Arithmetical CertaintiesA Few Exceptions Among Countless Knowledge-Statements

  1. José María Ariso Salgado 1
  1. 1 Universidad Internacional de La Rioja
    info

    Universidad Internacional de La Rioja

    Logroño, España

    ROR https://ror.org/029gnnp81

Revue:
Thémata: Revista de filosofía

ISSN: 0212-8365,  2253-900X

Année de publication: 2022

Número: 66

Pages: 142-158

Type: Article

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D'autres publications dans: Thémata: Revista de filosofía

Résumé

In this paper I disagree with Kusch (2016) on three issues concerning expressions of arithmetical certainties – in Wittgenstein’s sense – and regular uses of arithmetical expressions. Specifically, I explain why calculations do not turn into certainties by the fact that they have been proved; I argue that proved calculations constitute knowledge-statements; and, last but not least, I conclude from this that such proved calculations are sayable, whilst arithmetical certainties are ineffable or unsayable.

Références bibliographiques

  • Ariso, José María. “The teacher as persuader: On the application of Wittgenstein’s notion of ‘persuasion’ in educational practice”, Educational Philosophy and Theory (2021). DOI: 10.1080/00131857.2021.1930529
  • Ariso, José María. “Religious Certainty: Peculiarities and Pedagogical Considerations”, Studies in Philosophy and Education 39 (2020): 657-669.
  • Ariso, José María. “Teaching Children to Ignore Alternatives is—Sometimes—Necessary: Indoctrination as a Dispensable Term”, Studies in Philosophy and Education 38 (2019a): 397-410.
  • Ariso, José María. “Can a culture of error be really developed in the classroom without teaching students to distinguish between errors and anomalies?”, Educational Philosophy and Theory 51 (2019b): 1030-1041.
  • Ariso, José María. “Can Certainties Be Acquired at Will? Implications for Children’s Assimilation of a World-picture”, Journal of Philosophy of Education 50 (2016): 573-586.
  • Ariso, José María. “Some variations of the certainty of one’s own death”, Linguistic and Philosophical Investigations 14 (2015): 82-96.
  • Ariso, José María. “Wittgenstein and the Possibility of Inexplicably Losing Certainties”, Philosophical Papers 42 (2013): 133-150.
  • Ariso, José María. Wahnsinn und Wissen. Zu Wittgensteins Lage und Denkbewegung. Würzburg: Königshausen & Neumann, 2012.
  • Boudry, Maarten and Jerry Coyne. “Disbelief in belief: On the cognitive status of supernatural beliefs”, Philosophical Psychology 29 (2016): 601-615.
  • Churchill, John. “Wittgenstein: The Certainty of Worldpictures”, Philosophical Investigations 11 (1998): 28-48.
  • Floyd, Juliet. Wittgenstein’s Philosophy of Mathematics. Cambridge: Cambridge University Press, 2021.
  • Goody, Jack R. The Domestication of the Savage Mind. Cambridge: Cambridge University Press, 1977.
  • Hand, Michael “Religious Upbringing Reconsidered”, Journal of Philosophy of Education 36 (2002): 545–557.
  • Kober, Michael. Gewissheit als Norm: Wittgensteins erkenntnistheoretische Untersuchungen in ‘Über Gewissheit’. Berlin and New York: De Gruyter, 1993.
  • Kusch, Martin. “Wittgenstein on Mathematics and Certainties”, International Journal for the Study of Skepticism 6 (2016): 120-142.
  • McGinn, Marie. Sense and Certainty: A Dissolution of Scepticism. Oxford: Basil Blackwell, 1989.
  • Moyal-Sharrock, Danièle. Understanding Wittgenstein’s On Certainty. Basingstoke: Palgrave Macmillan, 2004.
  • Pritchard, Duncan: “Wittgenstein’s On Certainty and Contemporary Anti-scepticism”. Readings of Wittgenstein’s On Certainty, eds. Danièle Moyal-Sharrock and William H. Brenner. Basingstoke: Palgrave Macmillan, 2007. 189-224.
  • Rodych, Victor. “Wittgenstein on Mathematical Meaningfulness, Decidability, and Application”, Notre Dame Journal of Formal Logic 38 (1997): 195-225.
  • Ryan, Julie and Julian Williams. Children’s Mathematics 4-15: Learning From Errors and Misconceptions. Maidenhead: Open University Press, 2007.
  • Shapin, Steven. “Proverbial Economies: How an Understanding of Some Linguistic and Social Features of Common Sense Can Throw Light on More Prestigious Bodies of Knowledge, Science For Example”, Social Studies of Science 31 (2001): 731-769.
  • Siegel, Harvey. Educating Reason: Rationality, Critical Thinking, and Education. New York and London: Routledge, 1988.
  • Verbin, Nehama K. “Uncertainty and religious belief”, International Journal for Philosophy of Religion 51 (2002): 1-37.
  • Weiberg, Anja. “‘12 × 12 = 144’: Psychologische Sicherheit versus logischer Ausschluss des Irrtums in Über Gewißheit am Beispiel des Rechnens”, Wittgenstein-Studien 11 (2020): 271-282.
  • Williams, Michael. “Wittgenstein, Truth and Certainty”. Wittgenstein’s Lasting Significance, eds. Max Kölbel and Bernhard Weiss. London: Routledge, 2004a. 247-281.
  • Williams, Michael. “Wittgenstein’s Refutation of Idealism”. Wittgenstein and Scepticism, ed. Denis McManus. London and New York: Routledge, 2004b. 76-96.
  • Williams, Michael. “Why Wittgenstein Isn’t a Foundationalist”. Readings of Wittgenstein’s On Certainty, eds. Danièle Moyal-Sharrock and William H. Brenner. Basingstoke: Palgrave Macmillan, 2007. 47-58.
  • Wittgenstein, Ludwig. Philosophical Investigations. Oxford: Blackwell, 2001.
  • Wittgenstein, Ludwig. On certainty. Oxford: Blackwell, 1997.
  • Wittgenstein, Ludwig. Philosophical Remarks. Oxford: Basil Blackwell, 1975.
  • Wittgenstein, Ludwig. Remarks on the Foundations of Mathematics. Oxford: Basil Blackwell, 1967.
  • Wright, Crispin. “Wittgensteinian Certainties”. Wittgenstein and Scepticism, ed. Denis McManus. London and New York: Routledge, 2004. 22-55.
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