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Synthetic Philosophy of Contemporary Mathematics

Urbanomic/Sequence Press (2012)

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  1. Conceptual Modelling, Combinatorial Heuristics and Ars Inveniendi: An Epistemological History (Ch 1 & 2).Tom Ritchey - manuscript
    (1) An introduction to the principles of conceptual modelling, combinatorial heuristics and epistemological history; (2) the examination of a number of perennial epistemological-methodological schemata: conceptual spaces and blending theory; ars inveniendi and ars demonstrandi; the two modes of analysis and synthesis and their relationship to ars inveniendi; taxonomies and typologies as two fundamental epistemic structures; extended cognition, cognitio symbolica and model-based reasoning; (3) Plato’s notions of conceptual spaces, conceptual blending and hypothetical-analogical models (paradeigmata); (4) Ramon Llull’s concept analysis and combinatoric (...)
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  • Deep Disagreement in Mathematics.Andrew Aberdein - 2023 - Global Philosophy 33 (1):1-27.
    Disagreements that resist rational resolution, often termed “deep disagreements”, have been the focus of much work in epistemology and informal logic. In this paper, I argue that they also deserve the attention of philosophers of mathematics. I link the question of whether there can be deep disagreements in mathematics to a more familiar debate over whether there can be revolutions in mathematics. I propose an affirmative answer to both questions, using the controversy over Shinichi Mochizuki’s work on the abc conjecture (...)
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  • Pragmaticism.Charles S. Peirce - 2024 - De Gruyter.
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