Definitions

from Wiktionary, Creative Commons Attribution/Share-Alike License

  • n. An extreme form of constructivism, according to which a mathematical object does not exist unless it can be constructed from natural numbers in a finite number of steps.

Etymologies

finite +‎ -ism (Wiktionary)

Examples

  • A second strong indication that the later Wittgenstein maintains his finitism is his continued and consistent treatment of

    Wittgenstein's Philosophy of Mathematics

  • The first, and perhaps most definitive, indication that the later Wittgenstein maintains his finitism is his continued and consistent insistence that irrational numbers are rules for constructing finite expansions, not infinite mathematical extensions.

    Wittgenstein's Philosophy of Mathematics

  • But Lavine has developed a sophisticated form of set-theoretical ultra-finitism which is mathematically non-revisionist (Lavine 1994).

    Philosophy of Mathematics

  • For example, a proof-theoretic analysis may contribute to establish if a certain theory complies with a given mathematical framework (e.g., predicativity, finitism, etc.).

    Set Theory: Constructive and Intuitionistic ZF

  • Nor is the “finitism” characteristic of Hilbert and Bernays 'later work present in Dedekind (an aspect developed in response both to the set-theoretic antinomies and to intuitionist challenges), especially if it is understood in a metaphysical sense.

    Dedekind's Contributions to the Foundations of Mathematics

  • Such finitism might have been acceptable to Dedekind as a methodological stance; but in other respects his position is strongly infinitary.

    Dedekind's Contributions to the Foundations of Mathematics

  • Although this idea was later adopted by the other structuralistic programs, it plays a unique rôle within Ludwig's meta-theory in connection with his finitism.

    Structuralism in Physics

  • This leads to a position that has been called ultra-finitism.

    Philosophy of Mathematics

  • Though commentators and critics do not agree as to whether the later Wittgenstein is still a finitist and whether, if he is, his finitism is as radical as his intermediate rejection of unbounded mathematical quantification (Maddy 1986, 300-301, 310), the overwhelming evidence indicates that the later Wittgenstein still rejects the actual infinite

    Wittgenstein's Philosophy of Mathematics

  • On Wittgenstein's intermediate finitism, an expression quantifying over an infinite domain is never a meaningful proposition, not even when we have proved, for instance, that a particular number n has a particular property.

    Wittgenstein's Philosophy of Mathematics

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