We are happy to announce a talk by Maciej Kłeczek (GU Frankfurt) at the Semantics Colloquium.
Please register beforehand (firstname.lastname@example.org) to receive the access data to zoom on Thursday shortly before the talk starts.
Title: Quine on variables
Date: July 15
Time: 4 pm – 6 pm ct
In this exegetical talk we reconstruct and critically discuss the Quine view on variable like symbols and first-order variables. This is a quintessential Quinean theme found in a series of papers [On the Logic of Quantification, Variables Explained Away, The Variable, Algebraic Logic and Predicate Functor Logic], and Quine’s seminal monograph Word Object. Quine has presented a rather coherent picture of variable like symbols and first-order variables. As a consequence, this picture generates a coherent interpretation of first-order languages conforming to an important Quine’s background philosophical assumption which is nominalism (or rather a propensity to nominalism).
We start our talk with Quine’s account of schematicity and contrast it with alternative more recent approaches. Next, we proceed to Quine’s explication of a first-order variable as a relative pronoun characteristic for relative clauses (or ‘such that’ clauses). After discussing syntactic subtleties surrounding ‘such that’ clauses we proceed towards Predicate Functor Logic. Predicate Functor Logic is designed to provide the full analysis of first-order variables and also deliver an algebraization of first-order logic. In particular, we reconstruct Quine’s translations algorithms and point out possibly problematic features of the translation algorithm sending expressions of Predicate Functor Logic to First-Order Logic. Also, we assess how far Quine succeeds in providing the full analysis of first-order variables in the framework of Predicate Functor Logic. Furthermore, we raise the issue to what degree Predicate Functor Logic can be regarded as an algebraization of first-order logic.
In the last part of the talk we raise the issue of a satisfactory criterion of ontological commitment in the vicinity of Predicate Functor Logic. Quine regards Predicate Functor Logic as a new canonical notation. The standard Quinean criterion of ontological commitment [On What There Is] turns out to be dependent on the choice of notation. Since theories expressed in Predicate Functor Logic do not contain variables the standard criterion is inapplicable. This triggers a need of finding a more general criterion of ontological commitment which is not notation bound. We introduce the Quinean way forward which essentially relies on Russell’s criterion of ontological commitment [Introduction to Mathematical Philosophy] given in terms of the satisfaction of predicates.
By and large the talk focuses on exegetical issues and contains some insights of historical nature. No new technical results are going to be presented.