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Parmenides is one of the dialogues of Plato. It is widely considered to be one of the more, if not the most, challenging and enigmatic of Plato's dialogues.  The Parmenides purports to be an account of a meeting between the two great philosophers of the Eleatic school, Parmenides and Zeno of Elea, and a young Socrates. The occasion of the meeting was the reading by Zeno of his treatise defending Parmenidean monism against those partisans of plurality who asserted that Parmenides' supposition that there is a one gives rise to intolerable absurdities and contradictions.
Discussion with Socrates 
The heart of the dialogue opens with a challenge by Socrates to the elder and revered Parmenides and Zeno. Employing his customary method of attack, the reductio ad absurdum, Zeno has argued that if as the pluralists say things are many, then they will be both like and unlike; but this is an impossible situation, for unlike things cannot be like, nor like things unlike. But this difficulty vanishes, says Socrates, if we are prepared to make the distinction between sensibles on the one hand and Forms, in which sensibles participate, on the other. Thus one and the same thing can be both like and unlike, or one and many, by participating in the Forms of Likeness and Unlikeness, of Unity and Plurality; I am one man, and as such partake of the Form of Unity, but I also have many parts and in this respect I partake of the Form of Plurality. There is no problem in demonstrating that sensible things may have opposite attributes; what would cause consternation, and earn the admiration of Socrates, would be if someone were to show that the Forms themselves were capable of admitting contrary predicates.
At this point, Parmenides takes over as Socrates' interlocutor and dominates the remainder of the dialogue. After establishing that Socrates himself has made the distinction between Forms and sensibles, Parmenides asks him what sorts of Form he is prepared to recognize. Socrates replies that he has no doubt about the existence of mathematical, ethical and aesthetic Forms (e.g., Unity, Plurality, Goodness, Beauty), but is unsure of Forms of Man, Fire and Water; he is almost certain, though admits to some reservations, that undignified objects like hair, mud and dirt do not have Forms. Parmenides suggests that when he is older and more committed to philosophy, he will consider all the consequences of his theory, even regarding seemingly insignificant objects like hair and mud.
For the remainder of the first part of the dialogue, Parmenides draws Socrates out on certain aspects of the Theory of Forms and in the process brings to bear five arguments against the theory.
Argument 1. (130e-131e) If particular things come to partake of the Form of Beauty or Likeness or Largeness they thereby become beautiful or like or large. Parmenides presses Socrates on how precisely many particulars can participate in a single Form. On the one hand, if the Form as a whole is present in each of its many instances, then it would as a whole be in numerically different places, and thus separate from itself. Socrates suggests that the Form might be like a day, and thus present in many things at one. Parmenides counters that this would be little different from a single sail covering a number of people, wherein different parts touch different individuals; consequently, the Form is many.
Argument 2. (132a-b) Socrates' reason for believing in the existence of a single Form in each case is that when he views a number of (say) large things, there appears to be a single character which they all share, viz. the character of Largeness. But consider the series of large things: x,y,z, Largeness itself. But the Large itself is also in some sense considered to be large, and if all members of this series partake of a single Form, then there must be another Large in which large things and the first Form of Large partake. But if this second Form of Large is also large, then there should be a third Form of Large over the large things and the first two Forms, and so on ad infinitum. Hence, instead of there being one Form in every case, we are confronted with an indefinite number. This Largeness regress is commonly known under the name given to it by Aristotle, the famous Third Man Argument (TMA).
Argument 3. (132b-c) To the suggestion that each Form is a thought existing in a soul, thus maintaining the unity of the Form, Parmenides replies that a thought must be a thought of something that is a Form. Thus we still have to explain the participation relation. Further, if things share in Forms which are no more than thoughts, then either things consist of thoughts and think, or else they are thoughts, yet do not think.
Argument 4. (132c-133a) Socrates now suggests that the Forms are patterns in nature (paradeigmata - paradigms) of which the many instances are copies or likenesses. Parmenides argues that if the many instances are like the Forms, then the Forms are like their instances. Yet if things are like, then they come to be like by participating in Likeness; therefore Likeness is like the likeness in concrete things, and another regress is generated.
Argument 5. (133a-134e) Called the "greatest difficulty" (133a) by Parmenides, the theory of Forms arises as a consequence of the assertion of the separate existence of the Forms. Forms do not exist in our world but have their being with reference to one another in their own world. Similarly, things of our world are related among themselves, but not to Forms. Just as Mastership has its being relative to Slavery, so mastership in our world has its being relative to slavery in our world. No terrestrial master is master of Slave itself, and no terrestrial master-slave relation has any relationship to the ideal Master-Slave relation. And so it is with knowledge. All our knowledge is such with respect to our world, not to the world of the Forms, while ideal Knowledge is knowledge of the things not of our world but of the world of the Forms. Hence, we cannot know the Forms. What is more, the gods who dwell in the divine world, can have no knowledge of us, and nor can their ideal mastership rule us.
In spite of Socrates' inability to defend the theory against Parmenides' arguments, in the following transitional section of the dialogue Parmenides himself appears to advocate the theory. He insists that without Forms there can be no possibility of dialectic, and that Socrates was unable to uphold the theory because he has been insufficiently exercised. There follows a description of the kind of exercise, or training, that Parmenides recommends. The remainder of the dialogue is taken up with an actual performance of such an exercise, where a young Aristoteles (later a member of the Thirty Tyrants, not to be confused with Plato's eventual student Aristotle) takes the place of Socrates as Parmenides' interlocutor.
Discussion with Aristoteles 
This difficult second part of the dialogue is generally agreed to be one of the most challenging, and sometimes bizarre, pieces in the whole of the Platonic corpus. It consists of an unrelenting series of difficult and subtle arguments, where the exchange is stripped of all but the bare essentials of the arguments involved. Gone are the drama and colour we are accustomed to from earlier dialogues.
The long, austere second half of the dialogue is organized as a series of eight (or alternatively, nine) deductions about the relation of the one to the many. The reasoning is often, as are Parmenides' arguments in the first section of the work, obscure, and at times appears to be blatantly fallacious. Further, the deductions appear to be set up in a way to deliberately produce antinomies, or mutually contradictory conclusions. A bare outline of the deductions runs as follows:
- Deduction 1 - Hypothesis: If it is one. Conclusion: The one is nothing, does not exist, and is not the object of perception, knowledge or opinion.
- Deduction 2 - Hypothesis: If the one is. Conclusion: The one is everything and is the object of perception, knowledge and opinion.
- Appendix to Deductions 1 and 2 - Hypothesis: If the one is one and many, neither one nor many, and in time. Conclusion: The one comes to be and passes away in an instant outside of time.
- Deduction 3 - Hypothesis: If the one is. Conclusion: The many have contrary properties.
- Deduction 4 - Hypothesis: If the one is. Conclusion: The one is not in the many and the many not in the one; the many have no properties.
- Deduction 5 - Hypothesis: If the one is not. Conclusion: The one comes to be and passes away and neither comes to be nor passes away.
- Deduction 6 - Hypothesis: If the one is not. Conclusion: The one is nothing and in no state.
- Deduction 7 - Hypothesis: If the one is not. Conclusion: The many have contrary properties.
- Deduction 8 - Hypothesis: If the one is not. Conclusion: Nothing exists.
A satisfactory characterisation of this part of the dialogue has eluded scholars since antiquity. Many thinkers have tried, among them Cornford, Russell, Ryle, and Owen; but few would accept without hesitation any of their characterisations as having got to the heart of the matter. Recent interpretations of the second part have been provided by Miller (1986), Meinwald (1991), Sayre (1996), Allen (1997), Turnbull (1998), Scolnicov (2003), and Rickless (2007). It is difficult to offer even a preliminary characterisation, since commentators disagree even on some of the more rudimentary features of any interpretation. The discussion, at the very least, concerns itself with topics close to Plato's heart in many of the later dialogues, such as Being, Sameness, Difference, and Unity; but any attempt to extract a moral from these passages invites contention.
Ancient Commentaries 
The Parmenides was the frequent subject of commentaries by Platonists and Neoplatonists. Important examples include those of Proclus and of Damascius, and an anonymous 3rd or 4th commentary possibly due to Porphyry. The 13th century translation of Proclus' commentary by Dominican friar William of Moerbeke stirred subsequent medieval interest (Klibansky, 1941). In the 15th century, Proclus' commentary influenced the philosophy of Nicolas of Cusa, and Neoplatonists Giovanni Pico della Mirandola and Marsilio Ficino penned a major commentaries. According to Ficino:
- "While Plato sprinkled the seeds of all wisdom throughout all his dialogues, yet he collected the precepts of moral philosophy in the books on the Republic, the whole of science in the Timaeus, and he comprehended the whole of theology in the Parmenides. And whereas in the other works he rises far above all other philosophers, in this one he seems to surpass even himself and to bring forth this work miraculously from the adytum of the divine mind and from the innermost sanctum of philosophy. Whosoever undertakes the reading of this sacred book shall first prepare himself in a sober mind and detached spirit, before he makes bold to tackle the mysteries of this heavenly work. For here Plato discusses his own thoughts most subtly: how the One itself is the principle of all things, which is above all things and from which all things are, and in what manner it is outside everything and in everything, and how everything is from it, through it, and toward it." (Klibansky, 1941)
See also 
- "The Parmenides has surely proven itself the most enigmatic of all Plato's dialogues. In spite of a sustained and extensive history of discussion, there is no positive consensus about the basic issues central to its interpretation." Miller 3
- Rickless b
- Gill, Mary Louise. Parmenides. p.1. Hackett 1996.
- Meinwald 367
- The third deduction is typically interpreted as a kind of appendix to the first two
Texts and Translations 
- Burnet, J., Plato Opera Vol. II (Oxford University Press, 1903). ISBN 978-0-19-814541-7 (Greek with critical apparatus).
- Fowler, H. N., Plato Vol. IV (Harvard University Press, 1926). ISBN 978-0-674-99185-9 (Greek and English)
- Zekl, H. G., Platon Parmenides (Meiner Verlag, 1972). ISBN 978-3-7873-0280-2 (Greek and German)
- Allen, R. E., Plato's Parmenides, Revised Edition (Yale University Press, 1997). ISBN 978-0-300-07729-2 (English with commentary)
- Cornford, F. M., Plato and Parmenides (Routledge, 1939). ISBN 978-0-415-22517-5 (English with commentary)
- Gill, M. L. and Ryan, P., Plato: Parmenides (Hackett Publishing, 1996). ISBN 978-0-87220-329-7 (English with notes)
- Scolnicov, S., Plato's Parmenides (University of California Press, 2003). ISBN 978-0-520-22403-2 (English with commentary)
- Turnbull, R., The Parmenides and Plato's Late Philosophy (University of Toronto Press, 1998). ISBN 978-0-8020-4236-1 (English with commentary)
- Bechtle, Gerald (ed.) An anonymous commentary on Plato's Parmenides. Oxford 1996.
- Cherniss, Harold: Parmenides and the Parmenides of Plato“, in: American Journal of Philology 53, 1932, S. 122–138.
- Doull, James (1999). "The Argument to the Hypotheses in "Parmenides"". Animus 4. ISSN 1209-0689. Retrieved August 9, 2011..
- Graeser, A. Prolegomena zu einer Interpretation des zweiten Teils des Platonischen Parmenides. Bern: Haupt, 1999.
- Graeser, Andreas: Platons Parmenides, Akademie der Wissenschaften und der Literatur, Mainz 2003
- Halfwassen, Jens: Der Aufstieg zum Einen - Untersuchungen zu Platon und Plotin, K.G. Saur Verlag, München und Leipzig 2006
- Klibansky, Raymond. "Plato’s Parmenides in the Middle Ages and the Renaissance: A Chapter in the History of Platonic Studies," Medieval and Renaissance Studies 1 (1941-3), 281-335.
- Kraut, Richard (eds). The Cambridge Companion to Plato. Cambridge. New York 1992.
- Lünstroth, Margarete: Teilhaben und Erleiden in Platons Parmenides. Untersuchungen zum Gebrauch von μετέχειν und πάσχειν Edition Ruprecht, Göttingen 2006, ISBN 978-3-7675-3080-5
- Malmsheimer, Arne: Platons Parmenides und Marsilio Ficinos Parmenides-Kommentar. Ein kritischer Vergleich (= Bochumer Studien zur Philosophie, Bd. 34), Amsterdam 2001. ISBN 90-6032-363-7 online
- Meinwald, Constance. "Goodbye to the Third Man" in Kraut pp. 365–396.
- Miller, Mitchell H. Jr. Plato's Parmenides: The Conversion of the Soul. Princeton 1986.
- Morrow, G.R., Dillon, J.M. (trs.), Proclus' commentary on Plato's Parmenides. Princeton University Press, 1987.
- Rickless, Samuel C.: Plato's forms in transition. A reading of the Parmenides, Cambridge 2007. ISBN 978-0-521-86456-5
- --"Plato's Parmenides" <http://plato.stanford.edu/entries/plato-parmenides/>
- Ryle, Gilbert: „Plato's Parmenides“, in: Mind 48, 1939, S. 129-51, 303-25.
- Suhr, Martin: Platons Kritik an den Eleaten. Vorschläge zur Interpretation des platonischen Dialogs ‚Parmenides‘, Hamburg, 1969.
- Turner, John D., Kevin Corrigan (ed.), Plato's Parmenides and Its Heritage, Volume 1: History and Interpretation from the Old Academy to later Platonism and Gnosticism. Writings from the Greco-Roman World Supplements 2. Atlanta: Society of Biblical Literature, 2010.
- Zekl, Hans Günter: Der Parmenides, N.G. Elwert Verlag, Marburg/Lahn, 1971.
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