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Mathematics, Mental Imagery, and Ontology: A New Interpretation of the Divided Line
in The International Journal of the Platonic TraditionSearch for other papers by Miriam Byrd in
Current site
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Abstract
This paper presents a new interpretation of the objects of dianoia in Plato’s divided line, contending that they are mental images of the Forms hypothesized by the dianoetic reasoner. The paper is divided into two parts. A survey of the contemporary debate over the identity of the objects of dianoia yields three criteria a successful interpretation should meet. Then, it is argued that the mental images interpretation, in addition to proving consistent with key passages in the middle books of the Republic, better meets those criteria than do any of the three main positions.
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-
Adam, J. 1902. The Republic of Plato. Vol. 2. Reprint. Cambridge: Cambridge University Press, 1929.
-
Annas, J. 1975. ‘On the Intermediates’. Archiv für Geschichte der Philosophie 57, 146-66.
-
Arsen, H.S. 2012. ‘A Case for the Utility of the Mathematical Intermediates’. Philosophia Mathematica 20, 200-223. http://dx.doi.org/10.1093/phimat/nks009.
-
Bedu-Addo, J.T. 1976. ‘A Theory of Mental Development: Plato’s Republic V-VII (Part 1)’. Platon 28, 288-300.
-
Bedu-Addo, J.T. 1979. ‘Dianoia and the Images of Forms in Plato’s Republic VI-VII’. Platon 31, 89-110.
-
Bedu-Addo, J.T. 1991. ‘Sense-experience and the Argument for Recollection in Plato’s Phaedo.’ Phronesis 36, 27-60.
-
Brentlinger, J.A. 1963. ‘The Divided Line and Plato’s “Theory of Intermediates”’. Phronesis 8, 146-66.
-
Burnyeat, M. 1987. ‘Platonism and Mathematics: A Prelude to a Discussion’, in Graeser (ed.), Mathematics and Metaphysics in Aristotle. Berne: Paul Haupt, 213-240.
-
Burnyeat, M. 2000. ‘Plato on Why Mathematics is Good for the Soul’. Proceedings of the British Academy 103, 1-81.
-
Byrd, M. 2007. ‘The Summoner Approach: A New Method of Plato Interpretation’. Journal of the History of Philosophy 45, 365-381. http://dx.doi.org/10.1353/hph.2007.0054.
-
Cherniss, H. 1945. The Riddle of the Early Academy. Berkeley and Los Angeles: University of California Press.
-
Cornford, F.M. 1932. ‘Mathematics and Dialectic in the Republic VI-VII’. Mind 41, 37-52.
-
Cresswell, M.J. 2012. ‘Mathematical Entities in the Divided Line’. The Review of Metaphysics 66, 89-104. http://dx.doi.org/10.1515/apeiron.2011.020.
-
Cross, R.C. and A.D. Woozley. 1964. Plato’s Republic: A Philosophical Commentary. Reprint, New York: St. Martin’s Press, 1966.
-
Denyer, N. 2007. ‘Sun and Line: The Role of the Good’, in G.R.F. Ferrari (ed.), The Cambridge Companion to Plato’s Republic, 284-309.
-
Ferrari, G.R.F., ed. 2007. The Cambridge Companion to Plato’s Republic. Cambridge: Cambridge University Press.
-
Fine, G. 1999. ‘Knowledge and Belief in Republic 5-7,’ in G. Fine (ed.), Plato 1: Metaphysics and Epistemology. Oxford: Oxford University Press, 215-246.
-
Fogelin, R.J. 1971. ‘Three Platonic Analogies’. The Philosophical Review 80, 371-382.
-
Foley, R. 2008. ‘Plato’s Undividable Line: Contradiction and Method in Republic VI.’ Journal of the History of Philosophy 46, 1-23. http://dx.doi.org/10.1353/hph.2008.1842.
-
Franklin, L. 2011. ‘Particular and Universal: Hypothesis in Plato’s Divided Line’. Apeiron 44, 335-358.
-
Franklin, L. 2012. ‘Inventing Intermediates: Mathematical Discourse and Its Objects in RepublicVII’. Journal of the History of Philosophy 50, 483-506. http://dx.doi.org/10.1353/hph.2012.0080.
-
Grube, G.M.A. and Reeve, C.D.C. trans. 1992. Plato: Republic. Indianapolis: Hackett Publishing Co.
-
Hackforth, R. 1942. ‘Plato’s Divided Line and Dialectic’. The Classical Quarterly 36, 1-9.
-
Hardie, W.F.R. 1936. A Study in Plato. Oxford: Clarendon Press.
-
Hare, R.M. 1965. ‘Plato and the Mathematicians’, in R. Bambrough (ed.), New Essays on Plato and Aristotle. London: Routledge Publishing, 21-38.
-
Klein, J. 1968. Greek Mathematical Thought and the Origin of Algebra. Trans. E. Brann. Cambridge: M.I.T. Press.
-
Miller, M. 2007. ‘Beginning the ‘Longer Way’, in G.R.F. Ferrari (ed.), The Cambridge Companion to Plato’s Republic, 310-344.
-
Morrison, J.S. 1977. ‘Two Unresolved Difficulties in the Line and Cave’. Phronesis 22, 212-231.
-
Murphy, N.R. 1951. The Interpretation of Plato’s Republic. Reprint, London: Oxford University Press, 1960.
-
Nettleship, R.L. 1961. Lectures on the Republic of Plato. Reprint, Honolulu: University Press of the Pacific, 2003.
-
Patterson, R. 1985. Image and Reality in Plato’s Metaphysics. Indianapolis: Hackett Publishing.
-
Pritchard, P. 1995. Plato’s Philosophy of Mathematics. Sankt Augustin: Academia Verlag.
-
Raven, J.E. 1965. Plato’s Thought in the Making. Cambridge; Cambridge University Press.
-
Reeve, C.D.C. trans. 2016. Metaphysics. Indianapolis: Hackett Publishing Company, Inc.
-
Robins, I. 1995. ‘Mathematics and the Conversion of the Mind: Republic vii 522c1-531e3’. Ancient Philosophy 15, 359-391.
-
Robinson, R. 1953. Plato’s Earlier Dialectic, 2nd ed. London: Oxford University Press.
-
Ross, D. 1951. Plato’s Theory of Ideas. Oxford: Clarendon Press.
-
Smith, N.D. 1981. ‘The Objects of Dianoia in Plato’s Divided Line’. Apeiron 15, 129-137.
-
Smith, N.D. 1996. ‘Plato’s Divided Line’. Ancient Philosophy 16, 25-46.
-
Wedberg, A. 1955. Plato’s Philosophy of Mathematics. Stockholm: Almqvist and Wiksell.
-
Wilson, J.C. 1904. ‘On the Platonist Doctrine of the ὰσύµβλητοι ἀριθµοί’. The Classical Review 18, 247-260. http://dx.doi.org/10.1017/S0009840X00990176.
| Insgesamt | Letzte 365 Tage | In den letzten 30 Tagen | |
|---|---|---|---|
| Aufrufe von Kurzbeschreibungen | 1148 | 127 | 12 |
| Gesamttextansichten | 521 | 6 | 0 |
| PDF-Downloads | 461 | 13 | 0 |
Mathematics, Mental Imagery, and Ontology: A New Interpretation of the Divided Line
in The International Journal of the Platonic TraditionSearch for other papers by Miriam Byrd in
Current site
Google Scholar
PubMed
Abstract
This paper presents a new interpretation of the objects of dianoia in Plato’s divided line, contending that they are mental images of the Forms hypothesized by the dianoetic reasoner. The paper is divided into two parts. A survey of the contemporary debate over the identity of the objects of dianoia yields three criteria a successful interpretation should meet. Then, it is argued that the mental images interpretation, in addition to proving consistent with key passages in the middle books of the Republic, better meets those criteria than do any of the three main positions.
| Insgesamt | Letzte 365 Tage | In den letzten 30 Tagen | |
|---|---|---|---|
| Aufrufe von Kurzbeschreibungen | 1148 | 127 | 12 |
| Gesamttextansichten | 521 | 6 | 0 |
| PDF-Downloads | 461 | 13 | 0 |
