１７ Incompleteness Theorem #universe #incompleteness

１７　Incompleteness Theorem　#universe #incompleteness

○The proposition which cannot judge correction exists.
・・・Gödel (Kurt Gödel, Austria 1906-78) proved in 1930.
・・・Then, Turing(Aan Mathison Turing, UK 1912-1954) proved that there is no unific method of confirming beforehand whether a certain proposition is a proposition which cannot judge truth.
Reference: 「世にも美しい数学入門」Masahiko Fujiwara／Youko Ogawa(p.147～151)

The first incompleteness theorem
No consistent system of axioms whose theorems can be listed by an effective procedure (i.e., an algorithm) is capable of proving all truths about the arithmetic of the statements.
For any such theorem, there will always be statements that are true, but that are unprovable within the theorem.
The second incompleteness theorem
An extension of the first, shows that the system cannot demonstrate its own consistency.

☆If there is a proposition which cannot confirm that verification is impossible and it is unverifiable, it can say, "Search is eternal." 
・・・Although nothing may remain even if it continues search throughout life・・・

☆If you can not prove everything with one theory, you can use with multiple theories.

【References】
1. Gödel's incompleteness theorems - Wikipedia



【Change log】
20170429　Addition of theorems
20170706 Proposal of a proof with multiple theories