A good place to begin is with a delineation of the sorts of questions that foundational frameworks for mathematics, as we conceive them, can usefully address and which motivate their development in the first place. This will in turn guide us in framing some important desiderata that such frameworks should try to meet.
Hellman, G. (2011)., Foundational frameworks, in G. Sommaruga (ed.), Foundational theories of classical and constructive mathematics, Dordrecht, Springer, pp. 53-69.
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