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| publisher = Harvard University Press
| title = From Frege to Gödel. A source book in mathematical logic, 1879–1931
| year = 1967}}.</ref> as a formalization of his [[finitist]] conception of the [[foundations of mathematics|foundations of arithmetic]], and it is widely agreed that all reasoning of PRA is finitist, even though it is also widely agreed that the reasoning of PRA is not ultrafinitist. Many also believe that all of finitism is captured by PRA,<ref>{{citation|authorlink=William W. Tait|last=Tait|first= W.W.|year=1981|title=Finitism|journal=[[The Journal of Philosophy]]|volume=78|pages=524–546|doi=10.2307/2026089}}.</ref> but others believe finitism can be extended to forms of recursion beyond primitive recursion, up to [[epsilon zero (mathematics)|ε<sub>0</sub>]],<ref>{{citation
| last = Kreisel | first = G. | author-link = Georg Kreisel
| contribution = Ordinal logics and the characterization of informal concepts of proof
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