Finitism is an extreme version of intuitionism that rejects the idea of potential infinity.
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Skolem distrusted the completed infinite and was one of the founders of finitism in mathematics.
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Becker argued that Hilbert could not stick with finitism, but had to assume the potential infinite.
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John Philoponus was probably the first to use the argument that infinite time is impossible in order to establish temporal finitism.
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In defending his finitism against mathematical objections, he argues that the " definitions " of geometry actually support his account.
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The notion of temporal finitism was inspired by the doctrine of creation shared by the three Abrahamic religions : Judaism, Christianity and Islam.
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"' Temporal finitism "'is the doctrine that time is Aristotelian conception of the eternal with the Genesis creation narrative.
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According to Finitism, a mathematical object does not exist unless it can be constructed from the natural numbers in a finite number of steps.
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The primitive recursive functions are closely related to mathematical finitism, and are used in several contexts in mathematical logic where a particularly constructive system is desired.
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In his book " The Infinite ", Moore offers a thorough discussion of the idea of infinity and its history, and a defence of finitism.
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