Truth, demonstration and knowledgea classical solution to the paradox of knowability

  1. Zardini, Elia 1
  1. 1 Arché y grupo LOGOS
Revista:
Theoria: an international journal for theory, history and foundations of science

ISSN: 0495-4548

Año de publicación: 2015

Título del ejemplar: History and Philosophy of Logic and Mathematics

Volumen: 30

Número: 3

Páginas: 365-392

Tipo: Artículo

DOI: 10.1387/THEORIA.14668 DIALNET GOOGLE SCHOLAR lock_openDialnet editor

Otras publicaciones en: Theoria: an international journal for theory, history and foundations of science

Resumen

After introducing semantic anti-realism and the paradox of knowability, the paper offers a reconstruction of the anti-realist argument from the theory of understanding. The proposed reconstruction validates an unrestricted principle to the effect that truth requires the existence of a certain kind of “demonstration”. The paper shows that the principle fails to imply the problematic instances of the original unrestricted knowability principle but that the overall view still has unrestricted epistemic consequences. Appealing precisely to the paradox of knowability, the paper also argues, against BHK semantics, for the non-constructive character of the demonstrations envisaged by anti-realists, and contends that, in such a setting, one of the most natural arguments in favour of a revision of classical logic loses all its force.

Referencias bibliográficas

  • Brouwer, Luitzen. 1907. Over de grondslagen der wiskunde. PhD thesis, University of Amsterdam, Amsterdam.
  • Burge, Tyler. 1979. "Individualism and the mental". Midwest Studies in Philosophy, 4:73-121.
  • Cozzo, Cesare. 1994. "What can we learn from the paradox of knowability?". Topoi, 13:71-78.
  • Dean, Walter and Kurokawa, Hidenori. 2010. "From the knowability paradox to the existence of proofs". Synthese, 176:177-225.
  • Dummett, Michael. 1969. "The reality of the past". Proceedings of the Aristotelian Society, 69: 239-258.
  • Dummett, Michael. 1975. "The philosophical basis of intuitionistic logic". In Harvey Rose and John Shepherdson, editors, Logic Colloquium '73, pages 5-40. North-Holland, Amsterdam.
  • Dummett, Michael. 1982. "Realism". Synthese, 52:55-112.
  • Dummett, Michael. 2001. "Victor's error". Analysis, 61:1-2.
  • Fitch, Frederic. 1963. "A logical analysis of some value concepts". The Journal of Symbolic Logic, 28:135-142.
  • Hand, Michael. 2010. "Antirealism and universal knowability". Synthese, 173:25-39.
  • Hart, Wilbur. 1979. "The epistemology of abstract objects. Access and inference". Proceedings of the Aristotelian Society Supplementary Volume, 53:153-165.
  • Heyting, Arend. 1934. Mathematische Grundlagenforschung. Intuitionismus. Beweistheorie. Springer Verlag, Berlin.
  • Incurvati, Luca and Murzi, Julien. 2008. "How basic is the basic revisionary argument?". Analysis, 68:303-309.
  • Kallestrup, Jesper. 2007. "If omniscient beings are dialetheists, then so are anti-realists". Analysis, 67:252-254.
  • Kolmogorov, Andrej. 1932. "Zur Deutung der intuitionistischen Logik". Mathematische Zeitschrift, 35:58-65.
  • López de Sa, Dan and Zardini, Elia. 2006. "Does this sentence have no truthmaker?". Analysis, 66: 154-157.
  • López de Sa, Dan and Zardini, Elia. 2007. "Truthmakers, knowledge and paradox". Analysis, 67: 242-250.
  • López de Sa, Dan and Zardini, Elia. 2011. "No-no. Paradox and consistency". Analysis, 71:472-478.
  • Martin-Löf, Per. 2013. "Verificationism then and now". In Maria van der Schaar, editor, Judgement and the Epistemic Foundation of Logic, pages 3-14. Springer, Dordrecht.
  • Milne, Peter. 2005. "Not every truth has a truthmaker". Analysis, 65:221-223.
  • Milne, Peter. 2007. "Omniscient beings are dialetheists". Analysis, 67:250-251.
  • Murzi. 2012, Julien. "Manifestability and epistemic truth". Topoi, 31:17-26.
  • Pagin, Peter. 1994. "Knowledge of proofs". Topoi, 13:93-100.
  • Prawitz, Dag. 1965. Natural Deduction. Almqvist och Wiksell, Stockholm.
  • Prawitz, Dag. 1987. "Dummett on a theory of meaning and its impact on logic". In Barry Taylor, editor, Michael Dummett, pages 117-165. Martinus Nijhoff Publishers, Dordrecht.
  • Prawitz, Dag. 1998a. "Comments on the papers". Theoria, 64:283-337.
  • Prawitz, Dag. 1998b. "Truth and objectivity from a verificationist point of view". In Harold Dales and Gianluigi Oli vieri, editors, Truth in Mathematics, pages 41-51. Clarendon Press, Oxford.
  • Salerno, Joe. 2009. "Knowability noir: 1945-1963". In Joe Salerno, editor, New Essays on the Knowability Paradox, pages 29-48. Oxford University Press, Oxford.
  • Tennant, Neil. 1997. The Taming of the True. Clarendon Press, Oxford.
  • Tennant, Neil. 2002. "Victor vanquished". Analysis, 62:135-142.
  • Williamson, Timothy. 1982. "Intuitionism disproved?". Analysis, 42:203-207.
  • Williamson, Timothy. 2003. "Understanding and inference". Proceedings of the Aristotelian Society Supplementary Volume, 77:249-293.
  • Wittgenstein, Ludwig. 1953. Philosophische Untersuchungen. Blackwell, Oxford.
  • Wright, Crispin. 1992. Truth and Objectivity. Harvard University Press, Cambridge MA.
  • Zardini, Elia. 2007. "Notes on the semantics and logic of factive knowability". In Xavier Arrazola and Jesús Larrazabal, editors, LogKCA-07: Proceedings of the First ILCLI International Workshop on Logic and Philosophy of Knowledge, Communication, and Action, pages 447-454. University of the Basque Country Press, Donostia/San Sebastián.
  • Zardini, Elia. 2008. "Truth and what is said". Philosophical Perspectives, 22:545-574.
  • Zardini, Elia. 2011. "Truth without contra(di)ction". The Review of Symbolic Logic, 4:498-535.
  • Zardini, Elia. 2012a. "Truth preservation in context and in its place". In Catarina Dutilh-Novaes and Ole Hjortland, editors, Insolubles and Consequences, pages 249-271. College Publications, London.
  • Zardini, Elia. 2012b. "Two diamonds are more than one: Transitivity and the factivity of feasible knowability In Shahid Rahman, Giuseppe Primiero and Mathieu Marion, editors, The Realism-Antirealism Debate in the Age of Alternative Logics, pages 325-341. Springer, Dordrecht.
  • Zardini, Elia. 2015a. "The opacity of truth". Topoi, 34:37-54.
  • Zardini, Elia. 2015b. "A and ω". In Alessandro Torza, editor, Quantifiers, Quantifiers and Quantifiers. Springer, D ordrecht. Forthcoming.
  • Zardini, Elia. 2015c. "Black boxes: The semantics and logic of obliterative modalities". ms.
  • Zardini, Elia. 2015d. "Further reflections on sentences saying of themselves strange things". ms.
  • Zardini, Elia. 2015e. "If every true proposition is knowable, then every believed (decidable) proposition is true, or the incompleteness of the intuitionist solution to the paradox of knowability". ms.
Fuente de los datos: Dialnet