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as classical finitists, and those who do not allow potentially infinite objects as strict finitists: for example, a classical finitist would allow statements...

some philosophers and theologians to solve the problem of evil. Most finitists accept the absolute goodness of God but reject omnipotence. Finitistic...

one is not involved in any contradiction. The present-day conventional finitist interpretation of ordinal and cardinal numbers is that they consist of...

considered the universe of finitist mathematics. Speaking anachronistically, one could suggest that the 19th-century finitist Leopold Kronecker was working...

theoretic functions like exponentiation over natural numbers. Like other finitists, ultrafinitists deny the existence of the infinite set N {\displaystyle...

mathematicians including most famously his teacher Leopold Kronecker—a confirmed finitist. The second of these was Gottlob Frege's effort to reduce all of mathematics...

co-authored by Karl-Georg Niebergall, Niebergall and Schirn presented Hilbert’s finitist proof-theoretic approach in a new light by paying close attention to the...

Encyclopedia of Philosophy Cooke, Martin C. (2003). "Infinite Sequences: Finitist Consequence". Br. J. Philos. Sci. 54 (4): 591–599. doi:10.1093/bjps/54...

contemporaries, for example by Leopold Kronecker, who strongly adhered to a finitist philosophy of mathematics and rejected the idea that numbers can form an...

as urelements the objects of any theory or of the physical universe. In finitist set theory, urelements are mapped to the lowest-level components of the...

Astronomer Alan Hale – CTV call-in (Knoxville Freethought Forum 4/23/13). finitist. Archived from the original on August 11, 2019. Retrieved September 11...

e. the claim that transfinite induction below ε0 is valid), and gave a finitist proof for the case where m ≤ b 1 b 1 b 1 {\displaystyle m\leq b_{1}^{b_{1}^{b_{1}}}}...

Hence, motion involves traversing an actual infinite ... Accordingly, the finitist of this stripe must be mistaken. Similarly, whenever some period of time...

Wittgenstein did not object to mathematical formalism wholesale, but had a finitist view on what Cantor's proof meant. The philosopher maintained that belief...

intuitionist stance against Cantor's work. Finally, Wittgenstein's attacks were finitist: he believed that Cantor's diagonal argument conflated the intension of...

required when computing distances or angle measures. For Wildberger, a finitist, this replacement has the purported advantage of avoiding the concepts...

1930s, which saw the development of metalogic, in the finitist system of Hilbert, and the non-finitist system of Löwenheim and Skolem, the combination of...

Hume's "system concerning space and time" features two main doctrines: the finitist doctrine that space and time are not infinitely divisible, and the relationist...

countably infinite objects as classical finitists, and those who deny even countably infinite objects as strict finitists. The most famous proponent of finitism...

methods of proof theory was therefore suggested: instead of a reduction to finitist methods of reasoning, it was required only that the arguments be of a constructive...