Geniuses -

genius gottlob frege

Gottlob Frege

I do not begin with concepts and put them together to form a thought or judgement; I come by the parts of a thought by analysing the thought.

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genius gottlob frege

What is it, in fact, that we are supposed to abstract from, in order to get, for example, from the moon to the number 1? By abstraction we do indeed get certain concepts, viz. satellite of the Earth, satellite of a planet, non-self-luminous heavenly body, heavenly body, body, object. But in this series 1 is not to be met with; for it is no concept that the moon could fall under.

genius gottlob frege

Thus the thought, for example, which we expressed in the Pythagorean theorem is timelessly true, true independently of whether anyone takes it to be true. It needs no bearer. It is not true for the first time when it is discovered, but is like a planet which, already before anyone has seen it, has been in interaction with other planets.

genius gottlob frege

A scientist can hardly encounter anything more desirable than, just as a work is completed, to have its foundation give way.

genius gottlob frege

Every good mathematician is at least half a philosopher, and every good philosopher is at least half a mathematician.