A complete theory of truth is impossible. Tarski noted that the attempt to formulate a complete theory of truth for a language within the language itself would lead to paradox. This is a technical result of major importance that contains a metaphysical insight of equal importance. It is that the attempt to give a complete account of the relationship between language and the world within language is doomed to failure. The paradoxes exhibit the failure in cases in which language is both the subject and vehicle of discourse. What should we conclude about truth? It is a notion that cannot be defined. We cannot give any perfectly general definition of truth that specifies the necessary and sufficient conditions for the truth of every true sentence.Keith Lehrer, Theory of Knowledge.
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