On Kripke’s proof of Kripke completeness (Melvin Fitting)

The Logic and Metaphysics Workshop will meet on March 13th from 4:15-6:15 (NY time) in-person at the Graduate Center (Room 9205) for a talk by Melvin Fitting (CUNY).

Title: On Kripke’s proof of Kripke completeness

Abstract: Saul Kripke announced his possible world semantics in 1959, and published his proof of axiomatic completeness for the standard modal logics of the time in 1963.  It is very unlike the standard completeness proof used today, which involves a Lindenbaum/Henkin construction and produces canonical models.  Kripke’s proof involved tableaus, in a format that is difficult to follow, and uses tableau construction algorithms that are complex and somewhat error prone to describe. I will first discuss Kripke’s proof, then the historical origins of the modern version.  Then I will show that completeness, proved Kripke style, could actually have been done in the Lindenbaum/Henkin way, thus simplifying things considerably.  None of this is new but, with the parts collected together it is an interesting story. “In my end is my beginning”.

Neopragmatism and logic: A deflationary proposal (Lionel Shapiro)

The Logic and Metaphysics Workshop will meet on February 27th from 4:15-6:15 (NY time) in-person at the Graduate Center (Room 9205) for a talk by Lionel Shapiro (UConn).

Title: Neopragmatism and logic: A deflationary proposal

Abstract: Neopragmatists seek to sidestep metaphysical puzzles by shifting the target of philosophical explanation from the objects we think and talk about to the functions of expressions and concepts in our cognitive economy. Logical vocabulary can serve as a target for neopragmatist inquiry, and it has also posed obstacles to neopragmatist accounts of other vocabulary. I will argue that the obstacles can be addressed by adopting a neopragmatist perspective toward logical relations, such as logical consequence, and toward propositional content. Doing so calls into question two purported constraints on explanations of the functions of logical connectives. I will sketch an account made possible by rejecting those constraints, one according to which logical connectives serve to express dialectical attitudes. The proposal is deflationary in two ways: it rests on an extension of deflationism from truth to logical relations, and it aims to deflate some of neopragmatists’ theoretical ambitions.

Lewis on accommodation and representation de re (Gary Ostertag)

The Logic and Metaphysics Workshop will meet on March 6th from 4:15-6:15 (NY time) in-person at the Graduate Center (Room 9206) for a talk by Gary Ostertag (CUNY/Mount Sinai).

Title: Lewis on accommodation and representation de re

Abstract: Recall Lumpl, the lump of clay out of which the statue Goliath is fashioned. While (1) ‘Lumpl could have survived a squashing’ is true, (2) ‘Goliath could have survived a squashing’ is false, it being after all essential to Goliath, but not to Lumpl, that it be a statue. We have here an example of what David Lewis (1986) called “the inconstancy of representation de re”. For Lewis, the inconstancy does not amount to inconsistency, but rather points to the context-sensitivity of de re modal predication: (1) and (2) make implicit, context-sensitive reference to different counterpart relations. Once we recognize this, Lewisians argue, it becomes clear how our intuitive truth-conditional judgments are fully consistent. As I show, however, the conversational rule that triggers the implicit reference not only fails to license the reference shift, it effectively prohibits it. The upshot is that counterpart theory is deprived of a central motivation.

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