David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Philosophy of Science 70 (2):359-382 (2003)
Some have suggested that certain classical physical systems have undecidable long-term behavior, without specifying an appropriate notion of decidability over the reals. We introduce such a notion, decidability in (or d- ) for any measure , which is particularly appropriate for physics and in some ways more intuitive than Ko's (1991) recursive approximability (r.a.). For Lebesgue measure , d- implies r.a. Sets with positive -measure that are sufficiently "riddled" with holes are never d- but are often r.a. This explicates Sommerer and Ott's (1996) claim of uncomputable behavior in a system with riddled basins of attraction. Furthermore, it clarifies speculations that the stability of the solar system (and similar systems) may be undecidable, for the invariant tori established by KAM theory form sets that are not d-.
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
Matthew W. Parker (2009). Computing the Uncomputable; or, the Discrete Charm of Second-Order Simulacra. Synthese 169 (3):447 - 463.
Similar books and articles
Brian Skyrms (2002). Signals, Evolution and the Explanatory Power of Transient Information. Philosophy of Science 69 (3):407-428.
Teed Rockwell (2005). Attractor Spaces as Modules: A Semi-Eliminative Reduction of Symbolic AI to Dynamic Systems Theory. [REVIEW] Minds and Machines 15 (1):23-55.
Justin Clarke-Doane (2013). What is Absolute Undecidability?†. Noûs 47 (3):467-481.
Michael Strevens (2006). Chaos. In D. M. Borchert (ed.), Encyclopedia of Philosophy, second edition.
Dror Ben-Arié & Haim Judah (1993). ▵1 3-Stability. Journal of Symbolic Logic 58 (3):941 - 954.
Peter Csermely (2009). Weak Links: The Universal Key to the Stability of Networks and Complex Systems. Springer.
R. Duncan Luce (1971). Similar Systems and Dimensionally Invariant Laws. Philosophy of Science 38 (2):157-169.
Alfred Tarski (1968/2010). Undecidable Theories. Amsterdam, North-Holland Pub. Co..
Eric Dietrich (2000). Analogy and Conceptual Change, or You Can't Step Into the Same Mind Twice. In Eric Dietrich Art Markman (ed.), Cognitive Dynamics: Conceptual change in humans and machines. Lawrence Erlbaum. 265--294.
Walter Elberfeld (2000). An Analysis of Stability Sets in Pure Coordination Games. Theory and Decision 49 (3):235-248.
Added to index2009-01-28
Total downloads10 ( #209,179 of 1,696,808 )
Recent downloads (6 months)3 ( #187,594 of 1,696,808 )
How can I increase my downloads?