Proving church's thesis
Philosophia Mathematica 8 (3):244--58 (2000)
| Abstract | Arguments to the effect that Church's thesis is intrinsically unprovable because proof cannot relate an informal, intuitive concept to a mathematically defined one are unconvincing, since other 'theses' of this kind have indeed been proved, and Church's thesis has been proved in one direction. However, though evidence for the truth of the thesis in the other direction is overwhelming, it does not yet amount to proof. | |||||||||
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Nachum Dershowitz & Yuri Gurevich (2008). A Natural Axiomatization of Computability and Proof of Church's Thesis. Bulletin of Symbolic Logic 14 (3):299-350.
Gualtiero Piccinini (2007). Computationalism, the Church–Turing Thesis, and the Church–Turing Fallacy. Synthese 154 (1):97-120.
John T. Kearns (1997). Thinking Machines: Some Fundamental Confusions. Minds and Machines 7 (2):269-87.
Selmer Bringsjord & Konstantine Arkoudas (2006). On the Provability, Veracity, and AI-Relevance of the Church-Turing Thesis. In A. Olszewski, J. Wole'nski & R. Janusz (eds.), Church's Thesis After Seventy Years. Ontos Verlag.
Carol Cleland (2006). The Church-Turing Thesis: A Last Vestige of a Failed Mathematical Program. In A. Olszewski, J. Wole'nski & R. Janusz (eds.), Church's Thesis After Seventy Years. Ontos Verlag.
Paolo Cotogno (2003). Hypercomputation and the Physical Church-Turing Thesis. British Journal for the Philosophy of Science 54 (2):181-223.
Tim Button (2009). Sad Computers and Two Versions of the Church–Turing Thesis. British Journal for the Philosophy of Science 60 (4):765-792.
B. Jack Copeland (2008). The Church-Turing Thesis. In Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy. The Metaphysics Research Lab, Stanford University.
Janet Folina (1998). Church's Thesis: Prelude to a Proof. Philosophia Mathematica 6 (3):302-323.
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