A second strong indication that the later Wittgenstein maintains his finitism is his continued and consistent treatment of. From Wordnik.com. [Wittgenstein's Philosophy of Mathematics] Reference
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. From Wordnik.com. [Wittgenstein's Philosophy of Mathematics] Reference
But Lavine has developed a sophisticated form of set-theoretical ultra-finitism which is mathematically non-revisionist (Lavine 1994). From Wordnik.com. [Philosophy of Mathematics] Reference
In Bernays's most mature presentations of finitism. From Wordnik.com. [Hilbert's Program] Reference
This leads to a position that has been called ultra-finitism. From Wordnik.com. [Philosophy of Mathematics] Reference
Usually the label strict finitism is used to describe the view sketched above. From Wordnik.com. [Finitism in Geometry] Reference
As might be expected, strict finitism is not a popular view in the philosophy of mathematics. From Wordnik.com. [Finitism in Geometry] Reference
A remark concerning the philosophical context in which Gödel presented his translation, namely finitism. From Wordnik.com. [Kurt Gödel] Reference
The question of what Hilbert thought the epistemological status of the objects of finitism was is equally difficult. From Wordnik.com. [Hilbert's Program] Reference
The thesis that finitism coincides with primitive recursive reasoning has received a forceful and widely accepted defense by. From Wordnik.com. [Hilbert's Program] Reference
This characterization of finitism as primarily to do with intuition and intuitive knowledge has been emphasized in particular by. From Wordnik.com. [Hilbert's Program] Reference
Such finitism might have been acceptable to Dedekind as a methodological stance; but in other respects his position is strongly infinitary. From Wordnik.com. [Dedekind's Contributions to the Foundations of Mathematics] Reference
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. From Wordnik.com. [Structuralism in Physics] Reference
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.). From Wordnik.com. [Set Theory: Constructive and Intuitionistic ZF] Reference
Whether such methods would be considered finitary according to the original conception of finitism or constitute an extension of the original finitist viewpoint is a matter of debate. From Wordnik.com. [Hilbert's Program] Reference
Usually outside finitism the potentially infinite is allowed, i.e., if a procedure or algorithm will (provably) terminate at some moment in the future, then the outcome is accepted as constructable. From Wordnik.com. [Finitism in Geometry] Reference
Together, Wittgenstein's finitism and his criterion of algorithmic decidability shed considerable light on his highly controversial remarks about putatively meaningful conjectures such as FLT and GC. From Wordnik.com. [Wittgenstein's Philosophy of Mathematics] Reference
Of crucial importance to both an understanding of finitism and of Hilbert's proof theory is the question of what operations and what principles of proof should be allowed from the finitist standpoint. From Wordnik.com. [Hilbert's Program] Reference
Gödel (1958) presented another extension of the finitist standpoint; the work of Kreisel mentioned above may be seen as another attempt to extend finitism while retaining the spirit of Hilbert's original conception. From Wordnik.com. [Hilbert's Program] Reference
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. From Wordnik.com. [Wittgenstein's Philosophy of Mathematics] Reference
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. From Wordnik.com. [Dedekind's Contributions to the Foundations of Mathematics] Reference
However, finitism goes one step further and argues that an indefinite outcome is not be accepted as an outcome, since, as all computational resources are finite, it could very well be that these resources have been used up before the outcome has been reached. From Wordnik.com. [Finitism in Geometry] Reference
The additional qualification serves to make the distinction with Hilbert's finitism which, roughly speaking, can be seen as a form of finitism on the meta-level (e.g., although mathematical theories can talk about infinite structures, still the proofs in such theories must have a finite length). From Wordnik.com. [Finitism in Geometry] Reference
Even if no finitary consistency proof of arithmetic can be given, the question of finding consistency proofs is nevertheless of value: the methods used in such proofs, although they must go beyond Hilbert's original sense of finitism, might provide genuine insight into the constructive content of arithmetic and stronger theories. From Wordnik.com. [Hilbert's Program] Reference
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. From Wordnik.com. [Wittgenstein's Philosophy of Mathematics] Reference
Gassendi, Pierre (Saul Fisher) gene (Hans-Jörg Rheinberger and Staffan Müller-Wille) generalized quantifiers (Dag Westerståhl) general relativity early philosophical interpretations of (Thomas A. Ryckman) genetics evolutionary (Michael Wade) genotype/phenotype distinction (Richard Lewontin) molecular (Ken Waters) population (Samir Okasha) geometry finitism in (Jean-Paul Van Bendegem) in the 19th century (Roberto Torretti). From Wordnik.com. [Table of Contents] Reference
Parsons 1998 on the epistemology of finitism.) 2.2 Finitarily meaningful propositions and finitary reasoning. From Wordnik.com. [Hilbert's Program] Reference
Wittgenstein's finitism, constructivism, and conception of mathematical decidability are interestingly connected at (RFM. From Wordnik.com. [Wittgenstein's Philosophy of Mathematics] Reference
Brouwer, Luitzen Egbertus Jan | finitism |. From Wordnik.com. [Intuitionistic Logic] Reference
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