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PROPOSITIONAL LEARNING: FROM IGNORANCE TO KNOWLEDGE

Published online by Cambridge University Press:  24 October 2018

Pierre Le Morvan
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Abstract

In this paper, I offer an account of propositional learning: namely, learning that p. I argue for what I call the “Three Transitions Thesis” or “TTT” according to which four states and three transitions between them characterize such learning. I later supplement the TTT to account for learning why p. In making my case, I discuss mathematical propositions such as Fermat's Last Theorem and the ABC Conjecture, and then generalize to other mathematical propositions and to non-mathematical propositions. I also discuss some interesting applications of the TTT, and reply to some noteworthy objections.

Type
Articles
Information
Episteme , Volume 17 , Issue 2 , June 2020 , pp. 162 - 177
Copyright
Copyright © Cambridge University Press 2018

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References

REFERENCES

Aczel, A. 2007. Fermat's Last Theorem. New York, NY: Basic Books.Google Scholar
Alexander, P. A., Schallert, D. L. and Reynolds, R. E. 2009. ‘What Is Learning Anyway? A Topographical Perspective Considered.’ Educational Psychologist, 44: 176–92.CrossRefGoogle Scholar
Antognazza, M. R. 2015. ‘The Benefit to Philosophy of the Study of its History.’ British Journal for the History of Philosophy, 23: 161–84.CrossRefGoogle Scholar
Audi, R. 2011. Epistemology: A Contemporary Introduction to the Theory of Knowledge, 3rd edition. New York, NY: Routledge.Google Scholar
Castelvecchi, D. 2015. ‘The Impenetrable Proof.’ Nature, 526: 178–81.CrossRefGoogle ScholarPubMed
Claveau, F. and Vergara Fernández, M. 2015. ‘Epistemic Contributions of Models: Conditions for Propositional Learning.’ Perspectives on Science, 23: 405–23.CrossRefGoogle Scholar
Dewey, J. 1933. How We Think. Chicago, IL: Henry Regnery.Google Scholar
DeNicola, D. 2017. Understanding Ignorance. Cambridge, MA: MIT Press.Google Scholar
Driscoll, M. P. 2005. Psychology of Learning for Instruction. New York, NY: Pearson Education.Google Scholar
Dutant, J. 2015. ‘The Legend of the Justified True Belief Analysis.’ Philosophical Perspectives, 29: 95–145.CrossRefGoogle Scholar
Edwards, H. 2000. Fermat's Last Theorem: A Genetic Introduction to Algebraic Number Theory. New York, NY: Springer-Verlag.Google Scholar
Gettier, E. 1963. ‘Is Justified True Belief Knowledge?’ Analysis, 23: 121–3.CrossRefGoogle Scholar
Hazlett, A. 2010. ‘The Myth of Factive Verbs.’ Philosophy and Phenomenological Research, 80: 497–522.CrossRefGoogle Scholar
Le Morvan, P. 2010. ‘Knowledge, Ignorance, and True Belief.’ Theoria, 76: 309–18.Google Scholar
Le Morvan, P. 2011. ‘On Ignorance: A Reply to Peels.’ Philosophia, 39: 335–44.CrossRefGoogle Scholar
Le Morvan, P. 2012. ‘On Ignorance: A Vindication of the Standard View.’ Philosophia, 40: 379–93.CrossRefGoogle Scholar
Le Morvan, P. 2013. ‘Why the Standard Conception of Ignorance Prevails.’ Philosophia, 41: 239–56.CrossRefGoogle Scholar
Le Morvan, P. 2015. ‘On the Ignorance, Knowledge, and Nature of Propositions.’ Synthese, 192: 3647–62.CrossRefGoogle Scholar
Le Morvan, P. 2016. ‘Knowledge and Security.’ Philosophy, 91: 411–30.CrossRefGoogle Scholar
Le Morvan, P. 2017. ‘Knowledge Before Gettier.’ British Journal for the History of Philosophy, 25: 1216–38.CrossRefGoogle Scholar
Masser, D. W. 1985. ‘Open Problems.’ In Chen, W. W. L. (ed.), Proceedings of the Symposium on Analytic Number Theory. London: Imperial College.Google Scholar
Mochizuki, S. 2017a. ‘Inter-universal Teichmüller Theory I: Construction of Hodge Theaters.’ http://www.kurims.kyoto-u.ac.jp/~motizuki/Inter-universal%20Teichmuller%20Theory%20I.pdf.Google Scholar
Mochizuki, S. 2017b. ‘Inter-universal Teichmüller Theory II: Hodge-Arakelov-theoretic Evaluation’ http://www.kurims.kyoto-u.ac.jp/~motizuki/Inter-universal%20Teichmuller%20Theory%20II.pdf.Google Scholar
Mochizuki, S. 2017c. ‘Inter-universal Teichmüller Theory III: Canonical Splittings of the Log-theta-lattice.’ http://www.kurims.kyoto-u.ac.jp/~motizuki/Inter-universal%20Teichmuller%20Theory%20III.pdf.Google Scholar
Mochizuki, S. 2017d. ‘Inter-universal Teichmüller Theory IV: Log-volume Computations and Set-theoretic Foundations.’ http://www.kurims.kyoto-u.ac.jp/~motizuki/Inter-universal%20Teichmuller%20Theory%20IV.pdf.Google Scholar
Noddings, N. 2016. Philosophy of Education, 4th edition. Boulder, CO: Westview Press.Google Scholar
Nola, R. and Irzik, G. 2005. Philosophy, Science, Education, and Culture. Dordrecht: Springer.Google Scholar
Oesterlé, J. 1988. ‘Nouvelles approches du ‘théorème’ de Fermat.’ Astérisque, Séminaire Bourbaki, 694: 165–86.Google Scholar
Reichenbach, H. 1938. Experience and Prediction. Chicago, IL: University of Chicago Press.Google Scholar
Singh, S. 2012. Fermat's Last Theorem. New York, NY: HarperCollins Publishers.Google Scholar
Stillwell, J. 2015. ‘What Does ‘Depth’ Mean in Mathematics?’ Philosophia Mathematica, 23: 215–32.CrossRefGoogle Scholar
Taylor, R. and Wiles, A. 1995. ‘Ring Theoretic Properties of Certain Hecke Algebras.’ Annals of Mathematics, 141: 553–72.CrossRefGoogle Scholar
Turri, J. 2011. ‘Mythology of the Factive.’ Logos & Episteme, II: 143–52.Google Scholar
Wiles, A. 1995. ‘Modular Elliptic Curves and Fermat's Last Theorem.’ Annals of Mathematics, 141: 443–551.CrossRefGoogle Scholar