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  1. Alice Ambrose (1935). Finitism in Mathematics (I). Mind 44 (174):186-203.
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  2. J. P. Bendegem (2012). A Defense of Strict Finitism. Constructivist Foundations 7 (2):141-149.
    Context: Strict finitism is usually not taken seriously as a possible view on what mathematics is and how it functions. This is due mainly to unfamiliarity with the topic. Problem: First, it is necessary to present a “decent” history of strict finitism (which is now lacking) and, secondly, to show that common counterarguments against strict finitism can be properly addressed and refuted. Method: For the historical part, the historical material is situated in a broader context, and for the argumentative part, (...)
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  3. Andrew Boucher, A Natural First-Order System of Arithmetic Which Proves Its Own Consistency.
    Herein is presented a natural first-order arithmetic system which can prove its own consistency, both in the weaker Godelian sense using traditional Godel numbering and, more importantly, in a more robust and direct sense; yet it is strong enough to prove many arithmetic theorems, including the Euclidean Algorithm, Quadratic Reciprocity, and Bertrand’s Postulate.
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  4. Marc A. Joseph (2001). Review of M. Marion, Wittgenstein, Finitism, and the Foundations of Mathematics. [REVIEW] Mind 110 (438):501-504.
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  5. Lydia Patton (2014). Hilbert's Objectivity. Historia Mathematica 41 (2):188-203.
    Detlefsen (1986) reads Hilbert's program as a sophisticated defense of instrumentalism, but Feferman (1998) has it that Hilbert's program leaves significant ontological questions unanswered. One such question is of the reference of individual number terms. Hilbert's use of admittedly "meaningless" signs for numbers and formulae appears to impair his ability to establish the reference of mathematical terms and the content of mathematical propositions (Weyl (1949); Kitcher (1976)). The paper traces the history and context of Hilbert's reasoning about signs, which illuminates (...)
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  6. David G. Stern (2001). Review of M. Marion, Wittgenstein, Finitism, and the Foundations of Mathematics. [REVIEW] Dialogue 40 (03):624-626.
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  7. W. W. Tait (2010). Gödel on Intuition and on Hilbert's Finitism. In Kurt Gödel, Solomon Feferman, Charles Parsons & Stephen G. Simpson (eds.), Kurt Gödel: Essays for His Centennial. Association for Symbolic Logic.
    There are some puzzles about G¨ odel’s published and unpublished remarks concerning finitism that have led some commentators to believe that his conception of it was unstable, that he oscillated back and forth between different accounts of it. I want to discuss these puzzles and argue that, on the contrary, G¨ odel’s writings represent a smooth evolution, with just one rather small double-reversal, of his view of finitism. He used the term “finit” (in German) or “finitary” or “finitistic” primarily to (...)
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  8. Eric Winsberg (2000). Review of M. Marion, Wittgenstein, Finitism, and the Foundations of Mathematics. [REVIEW] Philosophy of Science 67 (3):533-.
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  9. Richard Zach (2003). The Practice of Finitism: Epsilon Calculus and Consistency Proofs in Hilbert's Program. Synthese 137 (1-2):211 - 259.
    After a brief flirtation with logicism around 1917, David Hilbertproposed his own program in the foundations of mathematics in 1920 and developed it, in concert with collaborators such as Paul Bernays andWilhelm Ackermann, throughout the 1920s. The two technical pillars of the project were the development of axiomatic systems for everstronger and more comprehensive areas of mathematics, and finitisticproofs of consistency of these systems. Early advances in these areaswere made by Hilbert (and Bernays) in a series of lecture courses atthe (...)
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