assistant Professor of Psychology and Psychiatry, Yale University
Martha Farah, Annenberg Professor of Natural Sciences, University of Pennsylvania
Kent Kiehl, Professor of Psychology and Neuroscience, University of New Mexico
Walter Sinnott-Armstrong, Chauncey Stillman Professor of Practical Ethics, Duke University
Discussant:
Jeffrey A. Fagan, Isidor and Seville Sulzbacher Professor of Law and Professor of Epidemiology, Columbia University
Moderator:
Federica Coppola, Presidential Scholar in Society and Neuroscience, Columbia University
Free and open to the public, but RSVP is required via Eventbrite. This event is part of the Seminars in Society and Neuroscience series.
14.30 – 15.30: Kit Fine: A Truthmaker Semantics for Conditional Imperatives
15.30 – 15.45: Coffee Break
15.45 – 16.45: Friederike Moltmann: Underspecification of Attitudes and Truthmaker
Semantics
16.45-17.00: Coffee Break
17.00 – 18.00: Federico Faroldi: Truthmaker Semantics for Justification Logics – Open
Problems (joint work with Tudor Protopopescu)
18.00-18.15: Coffee Break
18.15 – 19.15: Cian Dorr: Truthmaking in the Object Language
K. Fine: A Truthmaker Semantics for Conditional Imperatives
I provide a truth-maker semantics for conditional imperatives and indicate how it might be extended to other conditional constructions.
F. Moltmann: Underspecification of Attitudes and Truthmaker Semantics
It has been argued that the satisfaction conditions of a desire can be underspecified by the complement clause. This provides support for the view according to which the complement clause gives a partial content of the reported desire, where partial content is formulated in terms of truthmaker theory. In this talk, I will discuss the extent of such underspecification and whether it truly supports a truthmaker-based approach to the content of attitudes.
Optional preparatory reading here.
F. Faroldi: Truthmaker Semantics for Justification Logics – Open Problems
Justification logics are a family of logic where "implicit" modal operators are substituted by explicit terms to get formulas of the form t : A, where t could be evidence, a reason, etc. why A is known, believed, obligatory, etc., thus resulting in an “objectual” approach to modalities. In this talk we explore how to give a truthmaker semantics for justification logics, we provide some philosophical reasons to do so, and note some technical open problems.
Cian Dorr: Truthmaking in the Object Language
I consider a simple language with Boolean connectives, sentential variables and quantifiers binding them, and a connective for propositional identity (‘for it to be the case that … is for it to be the case that …’). Using familiar techniques, the possible-worlds model theory for such a language can be ‘internalised’ to derive a theory stated in the language itself, based on the definition of ‘world-proposition’ as ‘maximal consistent proposition’, and this theory can be shown to follow from the theory that propositions form a complete atomic Boolean algebra. In this paper, I will consider to what extent something similar can be done for Fine’s truthmaker semantics. This will involve looking for a way of picking out a class of special propositions to serve as surrogates for the states, and a binary relation among propositions to serve as a surrogate for the verification relation, and using these definitions to rewrite the metalinguistic definition of a model as theory in the object-language. I will make a start at considering to what extent the axioms of this theory can be derived from an independently natural weakening of the theory that propositions form a complete atomic Boolean algebra.
Speakers:
Cristina Alberini (NYU, Neural Science)
Heather Berlin (Mt. Sinai, Psychiatry)
Mark Solms (Cape Town, Neuropsychology)
Robert Stickgold (Harvard, Psychiatry)
Conference Schedule
10AM Teddy Seidenfeld – Conditional Probability, Conditionalization, and Total Evidence
11AM Eleonora Cresto – Beyond Indeterminate Utilities. The Case of Neurotic Cake-Cutting
11:20AM Ignacio Ojea Quintana – Unawareness and Levi’s Consensus as Common Ground
11:40AM Rush Stewart – Uncertainty, Equality, Fraternity
1PM Nils-Eric Sahlin – Levi’s Decision Theory: Lessons Learned
1:45PM Wilfried Sieg – Scientific Theories as Set-Theoretic Predicates?
2:45PM Panel Discussion – Learning from Levi
Abstracts available in attached documents under “Supporting material.”
Memorial
A memorial service will be held at 5PM at St. Paul’s Chapel on the Columbia campus. Reception to follow on the 7th floor of Philosophy Hall.
Scholars working under the broad umbrella of New Materialism have offered compelling reappraisals of the ways in which we know, interact with, and exist in the world. This scholarship also intersects with recent work on music and sound, which raises rich sets of questions regarding human agency, material, ethics, aesthetics, embodiment, and the subject/object dichotomy, among other issues.
We invite scholars working in the humanities, arts and sciences to submit proposals for papers and performances that engage with the themes of sound and new materialism, broadly construed. We welcome work that adopts historical, technological, analytical, philosophical, materialist, and creative vantage points, among others. Overall, this conference will direct these diverse disciplinary and methodological perspectives towards convergent and critical issues, creating new, interdisciplinary lines of enquiry and generating original research.
The one-day conference will consist of panels that comprise of papers with short reflections by a moderator, as well as an evening concert that includes opportunities for discussion. The concluding concert of work that engages with these themes from creative perspectives will afford attendees with an opportunity to consider and discuss issues concerning sound, material, and agency in a forum that contrasts with, but also complements, our events during the day. Conference participants are strongly encouraged to attend both the daytime and evening portions of the conference.
Proposals are called for:
Paper presentations of 20 minutes with 10 minutes of Q&A.
Artistic presentation of 20 minutes with 10 minutes of discussion
Submission: Proposals of no more than 500 words (300 words for artistic presentation) should be submitted as a PDF by August 14th 2019 to jc5036@columbia.edu
and include “NMAS Submission” in the subject line. If you’re applying for an artistic presentation please include three representative 2 minute audio/video examples. Please also include the title of your proposed paper and anonymize your submission. Include your name, affiliation, and contact information in the body of the email, and also nominate any audio/visual requirements for your paper or performance.
Over the last decades, the humanities have come under pressure from the scientific worldview. To many, it seems as if the humanities provide us at best with less-than-objective knowledge claims. Arguably, there are at least two overall reasons for this. On the one hand, the scientific worldview tends to associate objectivity with the kind of knowledge-acquisition, explanation, and justification characteristic of the natural sciences. On the other hand, the humanities themselves have contributed to the impression that they might be less relevant than the natural sciences to epistemic progress due to internal problems having to do with the very concept(s) of knowledge, reality and objectivity.
New Realism is a term for a whole series of current trends in philosophy that has important consequences for our understanding of knowledge in general. In particular, it reshapes our account of the human being qua source and object of knowledge claims. In this context, New Realism draws on a crucial indispensability thesis: we simply cannot eliminate the standpoint from which humans gather information about human and non-human reality alike from our account of reality itself. In light of this thesis, it turns out that the humanities are fully-fledged contributions to objective knowledge about reality – a fact we cannot ignore without succumbing to illusion. Against this background, the talk concludes that the so-called “scientific worldview” is untenable: it is built upon a denial of knowledge we actually possess, and so, by not being scientific enough, it fails to respect its own premises.
About the speaker:
Markus Gabriel holds the chair in epistemology, modern and contemporary philosophy at the University of Bonn. He is the director of the International Center for Philosophy and the multidisciplinary Center for Science and Thought. With Jocelyn Benoist he also directs Bonn-Paris Center for Research on New Realisms. His work focuses on contemporary philosophy, in particular epistemology and ontology, in an attempt to spell out the consequences of various trends in philosophy in a conversation with the humanities. Currently, he is working on a book called Fictions which deals with topics at the intersection of philosophy, literary studies and sociology.
The NYU Department of German and Deutsches Haus at NYU present “Objectivity and the Humanities – Prospects for a New Realism,” a talk by Professor Markus Gabriel.
Attendance information:
Events at Deutsches Haus are free of charge. If you would like to attend this event, please send us an email to deutscheshaus.rsvp@nyu.edu. Space at Deutsches Haus is limited; please arrive ten minutes prior to the event. Thank you!
“Objectivity and the Humanities – Prospects for a New Realism” is a DAAD-supported event.
This will be the third (and, time permitting, some material from the fourth) of a series of lectures that I aim to write up formally as a book. We will begin with a brief review of the most familiar theory of Chinese aesthetics: works of art are the products of sensitive human beings who cannot suppress their sincere responses to emotional stimuli. If art is understood as a sincere statement of this kind by a great genius, it stands to reason that, by correctly interpreting the work, one can communicate with that genius’s mind (xin 心) even after his or her death–and, likewise, that an artist today can communicate with audiences yet unborn. Art is thus timeless and offers the possibility of incorporeal immortality. If there is extra time, I will also survey two interrelated phenomena that I call meta-criticism and meta-writing (since there are no technical terms for them in Chinese). Meta-criticism, i.e. criticism of criticism, is a major feature of Chinese theories about art. Meta-criticism must be related to meta-writing, or the practice of writing about writing while exemplifying the very styles and techniques that one recommends: for example, artfully rhyming a couplet about rhyming.
With responses from: SANDRA SHAPSHAY (Hunter College, CUNY)
The Fall dates for the Comparative Philosophy seminar:
September 20 – Justin Tiwald (San Francisco State University)
October 11 – Richard Kim (Loyola University, Chicago
November 8 – Sungmoon Kim (City University of Hong Kong)
December 6 – Paul R. Goldin (University of Pennsylvania)
More details (such as titles, abstracts, and respondents) to follow. Looking forward to seeing you soon.
Hagop Sarkissian
Associate Professor & Chair, Department of Philosophy, The City University of New York, Baruch College
Associate Professor, Department of Philosophy, CUNY Graduate Center
Co-Director, Columbia Society for Comparative Philosophy
https://www.cbs.columbia.edu/cscp/
The notion of an occurrence of a proposition in discourse is the subject of the following observation:
(O) A proposition may occur in discourse, now asserted, now unasserted, and yetbe recognizably the same proposition.
I shall argue that the true significance of this observation is utterly distorted by Geach’s manner of construing of it — a construal widely known today as “the Frege-Geach point”. Though it serves as a basis for a contemporary understanding of logical form, strictly thought through, this way of construing (O) can be shown to lead to absurdity. I will further argue that a straightforward, undistorted, acceptance of (O) is the key to a genuine philosophical logic.
— Irad Kimhi (The Committee on Social Thought, University of Chicago)
Reception to follow.