Hilary Putnam once suggested that “the actual existence of sets as ‘intangible objects’ suffers… from a generalization of a problem first pointed out by Paul Benacerraf… are sets a kind of function or are functions a sort of set?” Sadly, he did not elaborate; my aim, here, is to do so on his behalf. There are well-known methods for treating sets as functions and functions as sets. But these do not raise any obvious philosophical or foundational puzzles. For that, we (...) first need to provide a full-fledged function theory. I supply such a theory: it axiomatizes the iterative notion of function in exactly the same sense that ZF axiomatizes the iterative notion of set. Indeed, this function theory is synonymous with ZF. It might seem that set theory and function theory present us with rival foundations for mathematics, since they postulate different ontologies. But appearances are deceptive. Set theory and function theory provide the very same judicial foundation for mathematics. They do not supply rival metaphysical foundations; indeed, if they supply metaphysical foundations at all, then they supply the very same metaphysical foundations. (shrink)

Scientific realism is usually presented as if metaphysical realism (i.e. the thesis that there is a structured mind-independent external world) were one of its essential parts. This paper aims to examine how weak the metaphysical commitments endorsed by scientific realists could be. I will argue that scientific realism could be stated without accepting any form of metaphysical realism. Such a conclusion does not go as far as to try to combine scientific realism with metaphysical antirealism. Instead, it amounts to the (...) combination of the former with a weaker view, called quietism, which is agnostic on the existence of mind-independent structures. In Sect. 2, I will argue that the minimal claim that brings together every scientific realist view is devoid of any metaphysical commitment. In Sect. 3, I will define metaphysical realism and antirealism. Such work will be instrumental in providing a more precise statement of quietism. Finally (Sect. 4), I will argue that assuming quietism, it is still possible to make sense of the debate between scientific realists and antirealists. (shrink)

Scientific realism is usually presented as if metaphysical realism (i.e. the thesis that there is a structured mind-independent external world) were one of its essential parts. This paper aims to examine how weak the metaphysical commitments endorsed by scientific realists could be. I will argue that scientific realism could be stated without accepting any form of metaphysical realism. Such a conclusion does not go as far as to try to combine scientific realism with metaphysical antirealism. Instead, it amounts to the (...) combination of the former with a weaker view, called quietism, which is agnostic on the existence of mind-independent structures. In Sect. 2, I will argue that the minimal claim that brings together every scientific realist view is devoid of any metaphysical commitment. In Sect. 3, I will define metaphysical realism and antirealism. Such work will be instrumental in providing a more precise statement of quietism. Finally (Sect. 4), I will argue that assuming quietism, it is still possible to make sense of the debate between scientific realists and antirealists. (shrink)