Abstract
This chapter of the book provides the last example of modern resources used to recreate the depth level of Plato’s meaning. This is a new hermeneutic approach which emphasizes Plato’s contribution to cultural progress, while avoiding the mistaken notion that modern research is a direct result of Plato’s text. In the Philebus Plato distinguishes between philosopher’s arithmetic and ordinary arithmetic. When philosophers count, they take into consideration the essence of the units involved in the process of counting. The capacity of thinking abstractly, separating your reasoning from the empirical realm, is proper to theoretical adults. The epistemology of theoretical adults is reconstructed using structuralism. Structuralism is based on a higher form of abstraction: it abstracts away from the numbers to the structural relations among them.
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Notes
- 1.
See the Tübingen school, note 15, chapter two.
- 2.
For the evolution of the mathematical thinking of the Greeks, from the use of mathematics for the solution of practical problems to abstract geometry and arithmetic, see Resnik. 1997. Mathematics as a Science of Patterns. Oxford: Clarendon Press, pp. 179–182.
- 3.
See also Shapiro, Philosophy of Mathematics: Structure and Ontology, op. cit., p. 78: “each mathematical object is a place in a particular structure.”
- 4.
Plato, in these lines, states that there is only one direction that our rational sight has to take into consideration in the process of learning: it is the direction of the truth understood thanks to the correct exercise of our rational capacities. Nonetheless, Plato is not saying that there exists only one possible way to look in the right direction. This confirms what it has been repeatedly emphasized in this research: Plato’s thought and indoctrination are antithetical.
References
Texts and Translations
Plato. Philebus. 1997. Translated by Frede, Dorothea. In Plato: Complete Works, edited by Cooper, J. M. Indianapolis: Hackett.
Plato. Republic. 1997. Translated by Grube, G.M.A. revised by Reeve, C.D.C. In Plato: Complete Works, edited by Cooper, J. M. Indianapolis: Hackett.
Recent Works
Chalmers, A. F. 1976. What Is This Thing Called Science? Indianapolis: Hackett.
Foley, R. 2008. “Plato’s Undividable Line: Contradiction and Method in Republic VI.” Journal of the History of Philosophy 46 (I): 1–24.
Resnik, M. 1997. Mathematics as a Science of Patterns. Oxford: Clarendon Press.
Shapiro, Stewart. 1997. Philosophy of Mathematics: Structure and Ontology. Oxford: Oxford University Press.
Shapiro, Stewart. 2000. Thinking about Mathematics: The Philosophy of Mathematics. Oxford: Oxford University Press.
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Saracco, S. (2017). Theoretical Adulthood. In: Plato and Intellectual Development. Palgrave Macmillan, Cham. https://doi.org/10.1007/978-3-319-52587-7_5
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