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Plato’s Parmenides

Thomas J. McFarlane
1 December 1998
Revised 3 March 2004

www.integralscience.org

ABSTRACT: Plato’s Parmenides is one of the most influential of all Platonic dialogues. At the same time, it is perhaps the most difficult to understand, and there is no scholarly consensus on its interpretation. By way of introduction to this important dialogue, the first part of this paper discusses the philosophies of Pythagoras, Parmenides of Elea, and Heraclitus. With this philosophical context in mind, we review Plato’s theory of Forms and then focus on the content and structure of the Parmenides dialogue itself. We conclude by examining several interpretations of the dialogue.

Pythagoras, Parmenides, and Heraclitus

Plato’s Parmenides is generally recognized to be among the most important of all Plato’s writings.[1] Yet, both ancient and modern scholars have differed more on the interpretation of Plato’s Parmenides than on any of Plato’s other dialogues.[2] Among the many influential thinkers throughout the course of Western history who have been profoundly influenced by Plato’s Parmenides are Plotinus, Proclus, Dionysius the Areopagite, Nicholas of Cusa, and Hegel. An understanding of this important dialogue, however, must begin with those ancient presocratic philosophers who were most influential to Plato’s philosophy and the Parmenides in particular: Pythagoras, Parmenides, and Heraclitus.

Pythagoras, the earliest of these figures, taught that all things are number, and that the cosmos is created and governed by numerical principles. In the Pythagorean cosmogenesis, the derivation of the multiplicity of things in the world from an original unity is identical to the derivation of the numbers from the numerical unit, one. Moreover, this identity is made manifest in the mathematical order of the cosmos, as exemplified in the mathematical ratios of the musical scales and the geometrical principles that govern spatial extension. The Pythagoreans saw in all things combinations of eternal principles, such as Limit and Unlimited, One and Many, At Rest and In Motion. This Pythagorean vision, which sees the material world of becoming as imitating the mathematical world of being, provided the seminal insight at the foundation of Western science, both ancient and modern, and continues to manifest its profound influence today. Its influence on ancients such as Parmenides, Heraclitus, and Plato, however, was equally important, as we will now see.

Heraclitus is most well known for his doctrine that 'all flows' (panta chorei). This flux of all things is a perpetual becoming of life and death, which are unified in this process. More generally, he taught the dynamic unity of all opposites, that the flux of existing things is characterized by the transformation between pairs of contrary principles. This teaching is in apparent contrast with the static separation of substantial entities, since everything is One through the dynamic transforming of opposites into each other. Yet, Heraclitus sees structure in this flux, the structure being represented by the Logos that is present in both the world and the mind:

Listening not to me but to the logos, it is wise to agree that all things are one...They [the ignorant] do not comprehend how, in differing, it agrees with itself — a backward-turning connection, like that of a bow and a lyre.[3]

Parmenides, like Heraclitus, affirmed the One. But while Heraclitus had affirmed a One that is a contradictory union of opposites, Parmenides affirmed a One that apparently admits no opposites. And while Heraclitus embraced becoming, Parmenides emphasized being. It was to Parmenides contrary to the logos for any real change to take place at all. In particular, it was impossible for a One Being to become many. For if the unity and being of the One are taken seriously, the One cannot in reality become other than what it already is—no manifold world can actually proceed out of the One, no opposites actually exist to transform into each other. Therefore plurality, becoming, change, motion, flux, and so on, are not real, despite what our senses may lead us to believe.[5] As Parmenides writes:

Being is ungenerated and indestructible, whole, of one kind and unwavering, and complete. Nor was it, nor will it be, since now it is, all together, one, continuous...That it came from what is not I shall not allow you to say or think — for it is not sayable or thinkable that it is not...How might what is then perish? How might it come into being? For if it came into being it is not, nor is it if it is ever going to be. Thus generation is quenched and perishing unheard of.[6]

Parmenides’ doctrine appears at first to be in dramatic contrast to Heraclitus’ doctrine that everything is in flux. However, these two doctrines can also be seen as two approaches to teaching the same thing, namely, that reality is not a plurality of static entities. For Parmenides, the only reality is the One, and the diverse appearances do not truly change because they do not truly exist in the first place. For Heraclitus, the diverse appearances change and therefore opposites do not exist independent of each other, thereby pointing to their unity in the One. Neither Heraclitus nor Parmenides, however, provided an entirely satisfactory philosophical solution to the problem of relating being and becoming. Without an explanation of how becoming relates to being, how the Many relates to the One, philosophers could find no rational understanding of diverse appearances. As J. N. Findlay put it, “Heracliteans...could predicate nothing of anything since all was in flux, whereas the Eleatics could predicate nothing of anything since what there was, was only itself. All these difficulties were afterwards to be made thematic in the late Dialogues Parmenides and Sophist, but Plato’s whole thought was, from the very beginning, a partial protest against it.”[7] Thus, it was left for Plato to provide an account (logos) of the relationship between being and becoming that acknowledges these subtleties.

Plato’s Theory of Forms

Plato’s theory of ideas, or forms, is generally regarded as the belief in eternal, unchanging, qualities or principles, existing independent of the changing world of phenomena.[8] Aristotle in Metaphysics A, 987 a 30 gives us a report of how Plato arrived at the theory of Forms:

From youth on, Plato had first been a disciple of Cratylus and his Heraclitean opinions: that all sensibles are ever in a state of flux, and that there is no knowledge concerning them. These theories he held later also. While Socrates was preoccupied with Ethics and not at all with nature as a whole, yet in the former he sought for the universal and was the first to reflect upon definitions. Plato, who had accepted the theories of Cratylus, was thus led to believe that the Socratic search was concerned with other than sensible things. For it was impossible for a universal definition to be that of a particular sensible, since sensibles are forever changing. It thus came about that he called this kind of reality Forms (eide) and maintained that sensibles exist side by side with them and are named after them.

The most famous account of the theory of forms by Plato himself is in the Republic, where the intelligible world of being is distinguished from the sensible world of becoming. Each of these two realms is then divided into higher and lower parts, resulting in a total of four, as shown in the diagram below. Note that the divisions apply not only to the objects of knowledge, but to the organs of knowledge as well, for the organ of knowledge must be suited to its object.

Intelligible	Highest forms represented only in the mind; Dialectical questioning of assumptions leading to insight (nous, noesis);
	Mathematical and other forms represented by sensible images; Logical reasoning and argumentation based on assumptions (dianoia)
Sensible	Objects of sensible world; Perceptions based on unquestioned belief (pistis) or opinion (doxa)
	Images and shadows of sensible objects; Capacity to receive sensible images (eikasia)

One description that Plato gives for the relationship between the intelligible forms and sensible objects is that a form is a general pattern that has various objects as specific instantiations. Another way of describing the relationship is to say that objects acquire intelligible properties by virtue of their participation in the forms corresponding to those properties. For example, a carpenter who is building a roof might join a collection of wooden beams to form a triangle. The carpenter might then construct several more of these triangles and fix them along the length of the roof with equal spacing between them. These wooden triangles are objects of the sensible world, and their shadows cast on the ground by the sun are images of sensible objects. Similarly, these wooden triangles are themselves sensible instantiations or physical representations of the mathematical form of a triangle. We only recognize the wooden triangles as triangles because we recognize that the beams partake of the properties of an intelligible triangle. This mathematical form is not an object of our sensible perceptions, however, but rather an object of reason. The carpenter, for example, may have reasoned and made mathematical calculations in order to clearly know the intelligible form of the triangle that needed to be used as a pattern for the wooden triangles. These reasonings, however, are based on assumptions, such as the axioms of Euclidean geometry. If these axioms are accepted and applied without question, then this knowledge of the triangle is tainted by belief and opinion. Such knowledge is, as it were, a shadow of the pure form of the triangle, which is approached only through dialectic and known completely only through unmediated insight. Yet, insofar as we recognize already a triangle at any of the lower levels, we participate, albeit imperfectly, in this complete knowledge of the pure form of the triangle.

Examples such as the one just given above illustrate the participation of objects at lower levels in forms at higher levels. These illustrations, however, do not make explicit the precise nature of participation, or how exactly sensible objects of becoming are related to unchanging intelligible forms. In particular, how does Plato’s theory of forms overcome the fundamental problems, pointed out by Parmenides and Heraclitus, associated with relating the realm of being with the realm of becoming? The answer to this question is to be found in the Parmenides, where Plato himself offers a serious critique of the theory of forms.

Parmenides, Part I: The Critique of the Forms

The first half of the Parmenides is a critique of the theory of forms. The main characters of the dialogue are Socrates (who was then quite young), Zeno (who was nearing forty), and Parmenides (who was well advanced in years). Zeno has just presented his argument that if there are a plurality of entities, they must be both like and unlike, which is impossible. The young Socrates replies that there is really nothing so absurd in the coincidence of opposites in sensible objects, for that happens all the time. What would really be amazing, Socrates suggests, is if there were such contradiction in the realm of the intelligible forms. At this point, Parmenides begins to question Socrates about the forms. The young Socrates answers that he believes that forms exist apart (choris) from the instances that share in them, and they provide unique patterns for things. This is the standard doctrine of the forms as presented in the Phaedo and the Republic.

With this admission by the young Socrates, Parmenides then begins a lengthy and thorough critique of this doctrine, showing all the various problems and contradictions that result from holding that the forms exist apart from each other and from sensible things. The last, and perhaps worst, of the problems is that if the forms exist in the realm of being apart from the changing objects of the sensible world, then there can be no intelligible relation between the two. Consequently, we cannot know the forms. In addition, even if there were supersensible gods who could know the forms, they could not know us or the world of sensible objects. Parmenides thus shows that the theory of forms, at least on the face of it, is not intelligible. Yet, he goes on to admit that the forms are necessary:

These difficulties and many more besides are inevitably involved in the forms, if these characters of things really exist and one is going to distinguish each form as a thing just by itself. The result is that the hearer is perplexed and inclined either to question their existence, or to contend that, if they do exist, they must certainly be unknowable by our human nature...But on the other hand, Parmenides continued, if, in view of all these difficulties and others like them, a man refuses to admit that forms of things exist or to distinguish a definite form in every case, he will have nothing on which to fix his thought, so long as he will not allow that each thing has a character which is always the same, and in so doing he will completely destroy the significance of all discourse.[9]

At this point in the dialogue, the young Socrates is at a total loss. Parmenides has decisively demolished the theory of forms, or at least Socrates’ understanding of it. Yet, without the forms, there is no possibility of any intelligible thought or discourse whatsoever, and our minds will become a Heraclitean flux of perpetually changing contradictions. At this point of aporia, Parmenides explains to the young Socrates where he went wrong:

You are undertaking to define ‘beautiful,’ ‘just,’ ‘good,’ and other particular forms, too soon, before you have had a preliminary training...You must make an effort and submit yourself, while you are still young, to a severer training in what the world calls idle talk and condemns as useless. Otherwise, truth will escape you.[10]

The young Socrates is in trouble because he has been reasoning about the forms as unquestioned axioms. In order to see the true nature of the forms, Socrates must train himself in dialectic and question the very nature of the forms themselves. Parmenides elaborates on the manner of dialectical exercise as follows:

If you want to be thoroughly exercised, you must not merely make the supposition that such and such a thing is and then consider the consequences; you must also take the supposition that that same thing is not...In a word, whenever you suppose that anything whatsoever exists or does not exist or has any other character, you ought to consider the consequences with reference to itself and to any one of the other things that you may select, or several of them, or all of them together, and again you must study these others with reference both to one another and to any one thing you may select, whether you have assumed the thing to exist or not to exist, if you are really going to make out the truth after a complete course of discipline...Most people are unaware that you cannot hit upon truth and gain understanding without ranging in this way over the whole field.[11]

With this prelude, Parmenides then proceeds with an illustration of the dialectical exercise, taking as his supposition the One.

Parmenides, Part 2: The Dialectical Exercise

The second half of the Parmenides is essentially a monologue by Parmenides. Based on what was stated in the first half of the dialogue, we can expect Parmenides to range over the whole field and hit upon the truth of the One. Based on the historical background, as well as the discussion of the forms in the first half, we can also expect this exercise to illuminate the nature of the forms and their relation to the sensible world.

The dialectical exercise is naturally divided into eight parts. For each of the two hypotheses, if the One is and if the One is not, we examine the consequences for the One, and the consequences for the Others. This alone would give four parts. Plato, however, adds a subtle but very important distinction to the exercise after it is started. He distinguishes between the One which has being and the bare One. There are then a total of eight hypotheses:

Hyp.	If...	Consequences for...	Results
I	One	the One	negative
II	One is	the One	positive
III	One is	the Others	positive
IV	One	the Others	negative
V	One is not	the One	positive
VI	not One	the One	negative
VII	One is not	the Others	positive
VIII	not One	the Others	negative

The results of the hypotheses follow a general pattern. In the case of hypotheses II, III, V, VII that predicate being of the One (or of the not One), the results deduced by Parmenides are positive. In these cases, predication is possible and positive statements are made of the One (or of the not One). In the case of hypotheses I, IV, VI, VIII that do not predicate being of the One (or of the not One), the results deduced by Parmenides are negative. In these cases, predication is not possible and nothing may be asserted of the subject.

Hypothesis I

This hypothesis demonstrates that from the bare One which negates all plurality, nothing can be deduced or evolved. It is interesting to observe at this point that the historical Parmenides, who asserted the absolute unity and indivisibility of the One, was logical in so far as he deduced that there could be no ‘Others’, no plurality of real things, and no world of sensible appearances. But he was not justified when he gave to his One various other attributes. As Plato has here shown, the true One cannot even exist or be the object of any kind of knowledge.[12] Thus, the bare One cannot give rise to the Pythagorean evolution, starting from this original One and leading to the sensible world.

Hypothesis II

Hypothesis III to VIII

Hypothesis VII and Hypothesis VIII are concerned with the consequences for the Others of the negative supposition that ‘there is no One’. The Hypothesis ‘if there is no One’ can be taken to mean ‘suppose that there exists nothing that can be called “one thing” (en)’. We can then inquire whether there is anything that, without being ‘one thing’ can nevertheless have some sort of existence. Alternatively, we can understand ‘if there is no One’ to mean: ‘suppose that no one thing has any sort of being’, where we take ‘one thing’ as equivalent to ‘an entity’. If there is no such thing as ‘an entity’, then there is not only no ‘One’ but no ‘Others’; in fact, there is nothing at all.[20]

Interpretations of Parmenides

The primary difficulty in the interpretation of the Parmenides is understanding the second half. Indeed, even to give a literal reading of the dialectical exercises poses problems and demands interpretation. Accordingly, the summary above has followed the modern interpretation of Cornford.

The standard interpretation of the Parmenides up until the nineteenth century was given in the Enneads of Plotinus. This ‘metaphysical’ interpretation of the Parmenides is given in Enn. V, 1 ‘On the Three Principal Hypostases’, which provides, from chapter 8 on, an exegesis of the latter part of the Parmenides, particularly of the First Hypothesis.[21] Proclus later provided another important Neoplatonic treatise in his Commentary on Plato’s Parmenides. On this interpretation, the hypotheses are not merely clarifications in the use of language, as modern analytical philosophers tend to view them. Cornford, for example, views the dialectical exercise as primarily designed to clarify ambiguities in language:

A main purpose of the whole exercise must be to point out that even the apparently simplest terms, such as ‘one’ and ‘being’, which will appear at the threshold of any metaphysical discussion, are dangerously ambiguous.[22]

There can be little doubt that Plato, whose philosophy places no small importance upon clear definitions, wrote the Parmenides with the intention to make certain subtle distinctions that Parmenides had failed to make. For the Neoplatonists such as Plotinus and Proclus, however, Plato’s purpose goes far beyond the making of subtle linguistic distinctions. The exercise in dialectic provides symbolic and numinous adumbrations of the nature of the superessential One and how one might approach it. The negative conclusions of the first Hypothesis, for example, are not illustrations of the nonsensical nature of the pure One. Rather, they demonstrate the failure of reason and language to grasp the ineffable non-relative One that rises above all forms of relative knowledge. The dialectical exercise, which ranges over the whole field of discourse and considers all the logical permutations of any proposition, is a meditation for freeing the mind from clinging to any one philosophical position or assumption, thereby opening it up to mystical illumination. It is the Platonic via negativa. As Proclus writes,

As by opinion we know the objects of opinion, and as we know by discursive intellect (dianoia) the objects of that faculty, and as by the intuitive intellectual element (noeron) in us we know the object of intellect, even so it is by the One that we know the One. This is the same as saying that it is by Not-Being that we know the One, and this in turn is equivalent to saying that it is by negation that we know the One.[23]

If we are to take seriously the more than two thousand years of metaphysical interpretation of Parmenides, and Plato’s philosophy in general, then we must at least be willing to consider the possibility that, in the words of J. N. Findlay, “The Platonic Dialogues...point beyond themselves, and without going beyond them they are not to be understood.”[24] Findlay is referring to two types of ‘pointing beyond’. Firstly, they literally point beyond themselves (e.g., in Phaedrus 275-6) by stating the superiority of oral over written exposition, and by repeatedly referring to a more thorough treatment that must occur ‘elsewhere’.[25] Secondly, in view of the fact that illuminated knowledge of supersensibles is part of Plato’s very philosophy, we should not expect to understand it if we insist on reducing it to a collection of concepts and words. As Findlay puts it, “Those unable or unwilling to draw conclusions from more or less palpable hints, or constitutionally unable to understand metaphysical or mystical utterances, or to enter into mystical feelings...should certainly never engage in the interpretation of Plato.”[26] With this intriguing perspective on Plato’s philosophy, let us take a closer look at Findlay’s interpretation of the Parmenides.

Regarding the purpose of the dialectic exercise, Findlay writes:

The lesson of the whole eightfold exercise carried out by Parmenides-Plato is, however, sufficiently clear: that talk about the Eide, as of some iridescent object, constantly challenges us to change our point of view, so that what is truly said at one position, and from one angle, has to be recanted at the next, the whole truth of the situation somehow lying in the complete round of our utterances.[27]

Findlay describes the truth lying in the First Hypothesis as follows:

What Plato-Parmenides is stressing in this First Hypothesis is that, in addition to their instantiability or eidetic causality, and in addition to their higher relations with one another, Eide also have an own-being, or narrowly intrinsic content, which distinguishes them from all other Eide, and which, in the case of the simpler, more ultimate Eide, can be simply enjoyed, but not further elucidated or talked about. To penetrate to this eidetic nucleus, through the penumbra of instantiation, and the corona of eidetic interrelations, is necessarily to perform a mystical or transcendental act par excellence, and almost necessarily to experience the characteristic aura of mysticism.[28]

With the emphasis on the mystical element in Plato, Findlay’s interpretation has clear kinship to that of Proclus and Plotinus. Findlay, however, is writing in the 20th century, and thus offers a unique version of the mystical interpretation. Let us, then, consider what insight he might provide into the problems of the forms that are the subject of the Parmenides:

It is incredibly wrong to treat Platonism as a form of dualism, as involving the postulation of a second world of detached meanings over against the solid world of particular things. If Plato believed or disbelieved anything, he disbelieved in the genuine being of particular things: eternal Natures may for him be changeably and inadequately instantiated, but there is nothing substantial, nothing ontically ontic, in such instantiations. They enter merely into the description of what Eide are and what they do.[29]

Platonism is the view that there are no instances...Eide alone are, and Eide are instantiated, but such instantiation does not create a shadowy world of Eidos-copies, in any other but a transformed reducible sense...The Eide are the living Meanings or Natures whose force is felt in all instantiation, and whose sense creates all understanding, and in neither existence or experience is there anything substantial to be laid hold of apart from them.[30]

The supremacy ascribed to the Principle of Unity or Good in the proposed dialectical deduction [of Eide from First Principles], shows that the system to be elaborated was only in appearance dualistic: the multidimensional media in which Unity disported itself must in the end prove to be wholly a reflex and an internal avocation of Unity Itself. The dialogue Parmenides goes some distance in suggesting how this can be so, and how in the most aloof notion of Unity Itself all multiplicity and variety is necessarily locked up.[31]

The Eide and the eidetic Knowledge of them are essentially two-sided: being what they are, and being all that anything is or could be, they have not only a side intrinsic to themselves, but also one that is extrinsic or for other things, and this second side can, on profounder reflection, be seen to be entirely dependent on the first side, so that knowing what an Eidos is goes with knowing how it could be instantiated and vice versa. This is, however, the lesson to be learnt from the dialectical exercise in the Second Part of the Dialogue.[32]

These passages suggest a non-dualistic interpretation of Plato’s theory of forms. As the Parmenides shows, it is a naive understanding of the forms to take them to be isolated, static patterns set in stark contrast with the changing phenomena of a sensory world. Instead, Findlay offers an interpretation on which the forms are interpenetrating principles that are not other than their own instantiations. The realms of being and becoming do not separate forms from sensible objects; rather, being and becoming are both implicit in the nature of the forms. As Plato wrote,

By Heaven, can we be ready to believe that the absolutely real has no share in movement, life, soul or wisdom? That it does not live or think, but in solemn holiness, unpossessed of mind, stands entirely at rest? That would be a dreadful thing to admit.[33]

Annotated Bibliography

Allen, R. E. (1983), Plato’s Parmenides: Translation and Analysis (Minneapolis: University of Minnesota Press).

This scholarly translation and interpretation of Parmenides uses the structure of the dialogue and a guide to interpreting individual passages. In addition to presenting his own interpretation, Allen critically discuses interpretations of other modern scholars.

Barnes, Jonathan (1987), Early Greek Philosophy (London: Penguin Books).

This anthology of major presocratic philosophical writings includes an introduction and overview of early Greek philosophy. In particular, it presents translations of surviving fragments by and about Parmenides and Zeno, who both appear as characters in the Parmenides.

Cornford, Francis M. (1957), From Religion to Philosophy: A Study in the Origins of Western Speculation (New York: Harper & Brothers).

This major work by a distinguished historian of ancient philosophy examines the religious and mythological roots of Greek philosophical thought. It provides insight into and background for early Greek philosophy in general.

Cornford, Francis M. (1939), Plato and Parmenides: Parmenides’ Way of Truth and Plato’s Parmenides (Indianapolis: The Bobbs-Merrill Company, Inc.).

This translation of Parmenides’ Way of Truth and Plato’s Parmenides is accompanied by an introduction and running commentary by F. M. Cornford. The introduction presents a useful overview of the various ancient and modern interpretations of Parmenides.

Findlay, J. N. (1974), Plato: The Written and Unwritten Doctrines (New York: Humanities Press).

This treatise on Plato’s philosophy is based on a combined study of Plato, Plotinus, the Metaphysics of Aristotle, as well as other ancient secondary sources on Plato’s written and unwritten doctrines. A chapter of the book is concerned with the Parmenides.

Grube, G. M. A. (1935), Plato’s Thought (London: Methuen).

This book is an introduction to Plato’s philosophy by a respected scholar. In addition to a detailed discussion of the theory of forms, it contains a discussion of Plato’s critique of this theory in the Parmenides.

Heidegger, Martin (1998), Parmenides , André Schuwer and Richard Rojcewicz, tr., (Bloomington: Indiana University Press).

This book is a translation of a lecture course delivered by Heidegger at the University of Freiburg during 1942-1943. Heidegger presents an original and provocative view of early Greek thought with a focus on the primordial understanding of truth in Parmenides’ didactic poem.

Honderich, Ted, ed. (1995), The Oxford Companion to Philosophy, (Oxford: Oxford University Press).

This comprehensive reference book contains entries on philosophers, schools of thought, and other subjects covering the whole history of philosophy.

Miller, Mitchell H., Jr. (1986), Plato’s Parmenides: The Conversion of the Soul (University Park: The Pennsylvania State University Press).

In this scholarly interpretation of Parmenides, the dialogue is interpreted with a view to its dramatic structure as well as its arguments. In particular, by recognition of the use of mimetic irony in the dialogue, Miller claims to resolve certain interpretive ambiguities.

Proclus (1987), Commentary on Plato’s Parmenides, Glenn R. Morrow and John M. Dillon tr., (Princeton: Princeton University Press).

This major work of the great Neoplatonist philosopher Proclus profoundly influenced medieval and Renaissance thought and thus represents the most historically important interpretation of Plato’s Parmenides.

Turnbull, Robert G. (1998), The Parmenides and Plato’s Late Philosophy: Translation of and Commentary on the Parmenides with Interpretive Chapters on the Timaeus, the Theaetetus, the Sophist, and the Philebus (Toronto: University of Toronto Press).

This book contains a scholarly translation and detailed commentary of Parmenides. Turnbull argues that in Parmenides Plato abandoned his theory of form participation presented in Phaedo. Turnbull’s interpretation rejects most modern accounts and draws from Aristotle, Euclid, and Plotinus.

End Notes

(c) 1998 Thomas J McFarlane