Without some affinity in human ideas art would certainly be impossible; but it can never be exactly determined how far the intentions of the poet are… - Gottlob Frege

Is it always permissible to speak of the extension of a concept, of a class? And if not, how do we recognize the exceptional cases? Can we always infer from the extension of one concept's coinciding with that of a second, that every object which falls under the first concept also falls under the second?

If the task of philosophy is to break the domination of words over the human mind [...], then my concept notation, being developed for these purposes, can be a useful instrument for philosophers [...] I believe the cause of logic has been advanced already by the invention of this concept notation.

A philosopher who has no connection to geometry is only half a philosopher, and a mathematician who has no philosophical vein is only half a mathematician.