Definitions
from Wiktionary, Creative Commons Attribution/ShareAlike License.
 noun mathematics An extreme form of
constructivism , according to which a mathematical object does not exist unless it can be constructed fromnatural numbers in afinite number of steps.
Etymologies
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Examples

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.

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

But Lavine has developed a sophisticated form of settheoretical ultrafinitism which is mathematically nonrevisionist (Lavine 1994).

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

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

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

Although this idea was later adopted by the other structuralistic programs, it plays a unique rÃ´le within Ludwig's metatheory in connection with his finitism.

This leads to a position that has been called ultrafinitism.

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, 300301, 310), the overwhelming evidence indicates that the later Wittgenstein still rejects the actual infinite

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.
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