David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Plato's theory of forms is developed and compared to the modern theory of recursion. I show how Plato's theory, as it applies to mathematical objects, is essentially a primitve version of modern recursion theory, which has all the essential elements of the ancient theory. However, Plato himself thought there was more than mathematics to his forms. He believed that form had a noncomposite, unanalyzable component. So, while recursion theory provides an adequate formalization of Plato's theory, it cannot be considered identical to it. I argue--drawing from material in the "Meno," "Phaedo," and "Republic"--that Plato's arguments for noncomposite form are largely fallacious. Plato would, I believe, have taken the computational version developed here seriously, since mathematics was his primary source for clear examples of forms (one could argue that it was his only source short of dipping into mysticism). In fact, there is a long-standing oral tradition that Plato developed a more formal version of his theory in lecture notes for courses he taught at the Academy (the university he founded in Athens). Any such notes, if they existed at all, have been lost. But if such a formal version did exist, it is tantalizing to wonder to what extent Plato may have anticipated modern theoretical computer science and metamathematics.
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library||
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
David Robjant (2012). The Earthy Realism of Plato's Metaphysics, Or: What Shall We Do with Iris Murdoch? Philosophical Investigations 35 (1):43-67.
Samuel Charles Rickless (2007). Plato's Forms in Transition: A Reading of the Parmenides. Cambridge University Press.
R. M. Dancy (2004). Plato's Introduction of Forms. Cambridge University Press.
Gail Fine (1993). On Ideas: Aristotle's Criticism of Plato's Theory of Forms. Oxford University Press.
Sheldon Wein (1986). Plato and the Social Contract. Philosophy Research Archives 12:67-77.
Vasilis Politis (2001). Anti-Realist Interpretations of Plato: Paul Natorp. International Journal of Philosophical Studies 9 (1):47 – 62.
Andrew S. Mason (2010). Plato. Acumen Pub. Ltd..
Plato & G. M. A. Grube (1949). Meno. New York, Liberal Arts Press.
Added to index2010-12-22
Total downloads9 ( #254,415 of 1,726,249 )
Recent downloads (6 months)0
How can I increase my downloads?