A Minimalist Foundation at Work

What is the nature of mathematics? The different answers given to this perennial question can be gathered from the different theories which have been put forward as foundations of mathematics. In the common contemporary vision, the role of foundations is to provide safe grounds a posteriori for the activity of mathematicians, which on the whole is taken as a matter of fact. This is usually achieved by reducing all concepts of mathematics to that of set, and by postulating sets to form a fixed universe, which exists by itself and is unaffected by any human activity. Thus it is a static vision.

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