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  1. Matthew E. Moore (2013). Peirce's Topical Theory of Continuity. Synthese:1-17.
    In the last decade of his life C.S. Peirce began to formulate a purely geometrical theory of continuity to supersede the collection-theoretic theory he began to elaborate around the middle of the 1890s. I argue that Peirce never succeeded in fully formulating the later theory, and that while that there are powerful motivations to adopt that theory within Peirce’s system, it has little to recommend it from an external perspective.
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  2. Matthew E. Moore (2009). Peirce on Perfect Sets, Revised. Transactions of the Charles S. Peirce Society: A Quarterly Journal in American Philosophy 45 (4):649-667.
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  3. Matthew E. Moore (2007). Naturalism, Truth and Beauty in Mathematics. Philosophia Mathematica 15 (2):141-165.
    Can a scientific naturalist be a mathematical realist? I review some arguments, derived largely from the writings of Penelope Maddy, for a negative answer. The rejoinder from the realist side is that the irrealist cannot explain, as well as the realist can, why a naturalist should grant the mathematician the degree of methodological autonomy that the irrealist's own arguments require. Thus a naturalist, as such, has at least as much reason to embrace mathematical realism as to embrace irrealism.
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  4. Matthew E. Moore (2007). The Completeness of the Real Line (La Completud de la Línea Real). Crítica 39 (117):61 - 86.
    It is widely taken for granted that physical lines are real lines, i.e., that the arithmetical structure of the real numbers uniquely matches the geometrical structure of lines in space; and that other number systems, like Robinson's hyperreals, accordingly fail to fit the structure of space. Intuitive justifications for the consensus view are considered and rejected. Insofar as it is justified at all, the conviction that physical lines are real lines is a scientific hypothesis which we may one day reject. (...)
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  5. Matthew E. Moore (2007). The Genesis of the Peircean Continuum. Transactions of the Charles S. Peirce Society 43 (3):425 - 469.
    : In the Cambridge Conferences Lectures of 1898 Peirce defines a continuum as a "collection of so vast a multitude" that its elements "become welded into one another." He links the transinfinity (the "vast multitude") of a continuum to the confusion of its elements by a line of mathematical reasoning closely related to Cantor's Theorem. I trace the mathematical and philosophical roots of this conception of continuity, and examine its unresolved tensions, which arise mainly from difficulties in Peirce's theory of (...)
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  6. Matthew E. Moore (2006). Naturalizing Dissension. Pacific Philosophical Quarterly 87 (3):325–334.
    Mathematical naturalism forbids philosophical interventions in mathematical practice. This principle, strictly construed, places severe constraints on legitimate philosophizing about mathematics; it is also arguably incompatible with mathematical realism. One argument for the latter conclusion charges the realist with inability to take a truly naturalistic view of the Gödel Program in set theory. This argument founders on the disagreement among mathematicians about that program's prospects for success. It also turns out that when disagreements run this deep it is counterproductive to take (...)
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  7. Matthew E. Moore (2002). A Cantorian Argument Against Infinitesimals. Synthese 133 (3):305 - 330.
    In 1887 Georg Cantor gave an influential but cryptic proof of theimpossibility of infinitesimals. I first give a reconstruction ofCantor's argument which relies mainly on traditional assumptions fromEuclidean geometry, together with elementary results of Cantor's ownset theory. I then apply the reconstructed argument to theinfinitesimals of Abraham Robinson's nonstandard analysis. Thisbrings out the importance for the argument of an assumption I call theChain Thesis. Doubts about the Chain Thesis are seen to render thereconstructed argument inconclusive as an attack on the (...)
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  8. Matthew E. Moore (2002). Archimedean Intuitions. Theoria 68 (3):185-204.
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