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.