Hilbert`s Program에 대해 쓴 논리학 최종 논문입니다.
3.Hilbert`s Finitary Standpoint
3-1.What is finitary reasoning?
3-2.What are the finitarily meaningful propositions?
4.Relationship between Incompleteness Theorem
Mathematic has a liberal property. We can think about something whether or not it exists, it can be an object of a mathematic field. That property differs Mathematic from other kind of science like Physics, Chemistry and Biology etc. Cantor said, "Mathematic nature stems from the liberal property". And that absolute property has a restriction, "inconsistency" of the object.
For a long period of time, it was believed that the Earth was flat, and that the Sun revolves around the Earth. To determine whether a proposition is correct or not may not be as easy as it seems. In modern logic,a proposition is characterized on whether it can be proven or not, rather than its correctness. We define S to be consistent when all A (AND) ~A cannot be deduced by S.
Hilbert was rather interested in the consistency of logic than "true or false" of proposition. He spent a lot of time trying to prove the consistency of axiom. Because it could be the great disaster for the Logical field, if whole mathematic is inconsistent. He had to keep the set theory like ZFC.
①Between The Finitary and The Ideal by Klaus Frovin Jorgensen, Roskilde University - Denmark(http://akira.ruc.dk/~frovin/finitary.pdf)
②Stanford Encyclopedia of Philosophy
④현대 수학의 아버지 힐베르트 by Constance Reed, 사이언스북스