Godel Thought, Absolutely Undecidable Proposition

The paper consists of three parts. In the first part, it begins with the introduction to incompleteness theorems and the outline of its proof; this basic knowledge is prepared for the two latter important parts. Godel's thought about absolutely undecidable questions and some philosophical deduction directly lead by it will be analyzed in the second part; and it involves the following problems:In what sense is mathematics inexhaustible? Are there absolutely undecidable propositions in number theory? Can evident axioms in mathematics included in finite rules? What is the relationship of and difference between human minds and machines? How do absolutely undecidable questions support the view of mathematics realism? The third part is mainly on the philosophical implication and corresponding deduction of absolutely undecidable questions and incompleteness theorems based on the thoughts mentioned above. Furthermore, it also involves other philosophers'views on absolutely undecidable questions and mathematics realism which differ from Godel's.