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  1. Computing the uncomputable; or, The discrete charm of second-order simulacra.Matthew W. Parker - 2009 - Synthese 169 (3):447-463.
    We examine a case in which non-computable behavior in a model is revealed by computer simulation. This is possible due to differing notions of computability for sets in a continuous space. The argument originally given for the validity of the simulation involves a simpler simulation of the simulation, still further simulations thereof, and a universality conjecture. There are difficulties with that argument, but there are other, heuristic arguments supporting the qualitative results. It is urged, using this example, that absolute validation, (...)
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  • Philosophical method and Galileo's paradox of infinity.Matthew W. Parker - 2008 - In Bart Van Kerkhove (ed.), New Perspectives on Mathematical Practices: Essays in Philosophy and History of Mathematics : Brussels, Belgium, 26-28 March 2007. World Scientfic.
    We consider an approach to some philosophical problems that I call the Method of Conceptual Articulation: to recognize that a question may lack any determinate answer, and to re-engineer concepts so that the question acquires a definite answer in such a way as to serve the epistemic motivations behind the question. As a case study we examine “Galileo’s Paradox”, that the perfect square numbers seem to be at once as numerous as the whole numbers, by one-to-one correspondence, and yet less (...)
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