Computing the uncomputable; or, the discrete charm of second-order simulacra

Synthese 169 (3):447 - 463 (2009)
Abstract
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, while highly desirable, is overvalued. Simulations also provide valuable insights that we cannot yet (if ever) prove.
Keywords Computability  Decidability  Undecidable  Computer simulation  Validation  Models  Chaos  Dynamical systems  Non-linear dynamics  Proof  Heuristics
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References found in this work BETA
Peter Koellner (2010). On the Question of Absolute Undecidability. In Kurt Gödel, Solomon Feferman, Charles Parsons & Stephen G. Simpson (eds.), Kurt Gödel: Essays for His Centennial. Association for Symbolic Logic. 153-188.
Adam Morton (1993). Mathematical Models: Questions of Trustworthiness. British Journal for the Philosophy of Science 44 (4):659-674.

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