Few texts of Plato have occasioned as much discussion and as many varying interpretations as his Parmenides.Footnote 1 The text is notoriously difficult to decipher, and this problem is only compounded by its unique portrayal of a young Socrates who is rather easily bested in debate by an older and wiser Parmenides, the dialogue's titular character. Among the many and various topics of dispute amongst scholars of Plato is the question of the so-called “Third Man” argument and its status both within the dialogue and on its own. The subject of a vast body of literature itself, the Third Man argument was referred to by Aristotle in his works Metaphysics Footnote 2 and Sophistical Refutations,Footnote 3 and taken up by subsequent Aristotelean commentators, among these being the medieval theologian Thomas Aquinas.Footnote 4 These numerous Aristotelean commentators, as well as those who have commented on the Parmenides, have produced a wealth of literature on the Third Man argument. In modern times, the publication of Gregory Vlastos's 1954 article “The Third Man Argument in the Parmenides”Footnote 5 has sparked a renewed interest in the topic and reinvigorated academic discussion on the Third Man.
The occurrence of the Third Man argument in the Parmenides is a curious one; it is presented as a crushing blow to the young Socrates' defense of the theory of Forms, and no refutation of the Third Man is offered or even attempted. As a result, Platonic scholars, such as the aforementioned Vlastos, have devoted much effort to analyzing the validity and soundness of the argument and to attempting to explain what Plato himself thought of it.Footnote 6 In a similar manner, Aristotle's few and brief mentions of the “third man”, in the context of criticizing Plato, have led many to attribute a Parmenides-esque Third Man argument to Aristotle, complete with infinite regress, and to view Aristotle (at least insofar as the Third Man goes) to stand or fall with the argument of the Parmenides.
Adding to the intrigue is Thomas's commentary on Aristotle's Metaphysics, wherein Thomas comments on three of the four uses of the “third man” therein: in none of these places does Thomas mention the concept of infinite regression, a concept which is central to the Parmenides' Third Man argument. As such, I will explore the Third Man arguments as they appear in Plato's Parmenides and Aristotle's Metaphysics. In doing so I will give special place to Thomas's commentary on the latter work as I believe it to provide a unique and hitherto ignored perspective on the Third Man argument. To this end, I will begin by examining the relevant section of the Parmenides before moving on to the text of Aristotle and to Thomas's commentary. Following this, the main modern interpretations of the Third Man argument will be considered. Finally, I will argue that the Third Man argument that appears in the Parmenides and those that are mentioned in Aristotle's work ought to be interpreted as separate arguments.
I. The Third Man in Plato
The Parmenides may be divided into two parts. The first part, which runs roughly from 126a to 137b, consists mainly of a young Socrates conversing with Zeno and Parmenides about Socrates' theory of Forms. The second part, running from roughly 137c to 166c, contains Parmenides' attempt to demonstrate for his audience a certain type of exercise which would allow for Socrates to salvage his theory. It is this second part which has proven famously and especially difficult for readers and commentators to understand, resulting in a myriad of widely differing interpretations. However, it is the first part which interests us here, since it is this part which contains the Third Man argument. As such, we will be focusing on the first part of the Parmenides to the exclusion of the second.Footnote 7
The Third Man argument appears as the second of five arguments that Parmenides brings against Socrates' theory of Forms. It should be noted that, as it appears here, the Third Man argument actually concerns the Form of Largeness or Greatness, and not of Man. The Third Man argument was so named after Aristotle's use of the term, who referred to such an argument in his Metaphysics. We will examine these shortly.
Parmenides begins the argument by probing Socrates: “I imagine that your reason for assuming one idea of each kind is as follows: - Whenever a number of objects appear to you to be great there doubtless seems to you to be one and the same idea (or nature) visible in them all; hence you conceive of greatness as one.”Footnote 8 Socrates agrees, to which Parmenides replies:
But now, if you allow your mind in like manner to embrace in one view this real greatness and those other great things, will not one more greatness arise, being required to account for the semblance of greatness in these?… Then another idea of greatness now comes into view over and above absolute greatness and the individuals which partake of it; and then another, over and above these, by virtue of which they will all be great, and so you will be left not with a single idea in every case, but with an infinite number.Footnote 9
Immediately one may see that Parmenides' objection rests on a multiplication of Forms that Socrates would find unacceptable. As Constance C. Meinwald writes, “[this] gives rise not only to a ‘Third Large,’ but is supposed to be reiterated to yield an unending series of Forms; Socrates regards such a result as unacceptable.”Footnote 10 The idea is that if a Form is invoked in order to explain what is common among sensible things (in this case, largeness or greatness), then we must for that reason invoke some additional Form which explains what is common between the sensible things and the original Form. Of course, this semblance between the additional Form and the original Form and the sensible things in question must be explained by some further Form, and so on ad infinitum. The result is that not only must there be some Form over-and-above, so to speak, sensible objects and the Form of said objects, but that this results in a vicious regress so that the Forms' explanatory power is reduced to nil.Footnote 11
There are a few more points to note before we move on to Aristotle and Thomas. First, the issue of how to successfully defend the theory of Forms against this attack is not taken up in the Parmenides, or indeed in any of Plato's works. However, some scholars, such as Meinwald, will argue that a solution may be gleaned from the text of the Parmenides when taken as a whole,Footnote 12 while others who are sympathetic to Meinwald's interpretation are not in agreement as to the types of predication which Meinwald identifies during the course of her treatment of the Third Man argument, or to their applications.Footnote 13
Second, the Third Man argument that appears in the Parmenides is woefully underspecified. According to Meinwald,
Not only does the text often not set out enough premises for the announced conclusion to follow, but there is just not enough information from which to determine exactly what we are supposed to understand as completing the arguments. And different ways of completing the arguments are not just trivially different…. The variety of formulations of the Third Man Argument that have been produced by careful interpreters is a sign of the extent to which that argument is underspecified, while the heat of their disagreement with each other indicates that the different formulations differ importantly.Footnote 14
At bottom, the Third Man argument that appears in the Parmenides is painfully short and underdeveloped; where one might hope for an extended treatise on the subject, only a few short lines are offered. The sheer amount of literature that has been produced on those short lines is a testament to the topic's endearing impact and to its depth as a philosophical well.Footnote 15
II. The Third Man in Aristotle and Thomas Aquinas
In all there are five instances of Aristotle referring to the Third Man argument in his body of work; these are: (1) Sophistical Refutations 178b36, (2) Metaphysics I.9, 990b17, (3) Metaphysics VII.13, 1039a1, (4) Metaphysics XI.1, 1059b8, and (5) Metaphysics XIII.4, 1079a13. Of these, Thomas commented on numbers 2 through 4. This, combined with the fact that the mentions in Sophistical Refutations and Metaphysics XIII are relatively minor and do not add anything substantial to our discussion here, has led me to leave mentions (1) and (5) aside for the purposes of this paper. We will focus, then, on Metaphysics I, VII, and XI in an attempt to understand Aristotle's Third Man argument and its intricacies. As stated above, we will rely heavily on Thomas's commentary for our interpretation.
a.) Metaphysics I.9, 990b17
The opening book of Aristotle's Metaphysics is well known for compiling a summary of the history of philosophers on the causes. Among those treated are the Platonists, who, Aristotle writes, posited the Forms as explanations of things. He continues, writing that “of the ways in which we prove that the Forms exist, none is convincing… of the more accurate arguments, some lead to Ideas of relations, of which we say there is no independent class, and others introduce the ‘third man’.”Footnote 16
Immediately we can note the brevity of the reference; no obvious extrapolation on the Third Man argument is offered by Aristotle in the following lines of the book. What little he does tell us is limited to the origins of the Third Man: Aristotle holds that the argument arises from certain “more accurate” arguments which purport to show (unconvincingly, according to Aristotle) the existence of the Forms.
When we move on to Thomas's commentary, we find the extrapolation which we might have hoped to find in Aristotle. Writes Thomas: “The second conclusion is one which follows from other most certain arguments, namely, that there is ‘a third man.’ This phrase can be understood in three ways.”Footnote 17 We will devote our attention to each of Thomas's three ways of understanding the “third man” phrase, as the analysis of these will allow us to say something substantial and, in the context of the modern commentary on the Third Man argument, new.
i.) The First Way of Understanding the Third Man
In scholastic fashion, Thomas divides his topic into a number of different sub-topics and immediately tackles the first. Writes Thomas: “First, it can mean that the ideal man is a third man distinct from two men perceived by the senses, who have the common name man predicated of both of them. But this does not seem to be what [Aristotle] has in mind… for this is the position against which he argues. Hence according to this it would not lead to an absurdity.”Footnote 18 Simply put, the first way of understanding the Third Man argument is just Plato's theory of Forms. That is, we might understand the Third Man to be the Form which explains how two sensible objects, in this case men, are related or similar: there is a “third man” or Form of man over and above them in which they participate and which accounts for what is common in them, i.e. their intelligible structure.
However, Thomas argues that this first way of understanding the argument cannot be what Aristotle means in mentioning the Third Man in book I, simply because Aristotle is here critiquing the arguments which the Platonists have put forward in order to establish the theory of Forms; it would be inappropriate and circular to claim that an argument in support of the theory of Forms is absurd because it leads to the theory of Forms. Thus, Aristotle cannot mean the “third man” to indicate this sense.
ii.) The Second Way of Understanding the Third Man
Thomas then moves on to the second way of understanding the Third Man argument; he writes the following:
The second way in which this expression can be understood is this: the third man means one that is common to the ideal man and to one perceived by the senses. For since both a man perceived by the senses and the ideal man have a common intelligible structure, like two men perceived by the senses, then just as the ideal man is held to be a third man in addition to two men perceived by the senses, in a similar way there should be held to be another third man in addition to the ideal man and one perceived by the senses. But neither does this seem to be what [Aristotle] has in mind here, because he leads us immediately to this absurdity by means of another argument. Hence it would be pointless to lead us to the same absurdity here.Footnote 19
This articulation of the Third Man argument is immediately recognizable as being quite similar to the version which appears in the Parmenides. Noticeably, however, the concept of infinite regression is absent. This second way of understanding the Third Man argument proceeds by noticing that what is common to a sensible man and the Form of man must be explained by some further instance, or Form, of man. Here there is simply no need for any sort of infinite regression, since the “third man” by itself is enough of an absurdity. Certainly, Plato would have viewed a “third man” as a serious objection to his theory of Forms and would have been unhappy with multiplying causal explanations beyond what he thought was necessary, namely, beyond the positing of a single Form of “man” over and above sensible men.
This form of the Third Man argument sheds some light on Aristotle's scathing critique of the theory of Forms which one finds in the beginning of chapter 9 of book I of the Metaphysics:
But as for those who posit the Ideas as causes, firstly, in seeking to grasp the causes of the things around us, they introduced others equal in number to these, as if a man who wanted to count things thought he would not be able to do it while they were few, but tried to count them when he had added to their number.Footnote 20
Aristotle is not here referring to the Third Man argument as such, but rather to the theory of Forms in general. His remarks here do, however, help us to understand his point of view in critiquing the theory of Forms and his mention of the Third Man in book I of the Metaphysics. Clearly in the second way of understanding the Third Man argument, we have an instance – right or not – of explanations being multiplied seemingly superfluously. Where the first way of understanding the Third Man viewed the third man as the Form which explained the likeness (or, intelligible structure) that is in common between sensible men – and in this Plato would find no disagreement – this second way of understanding the Third Man posits a Form which explains the likeness (or, intelligible structure) that is common between a sensible man (or men) and the Form of man – and to this Plato would object. Thus, we need not posit an infinite regress of men, since the third man over and above sensible man and the Form of man is enough to, at the least, damage Plato's theory of Forms. Moreover, it is noteworthy that this instance of the Third Man argument does not include a plurality of sensible men; indeed, just one sensible man is referred to, and only one is needed in order to get the argument off of the ground, in contrast to the first way of understanding the argument. This will be a recurring theme as we consider more instances of the Third Man argument below.
Yet Thomas writes that this way of understanding the Third Man argument is not what Aristotle has in mind here in book I of the Metaphysics. Thomas's reasoning is rather interesting, and speaks to his remarkable talent as an exegete. According to Thomas, Aristotle cannot mean to refer to this way of understanding the Third Man argument because Aristotle immediately moves on to articulate this very argument; hence, Thomas reasons, Aristotle must mean by “the third man” some other argument.
Let us digress for a moment to consider Aristotle's articulation of this second way of understanding the Third Man argument and Thomas's commentary thereupon. Writes Aristotle:
And if the Ideas and the particulars that share in them have the same form, there will be something common to these; for what should ‘2’ be one and the same in the perishable 2's or in those which are many but eternal, and not the same in the ‘2 itself’ as in the particular 2? But if they have not the same form, they must have only the name in common, and it is as if one were to call both Callias and a wooden image a ‘man’, without observing any community between them.Footnote 21
Again, we can see that the concept of infinite regression does not come into the argument; it is enough of a critique of Plato's theory of Forms, thinks Aristotle, that there would be “something common to these”. When we turn to Thomas, we find that his commentary on these brief lines of Aristotle's to be comparatively lengthy. Nevertheless, a study of Thomas's commentary, if only in part, will help us to better understand the argument of the Parmenides, even if the concept of infinite regression is missing from Aristotle and Thomas.
Thomas begins by providing a summary of Aristotle's argument,Footnote 22 after which he provides a detailed explanation of, in Thomas's words, “[the] need for positing a one apart from both sensible substances and the Forms”.Footnote 23 Writes Thomas:
the Ideas and the sensible things which participate in them either belong to one class or not. If they belong to one class, and it is necessary to posit, according to Plato's position, one common separate Form for all things having a common nature, then it will be necessary to posit some entity common to both sensible things and the Ideas themselves, which exists apart from both.Footnote 24
Next, Thomas considers two ways in which one might defend the theory of Forms against such an attack; and as to the first of these Thomas responds by bringing in an argument which has little direct bearing on the topic at hand, we will leave it aside.Footnote 25 The second counter-argument to the second way of understanding the Third Man which Thomas considers is that “sensible things, which participate in the Ideas, do not have the same form as the Ideas”.Footnote 26 This counter-argument is significant since, if it is successful, it would destroy the need for a “third man” completely, as there would be no “common nature” shared between sensible things and the Form thereof, and thus no need to posit some third entity which is common to these. Thomas replies in the following manner:
it follows [from this] that the name which is predicated of both the Ideas and sensible substances is predicated in a purely equivocal way. For those things are said to be equivocal which have only a common name and differ in their intelligible structure. And it follows that they are not only equivocal in every way but equivocal in an absolute sense, like those things on which one name is imposed without regard for any common attribute, which are said to be equivocal by chance; for example, if one were to call both Callias and a piece of wood man.Footnote 27
In short, if the sensibles and the Form in question do not share the same form, then the name that is predicated of them in common would be used purely equivocally; yet this is unacceptable, especially for Plato.
iii.) The Third Way of Understanding the Third Man
Thomas next considers the third way of understanding the Third Man argument, which he holds Aristotle to intend when the latter mentions “the third man” in book I of the Metaphysics. Writes Thomas:
Plato posited three kinds of entities in certain classes of things, namely, sensible substances, the objects of mathematics and the Forms. He does this, for example, in the case of numbers, lines and the like. But there is no reason why intermediate things should be held to exist in certain classes rather than others. Hence in the class of man it was also necessary to posit an intermediate man, who will be a third man midway between the man perceived by the senses and the ideal man.Footnote 28
The argument that Thomas presents here is rather unique; as far as “third man” arguments go, this one articulated by Thomas is without a doubt of the least known. It begins by noting that in the class of numbers, lines, and the like, Plato had posited sensibles, Forms, and intermediaries between these two.Footnote 29 But, Thomas argues, there is no reason not to posit intermediaries in other classes of things as well, and as such we are just as justified in positing an intermediate “man” in between a sensible man and the Form of man.
Once again, the reader will notice that the concept of infinite regression is absent. And once again, we might imagine Aristotle's critique of the theory of Forms from Metaphysics I.9, 990a34-990b4 as shedding some light onto our understanding of the Third Man argument: in seeking to explain the common intelligible structure of sensible objects, causes are multiplied beyond necessity. Notably, the exact manner in which the “third man” is supposed to arise is different here than it is in the second way of understanding the argument and in the Parmenides. Here, the “third man” appears as an intermediary, whereas in our previous examinations we saw that it appears as a necessary explanation of sorts, being “over and above” the sensibles and the Form, so to speak. Likewise, one might do away with this third version of the Third Man argument entirely by rejecting Plato's doctrine of the objects of mathematics being intermediaries, while the other versions of the Third Man argument that we have seen are entirely neutral to said objects.
It is worth asking: Does this version of the Third Man argument allow for an infinite regress in the similar way that the second version might? That is, might we posit a “fourth man” that is intermediate between the sensible man and the “third man”, and a “fifth man” that is intermediate between the “third man” and the Form of man, and so on ad infinitum? I am not convinced that this way of formulating the Third Man argument works. The third way of understanding the Third Man argument that Thomas is working with, and that he thinks Aristotle is working with, is based upon the Platonic idea of the objects of mathematics being intermediaries in certain classes of things, and Plato did not posit infinite intermediaries in these classes. Hence, if Aristotle and Thomas are to base the Third Man argument specifically on the line of reasoning that Plato uses in certain classes of things – lines, numbers, and the like – and carrying it over to other classes of things – man, horse, and whatever else has a Form – then we would not be justified in positing an infinite regress in this “fourth” way of understanding the Third Man argument, since neither did Plato posit an infinite regress in his doctrine of intermediaries.
b.) Metaphysics VII.13, 1039a1
We move on now to the second instance of the Third Man argument in the Metaphysics. For context, during the seventh book of the Metaphysics Aristotle attempts to show that “no universal attribute is a substance, and this is plain also from the fact that no common predicate indicates a ‘this’, but rather a ‘such’.”Footnote 30 He continues, arguing that if we deny this, “many difficulties follow and especially the ‘third man’.”Footnote 31 No explanation is offered by Aristotle.
Thomas's commentary is curious: “[Aristotle] says that, if the preceding conclusion is not admitted, many absurdities will follow, and one of these will be the need to posit a third man. This can be explained in two ways.”Footnote 32 Immediately we may ask: Why are there not three ways of understanding Aristotle's use of the phrase “third man”, as there were three in book I of the Metaphysics? Thomas continues: “First, it can mean that besides the two singular men, Socrates and Plato, there is a third man, who is common to both. This is not absurd according to those who posit Ideas, although it seems absurd from the viewpoint of right reason.”Footnote 33 The reader will recognize this as the first way of understanding the Third Man argument from book I of the Metaphysics. This explanation is simply Plato's theory of Forms, hence the reason why Thomas writes that this explanation of the Third Man “is not absurd according to those who posit Ideas”, since it just is a very simple version of the theory of Forms. Moving on, Thomas considers a second explanation of “the third man”:
Second, it can be explained as meaning that there is posited a third man besides a singular man and man in common, since they have a common name and intelligible expression, just as do two singular men in addition to whom a third common man is posited; and the reason is that they have a common name and definition.Footnote 34
It is clear that this explanation is the second way of understanding the Third Man argument from book I of the Metaphysics, and here Thomas is just as explicit with drawing out the argument; if we accept Plato's theory of Forms, then in the same way that there must be posited a third man in common between two sensible men, so there must also be posited a third man in addition to a single sensible man and man in common. Again, the reason is that what motivates us to posit a third man in the first case – a common name and intelligible expression or structure among the entities in question – is exactly the same thing that motivates us in the second case to posit a third man. And again, where Plato in the first case would be in agreement with the conclusion of the chain of reasoning, in the second case he would reject the conclusion (regardless of any “lack” of an infinite regress).
This is all well and fine, yet it is not obvious why Thomas neglects to mention the third way of understanding the Third Man argument here. We have seen the first two ways represented, yet here after considering the second argument, Thomas moves on to continue his commentary on Aristotle. What might explain this? I believe that the answer lies in the context of the various passages in question. Recall that in book I of the Metaphysics Aristotle mentions “the third man” in reference to “the more accurate arguments” which purported to show the reality of the Forms, specifically asserting that some of these “more accurate arguments” introduce “the third man”.Footnote 35 Thus, Thomas's commentary on this excerpt of Aristotle's was required to be rather broad in character. Moreover, as we saw above, Thomas held that the book I mention of the Third Man argument did not refer to what we've called the second way of understanding the argument that reappears here in book VII of the Metaphysics. In contrast, this book VII mention of the Third Man is in a much more specific context; Aristotle is articulating the consequences of denying a specific proposition: the proposition that “no universal attribute is a substance”.Footnote 36 If we see Thomas's commentary as informed by this proposition, it becomes easier to see why Thomas included the first two ways of understanding the Third Man argument in his commentary and not the third. The first two have direct bearing on the denial of the proposition that no universal attribute is a substance, since to deny this would be to claim that there is a universal attribute which is a substance, at which point the first two ways of understanding the Third Man would apply, according to Aristotle and Thomas, since this universal attribute would both have an intelligible structure (being a substance) and share this structure in common with other entities (being a universal). On the other hand, the assertion of the claim that there is a universal attribute that is a substance (no matter how many) does not imply or exclude the reality of the objects of mathematics as intermediaries between sensible substances and Forms. Indeed, it would be absurd for Thomas to bring in intermediaries in connection with the denial of the proposition “no universal attribute is a substance”, since intermediaries have no bearing on the question at hand – unlike in book I of the Metaphysics, where the discussion is much more broad, and where Thomas is clear that the first two ways of understanding the Third Man argument cannot be what Aristotle means in mentioning it there. It is consistent, then, for Thomas to refer to the third way of understanding the Third Man in book I of the Metaphysics and not here in book VII.
c.) Metaphysics XI.1, 1059b8
Aristotle's final mention of the Third Man that we will examine is in book XI of the Metaphysics. Aristotle writes:
evidently the Forms do not exist. [But] it is hard to say, even if one suppose them to exist, why in the world the same is not true of the others things of which there are Forms, as the objects of mathematics. I mean that these thinkers place the objects of mathematics between the Forms and perceptible things, as a kind of third set of things apart both from the Forms and from the things in this world; but there is not a third man or horse besides the ideal and the individuals.Footnote 37
Here Aristotle is explicit with his articulation of the Third Man argument. While it may be suggested that Aristotle never extrapolated on the Third Man argument, instead only mentioning it offhand, and that one might thereby equate Aristotle's view of the Third Man with the argument that appears in the Parmenides, this brief passage from the Metaphysics suggests otherwise.
The argument which Aristotle presents here is nuanced. It begins by assuming that the Forms exist. From here, Aristotle asks why, from the assumed premise, the same thing would not be true of things as is true of the objects of mathematics. He then explains his reasoning further, explicitly stating that, in the case of the objects of mathematics, the Platonists place these “as a kind of third set of things” between sensibles and the Forms. Aristotle then states the Platonic position: There is no third man besides the Form of man; yet it would appear that we are justified in assuming that there is. The reasoning, we have seen already, is that there is no reason why one ought to posit intermediaries in one class of things and not in another, and so we must also posit (or at least, we are just as justified in positing) intermediaries in the class of man, horse, etc. What we have here is clearly and explicitly an instance of Aristotle articulating a full version of the Third Man argument.
It is plain to see why Thomas thought to interpret a third way of understanding the Third Man in book I of the Metaphysics. Indeed, during his commentary there he refers forward to this argument.Footnote 38 His commentary here on book XI is not brief, but it is worth quoting at length:
since [Aristotle] had said that there are evidently no separate Forms, he poses the question whether the objects of mathematics are separate. First, he shows that they are not. For if one claims that there are separate Forms and separate mathematical entities over and above sensible substances, why is not the same thing true of all things which have Forms as is true of the objects of mathematics? So that just as the objects of mathematics are assumed to be intermediate between the separate Forms and sensible substances as a third class of things over and above the separate Forms and the singular things which exist here (for example, a mathematical line over and above the Form of a line and the perceptible line), in a similar fashion there should be a third man and third ‘horse over and above man-in-himself and horse-in-itself’ (i.e., the ideal man and the ideal horse, which the Platonists called Ideas) and individual men and horses. But the Platonists did not posit intermediates in such cases as these but only in that of the objects of mathematics.Footnote 39
Thomas ties this version of the Third Man argument to the question of the separation of the Forms as well as to the separation of the objects of mathematics. The Third Man argument, to Thomas's mind, is not just the result of the Platonists positing the Forms, but also of their positing the separation of the objects of mathematics as intermediaries. The Third Man argument, as Thomas interprets Aristotle in presenting it here in book XI of the Metaphysics (as well as in book I), is quite different from the argument which appears in the Parmenides. That is not to say that Plato's own “Third Man” argument in the Parmenides is completely unrelated to what we now call the “Third Man”; Thomas's commentary on book I of the Metaphysics is enough to show us that among the many ways to interpret the Third Man, the version of the Parmenides (with or without the infinite regress) is not without merit – and I am leaving aside the question of the soundness of any Third Man argument. It is interesting to note, however, that nowhere in the text of the Metaphysics, or indeed in Thomas's commentary thereon, does the concept of infinite regression arise with connection to the Third Man argument.
III. Modern Interpretations
I now wish to consider other commentators on Plato, Aristotle, and the Third Man argument. Unfortunately, I have been unable to locate any English secondary literature on Thomas's interpretation of the Third Man. The state of the current literature on the argument, at least as far as Plato and Aristotle are concerned, is overwhelming in its sheer volume, yet, I would argue, significantly less overwhelming with respect to its depth. Among this literature the common theme is that Aristotle's Third Man argument is at the least very similar to that which appears in the Parmenides, and that in order to answer the Third Man argument, one must delve into the philosophical depths of the Platonic and Aristotelean theories of predication.
For example, Joan Kung indicates that “there is little doubt that Aristotle would regard the regress engendered by the [Third Man argument] as unacceptable.”Footnote 40 Indeed. Yet, the reader will notice, Aristotle nowhere mentions infinite regression when discussing the Third Man argument, neither in the texts we have considered in this paper, nor in the texts which we have acknowledged and bypassed. And while it might be protested that Aristotle only gives brief mentions of the Third Man, the fact remains that the one time he does present an explicit version of the Third Man argument, infinite regression entirely absent. Moreover, Kung consistently gives the impression that Aristotle's attack against the theory of Forms in the Third Man argument is one which is based upon predication.Footnote 41 Now, this might be true of what I have called the second way of understanding the Third Man argument, but it is not clear that the third way of understanding the argument is so based; at the very least argumentation is required in order to show this.
Kung is not alone in her thinking; it is representational of the current state of scholarship on Aristotle and the Third Man argument. One sees this explicitly in Gail Fine, who writes that Aristotle's Third Man argument “purports to show that a theory of forms is vulnerable to a vicious infinite regress… the [Third Man argument] purports to show that, if there is one form corresponding to ‘F’, there are an infinite number of them.”Footnote 42 Interestingly, Fine also mentions the passage from Metaphysics VII, during which, of course, there is no mention of infinite regress, and she neglects to mention the passage from Metaphysics XI, the only passage of Aristotle's where he explicitly gives his version of the Third Man argument, and which, again, has no mention of an infinite regress. Indeed, nowhere in her paper discussing Aristotle and the Third Man argument does she mention Metaphysics XI or the objects of mathematics as intermediaries.
Likewise, the tendency to view Aristotle's version of the Third Man argument as what I have called the second way of understanding it is extremely strong in the secondary literature post-Vlastos. Robert Barford, in his treatment of Aristotle and the Third Man, cannot help but assume this,Footnote 43 while other scholars, such as MeinwaldFootnote 44 and James C. Dybikowski,Footnote 45 heavily imply this by treating Aristotle's critique as one that is fundamentally about predication.
This is not to say that no Aristotelean version of the Third Man argument revolves around the issue of predication; we have seen that the second way of understanding the argument does just this. The issue is with scholars ignoring – in most cases, completely ignoring – the only instance in Aristotle's texts of him actually explicitly stating the argument, and the fact that this explicit statement of the argument revolves around the inconsistent use of intermediates in Plato's ontology and not around predication (in any obvious sense, at least).
However, I have come across one scholar who has come quite close to noticing just this, that scholar being Vlastos, who began the modern flood of literature on the Third Man; unfortunately, those who have written after him have missed this aspect of Vlastos' article, and the point appears to never have been taken up. Vlastos discerns two separate versions of the Third Man argument in the Parmenides, adding that Aristotle supplied a third.Footnote 46 And where at first Vlastos indicates that he is taking this third Aristotelean version of the argument from Peri Ideōn,Footnote 47 later in the same paper he indicates that he is aware of the argument of Metaphysics XI,Footnote 48 although this remark is only offhand and does not derail the discussion of predication. The result is that Vlastos has come frustratingly close to touching on the Aristotelean Third Man argument (and what would be, in his eyes, a fourth version of the argument), only to abruptly change direction and avoid it altogether.
What explains this phenomenon? What explains the seemingly willful ignorance of modern scholars of the Aristotelean explanation of the Third Man argument? When it comes to Aristotle, why do so many scholars prefer to satisfy themselves with “third man” name drops and a text of disputed authenticity, especially when an explicit Aristotelean explanation of the Third Man exists? Perhaps part of this may be explained by the fact that the Platonic doctrine of intermediaries in the objects of mathematics remains itself so vague and disputed. Regardless, we have a steady guide in Thomas, and if we are to take Thomas's commentary on Aristotle seriously, we may discern three important points in closing out this paper. First, the third way of understanding the Third Man argument is the quintessential Aristotelean Third Man argument, as evidenced by books I and XI of the Metaphysics. Second, the second way of understanding the Third Man argument is another legitimate interpretation of the argument, although it is most properly understood as arising out of a specific set of premises surrounding the theory of Forms, as evidenced by book VII of the Metaphysics. Third and finally, none of the three ways of understanding the Third Man augment involve an infinite regress (at least for Aristotle; Plato is another story), and neither does the third version revolve around the concept of predication – at least not to the degree which the second version does. For bringing these points to light, Thomas's commentary is invaluable.
Conclusion
The preceding considerations have led me to conclude that the Third Man arguments that one finds in the Parmenides and in Aristotle ought to be interpreted as separate arguments. The modern tendency to equate them is unfortunate, since in the case of Aristotle's mentions of a “third man”, there is either little on the surface to suggest that they are either the same or different arguments as the Parmenides argument, or there is much to suggest that the arguments are fundamentally different, as is the case with the Metaphysics book XI argument. If the conclusion that the Parmenides and the Aristotelean Third Man arguments ought to be interpreted as separate arguments is correct, then it raises the question: What led Plato and Aristotle to critique the theory of Forms in such different ways? Why was Plato so concerned with infinite regress? Why was Aristotle not? Certainly, these questions, insofar as they touch upon Plato, are intimately tied up with the very difficult to interpret Parmenides. Yet perhaps we may find some answers to these questions in Plato's and Aristotle's respective philosophical projects and methodologies. In any event, it has been my primary intention in this paper to indicate a shift in “Third Man studies” that must occur in modern scholarship.
