Volume 10, Issue 1, 2013
A Journal of Analytic Scholasticism
John Mair on Semantic Paradoxes
Alethic Modalities and Validity in Paradoxical Contexts
Conceptual analysis of logical consequence can be regarded as a crucial part of any logical theory. The present paper focuses on John Mair’s approach to this issue from both historical and systematic point of view. Mair’s task is to analyse the concepts of modality and validity in universal token-based languages with non-compositional semantics based on network evaluation. To fulfil it, Mair addresses modal paradoxes, validity paradoxes and inferences with paradoxical components. Both truth and modality and truth and validity, when conceived as semantic properties, turn out to be mutually independent as a result of Mair’s semantics: there are true impossible propositions and possible propositions which cannot be true and truth-preservation turns out to be neither a sufficient nor a necessary condition for validity.