Foundations of mathematics
The foundation mathematich very important. This is used to some field of mathematich. Such as mathematical logic, axiomatic set theory, proof theory, model theory, and recursion theory.
The foundation give much assumption from philosophy of mathematich. For example the the assumstion from plato, aristoteles, brouwer, immanuel kant, etc .
The main of Foundation of mathematich it is :
1. Platonism..
Platonism is from plato. Platonism is veru important for mathematich method. He is the son of Ariston and Perictione, was born in Athens. The foundational philosophy of Platonist mathematical realism, as give by mathematician Kurt Gödel. The platonism is term of plato cave. The Follow of plato mathematic as ideal’s. This mathematic are be found in your idea.
2. Intuitionism
Intuitionism is from LEJ Brouwer, it is contends the primary objects of mathematical discourse are mental constructions governed by self-evident laws. Intuitionists have challenged many of the oldest principles of mathematics as being nonconstructive and hence mathematically meaningless. intuitionism is a program of methodological reform whose motto is that "there are no non-experienced mathematical truths. In intuitionism, the term "explicit construction" is not cleanly defined, and that has led to criticisms






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