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
8 February @Columbia
Patricia Kitcher: The Fact of Reason in Kant’s Moral Psychology
Response: Jessica Tizzard
22 February @NSSR
5 April @Columbia
Beatrice Longuenesse: Residues of First Nature
19 April @NSSR
Angelica Nuzzo: Approaching Hegel’s Logic Obliquely: Melville, Moliere, Beckett
Response: David Carlson
10 May @Columbia
Amy Allen: Turning Dead Ends into Through Streets: Psychoanalysis and the Idea of Progress
8 February @Columbia
Patricia Kitcher: The Fact of Reason in Kant’s Moral Psychology
Response: Jessica Tizzard
22 February @NSSR
5 April @Columbia
Beatrice Longuenesse: Residues of First Nature
19 April @NSSR
Angelica Nuzzo: Approaching Hegel’s Logic Obliquely: Melville, Moliere, Beckett
Response: David Carlson
10 May @Columbia
Amy Allen: Turning Dead Ends into Through Streets: Psychoanalysis and the Idea of Progress
The REC is a pre-read conference. The papers will be made available on April 15.
Friday, May 3, 2019
1:30 – 3:15 pm
Alex Byrne (MIT)
Chair: TBD
Coffee Break
3:45 – 5:30 pm
Susanna Rinard (Harvard)
Chair: TBD
Dinner
7:30 – 9:15 pm
Jonathan Kvanvig (Washington University St Louis)
Chair: TBD
Reception 9:30 – 11:00 PM
Saturday, May 4, 2019
9:30 – 11:15 am
Anil Gupta (University of Pittsburgh)
Chair: TBD
Coffee Break
11:45 – 1:30 pm Winner of the Young Epistemologist Prize
TBD
Chair: TBD
Lunch
2:45 – 4:30 pm
Maria Lasonen-Aarnio (University of Helsinki)
Chair: TBD
Discussants
Heather Battaly (University of Connecticut)
John Bengson (University of Wisconsin-Madison)
Annalisa Coliva (University of California Irvine)
Thomas Kelly (Princeton)
Participants
Chris Copan, Andy Egan, Megan Feeney, Peter Klein, Matthew McGrath, Susanna Schellenberg, Ernie Sosa
The REC is a pre-read conference, so papers are to be read in advance. There is no registration fee for the conference, but please notify Megan Feeney, the conference manager, if you plan to attend by sending an email to rutgersepistemologyconference@gmail.com. If you wish to participate in the meals, please send a check made out to “Rutgers University” to Megan Feeney by April 15 ($80 if you are a faculty member or a postdoc; $60 if you are a graduate student or an undergraduate): Megan Feeney; Rutgers Epistemology Conference; 106 Somerset St, 5th Floor; New Brunswick, NJ 08901.
8 February @Columbia
Patricia Kitcher: The Fact of Reason in Kant’s Moral Psychology
Response: Jessica Tizzard
22 February @NSSR
5 April @Columbia
Beatrice Longuenesse: Residues of First Nature
19 April @NSSR
Angelica Nuzzo: Approaching Hegel’s Logic Obliquely: Melville, Moliere, Beckett
Response: David Carlson
10 May @Columbia
Amy Allen: Turning Dead Ends into Through Streets: Psychoanalysis and the Idea of Progress
This essay tries to develop a “black radical Kantianism” – that is, a Kantianism informed by the black experience in modernity. After looking briefly at socialist and feminist appropriations of Kant, I argue that an analogous black radical appropriation should draw on the distinctive social ontology and view of the state associated with the black radical tradition. In ethics, this would mean working with a (color-conscious rather than colorblind) social ontology of white persons and black sub-persons and then asking what respect for oneself and others would require under those circumstances. In political philosophy, it would mean framing the state as a Rassenstaat (a racial state) and then asking what measures of corrective justice would be necessary to bring about the ideal Rechtsstaat.
Response by César Cabezas Gamarra.
Presented by the German Idealism Workshop
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.
In 1804 Schelling diagnosed our impending “annihilation of nature” due to our conceptual detachment from and consequent economic exploitation of our natural world. His critique of Modernity’s Cartesian Idealisms, effected through his inversion of the Kantian categories, results in a philosophical project whose relevance to our ongoing climate crisis is difficult to overstate.
Bruce Matthews
Bard College/BHSEC, professor of philosophy, research in German Idealism and Romanticism, with a focus on life and thought of F.W.J. Schelling, whose recent work revolves around Schelling’s critique of modernity with its anticipation of, as he wrote in 1804, ‘the annihilation of nature,’ and its relevance to the Anthropocene.
“Schelling in the Anthropocene: A New Mythology of Nature,” (Symposium: Canadian Journal of Continental Philosophy, 2015), “Schelling: A Brief Biographical Sketch of the Odysseus of German Idealism,” in The Palgrave Handbook to German Idealism (2014), and “The New Mythology: Between Romanticism and Humanism,” in The Relevance of Romanticism (Cambridge University Press, 2014). Books include the forthcoming intellectual biography, Schelling: Heretic of Modernity (2018), Schelling’s Organic Form of Philosophy: Life as the Schema of Freedom (SUNY 2011).
Presented by the Philosophy Department at The New School for Social Research