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Please do read further on Tarski's work. Specifically, Tarski's Undefinability of Truth is a formal result which says that the typical language that we use to d
by Kednicma 6y ago
Please do read further on Tarski's work. Specifically, Tarski's Undefinability of Truth is a formal result which says that the typical language that we use to describe the world is so powerful that it cannot define its own notion of truth when analyzed formally. It is part of a family of results which destabilized the logicist dreams of the era and led to our modern vision of mathematics as a branching tree of many different logics.
Edit: https://www.logicmatters.net/resources/pdfs/godelbook/GodelBookLM.pdf https://www.logicmatters.net/resources/pdfs/godelbook/GodelB... is quite good and includes Tarski's results. There's also GEB, of course.
- hyperpape 6y agoWhat you said was "The former program destroyed any belief that we might be able to use formal tactics to analyze truth or other semantics." That description is quite vague, which was what my question suggested. Tarski's work described a criterion for a theory of truth for a language, and showed how to give a compositional semantics for some formal languages. As you noted, that language does not define its own truth predicate, to avoid paradox, but this is a formal analysis of truth. His work, along with Gödel's, ended the logicist program, but not formal treatments of semantic concepts. P.S. Don't assume what others have or haven't read. I can't claim any expertise, but I took a graduate seminar on the theory of truth taught by Anil Gupta. That doesn't mean I'm right, of course.