Math without grounds, but with philosophy

31 March, 2022

Mathematics is paradoxical. It helps to explore reality, but its objects are not in reality. It is the most reliable science, but it cannot prove its own authenticity. This episode is about the philosophical problems of the Queen of Sciences.

Guest — philosopher Vladislav Shaposhnikov
Moderator — Anton Kuznetsov


00:00 - Introduction
00:58 - Why do we need a philosophy of mathematics?
03:51 - Numbers and tribes of the Amazon. The math is not obvious
05:48 - The problem of formal and informal. Let's get rid of intuitions!
12:48 - What is the search for the foundations of mathematics?
15:46 - No foundation was sought until the 19th century. They are in the divine
18:15 - Does the problem of foundations arise because mathematicians have become atheists?
20:14 - Mathematics has not been the same at all times
22:15 - The gap between mathematics and reality
28:30 - Formalization of mathematics and its foundations
30:50 - Confrontation between formalists and intuitionists
37:54 - Handel. Why the grounds have not been found and most likely will not be found
41:46 - Conclusion from Mary

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