Constituted Platonism, Reason, and Mathematical Knowledge

Richard Tieszen

in After Gödel

Published in print May 2011 | ISBN: 9780199606207
Published online May 2011 | e-ISBN: 9780191725500 | DOI:
Constituted Platonism, Reason, and Mathematical Knowledge

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Many of the ideas in the previous chapters are brought together in the account of the knowledge of abstract mathematical objects presented in this chapter. The chapter commences with a description of acts of reason as “founded” acts of consciousness. Following ideas of Husserl that interested Gödel, it is shown how the meaning of being of abstract mind-independent mathematical objects is supposed to be constituted in founded acts of reason of (human) monads. The place of mathematical intuition (as a kind of rational intuition) in providing knowledge and objectivity is discussed. An example of illusion in set theory, and of the correction of illusion, is presented. A final section covers various analogies between ordinary sense perception and mathematical intuition that are alleged to hold by Gödel. The chapter provides an extended response to the old problem of bridging the supposed gap between human subjectivity and mathematical objectivity.

Keywords: founded; abstraction; perception; reason; platonism; intuition; constitution; monads; objectivity; analogies

Chapter.  20601 words.  Illustrated.

Subjects: History of Western Philosophy

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