Mathematical Perspectives on Liar Paradoxes

The liar paradox is a famous and ancient paradox related to logic and philosophy. It shows it is perfectly possible to construct sentences that are correct grammatically and semantically but that cannot be true or false in the traditional sense. In this paper the authors show four approaches to interpreting paradoxes that illustrate the influence of: (a) the levels of language, (b) their belonging to indeterminate compatible propositions (ICP) or indeterminate propositions (IP), (c) being based on universal antinomy and (d) the theory of dialetheism.