They are truisms—in principle they are statements that are entirely redundant as one could in principle work out the truth of them without being told anything. However, principle and practice are rather different here—just because we could in principle reinvent mathematics from scratch doesn’t mean that in practice we could. Consequently these beliefs are presented to us as external information rather than as the inevitable truisms they actually are.
They are truisms—in principle they are statements that are entirely redundant as one could in principle work out the truth of them without being told anything. However, principle and practice are rather different here—just because we could in principle reinvent mathematics from scratch doesn’t mean that in practice we could. Consequently these beliefs are presented to us as external information rather than as the inevitable truisms they actually are.