|
The Generality of Logic and the Problem of Logical Constants| old_uid | 8914 |
|---|
| title | The Generality of Logic and the Problem of Logical Constants |
|---|
| start_date | 2010/06/15 |
|---|
| schedule | 09h30-12h30 |
|---|
| online | no |
|---|
| details | conférence 5/6 |
|---|
| summary | To account for our informal notion of logical consequence, it is not sufficient to provide a conceptually motivated definition of logical consequence. The definition of logical consequence has to be supplemented with a conceptually motivated division between logical symbols and extra-logical symbols. In connection with the problem of motivating this divide, the main aim of this talk is to investigate two related ideas. The first one is that being a possible interpretation for a logical constant amounts to satisfying some invariance criterion. The second one is that such a characterization can be vindicated by appealing to the generality of logic.
I will present the first characterization of this kind given by Tarski himself in 1966, as a late follow-up to his 1936 paper on logical consequence. No matter how attractive the simplicity of Tarski's proposal is, the analysis of generality in terms of invariance has proven to be more involved than Tarski had thought. So I will develop on an objection to Tarski's analysis and recalls an alternative characterization I had given which aims at fixing the problem. The corresponding invariance criterion has recently been challenged by Feferman in 2009. In the final part of the talk, I argue that Feferman's criticisms can (partly) be met by redesigning the framework for invariance. This is shown to yield an invariance characterization of first-order definable operations, which can be justified in terms of generality. |
|---|
| responsibles | Tessier Cardon |
|---|
| |
|