dorsal/arxiv
View SchemaStrong Determinism vs. Computability
| Authors | C. Calude, D. I. Campbell, K. Svozil, D. Ştefănecu |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9412004 |
| URL | https://arxiv.org/abs/quant-ph/9412004 |
| Journal | The Foundational Debate. Complexity and Constructivity in Mathematics and Physics. Vienna Circle Institute Yearbook, Vol. 3, ed. by Werner DePauli Schimanovich, Eckehart Koehler and Friedrich Stadler (Kluwer, Dordrecht, Boston, London, 1995), p. 115-131. |
Abstract
Are minds subject to laws of physics? Are the laws of physics computable? Are conscious thought processes computable? Currently there is little agreement as to what are the right answers to these questions. Penrose goes one step further and asserts that: {\it a radical new theory is indeed needed, and I am suggesting, moreover, that this theory, when it is found, will be of an essentially non-computational character.} The aim of this paper is three fold: 1) to examine the incompatibility between the hypothesis of strong determinism and computability, 2) to give new examples of uncomputable physical laws, and 3) to discuss the relevance of G\"odel's Incompleteness Theorem in refuting the claim that an algorithmic theory---like strong AI---can provide an adequate theory of mind. Finally, we question the adequacy of the theory of computation to discuss physical laws and thought processes.
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"abstract": "Are minds subject to laws of physics? Are the laws of physics computable? Are\nconscious thought processes computable? Currently there is little agreement as\nto what are the right answers to these questions. Penrose goes one step further\nand asserts that: {\\it a radical new theory is indeed needed, and I am\nsuggesting, moreover, that this theory, when it is found, will be of an\nessentially non-computational character.} The aim of this paper is three fold:\n1) to examine the incompatibility between the hypothesis of strong determinism\nand computability, 2) to give new examples of uncomputable physical laws, and\n3) to discuss the relevance of G\\\"odel\u0027s Incompleteness Theorem in refuting the\nclaim that an algorithmic theory---like strong AI---can provide an adequate\ntheory of mind. Finally, we question the adequacy of the theory of computation\nto discuss physical laws and thought processes.",
"arxiv_id": "quant-ph/9412004",
"authors": [
"C. Calude",
"D. I. Campbell",
"K. Svozil",
"D. \u015etef\u0103necu"
],
"categories": [
"quant-ph",
"chao-dyn",
"nlin.CD"
],
"journal_ref": "The Foundational Debate. Complexity and Constructivity in\n Mathematics and Physics. Vienna Circle Institute Yearbook, Vol. 3, ed. by\n Werner DePauli Schimanovich, Eckehart Koehler and Friedrich Stadler (Kluwer,\n Dordrecht, Boston, London, 1995), p. 115-131.",
"title": "Strong Determinism vs. Computability",
"url": "https://arxiv.org/abs/quant-ph/9412004"
},
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