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Theoretical Childhood and Adulthood: Plato’s Account of Human Intellectual Development

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Abstract

The Platonic description of the cognitive development of the human being is a crucial part of his philosophy. This account emphasizes not only the existence of phases of rational growth but also the need that the cognitive progress of the individuals is investigated further. I will reconstruct what rational growth is for Plato in light of the deliberate choice of the philosopher to leave incomplete his schematization of human intellectual development. I will argue that this is a means chosen by Plato to stimulate his readers to use his text as a starting point for an enquiry into the capabilities of human intellection. I will illustrate the presence of two phases in the process of human rational growth, highlighting the different techniques utilized by Plato to promote cognitive development during each of them. When the individuals are in the first phase of intellectual growth, they are rationally stimulated via conventional discursive material transmitted in written form. Human rational progress at the level of sophistication of theoretical adulthood is promoted through mathematics.

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Notes

  1. Republic, VI 509 d-510.

  2. Republic, VII 534 a.

  3. R. Foley, Plato’s Undividable Line: Contradiction and Method in Republic VI, «Journal of the History of Philosophy», vol. 46, no. I, 2008, p. 23. My emphasis.

  4. Ibid.

  5. The method that Plato uses to require his readers to engage with the text of the dialogues, completing it with their own thinking, is not the subject of this paper.

  6. Republic, VI 509 d-510.

  7. R. Foley, art. cit., p. 1.

  8. My purpose here is not that of listing all the clues which go in this direction, because this would require a description of my reinterpretation of fundamental components of Platonic philosophy, which goes beyond the goals of this paper. This does not mean that I do not want to offer to the reader the textual justification of my claims. On the contrary, knowing that this justification comprises of textual excerpts, taken from Plato’s dialogues, and the explanation of my novel interpretation of them, I have decided to devote separate pieces to the analyses of specific elements of Plato’s thought, that point to the existence of a broader schematization of intellectual development than that which is usually taken into consideration in a standard reading of Plato.

  9. For the connection of theoretical childhood with physical adult age see Republic, III 409 b 5 and Sophist, 251 b 6 where it is explained that you can begin to learn “late in life”.

  10. Republic, VI 509 d- 510.

  11. Where and if the human intellectual journey could end for Plato is not the subject of this work.

  12. Republic, VI 509 d.

  13. Ibid.

  14. A. F. Chalmers, What is this Thing Called Science?, Indianapolis, Hackett, 1976, p. 78.

  15. Republic, VI 509 d-510.

  16. Republic, VII 534 a.

  17. This is “The Revisionist Interpretation” as Foley, art. cit., describes it on pages 8–9.

  18. See “The Demarcation Interpretation”, described by Foley, art. cit., pp. 9–12.

  19. See Foley, art. cit., p. 10.

  20. See “The Gaffe Interpretation”, Foley, art. cit., pp. 12–15.

  21. See “The Dissolution Interpretation”, Foley, art. cit., pp. 15–18.

  22. Republic, VI 509 d-510.

  23. Republic, I 328–331.

  24. Republic, I 336–352.

  25. Republic, I 331 c.

  26. Ibid.

  27. Republic, I 339.

  28. Socrates’ objection is that if justice is obeying the will of the ruler it could happen that our actions are involuntarily against the advantage of the stronger because we are obeying his wrong orders. Thrasymachus defends his thesis stating that no real ruler errs. This reply is designed simply to get around Socrates’ remarks and it does confirm that Thrasymachus is a theoretical child. I will not analyze here the last concept of justice proposed by Thrasymachus and if and why his thought can be associated with that of Callicles in the Gorgias.

  29. Phaedrus, 275 a-b.

  30. Phaedrus, 275 a.

  31. This seems to find confirmation in Republic, II 381 a: “And the most courageous and the most rational soul is least disturbed or altered by any outside affection.”

  32. Republic, VII 518 c-d.

  33. S. Cavell, The Availability of Wittgenstein’s Later Philosophy, «The Philosophical Review», Vol. 71, No 1, 1962, p. 74. My emphasis.

  34. Republic, X 598 e-599 a.

  35. S. Cavell, op. cit., p. 87. My emphasis.

  36. W. James, Pragmatism: A New Name for Some Old Ways of Thinking, New York, Longman, Green and Co, 1907.

  37. W. James, op. cit., p. 45.

  38. W. James, op. cit., p. 43.

  39. W. James, op. cit., p. 44. My emphasis.

  40. Dewey, How we Think, Lexington, Mass: D.C., Heath, 1910.

  41. Dewey, op. cit., p. 176. My emphasis.

  42. Foley, art. cit., p. 12.

  43. T. Heath, A History of Greek Mathematics, Oxford, The Clarendon Press, 1921, p. 290. My emphasis

  44. Ibid.

  45. M. J. Greenberg, Euclidean and Non-Euclidean Geometries: Development and History, San Francisco, W. H Freeman and Co., 1974, p. 8.

  46. M. J. Greenberg, op. cit., p. 9.

  47. John Casey, The First Six Books of the Elements of Euclid, Dublin, Hodges, Figgis & Co, 1885, p. 8.

  48. John Casey, op. cit, p. 6.

  49. D. R. Hofstadter, Gödel, Escher, Bach: an Eternal Golden Braid, New York, Basic Books, 1979, p. 90.

  50. John Casey, op. cit, p. 8.

  51. John Casey, op. cit, p. 5: “a circle is a plane figure formed by a curved line called the circumference, and is such that all right lines drawn from a certain point within the figure to the circumference are equal to one another. This point is called the centre.”

  52. John Casey, op. cit, p. 4: “A triangle whose three sides are unequal is said to be scalene…, a triangle having two sides equal, to be isosceles…, and having all its sides equal, to be equilateral…”

  53. M. J. Greenberg, op. cit., p. 18.

  54. Ibid.

  55. M. J. Greenberg, op. cit., p. 16. P. J. Ryan, Euclidean and Non-Euclidean Geometry: An Analytical Approach, Cambridge, Cambridge University Press, 1986, p. 2, stresses that “ Many ‘proofs’ of the fifth postulate were proposed, but they usually contained a hidden assumption equivalent to what was to be proved. Three such equivalent conditions were:

    i. Two intersecting straight lines cannot be parallel to the same straight line. (Playfair)

    ii. Parallel lines remain at a constant distance from each other. (Proclus)

    iii. The interior angles of a triangle add up to two right angles. (Legendre)”

  56. See M. J. Greenberg, op. cit., p. 250.

  57. Kant, The Critique of Pure Reason, trans. Norman Kemp Smith, New York, Modern Library, 1958, pp. 25-38.

  58. Kant, op. cit., pp. 33-34.

  59. J. R. Brown, Philosophy of Mathematics: A Contemporary Introduction to the World of Proofs and Pictures, Routledge, London and New York, 1999, p. 85. See also Mark Colyvan, An Introduction to the Philosophy of Mathematics, Cambridge, Cambridge University Press, 2012, pp. 156-157. I want to thank Mark Colyvan for this suggestion.

  60. D.R. Hofstadter, ei, p. 127.

  61. Gordon Rice, Recursion and Iteration, «Communications of the ACM», Vol. 8, No 2, 1965, p. 114.

  62. Ibid.

  63. Ibid.

  64. The part of my research relative to Arabic and Roman notation and recursion has been developed thanks to Mark Colyvan’s intuitions. I am grateful to him for having shared them with me.

  65. See the “Hilbert Problems,” those unresolved problems in mathematics which is crucial to prove; in particular, see the number one in the list, the continuum hypothesis (M. Colyvan, op. cit, p. 34). The question of the size of the continuum is an independent question, a question which is left unanswered by the relevant mathematical theory (M. Colyvan, op. cit, p. 33), as it is emphasized by Kurt Gödel’s words in What is Cantor’s Continuum Problem?, in Philosophy of Mathematics, edited by Paul Benacerraf and Hilary Putnam, Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1964. p. 260: “not even an upper bound, however large, can be assigned for the power of the continuum. Nor is the quality of the cardinal number of the continuum known any better than its quantity.”

  66. See Bertrand Russell, The Regressive Method of Discovering the Premises of Mathematics, in Essays in Analysis, by Bertrand Russell edited by Douglas Lackey, London, George Allen & Unwin Ltd, 1973, in particular pp. 273-274.

  67. These two species of knowledge, one which needs the mediation of the tangible to exist and the other one which has reached a superior degree of refinement, leave open questions about the compatibility of human nature with a kind of knowledge which has totally abandoned the empirical, which can be located in the D’ sector of my extended line segment. Whether a human being can reach a level of intellectual sophistication which totally separates her thinking from the tangible, is a question which exceeds the scopes of this research.

  68. Foley, art. cit., p. 22.

  69. Republic, VI 509 d-510.

References

  • Plato, Phaedrus, trans. Alexander Nehamas and Paul Woodruff, in Plato: Complete Works, edited by J. M. Cooper, Indianapolis, Hackett, 1997.

  • Plato, Republic, trans. G.M.A. Grube, revised by C.D.C. Reeve, in Plato: Complete Works, edited by J. M. Cooper, Indianapolis, Hackett, 1997.

  • Plato, Sophist, trans. Nicholas P. White, in Plato: Complete Works, edited by J. M. Cooper, Indianapolis, Hackett, 1997.

ᅟ

  • Brown, J. R. (1999). Philosophy of mathematics: A contemporary introduction to the world of proofs and pictures. London and New York: Routledge.

  • Casey, J. (1885). The first six books of the elements of euclid. Dublin: Hodges, Figgis & Co.

  • Cavell, S. (1962). The availability of Wittgenstein’s later philosophy. The Philosophical Review, 71(1), 67–93.

  • Chalmers, A. F. (1976). What is this thing called science? Indianapolis: Hackett.

  • Colyvan, M. (2012). An introduction to the philosophy of mathematics. Cambridge: Cambridge University Press.

  • Dewey. (1910). How we think. Lexington, Mass: D.C., Heath.

  • Foley, R. (2008). Plato’s undividable line: Contradiction and method in republic VI. Journal of the History of Philosophy, 46(1), 1–23.

  • Gödel, K. (1964). What is Cantor’s continuum problem? In P. Benacerraf & H. Putnam (Eds.), Philosophy of mathematics. Englewood Cliffs: Prentice-Hall, Inc.

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  • Greenberg, M. J. (1974). Euclidean and non-euclidean geometries: Development and history. San Francisco: W. H Freeman and Co.

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  • Hofstadter, D. R. (1979). Gödel, Escher, Bach: An eternal Golden Braid. New York: Basic Books.

  • James, W. (1907). Pragmatism: A new name for some old ways of thinking. New York: Longman, Green and Co.

  • Kant. (1958). The critique of pure reason. Trans. N. Kemp Smith. New York: Modern Library.

  • Rice, G. (1965). Recursion and iteration. Communications of the ACM, 8(2), 114–115.

  • Russell, B. (1973). The regressive method of discovering the premises of mathematics. In R. Bertrand & L. Douglas (Eds.), Essays in analysis. London: George Allen & Unwin Ltd.

  • Ryan, P. J. (1986). Euclidean and non-euclidean geometry: An analytical approach. Cambridge: Cambridge University Press.

  • Wittgenstein. (1998). Philosophical Investigations, (trans: G. E. M. Anscombe), 2nd edition. Oxford: Blackwell, reprinted.

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    Susanna Saracco

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Saracco, S. Theoretical Childhood and Adulthood: Plato’s Account of Human Intellectual Development. Philosophia 44, 845–863 (2016). https://doi.org/10.1007/s11406-016-9698-7

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