Mathematics MOC

Foundation of mathematics

According to Vladimir Voevodsky¹, a foundation of mathematics as three components:

1. A formal deduction system: language and rules of manipulating sentences in this language that are purely formal, such that a record of such manipulations can be verified by a computer program;
2. A structure that provides a meaning to the sentences of this language in terms of mental objects intuitively comprehensible to humans;
3. A structure that enables humans to encode mathematical ideas in terms of the objects directly associated with the language.

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Footnotes

1. 2014. The origins and motivations of Univalent Foundations: A personal mission to develop computer proof verification to avoid mathematical mistakes ↩