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Tableaux for Lewis’s V-family (Yale Weiss)

The Logic and Metaphysics Workshop will meet on October 15th from 4:15-6:15 in room 6494 of the CUNY Graduate Center for a talk by Yale Weiss (GC).

Title: Tableaux for Lewis’s V-family

Abstract: In his seminal work Counterfactuals, David Lewis presents a family of systems of conditional logic—his V-family—which includes both his preferred logic of counterfactuals (VC/C1) and Stalnaker’s conditional logic (VCS/C2). Graham Priest posed the problem of finding systems of (labeled) tableaux for logics from Lewis’s V-family in his Introduction to Non-Classical Logic (2008, p. 93). In this talk, I present a solution to this problem: sound and complete (labeled) tableaux for Lewis’s V-logics. Errors and shortcomings in recent work on this problem are identified and corrected (especially close attention is given to a recent paper by Negri and Sbardolini, whose approach anticipates my own). While most of the systems I present are analytic, the tableaux I give for Stalnaker’s VCS and its extensions make use of a version of the Cut rule and, consequently, are non-analytic. I conjecture that Cut is eliminable from these tableaux and discuss problems encountered in trying to prove this.

Ontological Reductions of First Order Models (Alfredo Freire)

The Logic and Metaphysics Workshop will meet on October 22nd from 4:15-6:15 in room 6494 of the CUNY Graduate Center for a talk by Alfredo Freire (Campinas).

Title: Ontological Reductions of First Order Models

Abstract: Since the discovery of the Loweinheim-Skolem theorem, it has been largely held that there is no purely formal way of fixing a model for any first order theory. Because of this, many have focused on having a relative account of models, establishing the expressive power of one model in its ability to internalize models for other theories. One can, for instance, define a plurality of models for PA from a given model for ZF, and this may be understood as evidence for the ontology of arithmetics being reducible to the ontology of set theory. In this presentation, I argue that a close attention to what it means to reduce an ontology shows that methods of reduction are generally not neutral and make it possible for weaker models to reduce stronger ones. For this, I analyze the known model-theoretical reduction of NBG into ZF proved by Novak, showing that a more demanding method makes it impossible for ZF to internalize NBG. We finish this presentation by showing how this view, together with some technical results, provide a positive account in defense of the multiversalist perspective on set theory.

Inconsistency and the Sorites Paradox (Otávio Bueno)

The Logic and Metaphysics Workshop will meet on October 1st from 4:15-6:15 in room 6494 of the CUNY Graduate Center for a talk by Otávio Bueno (Miami).

Title: Inconsistency and the Sorites Paradox

Abstract: The Sorites paradox offers an unsettling situation in which, in light of its premises and the apparent validity of the argument, one may be inclined to take the argument to be sound. But this entails that vague concepts, ubiquitous and indispensable to express salient features of the world, are ultimately inconsistent, or at least the application conditions of these concepts seem to lead one directly into contradiction. In what follows, I argue that this inconsistent understanding of vagueness is difficult to resist, but it is also hard to accept. First, I point out that a number of approaches to vagueness that try to resist this conclusion ultimately fail. But it is also difficult to accept the inconsistency approach. After all, vague concepts do not seem to be inconsistent. Second, even if the inconsistency view turned out to be true, the phenomenology of vague concepts (and such concepts, after all, do not seem to be inconsistent at all) can be accommodated. Contextual factors force one to apply inconsistent concepts consistently by arbitrarily resisting to apply the concepts once a locally determined threshold is met. This yields the impression that vague concepts are consistent. As a result, in light of the apparent non-inconsistent nature of vagueness, on the one hand, and the Sorites argument that supports the opposite view, on the other, it is unclear how to establish whether vague concepts ultimately are inconsistent or not. This explains why the Sorites paradox, despite centuries of reflection, does not go away, and why it is unclear how to settle, in one way or another, a significant aspect of the nature of vagueness.