In my previous post, I noted the most obvious problem with Tarski’s (or almost anybody’s) argument that natural languages are inconsistent – if natural languages are in fact inconsistent, then everything is provable within natural languages and so the argument they are inconsistent does not establish anything.
Tarski’s response to his belief that natural languages are inconsistent was to define a formal concept of truth that could be used in place of the natural language concept of truth. There is a further problem with this approach that follows from the more obvious point above. If natural languages are in fact inconsistent, then any proof within a natural language will not establish any truth. This means that the proofs necessary to define, and determine the properties of, any defined formal language will not establish any truths about those languages. In other words, if natural languages are inconsistent, then it is not possible to define any meaningful formal languages that embody anything true.
The premise of Tarski’s approach, that it is possible to replace natural language use with a formal language, is not consistent with Tarski’s basic assumption – that natural languages are inconsistent.