ПРАКТИКА КОМПЬЮТЕРНЫХ ДОКАЗАТЕЛЬСТВ И ЧЕЛОВЕЧЕСКОЕ ПОНИМАНИЕ: ЭПИСТЕМОЛОГИЧЕСКАЯ ПРОБЛЕМАТИКА

科研成果: Article同行评审

摘要

In recent decades, some epistemological issues have become especially acute in mathematics. These issues are associated with long proofs of various important mathematical results, as well as with a large and constantly increasing number of publications in mathematics. It is assumed that (at least partially) these difficulties can be resolved by referring to computer proofs. However, computer proofs also turn out to be problematic from an epistemological point of view. With regard to both proofs in ordinary (informal) mathematics and computer proofs, the problem of their surveyability appears to be fundamental. Based on the traditional concept of proof, it must be surveyable, otherwise it will not achieve its main goal - the formation of conviction in the correctness of the mathematical result being proved. About 15 years ago, a new approach to the foundations of mathematics began to develop, combining constructivist, structuralist features and a number of advantages of the classical approach to mathematics. This approach is built on the basis of homotopy type theory and is called the univalent foundations of mathematics. Due to its powerful notion of equality, this approach can significantly reduce the length of formalized proofs, which outlines a way to resolve the epistemological difficulties that have arisen.
投稿的翻译标题COMPUTER PROOFS PRACTICE AND HUMAN UNDERSTANDING: EPISTEMOLOGICAL ISSUES
源语言Russian
页(从-至)5-19
页数15
期刊Вестник Пермского университета. Философия. Психология. Социология
1
DOI
Published - 2021

Level of Research Output

  • VAK List

指纹 探究 'ПРАКТИКА КОМПЬЮТЕРНЫХ ДОКАЗАТЕЛЬСТВ И ЧЕЛОВЕЧЕСКОЕ ПОНИМАНИЕ: ЭПИСТЕМОЛОГИЧЕСКАЯ ПРОБЛЕМАТИКА' 的科研主题。它们共同构成独一无二的指纹。

引用此