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From Freudenthal (1983), p. 28

I start with the antithesis - if it really is an antithesis -
between nooumenon (thought object) and phainomenon.
The mathematical objects are nooumena, but a piece of mathematics
can be experienced as a phainomenon; number are nooumena,
but working with numbers can be a phainomenon.

The definitions found in Kantian philosophy:

  • nooumenon: a thing as it is in itself, unable to be known through perception but postulated as the intelligible ground of a phenomenon
  • phenomenon: a thing as it appears in perception as distinguished from the thing as it is in itself independent of sense experience


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