{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,6,25]],"date-time":"2024-06-25T05:19:39Z","timestamp":1719292779274},"reference-count":40,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2009,8,1]],"date-time":"2009-08-01T00:00:00Z","timestamp":1249084800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Minds & Machines"],"published-print":{"date-parts":[[2009,8]]},"DOI":"10.1007\/s11023-009-9161-7","type":"journal-article","created":{"date-parts":[[2009,10,12]],"date-time":"2009-10-12T14:20:18Z","timestamp":1255357218000},"page":"391-405","source":"Crossref","is-referenced-by-count":4,"title":["A Brief Critique of Pure Hypercomputation"],"prefix":"10.1007","volume":"19","author":[{"given":"Paolo","family":"Cotogno","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2009,10,13]]},"reference":[{"key":"9161_CR1","unstructured":"Akl, S. G., & Fraser, R. (2006). Accelerating machines. Technical Report 2006-510. Kingston, Ontario: Queen\u2019s University."},{"key":"9161_CR2","doi-asserted-by":"crossref","first-page":"903","DOI":"10.1090\/S0025-5718-97-00856-9","volume":"66","author":"D. H. Bailey","year":"1997","unstructured":"Bailey, D. H., Borwein, P. B., & Plouffe, S. (1997). On the rapid computation of various polylogarithmic constants. Mathematics of Computation, 66, 903\u2013913.","journal-title":"Mathematics of Computation"},{"key":"9161_CR3","volume-title":"The infinite book","author":"J. D. Barrow","year":"2005","unstructured":"Barrow, J. D. (2005). The infinite book. London: Jonathan Cape."},{"key":"9161_CR4","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1016\/j.entcs.2005.11.049","volume":"155","author":"A. Bauer","year":"2006","unstructured":"Bauer, A. (2006). First steps in synthetic computability theory. Electronic Notes in Theoretical Computer Science, 155, 5\u201331.","journal-title":"Electronic Notes in Theoretical Computer Science"},{"key":"9161_CR5","doi-asserted-by":"crossref","first-page":"765","DOI":"10.2307\/2023500","volume":"59","author":"P. Benacerraf","year":"1962","unstructured":"Benacerraf, P. (1962). Tasks, super-tasks, and the modern eleatics. The Journal of Philosophy, 59, 765\u2013784.","journal-title":"The Journal of Philosophy"},{"key":"9161_CR6","doi-asserted-by":"crossref","first-page":"72","DOI":"10.1016\/j.amc.2005.09.072","volume":"178","author":"S. B. Cooper","year":"2006","unstructured":"Cooper, S. B. (2006). Definability as hypercomputational effect. Applied Mathematics and Computation, 178, 72\u201382.","journal-title":"Applied Mathematics and Computation"},{"key":"9161_CR7","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1093\/bjps\/54.2.181","volume":"54","author":"P. Cotogno","year":"2003","unstructured":"Cotogno, P. (2003). Hypercomputation and the physical Church-Turing thesis. The British Journal for the Philosophy of Science, 54, 181\u2013223.","journal-title":"The British Journal for the Philosophy of Science"},{"key":"9161_CR8","unstructured":"Cotogno, P. (2007). A note on G\u00f6del\u2019s theorem and the rejection of Hilbert\u2019s programme. Poster Presented at the G\u00f6del Centenary Symposium. University of Vienna."},{"key":"9161_CR9","volume-title":"Computability and Unsolvability, (revised edition)","author":"M. Davis","year":"1982","unstructured":"Davis, M. (1982). Computability and unsolvability, (revised edition). New York: Dover."},{"key":"9161_CR10","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1007\/978-3-662-05642-4_8","volume-title":"Alan turing: The life and legacy of a great thinker","author":"M. Davis","year":"2004","unstructured":"Davis, M. (2004). The myth of hypercomputation. In C. Teuscher (Ed.), Alan turing: The life and legacy of a great thinker (pp. 195\u2013212). Berlin: Springer."},{"key":"9161_CR11","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1007\/88-470-0472-1_6","volume-title":"Imagination and rigor","author":"M. Davis","year":"2006","unstructured":"Davis, M. (2006a). Computability, computation, and the real world. In S. Termini (Ed.), Imagination and rigor (pp. 63\u201370). Milan: Springer."},{"key":"9161_CR12","doi-asserted-by":"crossref","first-page":"4","DOI":"10.1016\/j.amc.2005.09.066","volume":"178","author":"M. Davis","year":"2006","unstructured":"Davis, M. (2006b). Why there is no such discipline as hypercomputation. Applied Mathematics and Computation, 178, 4\u20137.","journal-title":"Applied Mathematics and Computation"},{"key":"9161_CR13","volume-title":"A profile of mathematical logic","author":"H. Delong","year":"1970","unstructured":"Delong, H. (1970). A profile of mathematical logic. Reading: Addison-Wesley."},{"key":"9161_CR14","doi-asserted-by":"crossref","first-page":"314","DOI":"10.1515\/9783110870299.314","volume-title":"The space of mathematics","author":"S. Feferman","year":"1992","unstructured":"Feferman, S. (1992). Turing\u2019s \u201cOracle\u201d: From absolute to relative computability\u2014and back. In J. Echeverria, A. Ibarra, & T. Mormann (Eds.), The space of mathematics (pp. 314\u2013348). Berlin: de Gruyter."},{"key":"9161_CR15","first-page":"709","volume":"10","author":"H. Gaifman","year":"2006","unstructured":"Gaifman, H. (2006). Naming and diagonalization, from Cantor to G\u00f6del to Kleene. Logic Journal of the Interest Group in Pure and Applied Logic, 10, 709\u2013728.","journal-title":"Logic Journal of the Interest Group in Pure and Applied Logic"},{"key":"9161_CR16","volume-title":"The treatment of ambiguity and paradox in mechanical language, Air Force Office of Scientific Research TN-603-61","author":"S. Gorn","year":"1961","unstructured":"Gorn, S. (1961). The treatment of ambiguity and paradox in mechanical language, Air Force Office of Scientific Research TN-603-61. Philadelphia: University of Pennsylvania."},{"key":"9161_CR17","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1007\/s11023-005-9006-y","volume":"16","author":"A. Hagar","year":"2006","unstructured":"Hagar, A., & Korolev, A. (2006). Quantum hypercomputability? Minds and Machines, 16, 87\u201393.","journal-title":"Minds and Machines"},{"key":"9161_CR18","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1093\/phisci\/axi108","volume":"56","author":"T. D. Kieu","year":"2005","unstructured":"Kieu, T. D., & Ord, T. (2005). The diagonal method and hypercomputation. British Journal for the Philosophy of Science, 56, 147\u2013156.","journal-title":"British Journal for the Philosophy of Science"},{"key":"9161_CR19","volume-title":"Introduction to metamathematics","author":"S. C. Kleene","year":"1974","unstructured":"Kleene, S. C. (1974). Introduction to metamathematics. Amsterdam: North-Holland."},{"key":"9161_CR21","doi-asserted-by":"crossref","first-page":"134","DOI":"10.1007\/BFb0080769","volume-title":"Category theory, homology theory and their applications II.","author":"F. W. Lawvere","year":"1969","unstructured":"Lawvere, F. W. (1969). Diagonal arguments and cartesian closed categories. In P. Hilton (Ed.), Category theory, homology theory and their applications II (pp. 134\u2013145). Berlin: Springer."},{"key":"9161_CR22","first-page":"1","volume":"15","author":"F. W. Lawvere","year":"2006","unstructured":"Lawvere, F. W. (2006). Author commentary. Reprints in Theory and Applications of Categories, 15, 1\u20132.","journal-title":"Reprints in Theory and Applications of Categories"},{"key":"9161_CR23","volume-title":"Conceptual mathematics: A first introduction to categories","author":"F. W. Lawvere","year":"2007","unstructured":"Lawvere, F. W., & Schanuel, S. H. (2007). Conceptual mathematics: A first introduction to categories. Cambridge: Cambridge University Press."},{"key":"9161_CR24","volume-title":"An introduction to the general theory of algorithms","author":"M. Machtey","year":"1978","unstructured":"Machtey, M., & Young, P. (1978). An introduction to the general theory of algorithms. New York: Elsevier."},{"key":"9161_CR25","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1023\/A:1005045200162","volume":"116","author":"W. J. McLaughlin","year":"1998","unstructured":"McLaughlin, W. J. (1998). Thomson\u2019s lamp is dysfunctional. Synthese, 116, 281\u2013301.","journal-title":"Synthese"},{"key":"9161_CR26","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1016\/j.amc.2005.09.076","volume":"178","author":"T. Ord","year":"2006","unstructured":"Ord, T. (2006). The many forms of hypercomputation. Applied Mathematics and Computation, 178, 143\u2013153.","journal-title":"Applied Mathematics and Computation"},{"key":"9161_CR27","doi-asserted-by":"crossref","first-page":"397","DOI":"10.1007\/BF01277482","volume":"31","author":"D. Pavlovi\u0107","year":"1992","unstructured":"Pavlovi\u0107, D. (1992). On the structure of paradoxes. Archives for Mathematical Logic, 31, 397\u2013406.","journal-title":"Archives for Mathematical Logic"},{"key":"9161_CR28","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1016\/j.tcs.2005.11.040","volume":"358","author":"P. H. Potgieter","year":"2006","unstructured":"Potgieter, P. H. (2006). Zeno machines and hypercomputation. Theoretical Computer Science, 358, 23\u201333.","journal-title":"Theoretical Computer Science"},{"key":"9161_CR29","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1016\/j.tcs.2003.12.007","volume":"317","author":"O. Shagrir","year":"2004","unstructured":"Shagrir, O. (2004). Super-tasks, accelerating Turing machines and uncomputability. Theoretical Computer Science, 317, 105\u2013114.","journal-title":"Theoretical Computer Science"},{"key":"9161_CR30","first-page":"2887","volume":"B36","author":"Z. Silagadze","year":"2005","unstructured":"Silagadze, Z. (2005). Zeno and modern science. Acta Physica Polonica, B36, 2887\u20132930.","journal-title":"Acta Physica Polonica"},{"key":"9161_CR31","volume-title":"Introduction to the theory of computation, 2nd edition","author":"M. Sipser","year":"2006","unstructured":"Sipser, M. (2006). Introduction to the theory of computation, (2nd ed). Boston: Thomson."},{"key":"9161_CR32","doi-asserted-by":"crossref","first-page":"184","DOI":"10.1016\/j.amc.2005.09.078","volume":"178","author":"W. D. Smith","year":"2006","unstructured":"Smith, W. D. (2006). Three counterexamples refuting Kieu\u2019s plan for \u201cquantum adiabatic hypercomputation\u201d, and some uncomputable quantum mechanical tasks. Applied Mathematics and Computation, 178, 184\u2013193.","journal-title":"Applied Mathematics and Computation"},{"key":"9161_CR33","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF01405490","volume":"2","author":"J. Soto-Andrade","year":"1984","unstructured":"Soto-Andrade, J., & Varela, F. J. (1984). Self-reference and fixed points: A discussion and an extension of Lawvere\u2019s theorem. Acta Applicandae Mathematicae, 2, 1\u201319.","journal-title":"Acta Applicandae Mathematicae"},{"key":"9161_CR34","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1093\/analys\/15.1.1","volume":"15","author":"T. Thomson","year":"1954","unstructured":"Thomson, T. (1954). Tasks and super-tasks. Analysis, 15, 1\u201313.","journal-title":"Analysis"},{"key":"9161_CR35","unstructured":"Toffoli, T. (1998). Non-conventional computers. Encyclopedia of Electrical and Electronics Engineering, 14, 455\u2013471. New York: Wiley."},{"key":"9161_CR36","unstructured":"Turing, A. M. (2004). Systems of logic based on ordinals. Proceedings of the London Mathematical Society 45, 161\u2013228 (1939). Reprinted in B. J. Copeland (Ed.), The essential turing (pp. 125-204). Oxford: Oxford University Press."},{"key":"9161_CR37","doi-asserted-by":"crossref","first-page":"739","DOI":"10.1093\/bjps\/55.4.739","volume":"55","author":"P. D. Welch","year":"2004","unstructured":"Welch, P. D. (2004a). On the possibility, or otherwise, of hypercomputation. British Journal for the Philosophy of Science, 55, 739\u2013746.","journal-title":"British Journal for the Philosophy of Science"},{"key":"9161_CR38","first-page":"223","volume-title":"Foundations of the Formal Sciences III","author":"P. D. Welch","year":"2004","unstructured":"Welch, P. D. (2004b). Post\u2019s and other problems in higher supertasks. In B. L\u00f6we, B. Piwinger, & T. R\u00e4sch (Eds.), Foundations of the formal sciences III (pp. 223\u2013237). Dordrecht: Kluwer."},{"key":"9161_CR39","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1016\/j.tcs.2003.12.011","volume":"317","author":"B. Wells","year":"2004","unstructured":"Wells, B. (2004). Hypercomputation by definition. Theoretical Computer Science, 317, 191\u2013207.","journal-title":"Theoretical Computer Science"},{"key":"9161_CR40","doi-asserted-by":"crossref","first-page":"443","DOI":"10.2307\/2118559","volume":"141","author":"A. Wiles","year":"1995","unstructured":"Wiles, A. (1995). Modular elliptic curves and Fermat\u2019s last theorem. Annals of Mathematics, 141, 443\u201355.","journal-title":"Annals of Mathematics"},{"key":"9161_CR41","doi-asserted-by":"crossref","first-page":"362","DOI":"10.2178\/bsl\/1058448677","volume":"9","author":"N. S. Yanofsky","year":"2003","unstructured":"Yanofsky, N. S. (2003). A universal approach to self-referential paradoxes, incompleteness and fixed points. Bulletin of Symbolic Logic, 9, 362\u2013386.","journal-title":"Bulletin of Symbolic Logic"}],"container-title":["Minds and Machines"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11023-009-9161-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11023-009-9161-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11023-009-9161-7","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,5,27]],"date-time":"2023-05-27T04:09:52Z","timestamp":1685160592000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11023-009-9161-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,8]]},"references-count":40,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2009,8]]}},"alternative-id":["9161"],"URL":"https:\/\/doi.org\/10.1007\/s11023-009-9161-7","relation":{},"ISSN":["0924-6495","1572-8641"],"issn-type":[{"value":"0924-6495","type":"print"},{"value":"1572-8641","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,8]]}}}