• Goethe's observation to Eckermann that, properly speaking, “our intellectual work lies not so much in thinking new thoughts as in thinking the old ones again” (229-30).

There is a saying by Dieudonne which is related to the view of Goethe:

• “What changes in Mathematics, as in all other sciences, is the point of view from which results already acquired, are assessed.”

Jean Dieudonne

The problem with the above sayings is: What is a point of view? Is it an interpretation? a metaphor? An appropriate Functor between a familiar category and an unfamiliar one?

Some examples: In axiomatic Set Theory, there is no randomness or fuzziness. The map f:A--→ [0,1], is just a map. If we change the point of view and regard this function as a generalized membership function, then this changed point of view give “fuzzy set theory”. Similarly with probability.

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