nounPhilosophy & Mathematics
Rejection of the belief that anything can actually be infinite.
- According to meaning finitism, the move to the next instance is not intuitive or interpretive but ‘blind’.
- Dummett concludes that one route to such a local revisionism is a hard-headed finitism in which one denies that there is a determinate fact concerning the outcome of a procedure that has not been carried out.
- The make believe world of predicate logic was a mere conservative extension of finitism.
- Example sentences
- This axiom is problematic in some systems, and some people, finitists such as Hilbert, wanted a consistent way to talk about infinity that stemmed from proofs using finitary means.
- The most unassailable way of reasoning is finitist.
- The hard-headed finitist has to restrict logic even further than the intuitionist does.
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