An Analysis of The Liar Paradox Withing The Framework of The Theory of Structured Propositions

The Liar is a self-referential sentence which says that it is false. In this article، we will first show that the main two traditional and well-known solutions of this paradox cannot survive a serious scrutiny. Then، we will use two important premises to introduce a new solution for the problem. The first premise is that “propositions” (rather than sentences) are truth-bearers (even though we sometimes assign truth value to sentences، when we do that، we are well aware that we are not talking accurately; but this kind of inaccuracy is allowed only as far as it doesn’t cause serious problems such as paradoxes). After adding this premise to the discourse، the Liar sentence will be rephrased in a more accurate way as a sentence which says that the proposition it expresses is false. The second premise is the theory of structured propositions according to which propositions are ordered sets (that is to say a proposition is of the ontological genre of sets). Then، using the regularity principle in set theory، we will show that no set can be a member of itself and since a proposition is a set، it can’t include itself as a member and can’t express its own falsehood. In this way، we prove that no such proposition exists and the Liar sentence is without content and meaningless. Taking propositions as truth bearers and using the theory of structured propositions lead to an acceptable solution for the Liar paradox which in its turn can be taken as an advantage of those theories about truth-bearers and the nature of propositions.