The problem of universals is a classic problem in philosophy; it concerns whether or not universals have an objective ontological status. Universals are general or abstract qualities, relations,properties, characteristics, or kinds that can be predicated on particulars. For example, a St. Bernard, a Yorkshire terrier, and a Beagle all share the universal quality of “being a dog.” The problem of universals has bothered philosophers since ancient times, and remains unsolved today (although, there are some accepted solutions that still require more refining, e.g. Conceptual Nominalism). Plato attempted to solve this problem, via Socrates; his theory of Forms, or Ideas, has influenced philosophers from antiquity to the present. Platonic Realism is one of the famous attempts at a solutions to the problem of universals; however, it has some fatal flaws.
I will lay out Plato’s general theory as accurately as my interpretation of the literature allows; after that I will describe the Aristotelian criticism of Plato’s solution.
In the Phaedo, Plato lays out some general concepts of his Theory of Forms. In this particular passage, Socrates is questioning Simmias with regard to the ontologically objective existence of the Ideal Form of Justice (the Just): What about the following, Simmias? Do we say that there is such a thing as the Just itself, or not? We do say so, by Zeus. And the Beautiful, and the Good? Of course. And have you ever seen any of these things with your eyes? In no way, he said. Or have you ever grasped them with any of your bodily senses? I am speaking of all things such as Bigness, Health, Strength, and, in a word, the reality of all other things, that which each of them essentially is. Is what is most true in them contemplated through the body, or is this the position: Whoever of us prepares himself best and most accurately to grasp that thing itself which he is investigating will come closest to the knowledge of it? Obviously (65d-66a).
Plato has laid out his position here with regard to universals; he has said that there are external universals, inaccessible by bodily senses, independent of the particular on which that universal is predicated. Basically, Plato is saying, for example, that the universal “bigness” exists as an immaterial entity, independent of the physical world. Since these entities are not accessible by our senses, they
must be immaterial. Plato seems to think that particulars participate in the form of X and receive the quality X that is shared between them; take, for example, this passage from the Phaedo: “Consider, he said, whether this is the case: We say that there is something that is equal. I do not mean a stick equal to a stick or a stone to a stone, or anything of that kind, but something else beyond all of these, the Equal itself. Shall we say that this exists or not? Indeed we shall, by Zeus, said Simmias, most definitely” (74a-74b). In this particular passage, Socrates is explaining to Simmias that the Equal itself is not to be found within the equality of two particulars, sticks to sticks, but exists somewhere else, transcendent to each of these particulars.
Plato thought that universals were separate from the particulars that they instantiate in the physical realm, as is explained in this quote from the Phaedo: “I assume the existence of a Beautiful itself by itself, of a Good and a Great and all the rest” (100b). Plato felt that simply describing the characteristics of the universal observed within particulars was not sufficient in establishing an actual
model of the universal’s ontologically objective status, since the particular only participates in the universal insofar as it receives the universal quality X, as is evidenced in this passage:Consider then, he said, whether you share my opinion as to what follows, for I think that, if there is anything beautiful besides the Beautiful itself, it is beautiful for no other reason than it shares in that Beautiful, and I say so with everything. Do you agree to this sort of cause? – I do. I no longer understand or recognize those other sophisticated causes, and if someone tells me that a thing is beautiful because it has a bright color or shape or any such thing, I ignore these other reasons – for all these confuse me – but I simply, naively, and perhaps foolishly cling to this, that nothing else makes it beautiful other than the presence of, or the sharing in, or however you may describe its relationship to that Beautiful we mentioned, for I will not insist on
the precise nature of the relationship, but that all beautiful things are beautiful by the Beautiful (100c-100e).
Plato, in the above passage, is explaining that the qualities of the particular do nothing to explain the universal that supplies the qualities of the particular, because these are simply a result of the particular receiving the shared qualities from the ontologically objective universal, which is that quality in itself.
Plato’s Ideal Forms even encompass the realm of numbers. In this passage, Plato sets up a conceptual framework for a Platonic Realism of Mathematics: “As we were saying just now, you surely know that what the Form of three occupies must be not only three but also odd. – Certainly” (104d).
Aristotle, Plato’s student and successor, did not accept the concept of a Form existing in itself,and laid out a few devastating arguments against the idea of Platonic Forms. Probably the most devastating argument against Platonism would be the Third Man Argument. I will quote from Aristotle’s version of the Third Man Argument as stated in On Ideas:If what is predicated truly of some plurality of things is also some other thing apart from the things of which it is predicated, being separated from them (for this is what those who posit the Ideas [i.e. Forms] think they prove; for this is why, according to them, there is such a thing as man-
itself, because the man is predicated truly of the particular men, these being a plurality, and it is other than the particular men) – but if this is so, there will be a third man. For if the
the particulars and the Idea. In the same way, there will also be a fourth
(F stands for any Ideal Form):
1) Forms are one-over-many: For any plurality of F things, there is a form of F-ness by virtue of partaking of which each member of that plurality is F (Republic 596a).
2) Forms are Self-predicating: Every possible form of F-ness is itself F (Parmenides 132a-1-b2, 132d1-133a6).
3) Forms are non-self-partaking: No form partakes in itself (Phaedo 100c4-6).
4) Forms are unique: For any property F there is only one form of F-ness.
5) Forms are pure: No form can have properties that are opposite or contrary of the Form itself (the property of being one and the property of being many are contrary).
6) One-ness of Forms: Every Form is one in itself (there are not many forms for the Many, but one form of Many) (Republic 476a2–6 and 524b7–11).
Number four follows logically from number six; if something is one in itself, nothing else can be like it,so that thing is unique. Number five would then follow from number two; if, for example the Large is large (self-predication), then that thing (the Large) could not, logically, be small also. So, following from
the purity of Forms (number five), the one-ness of forms would indicate that one Form cannot also be many because being many would not be consistent with being one. After laying out Plato’s theory in this way, we can see that it contains some problems. Aristotle’s contention would go like this: If we have
three men, they form the plurality (M1,M2,M3) since they all partake in the universal human. The plurality would partake in the Form of human, which would be a perfect human, in itself. Now we have encountered the problem; this perfect human would have the aspect of human-ness, and since a Form cannot partake in itself (number three), we have to add this human to the plurality of (M1,M2,M3)
because he has the universal aspect of human-ness which he cannot receive from himself (number three). Now we have the plurality (M1,M2,M3,P1) which needs to participate in a Form to receive the universal “human-ness”, which would be a perfect human according to Plato. But we also have a third man that the plurality has to partake in; the problem gets worse, since this new “perfect human” must get his “human-ness” from somewhere, and he cannot get it from himself (number three), so there must be a fourth man where he gets his “human-ness” from. So, you add the fourth man to the plurality, (M1,M2,M3,P1,P2) and so on endlessly. The Third Man Argument basically reduces the Theory of Forms to a series of infinite regress because any plurality of things that receives their universal aspect from a form of the aspect-in-itself, must be added to the plurality because that aspect-in-itself (the perfect human) has to receive its aspect from somewhere other than itself (number three). A more concise and logical version of this argument comes from Parmenides; I will rephrase the argument and use the concept of a man (man-ness or human-ness), rather than “large-ness” to remain consistent with the above argument. Consider a plurality of men, A, B, and C. According to the principle of One-over-Many (number one), there is form of Man (let’s call it “M1”) which A, B, and C partake in. According to the principle of Self-Predication (number two), M1 is a man. So there is now a new plurality of men, A, B, C, and M1. Thus, according to the principle of One-over-Many, there is another form of “Man-ness” (Human-ness) (let’s call it “M2”) from which A, B, C, and M1 also derive their “Man-ness” from. Hence M1 partakes in M2. According to the Theory of Forms, no Form is identical to anything that partakes in it, the term used in Parmenides is Non-Identity, which is clearly stated in principles four, five, and six. Based on the fact that M1 partakes in M2, the principle of Non-Identity requires that M2 be numerically distinct from M1. Thus, there must be at least two forms of man, M1 and M2. But this is not all; according to Self-Predication, M2 is a man. So there is now a new plurality of men, A, B, C, M1, and M2. Thus, according to One-Over-Many, there is another form of “Man-ness” (Human-ness) (let’s call it “M3) which A, B, C, M1, and M2 also partake in. Hence M1 and M2 both partake in M3. But according to Non-Identity, M3 is numerically distinct from both M1 and M2. Thus, there must be at least three forms of man, M1, M2, and M3. Repetition of this reasoning will result in an infinite regress.
So, Plato’s Theory of Forms has a fatal flaw – namely, the infinite regress. Aristotle did not formulate this argument; he borrowed it from Plato’s dialogue Parmenides. Plato actually subjected his own theory to one of the harshest self-criticisms that the philosophical world has ever seen. In the dialogue Parmenides, a young Socrates is being questioned by Parmenides with regard to the Theory of Forms Socrates has just presented. What follows are a few of Parmenides’ objections, but the most note-worthy is the Third Man Argument (Parmenides 132a-1-b2, 132d1-133a6). The young Socrates has no rebuttal to any of Parmenides’ objections, but seems to remain rather puzzled over the conundrums they present. There are many other objections to the Theory of Forms, but the TMA (Third Man Argument) is the most famous, and devastating. Regardless of the flaws in Plato’s theory, he was one of the first philosophers in antiquity to address this problem and attempt to create a coherent solution. The problem of universals has plagued philosophy for millennia, and will probably continue to do so for many years to come.
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