Gil Sagi: Extensionality and Logicality

Tarski has characterized logical notions as invariant under permutations of the domain. Tarski proposed this characterization as an extension of Klein’s Erlanger Program, where various geometrical disciplines are characterized by invariance under certain kinds of transformations. The idea was that logical notions are more general than any of the geometrical notions, and are thus invariant under the most general class of transformations.

In this paper, I take Tarski’s logical notions from the geometrical context, and place them in a linguistic setting. We look at a scale inspired by Ruth Barcan Marcus of various levels of meanings: extensions, intensions and hyperintensions. On this scale, the lower the level of meaning, the more coarse-grained and less “intensional” it is. I propose to extend this scale to accommodate logical notions. Thus, below the level of extension, we will have a more coarse-grained level of form. I employ a semantic conception of form, adopted from Sher, where forms are features of things “in the world”. Each expression in the language has a form, and by the definition we give, forms will be invariant under permutations and thus Tarskian logical notions. Logical notions can thus be thought of as the most general in the scale of meaning. We then define the logical constants of a language as those terms whose extension can be determined by their form. Logicality will be shown to be a lower level analogue of rigidity.

I explain how forms fare on Marcus’s proposed scale of extensionality and intensionality, employing her principles of explicit and implicit extensionality. Surprisingly, permutation-invariant notions fit neatly into this picture. Thus, for instance, Marcus’s principles of implicit extensionality concern the types of contexts in which expressions with the same meaning can be substituted salva veritate. I employ McGee’s theorem concerning permutation invariance and definability in L∞∞ (McGee, 1996) to show that expressions with equal forms can be substituted salva veritate in L∞∞-sentences where the rest of the terms are logical.

Gil Sagi

Gil Sagi is a Postdoctoral Fellow at the Ludwig-Maximilians-Universität München . She completed her BSc degree in mathematics and philosophy as well as her MA and PhD degree in Philosophy at the Hebrew University in Jerusalem. Her research interests are in the philosophy of logic (logical consequence, formality, logical terms, logic and natural language), the philosophy of language (the analytic/synthetic distinction), the philosophy of mathematics (optimism in mathematics), and the history of the philosophy of logic (Frege, Tarski, Carnap). Gil Sagi has received various awards as a Bachelor and Master student of the Hebrew University and as a visiting student abroad. As a PhD student she received the Polonsky PhD fellowship (2009-2013) and the Yael Cohen memorial prize for excellency in philosophical research.

When & Where?

Thursday, 9 April 2015, 3.15-5 pm
Faculty of Philosophy, Room Beta