著者

宇野 光範

出版者

香川高等専門学校

雑誌

高松工業高等専門学校研究紀要 (ISSN:03899268)

巻号頁・発行日

vol.40, pp.47-59, 2005-03

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There is a huge gap between a sentence being undecidable and a true sentence being unprovable. Although being a Platonist, Godel had been reluctant to explain his incompleteness theorems in terms of the notion of truth. Instead, he mentions on absolutely undecidable Diophantine problems with regard to his first incompleteness. This together with his distinction of objective/subjective mathematics, Godel's intended philosophical implications of his theorems are discussed. Difficulties under subjective math, when no Platonism is presupposed, are examined.