The theory itself is attacked from four specific areas that deserve detailed treatment. But it may also be speculated that the dialogue Philebus is a mature response to the problems of the forms. This paper will attempt to link the criticism of the Parmenides with the likely solution in the Philebus, where some have held that the forms disappear altogether. If the Philebus represents Platos mature thought, then one may conclude that it is his later way of dealing with the criticism of the Parmenides.
The first argument that Parmenides offers (130e 4 131e) deals with the fundamental relation of the form itself to the particular. Parmenides offers two options: that the form is completely present in the particular, or that the form is divided into pieces in each particular. Of course, stated baldly like that, the theory cannot recover. If the former option, than the forms themselves must be replicated as many times as there are particulars. If the latter, the theory of forms is reduced to absurdity, since each particular has a slight sliver of the form.
One might hold that this entails the later Aristotelian theory of forms, where forms are instantiated individually in a specific thing. This entails for Aristotle that the universal be different from the form (in Plato, they are one in the same), while the form itself identifies the individual as individual only. Though it is hard to see how Parmenides actually meant this, or that Plato was beginning to lean toward what will become the Aristotelian theory of substance. But this concept may lead us to the eccentric argument in the Philebus.
Secondly, Socrates seems to respond that the forms are merely in the mind, that they are purely conceptual objects without any physical or spiritual reality outside the mind. This is a form of nominalism where only particulars actually exist, but the mental forms simply serve as regulative qualities, that is, serve as means of categorizing physical existence. But Parmenides retorts that such a view must be based on something. It must be based on a form. The argument here seems to be an argument for the forms than anything else.
If one holds the basic nominalist position that universals/forms are held only in the mind and exist nowhere else, then it does make sense to hold that such objects must refer to something, namely a form. This is an argument for the forms in that, since all people have universal objects in mind when categorizing the universe, these universal objects must have actual correlates. If this latter is not posited, then one is left in the Lockian position where a mechanism is theorized in the mind where the particular sensations are categorized into universals.
But holding that forms exist seems to be a simpler explanation than imagining the internal machine, some sort of modern agent intellect, that generates universals out of particulars. Third, Parmenides holds, in his most famous argument, that, as Socrates claims, participation is really another name for resemblance, then a serious problem arises. This problem is that resemblance implies that two objects resemble one another in at least one respect. But this resemblance cannot be left as a dyad, and hence, a third thing must join the two together.
This is the famed third man argument. If a form resembles a particular in the quality large for example, then there must be a third entity that itself is large. The relationship itself must have a form, in other words (Runciman, 1959). This leads to an infinite regress, the exact regress that the forms were partially designed to stop. The form, by definition is the ultimate entity that is uncreated. Lastly, Parmenides holds that something as pure as a form cannot exist in the present mixed world (133a 11-135).
It is the mixed idea that will become paramount in the Philebus much later. In other words, nothing in this world is pure form, and one could also say that nothing in this world is pure particular. This essay is willing to hold that this view is precisely what motivated the Philebus much later. It is the latter issue that is most important, namely, that a particular is not really a particular. Any particular, a tree for example, is a universal: it is a complex mix of chemistry, electricity and biology that go into making the tree itself.
It is a complex of things, not a particular. If there are no pure universals, there are no particulars. But the point concerning the Parmenides is that what Socrates has done in his theory of forms is to posit another world that, due to the mixed nature of this world, cannot have any direct contact with it. The forms correlate with one another, the particulars (so called) correlate with one another, and they do not meet (Scoon, 1942). The forms exist merely as models that may have had relevance to the Demiurgos, but not human beings.
Hence, again, the mixed world of the Philebus is called upon later in Platos career to deal with these problems. Dealing with these problems caused Plato a great amount of trouble, and the final statement on it is in the Philebus. Nevertheless, prior to getting to the latter dialogue (if it can be called that) a few comments on Parmenides are in order. There is a concept of the forms that undercuts each of Parmenides statements without having to respond to each in turn. Parmenides has misread the theory of forms, and Plato likely knew this as he was writing the arguments of Parmenides.
The Philebus serves as Platos final expression of the topic, where the forms are no where to be found, but a new ontology is laid out that may well express the experience of the transcendent more powerfully than the forms. The transcendent still remains, but the mode of expressing it changes. The Philebus alters the Platonic ontology. The forms are now transformed into regulating causes, and the ontological universe has now been reduced to four things: the unlimited, the limited, the divine cause and the mixed entity, or the particular. The unlimited seems to refer to the flux of becoming coming into being.
But the limit is that which makes being out of the flux of becoming (25a). The mixture is the actual particular, and there is a divine cause that beings this mixture about, the creator (or architect, to be more accurate) of the material universe. But what does this have to do with either the forms or answering Parmenides? Everything: the limited and unlimited are responses to the problems Parmenides raises, it is a way of maintaining the unchanging truth of things (and hence maintaining a front against the sophists), but avoiding the problems Parmenides raises against the forms.
It may be that the concept of the limited and unlimited was germinating in Platos mind, leading precisely to this self-criticism that turned out to be the Parmenides. Nevertheless, the transcendent forms have been simplified and redesigned to deal with Parmenides. In 28e8ff, Plato gives the example of bodily health (relative to pleasure) that lies at the heart of the ontological system. The unlimited is the flux of reality: the whole spectrum from hot to cold, moist to dry, etc. The limit is the proportion of these things that create the equilibrium necessary in the human body to create health.
The mixed state is health itself, or the limit placing a proportion upon the flux of qualities, qualities that, without limit, would be merely relative, always changing, and never actually known. The limit brings the flux and relativity of reality to its proper equilibrium, that is, the universe that we can experience. All of this is regulated by the divine nous that has ordained the nature of these entities (Lemberg, 1940). Therefore, there is no question as to the forms relation to the particular, or even the concept of a particular as a solid, single entity at all.
Material reality is the result of a limit being placed on the flux of qualities. One might even say that this precedes Kants idea of the categories placing a limit on the manifold, or the flux of unknowable qualities. The forms are no long is a separate world, since the limit is the very principle of individuation and stability. In many ways, one can see a slow immenitization of the forms, not in an Aristotelian sense, but in a unique proto-Kantian sense. One sees a world of particular things.
Particular is really a metaphor, since they are not particulars, but a relatively stable limitation placed on an otherwise unknowable swirl of qualities. Hence, the problem of the relation of universal and particular is solved, since the observable object is neither and both: it is universal in that it is taken from the eternal becoming of things, and it is particular in that it is a stable, particular things. It does change, but this change is the result of the mathematical ratio that the limit places on the practically infinite swirl of qualities and their equally infinite relations.
Hence, the universal is (in some sense) instantiated, and the particular is understood not to be a single thing, but in reality, referring to a ratio, a balance of forces and qualities that create the stable universe. Hence, all things good, all things pleasurable, can be reduced to the world of mathematical forms, numbers rather than abstractions that served to provoke Parmenides. The forms are reduced to a ratio, numbers; the very mathematics where Plato is most comfortable. The forms as stated by Parmenides are untenable.
Plato, or so this paper contends, attacked his own theory precisely as the ratio idea was germinating in his mind. The forms will be abandoned, but the transcendent will not. The transcendent will become the ratio that the limit places on the unlimited, thereby undercutting the entire argument of Parmenides, which assumes a participatory relationship between form and particular. The Philebus is the domination of number, the creativity of number, measure and mathematics on reality that save the transcendent while eliminating the attacks of Parmenides.
Hence, the latter was a necessary negation so that the later theory can develop. If anything, then, the theory of forms itself is the unlimited, the Parmenides is the limit, and the mixed entity is the Philebus. The nous is, of course, Plato himself. The limit is a negation in the sense that it takes the flux of reality and provides it with form. But it is positive in that it represents the old Pythagorean idea of number, that objects exist in relatively stable form on this earth because they represent a ratio: a balance of forces.
If the forms remain at any level, they are now reduced to numbers, and hence, have no relation to the attacks of Parmenides. It is roughly the later approach of Aristotle, and the Philebus should be used more often as the transition piece that connects Plato to Aristotle. The mixed state of things is their observable form: not universal, not particular, but an equilibrium, a ratio created by the limit, and hence, beyond the criticism of Parmenides.
What remains is number, ratio and relative stability of the observable that is mixed in that is not purely universal, and not purely particular, since neither of these pure forms exists in our world. Bibliography: Lemberg, Meyer W. The Unity of the Philebus. Classical Philology, 35, 1940, 154-179 Plato. Philebus. Trans. Dorothea Frede. Hackett, 1992 Plato. Parmenides. Complete Works of Plato. John Cooper, ed. Hackett, 1997 Runciman, Walker. Platos Parmenides. Harvard Studies in Classical Philology, 64, 1959, 89-120 Scoon, Robert. Platos Parmenides. Mind, 57, 1942, 115-133