I probably need to justify my claim in the last post that Tarski was brilliant on logical analysis but pretty average when it comes to philosophy. I will argue this based on Tarski’s claims about the consistency of natural languages, in two papers of his: “The Concept of Truth in Formalized Languages” and “The Semantic Conception of Truth and the Foundations of Semantics”.
In “The Concept of Truth…..”, Tarski offers a philosophical justification for pursuing the logical task of a formal definition of truth. To paraphrase, the philosophical justification is that natural languages are necessarily inconsistent when they come to use the concept of truth. The argument is the familiar argument from the Liar Paradox. In “The Semantic Conception of Truth…”, Tarski offers a clear logical argument for this claim: any language that is ‘semantically closed’, i.e. the language contains a properly defined concepttrue, and which contains the normal laws of logic, is inconsistent. Natural languages satisfy both of these and so are inconsistent.
Tarski’s argument about the inconsistency of semantically closed languages is clear and insightful. The conclusion that natural languages are inconsistent is philosophically disastrous. The most obvious problem is that, if English (or German) is inconsistent when it uses the concept of truth, then nothing can be proven using those languages. This is because everything is provable in inconsistent languages (which obey the normal laws of logic). The result of this is that, if natural languages are inconsistent, Tarski’s argument occurs in an inconsistent language so does not actually prove anything.
Any argument in a natural languages that natural languages are inconsistent is self-defeating. It cannot establish that natural languages are in fact inconsistent. This does not mean that natural languages are consistent though.