•  481
    Does the solar system compute the laws of motion?
    with Douglas Ian Campbell
    Synthese 198 (4): 3203-3220. 2019.
    The counterfactual account of physical computation is simple and, for the most part, very attractive. However, it is usually thought to trivialize the notion of physical computation insofar as it implies ‘limited pancomputationalism’, this being the doctrine that every deterministic physical system computes some function. Should we bite the bullet and accept limited pancomputationalism, or reject the counterfactual account as untenable? Jack Copeland would have us do neither of the above. He att…Read more
  •  46
    The minimal e-degree problem in fragments of Peano arithmetic
    with M. M. Arslanov, C. T. Chong, and S. B. Cooper
    Annals of Pure and Applied Logic 131 (1-3): 159-175. 2005.
    We study the minimal enumeration degree problem in models of fragments of Peano arithmetic () and prove the following results: in any model M of Σ2 induction, there is a minimal enumeration degree if and only if M is a nonstandard model. Furthermore, any cut in such a model has minimal e-degree. By contrast, this phenomenon fails in the absence of Σ2 induction. In fact, whether every Σ2 cut has minimal e-degree is independent of the Σ2 bounding principle
  •  25
    A nonlow2 R. E. Degree with the Extension of Embeddings Properties of a low2 Degree
    with R. A. Shore
    Mathematical Logic Quarterly 48 (1): 131-146. 2002.
    We construct a nonlow2 r.e. degree d such that every positive extension of embeddings property that holds below every low2 degree holds below d. Indeed, we can also guarantee the converse so that there is a low r.e. degree c such that that the extension of embeddings properties true below c are exactly the ones true belowd.Moreover, we can also guarantee that no b ≤ d is the base of a nonsplitting pair
  •  10
    Ct Chong
    with C. T. Cl-Iong
    In Edward R. Griffor (ed.), Handbook of Computability Theory, Elsevier. pp. 140--298. 1999.