In Defense of the Unprovability of the Church-Turing Thesis

One of us has previously argued that the Church-Turing Thesis (CTT), contra Elliot Mendelson, is not provable, and is — light of the mind’s capacity for effortless hypercomputation — moreover false (e.g., [13]). But a new, more serious challenge has appeared on the scene: an attempt by Smith [28] to prove CTT. His case is a clever “squeezing argument” that makes crucial use of Kolmogorov-Uspenskii (KU) machines. The plan for the present paper is as follows. After covering some necessary preliminaries regarding the nature of CTT, and taking note of the fact that this thesis is “intrinsically cognitive” (§2), we: sketch out, for context, an open-minded position on CTT and related matters (§3); explain the formal structure of squeezing arguments (§4); after a review of KU-machines, formalize Smith’s case (§5); give our objections to certain assumptions in Smith’s argument (§6); support these objections with some evidence from general but limited-agent problem solving (§7); and explain why Smith’s argument is inconclusive (§8). We end with some brief, concluding remarks, some of which point toward near-future work that will build on the present paper (§9)
Keywords No keywords specified (fix it)
Categories (categorize this paper)
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history Request removal from index Translate to english
Download options
PhilPapers Archive

Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 9,357
External links
  •   Try with proxy.
  • Through your library Only published papers are available at libraries
    References found in this work BETA

    No references found.

    Citations of this work BETA

    No citations found.

    Similar books and articles
    Tim Button (2009). Sad Computers and Two Versions of the Church–Turing Thesis. British Journal for the Philosophy of Science 60 (4):765-792.
    Paolo Cotogno (2003). Hypercomputation and the Physical Church-Turing Thesis. British Journal for the Philosophy of Science 54 (2):181-223.
    B. Jack Copeland (2008). The Church-Turing Thesis. In Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy. The Metaphysics Research Lab, Stanford University.

    Monthly downloads

    Added to index


    Total downloads

    23 ( #63,349 of 1,088,623 )

    Recent downloads (6 months)

    1 ( #69,601 of 1,088,623 )

    How can I increase my downloads?

    My notes
    Sign in to use this feature

    Start a new thread
    There  are no threads in this forum
    Nothing in this forum yet.