The Logic and Metaphysics Workshop will meet on September 30th from 4:15-6:15 in-person at the Graduate Center (Room 4419) for a talk by Daniel West (CUNY).

Title: The disjunction property for operational relevance logics

Abstract: A logic has the disjunction property just in case whenever a disjunction is valid, at least one of its disjuncts is valid. The disjunction property is important to constructivists and is a well-known feature of intuitionistic logic. In this talk I present joint work with Yale Weiss in which we use model-theoretic techniques to show that the disjunction property also holds in Urquhart’s operational relevance logics. This is a known result in the case of the positive semilattice logic, but the proof is quite different, being proof-theoretic rather than semantic. These results suggest that operational relevance logics merit further attention from a constructivist perspective. Along the way, we also provide a novel proof that the disjunction property holds in intuitionistic logic.

Note: This is joint work with Yale Weiss (CUNY).

The Logic and Metaphysics Workshop will meet on September 23rd from 4:15-6:15 in-person at the Graduate Center (Room 4419) for a talk by Rohit Parikh (CUNY).

Title: Value and freedom

Abstract: In order to decide how good a society is, we need some measure of goodness. And the goodness of a society is typically obtained by somehow summing up the well beings of its members. Various approaches include Utilitarianism and Rawlsianism as well as the Leximin approach suggested by Amartya Sen. But Sen and Nussbaum have suggested that the Capability of an individual, what the individual can do, should be the real measure of well being. Another issue is that of freedom. My freedom can be diminished by some restrictive laws. But it can also be diminished by some handicap, or by certain social methods not being available. How to measure the amount of freedom I have? Is it simply the number of options I have, or does the value of the options also matter? And what is the mathematics of freedom?

Note: An extended abstract is available here.

The Logic and Metaphysics Workshop will meet on September 16th from 4:15-6:15 in-person at the Graduate Center (Room 4419) for a talk by Mel Fitting (CUNY).

Title: Simple tableaus for simple logics

Abstract: Consider those many-valued logic models in which the truth values are a lattice that supplies interpretations for the logical connectives of conjunction and disjunction, and which has a De Morgan involution supplying an interpretation for negation. Assume the set of designated truth values is a prime filter in the lattice. Each of these structures determines a simple many-valued logic. We show there is a single Smullyan style signed tableau system appropriate for all of the logics these structures determine. Differences between the logics are confined entirely to tableau branch closure rules. Completeness, soundness, and interpolation can be proved in a uniform way for all cases. Since branch closure rules have a limited number of variations, in fact all the semantic structures determine just four different logics, all well-known ones. Asymmetric logics such as strict/tolerant, ST, also share all the same tableau rules, but differ in what constitutes an initial tableau. It is also possible to capture the notion of anti-validity using the same set of tableau rules. Thus a simple set of tableau rules serves as a unifying and classifying device for a natural and simple family of many-valued logics.

The Logic and Metaphysics Workshop will meet on September 9th from 4:15-6:15 in-person at the Graduate Center (Room 4419) for a talk by Hartry Field (NYU).

Title: Well-behaved truth

Abstract: Common-sense reasoning with truth involves both the use of classical logic and the assumption of the transparency of truth (the equivalence between a sentence and the attribution of truth to it). The semantic paradoxes show that at least one of these must go, and different theorists make different choices. But whatever one’s choice, it’s valuable to carve out one or more domains where both classical logic and transparency can be assumed; domains where everything is *well-behaved*.  In this talk I’ll explore a method of adding a predicate of well-behavedness to various truth theories, which works for both classical and nonclassical theories (including non-classical theories with special conditionals). With such a predicate, one can reason more easily, and formulate and prove generalizations that are unavailable without such a predicate. Besides their intrinsic interest, these generalizations greatly increase the proof-theoretic strength of axiomatic theories.  (There are some previous proposals for adding a well-behavedness predicate to specific classical theories, and others for adding one to non-classical theories without special conditionals.  The current proposal, besides being general, is also more satisfactory in the individual cases, and is the only one I know of for non-classical theories with conditionals.)

The Logic and Metaphysics Workshop will be meeting on Mondays from 4:15 to 6:15 unless otherwise indicated. Talks will be in-person only at the CUNY Graduate Center (Room 4419). The provisional schedule is as follows:

Sep 2. NO MEETING

Sep 9. Hartry Field (NYU)

Sep 16. Mel Fitting (CUNY)

Sep 23. Rohit Parikh (CUNY)

Sep 30. Daniel West (CUNY)

Oct 7. Cian Dorr (NYU)

Oct 14. NO MEETING

Oct 21. Thomas M. Ferguson (Rensselaer)

Oct 28. Roundtable Discussion and Dinner celebrating the 10th Anniversary of the Workshop (Details TBA)

Nov 4. Elena Ficara (Paderborn)

Nov 11. Friederike Moltmann (CNRS)

Nov 18. Damiano Costa (Lugano)

Nov 25. Damian Szmuc (Buenos Aires)

Dec 2. Sam Burns (Columbia)

Dec 9. Walter Carnielli (Campinas)