РАСПРЕДЕЛЕННОЕ ПОЗНАНИЕ И МАТЕМАТИЧЕСКАЯ ПРАКТИКА В ЦИФРОВОМ ОБЩЕСТВЕ: ОТ ФОРМАЛИЗАЦИИ ДОКАЗАТЕЛЬСТВ К ПЕРЕСМОТРУ ОСНОВАНИЙ
Ключевые слова:
распределенное познание, коммуникация, цифровое общество, математическая практика, формальное доказательство, основания математики
Аннотация
В статье сделана попытка посмотреть на современную математическую практику через призму концепции распределенного познания. Характерное для цифрового общества повсеместное использование персональных компьютеров и сети интернета рассмотрено как способ достичь более эффективного распределения познавательной активности человека. В качестве решающего вызова, определяющего магистральное направление трансформации математической практики, в статье выделяется «проблема сложности». Современная тенденция к полной формализации математических доказательств на основе цифровых технологий рассматривается как одна из реакций на указанный вызов. Показано, что названная тенденция ведет к проекту переосмысления и перестройки самих оснований математики в целях обеспечения более эффективной коммуникации, а, тем самым, и надежности современной математики.
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Литература
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Tymoczko, T. "Making Room for Mathematicians in the Philosophy of Mathematics", The Mathematical Intelligencer, 1986, vol. 8, no. 3, pp. 44-50.
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Baker, A. "Non-Deductive Methods in Mathematics" (2009; substantive revision -2015), in: Zalta, E.N. (ed.), The Stanford Encyclopedia of Philosophy.
Boyer, R.S., de Bruijn, N.G., Huet, G., Trybulec, A. "Panel Discussion: Mechanically Proof-Checked Encyclopedia of Mathematics: Should We Build One? Can We?", in: Bundy, A. (ed.), Automated Deduction -CADE-12: 12th International Conference on Automated Deduction. Nancy, France, June 26 -July 1, 1994. Proceedings. Berlin: Springer-Verlag, 1994, pp. 237-251.
Davies, E.B. "Whither Mathematics?", Notices of the American Mathematical Society, 2005, vol. 52. no. 11, pp. 1350-1356. de Bruijn, N.G. "Checking Mathematics with Computer Assistance", Notices of the American Mathematical Society, 1991, vol. 38, no. 1, pp. 8-15.
Giddens, A. Posledstviya sovremennosti . Moscow: Praksis, 2011. 352 pp.
Hales, T.C. "Formal Proof", Notices of the American Mathematical Society, 2008, vol. 55, no. 11, pp. 1370-1380.
Homotopy Type Theory: Univalent Foundations of Mathematics. The Univalent Foundations Program, Institute for Advanced Study, 2013. 469 pp.
Hutchins, E. Cognition in the Wild. Cambridge, MA: The MIT Press, 1995. 379 pp.
Lakatos, I. "Infinite Regress and Foundations of Mathematics", in: Lakatos, I. Mathematics, Science, and Epistemology. Philosophical Papers. Vol. 2. Ed. by J. Worrall, G. Currie. Cambridge, UK: Cambridge University Press, 1978, pp. 3-23.
Lamb, E. "Maths Proof Smashes Size Record: Supercomputer Produces a 200-Terabyte Proof -But Is It Really Mathematics?", Nature, vol. 534, 2 June 2016, pp. 17-18.
Latour, B. "Cogito ergo sumus! Or Psychology Swept Inside Out by the Fresh Air of the Upper Deck... A Review of Ed Hutchins", Cognition in the Wild, Cambridge, MA: The MIT Press, 1995", Mind, Culture, and Activity, 1996, vol. 3, no. 1, pp. 54-63.
MacKenzie, D. Mechanizing Proof: Computing, Risk, and Trust. Cambridge, MA: The MIT Press, 2001. 439 pp.
Monroe, D. "A New Type of Mathematics? New Discoveries Expand the Scope of Computer-Assisted Proofs of Theorems", Communications of the ACM, 2014, vol. 57, no. 2, pp. 13-15.
Norman, D.A. Things That Make Us Smart: Defending Human Attributes in the Age of the Machine. Reading, MA: Addison-Wesley Publishing Company, 1993. 304 pp.
Perry, M. "Distributed Cognition", in: Paschler, H. (ed.), Encyclopedia of the Mind. Thousand Oaks, CA: SAGE Publications, 2013, pp. 258-260.
Rheingold, H. Net Smart: How to Thrive Online, Cambridge, MA: The MIT Press, 2012. 332 pp.
Rodin, A. "On the Constructive Axiomatic Method", Logique et Analyse, 2018, vol. 61, no. 242, pp. 201-231.
Shaposhnikov, V.A. "Matematicheskaya praktika v usloviyakh sotsiotsifrovoy revolyutsii" , in: Ershova, R.V. (ed.) TSifrovoye obshchestvo kak kul’turno-istoricheskiy kontekst razvitiya cheloveka, 14-17 fevralya 2018, Kolomna . Kolomna: Gosudarstvennyy sotsial’no-gumanitarnyy universitet, 2018, pp. 431-436.
Streicher, T. "Review: Paul Taylor, Practical Foundations of Mathematics, Cambridge University Press, 1999", Science of Computer Programming, 2000, vol. 38, no. 1-3, pp. 155-157.
Taylor, P. Practical Foundations of Mathematics. Cambridge, UK: Cambridge University Press, 1999. 584 pp.
Tsementzis, D. "Univalent Foundations as Structuralist Foundations", Synthese, 2017, vol. 194, no. 9, pp. 3583-3617.
Tymoczko, T. "Making Room for Mathematicians in the Philosophy of Mathematics", The Mathematical Intelligencer, 1986, vol. 8, no. 3, pp. 44-50.
Voevodsky, V. "Univalent Foundations of Mathematics", in: Beklemishev, L.D., de Queiroz, R. (eds.), Logic, Language, Information and Computation: 18th International Workshop, WoLLIC 2011, Philadelphia, PA, USA, May 18-20, 2011. Proceedings (LNAI 6642). Berlin: Springer-Verlag, 2011, p. 4.
Weiss, I. "The QED Manifesto after Two Decades -Version 2.0", Journal of Software, 2016, vol. 11, no. 8, pp. 803-815.
Wiedijk, F. "The QED Manifesto Revisited", Studies in Logic, Grammar and Rhetoric, 2007, vol. 10 (23), pp. 121-133.
Опубликован
2019-03-21
Как цитировать
Шапошников В. А. РАСПРЕДЕЛЕННОЕ ПОЗНАНИЕ И МАТЕМАТИЧЕСКАЯ ПРАКТИКА В ЦИФРОВОМ ОБЩЕСТВЕ: ОТ ФОРМАЛИЗАЦИИ ДОКАЗАТЕЛЬСТВ К ПЕРЕСМОТРУ ОСНОВАНИЙ // Эпистемология и философия науки. 2019. Т. 55. № 4. С. 160–173.
Раздел
Case studies - Science Studies
