 Most viewpoints in the philosophy of mathematics accept the existence of all of the finite and infinite objects mentioned so far in exactly the same way that they accept the existence of finite integers. (Platonists might accept that this is literal existence, while fictionalists accept this as some sort of fictional existence, and others might have a different idea of what this means.) Standard set theories can prove the existence of all these objects, and for most mathematicians and philosophers, this is all that is needed. Logicist and neologicist accounts of mathematics may obtain the existence of infinite sets or infinitely many numbers by explicit postulation (as in the case of the axiom of infinity in Whitehead and Russell’s Principia Mathematica) or as the outcome of an implicit postulation (such as Hume’s Principle in Scottish neologicism, see Hale and Wright 2001, Heck 1997, 2011). While the axiom of infinity is easily stated and understood, Hume’s Principle has a peculiar form, for it postulates the existence of a function \(\#\) that sends concepts into objects while respecting an equivalence relation \(\approx\) among concepts. Formally it is stated as follows: