Question

I have thought a lot a about mathematics and it's foundations. There have been several attempts to give it a solid foundation, and they all failed. Frege / Russell logical atomist approach failed, intuitionist logic failed, set theory did succeed to some extend, but it lead to extremely bizarre conclusions that many mathematicians think have nothing to do with reality (like infinite hierarchies of infinities and similar nonsense).

The more I think about it, the more it seems to me that all these projects failed because modern mathematics (with some exceptions like elementary number theory and classical geometry because they originated in ancient Greece) is nothing but medieval scholasticism in a different flavour. Real/complex analysis, set theory, modal logic and other related fields have nothing to do with reality, they are just hyper-logical nonsense abstraction for abstraction's sake.

Is mathematics, or a part of it scholasticism?

Answer 1

Mathematics is not scholasticism and has practical applications in various fields. It provides a framework for understanding and solving real-world problems.

Step-by-step explanation:

Mathematics has evolved over time and has undergone various attempts to provide it with a solid foundation. While different approaches have been made, it is important to note that mathematics is not scholasticism. Scholasticism refers to a medieval school of thought that aimed to reconcile faith and reason, whereas mathematics is a discipline that utilizes logical reasoning and abstraction to study concepts and relationships.

Modern mathematics is not just an abstract concept but has practical applications in various fields such as physics, engineering, and computer science. Real and complex analysis, set theory, modal logic, and other fields within mathematics are not merely hyper-logical nonsense abstractions but provide a framework for understanding and solving real-world problems.

While there may be some debate about the extent to which mathematics reflects reality, it is important to recognize that mathematics has proven to be an incredibly powerful tool for understanding and describing the world around us.