The Independent Existence of Mathematical Objects

Quine's famous assertion that "to be is to be the value of a bound variable" translates, in syntactic form, the way in which first-order formal logic correctly expresses existence, which can no longer be taken as a real predicate since Kant. However, this operation of quantification does not exhaust the metaphysical breadth of the theme of Being, involved by dragging through the use of the verb "to be". In particular, when it comes to mathematical objects, it is verified that quantification depends on the reality of non-empirical and non-mental domains, which support the truth of mathematical propositions. This work seeks to demonstrate that such domains must have an autonomous, independent, abstract and necessary way of being, which implies the adoption of mathematical Platonism in a strong sense, a position similar to that adopted by G. Frege in the proposition of his thesis of the "Third Kingdom" ("drittes Reich") in his famous article Der Gedanke.