Seminar in Logic - A

Semantic and set-theoretic paradoxes

The notions of truth and set are two of the most fundamental notions in the philosophy of logic and mathematics. Famously, however, efforts to formalize these notions have revealed a crucial difficulty: although apparently harmless at an informal level, once formalized they are limited by the possibility of giving rise to so-called semantic and set-theoretic paradoxes. A paradox, as Mark Sainsbury puts it, is an argument in which "an evidently unacceptable conclusion (...) follows from evidently acceptable premisses by means of evidently acceptable reasoning." The paradoxes relating to the notions of truth and set have, on the one hand, triggered the so-called "foundational crisis" in the philosophy of mathematics and, on the other, have inspired several explanations and solutions, sometimes incompatible with each other. The most famous of the latter will be the subject of this course, which will investigate their logico-philosophical limits and advantages.

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Mixed

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Evaluation method: Essay.