Доклад Нозона Янофского «Self-Referential Paradoxes»

31 января Нозон Янофский выступил с докладом «Self-Referential Paradoxes» на теоретическом семинаре МЛ ЛогЛинФФ «Формальная философия». 

фото МЛ ЛогЛинФФ

Аннотация. 

Over the past 150 years, some of the most profound and influential theorems in mathematics and computer science have emerged from self-referential paradoxes. These theorems deal with systems that exhibit self-reference, challenging our understanding of fundamental concepts. This presentation will explore:

1. Georg Cantor's Theorem: Demonstrating the existence of different levels of infinity.
2. Bertrand Russell's Paradox: Exposing inconsistencies in naive set theory.
3. Kurt Gödel's Incompleteness Theorems: Revealing inherent limitations in formal systems and the notion of mathematical proof.
4. Alan Turing's Halting Problem: Proving the existence of unsolvable computational problems.

Remarkably, these diverse theorems, along with several others, can be understood as manifestations of a single, elegant theorem from basic category theory. This presentation will elucidate this theorem and demonstrate its various instances.