(>>823再録) (参考) https://en.wikipedia.org/wiki/Finitism Finitism Hilbert did not give a rigorous explanation of what he considered finitistic and referred to as elementary. However, based on his work with Paul Bernays some experts such as William Tait have argued that the primitive recursive arithmetic can be considered an upper bound on what Hilbert considered finitistic mathematics.
In the years following Godel's theorems, as it became clear that there is no hope of proving consistency of mathematics, and with development of axiomatic set theories such as Zermelo?Fraenkel set theory and the lack of any evidence against its consistency, most mathematicians lost interest in the topic. Today most classical mathematicians are considered Platonist and readily use infinite mathematical objects and a set-theoretical universe.[citation needed]
https://en.wikipedia.org/wiki/Platonism Platonism Platonism is the philosophy of Plato and philosophical systems closely derived from it, though contemporary platonists do not necessarily accept all of the doctrines of Plato.[1] Platonism at least affirms the existence of abstract objects, which are asserted to exist in a third realm distinct from both the sensible external world and from the internal world of consciousness, and is the opposite of nominalism.[1] This can apply to properties, types, propositions, meanings, numbers, sets, truth values, and so on (see abstract object theory).
https://en.wikipedia.org/wiki/Abstract_object_theory Abstract object theory Abstract object theory (AOT) is a branch of metaphysics regarding abstract objects.[1] Originally devised by metaphysician Edward Zalta in 1981,[2] the theory was an expansion of mathematical Platonism. (引用終り) 以上
