Computational Platonism

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)
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history
Request removal from index
Translate to english
Download options
Our Archive

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 29,511
External links

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.

Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles
Plato and the Social Contract.Sheldon Wein - 1986 - Philosophy Research Archives 12:67-77.
Anti-Realist Interpretations of Plato: Paul Natorp.Vasilis Politis - 2001 - International Journal of Philosophical Studies 9 (1):47 – 62.
Plato.Andrew S. Mason - 2010 - Acumen Publishing.
Meno. Plato & G. M. A. Grube - 1949 - New York: Liberal Arts Press.
Plato: Meno and Phaedo. Plato - 1980 - Cambridge University Press.
Added to PP index

Total downloads
9 ( #468,974 of 2,180,737 )

Recent downloads (6 months)

How can I increase my downloads?

Monthly downloads
My notes
Sign in to use this feature

There  are no threads in this forum
Nothing in this forum yet.

Other forums