2 October 2015, Cool Logic, Stella Moon

In the early 1900s, some paradoxes were discovered regarding the notion of truth. This led some philosophers to suggest abandoning truth entirely. However, Tarski's ground breaking paper “The concept of truth in formalized languages” (1935) reintroduced the concept of truth as a respectable notion. He introduced the notion of metalanguage and object language to avoid the paradoxes. This also led to a view called deflationism. Deflationism is a view that the assertion of truth should not assert more than the statement itself.

Since then, there have been attempts to formalise the concept of truth. There are two ways of formalising the concept: semantic and axiomatic theories of truth. Semantic theories use models of formal theories to state whether a sentence is true or false. This is generally accepted and used in model theory. Axiomatic theories introduce truth into the language of the theory.

We will use Peano Arithmetic (PA) as our base theory, the theory of the object language. We can show Goedel's theorems in PA and discuss truth in arithmetic. To respect deflationists' view on truth, I will introduce proof theoretic and model theoretic conservativities, and discuss the compositional axioms of truth.

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