Recursive Synthesis and the Foundations of Mathematics

Details Recursive Synthesis and the Foundations of Mathematics Recursive Synthesis and the Foundations of Mathematics

2002-08-23

arxiv.org/abs/math/0208184v1

Mathematics

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20 pages

Scientific paper

This paper presents mathematics as a general science of computation in a way different from the tradition. It is based on the radical philosophical standpoint according to which the content, meaning and justification of experience lies in its precise formulation. The requirement on precise, formal content discloses the relational structure of (mathematical) experience, and gives a new meaning to the `ideal' objects beyond concrete forms. The paper also provides a systematic reason why set theory represents an ultimate stage in mathematical technology.

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