Such scrutiny can scarcely help relying on philosophical ideas and principles.
In practice this usually means scrutinizing the logical and linguistic tools mathematicians wield.
On the other hand, some philosophers, logicians and mathematicians have tried or are trying to subject the very concepts which mathematicians are using in their work to critical scrutiny. On the one hand, some philosophers (and some mathematicians) take the nature and the results of mathematicians' activities as given, and go on to ask what philosophical morals one might perhaps find in their story. One can distinguish, roughly speaking, two different approaches to the philosophy of mathematics.
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