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Penrose and platonism

In Emily Grosholz & Herbert Breger (eds.), The growth of mathematical knowledge. Boston: Kluwer Academic Publishers. pp. 133--141 (2000)

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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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  • Non-deductive Logic in Mathematics: The Probability of Conjectures.James Franklin - 2013 - In Andrew Aberdein & Ian J. Dove (eds.), The Argument of Mathematics. Dordrecht, Netherland: Springer. pp. 11--29.
    Mathematicians often speak of conjectures, yet unproved, as probable or well-confirmed by evidence. The Riemann Hypothesis, for example, is widely believed to be almost certainly true. There seems no initial reason to distinguish such probability from the same notion in empirical science. Yet it is hard to see how there could be probabilistic relations between the necessary truths of pure mathematics. The existence of such logical relations, short of certainty, is defended using the theory of logical probability (or objective Bayesianism (...)
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  • Mathematics as the art of abstraction.Richard L. Epstein - 2013 - In Andrew Aberdein & Ian J. Dove (eds.), The Argument of Mathematics. Dordrecht, Netherland: Springer. pp. 257--289.
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