Parmenides () is one of the dialogues of Plato. It is widely considered to be the most challenging and enigmatic of Plato's dialogues."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, p. 3.Gill, Mary Louise. Parmenides. p. 1. Hackett 1996.Meinwald, p. 367. 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. The dialogue is set during a supposed meeting between Parmenides and Zeno of Elea in Socrates' home city of Athens. The dialogue is chronologically the earliest of all, as Socrates is only nineteen years old, so he takes the unusual position of the student, while Parmenides serves as the lecturer.
Most scholars agree that the dialogue does not record historic conversations and is most likely an invention by Plato.
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 a distinction between sensibles, on one hand, and Forms (in which sensibles participate) on the other—then it is the Form of Likeness that cannot be, and is not, unlike, while one and the same sensible thing can indeed be simultaneously like and unlike (or one and many), by participating in the Forms of both Likeness and Unlikeness (or both Unity and Plurality):
Hence, concludes Socrates, there is no problem in demonstrating that sensible things may have opposite attributes; what would cause consternation—and earn his admiration—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; these can be summarized as follows:
Argument 1. (130e–131e) If particular things come to partake of the Form of Beauty or Likeness or Largeness, they thereby become beautiful or alike or large. Parmenides presses Socrates on how, precisely, many particulars can participate in a single Form. On 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 places at once. 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 that they all share—viz., the character of Largeness. But if Largeness is also, in some sense, considered to be large, then there is a further series of large things: the original set, plus Largeness itself; and if all members of this series partake of a single Form, then there must be another Largeness, of which large things and the first Form of Largeness partake. But if this second Form of Largeness is also large, then there should be a third Form of Largeness 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 more famously known under the name given to it by Aristotle: that is, as the Third Man Argument.
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 that 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 (; "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) Parmenides calls this argument the "greatest" of the "difficulties" to which the theory of Forms is subject, and so it has often been dubbed the "greatest difficulty" (Gk. , megístē aporía—though Plato himself never uses exactly this phrase) argument. Interpretation of this argument is particularly divisive; what follows is one possible reconstruction: Forms are separate from the sensible world; if a given Form is essentially relative—i.e., cannot be defined without reference to another entity, as "master" cannot be defined without something of which to be master—it must be other Forms to which it is relative. Similarly for the sensible things of our world: if such a thing is what it is relative to something else, the "something else" must also be of the sensible realm. The Form of Mastership has its being relative to the Form of Slavery; a master in our world, however, can only be master of a particular slave or set of slaves—no terrestrial master is master of Slave itself, and no terrestrial slave is subject to Mastership itself. So it is with knowledge, which too is essentially relational (being always knowledge of something): all our knowledge is such with respect to our world, not to the world of the Forms; ideal Knowledge, conversely, is knowledge not of the things 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 neither can their ideal mastership rule us.
In spite of Socrates' inability to defend the theory against Parmenides' arguments, in the succeeding 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. One of the second part is "whether Plato was committed to any of the arguments developed in the second part of the dialogue." 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 second part of the dialogue can be divided thus:
Hypothesis/Deduction n. 1 (137c-142a): If it is one. The one cannot be made up of parts, because then the one would be made of many. Nor can it be a whole, because wholes are made of parts. Thus the one has no parts and is not a whole. It has not a beginning, a middle nor an end because these are parts, it is therefore unlimited. It has no shape because it is neither linear nor circular: a circle has parts all equidistant from the centre, but the one has no parts nor a centre; It is not a line because a line has a middle and two extremes, which the one cannot have. Thus the one has no shape. The one cannot be in anything nor in itself. If it was in another it would be all surrounded and by what it is inside and would be touched at many parts by what contains it, but the one has no parts and thus cannot be inside something else. If it were in itself it would contain itself, but if it is contained then it is different from what contains it and thus the one would be two. The one cannot move because movement is change or change in position. It cannot change because it has no parts to change. If it moves position it moves either circularly or linearly. If it spins in place its outer part revolves around its middle but the one has neither. If it moves its position it moves through something else, which it cannot be inside. Thus the one does not move. The one must be itself and cannot be different from it. The one does not take part in the flowing of time so it is imperishable.
Hypothesis/Deduction n. 2 (142b–155e): If the one is. The one is, it must be and it is part of being. The one is part of being and vice versa. Being is a part of the one, the one is a whole that is a group of sections. The one does not participate in the being, so it must be a single part. Being is unlimited and is contained in everything, however big or small it is. So, since the one is part of being, it is divided into as many parts as being, thus it is unfinished. The parts are themselves sections of a whole, the whole is delimited, confirming the presence of a beginning, a centre, and an end. Therefore, since the centre is itself at the same distance from the beginning and the end, the one must have a form: linear, spherical, or mixed. If the whole is in some of its parts, it will be the plus into the minus, and different from itself. The one is also elsewhere, it is stationary and in movement at the same time.
The Appendix to the First Two Deductions 155e–157b