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  1. Restructuring the Sciences: Peirce's Categories and His Classifications of the Sciences.Richard Kenneth Atkins - 2006 - Transactions of the Charles S. Peirce Society 42 (4):483-500.
    : This essay shows that Peirce's (more or less) final classification of the sciences arises from the systematic application of his Categories of Firstness, Secondness and Thirdness to the classification of the sciences themselves and that he does not do so until his 1903's "An Outline Classification of the Sciences." The essay proceeds by: First, making some preliminary comments regarding Peirce's notion of an architectonic, or classification of the sciences; Second, briefly explaining Peirce's Categories of Firstness, Secondness and Thirdness; Third, (...)
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  • "Merely a Veil Over the Living Thought": Mathematics and Logic in Peirce's Forgotten Spinoza Review.Shannon Dea - 2006 - Transactions of the Charles S. Peirce Society 42 (4):501-517.
    This paper considers Peirce's striking remarks about mathematics in a little-known review of Spinoza's Ethics within the larger context of his philosophy of mathematics. It argues that, for Peirce, true mathematical reasoning is always at the vanguard of thought, and resists logical demonstration. Through diagrammatic thought and her pre-theoretical innate faculty of logica utens, the great mathematician is able to see a theorem as true long before the logical apparatus necessary to demonstrate its truth exists. For Peirce, true mathematical thought (...)
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  • The Historicity of Peirce’s Classification of the Sciences.Chiara Ambrosio - 2016 - European Journal of Pragmatism and American Philosophy 8 (2).
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  • Imagination, Concentration, and Generalization: Peirce on the Reasoning Abilities of the Mathematician.Daniel G. Campos - 2009 - Transactions of the Charles S. Peirce Society 45 (2):135-156.
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  • Peirce’s Philosophy of Mathematical Education: Fostering Reasoning Abilities for Mathematical Inquiry.Daniel G. Campos - 2010 - Studies in Philosophy and Education 29 (5):421-439.
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  • The Framing of the Fundamental Probability Set: A Historical Case Study on the Context of Mathematical Discovery.Daniel G. Campos - 2009 - Perspectives on Science 17 (4):pp. 385-416.
    I address the philosophical debate over whether the mathematical theory of probability arose on the basis of empirical observations or of purely theoretical speculations. The debate tends to pose a strict dichotomy between empirical problem-solving and pure theorizing. I alternatively suggest that, in the case of mathematical probability, an empirical problem-context acted as an enabling condition for the possibility of mathematical innovation, but that the activity of the early mathematical probabilists gradually became the study of a theoretical system of ideas. (...)
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  • Peirce on the Role of Poietic Creation in Mathematical Reasoning.Daniel G. Campos - 2007 - Transactions of the Charles S. Peirce Society 43 (3):470 - 489.
    : C.S. Peirce defines mathematics in two ways: first as "the science which draws necessary conclusions," and second as "the study of what is true of hypothetical states of things" (CP 4.227–244). Given the dual definition, Peirce notes, a question arises: Should we exclude the work of poietic hypothesis-making from the domain of pure mathematical reasoning? (CP 4.238). This paper examines Peirce's answer to the question. Some commentators hold that for Peirce the framing of mathematical hypotheses requires poietic genius but (...)
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  • Philosophy of Mathematics: Selected Writings.Charles S. Peirce - 2010 - Indiana University Press.
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