Let us look at some specific examples of mathematical work and see what philosophical lessons we can draw from them. We will find that the activity of mathematical research forces a recognition of the objectivity of mathematical truth. The "Platonism" of the working mathematician is not really a belief in Plato's myth; it is just an awareness of the refractory nature, the stubbornness of mathematical facts. They are what they are, not what we wish them to be.
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