Parmenides ’ first and second hypotheses , αὐ τὰ τὰ ὅ μοιά , and Socrates ’ astonishment As duas

In this paper, I propose a new interpretation for two of the most debated passages of Plato’s Parmenides: Socrates’ long speech (128e5–130a2) and Parmenides’ first antinomy (137c-155e). My aim is to demonstrate: 1) that Socrates’ speech can only make sense if we understand αὐ τὰ τὰ ὅ μοιά as a third kind of entity, the immanent property sensibles have by participating in the form of Likeness; 2) that the first two hypothesis of the second part of the dialogue (137c-155e), together with Parmenides’ criticism in the first part of the dialogue (130b-134e), is an answer to Socrates’ challenge (128e-130a). Parmenides’ arguments aim to show that, according to Socrates’ own premises, it is not possible for forms or immanent properties to be the kind of unity Socrates wants them to be. Finally, 3) I will use these results to suggest an innovative answer to the vexed question about the relation between the first and second parts of the Parmenides. According to my interpretation, the exercise of the second part of the dialogue does not provide the solution to Parmenides’ criticism of the theory of forms, despite what the majority think today. Rather, it radicalizes this criticism by pointing to a fundamental miscomprehension on Socrates’ conception of what it is to be a unity.

In order to solve this paradox, Socrates opens his ontological toolkit. Deploying his distinction between sensible things and Forms, Socrates elucidates to Zeno that there is no surprise in sensible things being subject to opposite predicates. Sensible things are charact erized by multiplicity. They are "the things we call many" (πολλὰ καλοῦμεν) both because they are numerically multiple, there are many beautiful things, as well as because they are internally complex, each one of them being a whole composed of multiple parts.
We can conclude that sensible things display these two asp ects of multiplicity (internal multiplicity and numerical multiplicity) from many textual indications. First of all, the very formulation of the pluralist' s thesis displays this ambiguity. Zeno describes their opponent' s hypothesis by one single expression "πολλά ἐστι τὰ ὄντα" (127e1). But this same Greek expression can mean two distinct theses. On the one hand, it can be translated as the English phrase "there are many things" , with the verb being applied to the subject "πολλά τὰ ὄντα" in an absolute sentence. In this reading, the phrase express numerical pluralism: there are (there exist) more than one thing. This is the sense of the phrase behind Parmenides' argument in 127e8-128a1. On the other hand, this same expression "πολλά ἐστι τὰ ὄντα" can be read as a regular predication with the predicate "πολλά" being applied to the subject "τὰ ὄντα" . In this reading, the pluralistic thesis is that the beings are multiple in the sense that they have multiple asp ects. This is the sense behind Socrates' comments in 129c 2 .
According to Socrates' explanation, sensible things have their properties by coming to share in a separate Form, and there is nothing wrong in getting a share of two opposite Forms. Therefore, Zeno' s conclusion does not generate any measure of paradox. As Socrates explains using himself as an example, as long as the opposite predicates are assigned to different elements of the same sensible thing, Zeno' s paradox will not bite. There is an element of Socrates that is the subject of likeness, and another element of him that is the subject of unlikeness. And there is no contradiction in different elements of the same subjects having opposite properties (cf. Prm. 129c5-129d2) 3 .
What is particular interesting in these opening arguments of the Parmenides is that Socrates here does not keep investigating his interlocutor's thesis, but rather brings the audience's attention to his own explanations and theories. In order to do that, Socrates' challenges his Eleatic friends to prove him wrong right after presenting his solution to Zeno's paradox. With the arrogance that charact erizes the young people, Socrates' does not see that this challenge will precipitate the venerable Parmenides into the debate, ultimately leading him to his own defeat. Socrates presents his challenges in a long sp eech in which many strong words such as τέρας and ἄτοπον are used to describe the state of awe Socrates would be if someone demonstrates to him some disturbing flaws within his theory (Prm. 128e5-130a2). But which problematic features are these that Socrates is so afraid to undermine his theory?
Following a tradition started with R. Allen (1994, p. 99-103), most part of the commentators believe that Socrates' challenge relies on just one question. Socrates has shown to Zeno how sensible things can have opposite properties without generating paradoxes. His solution dwells on the fact that opposite properties within sensible particulars are caused by separate Forms. But the Forms themselves do not suffer from the same problem, being freed from the co-presence of opposites. He would then be amazed if someone could show him that his Forms are also subject to the co-presence of opposite, since that would reest ablish Zeno's paradox 4 .
Despite the almost unanimous acceptance of this reading, I think this interpretation shows serious flaws.

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The most important problem with this reading is that it makes Socrates' speech rather tautological. According to this interpretation, Socrates would be restating the same point with different words one time after another for nothing less than 25 consecutive lines. Although that could be the case, I gather that an interpretation that underlines differences within this long passage would be, for the start, preferable. In this paper, I will defend that Socrates puts forward four different challenges in these same lines. Furthermore, I will propose that these different challenges represent a summary of the criticism that will be developed by Parmenides during the rest of the dialogue. First, let me outline the sentences that Socrates uses to defy his Eleatic companions: 1) 129b1-2: "If someone showed that the likes themselves (αὐτὰ τὰ ὅμοιά) come to be unlike or the unlikes (τὰ ἀνόμοια) like -that, I think, would be a marvel (τέρας ἂν οἶμαι ἦν)".
Although it is clear that these challenges have to do with opposite properties, the words used by Socrates in each one of them uncover sp ecificities that make them radically distinct in terms of ontology.
In the first sentence, for instance, Socrates uses the rather unusual expression αὐτὰ τὰ ὅμοιά. The construction is rare; locutions such as this one, composed of αὐτὰ τὰ + plural adjective only happens two times in discussions about forms within the entire platonic corpus (Phd 74c1: αὐτὰ τὰ ἴσα / Prm. 129b1: αὐτὰ τὰ ὅμοιά). What is surprising in such kind of construction is that it displays a plural to apparently designate a Form. Forms are supposed to be singular, unique entities. While we have many beautiful things, there is only one Beauty. But, if so, why the plural?
The oldest commentator to deal with this problem that we know of is Olympiodorus. And he solves the question by pointing to a third kind of entity (i.e. in addition to Forms and sensibles) as the reference of the expression. Olympiodorus suggests that this kind of construction designate not the form but the several thoughts or mental representations of the Form in various persons' minds (τὰ ἐν τῇ ψυχῇ εἴδη). But for modern interpreters of the Parmenides another option for the designation of this expression comes naturally to mind. During his conversation with Parmenides, Socrates distinguishes not only Forms from things, but also Forms (the Likeness itselfαὐτὸ καθ'αὑτὸ εἶδός τι ὁμοιότητος) from the "likeness we have" (ἡμεῖς ὁμοιότητος ἔχομεν).
The "likeness we have" represent the share a sensible particular receive by participating in a Form. Zeno' s paradox does not work for a Socratic ontology because, by participating in Likeness, a sensible thing comes to have a share of Likeness, and by participating in Unlikeness, the same thing receives a share of Unlikeness. These shares the sensible particulars receive through participation in the Forms are sometimes called "immanent charact ers" or "Form-copies" (cf. Gill & Ryan, 1996, p. 19-27).
Socrate's proposed ontology is therefore composed of three different kinds of entities. Each sensible thing is a whole composed of many elements, each property it has represents one of its immanent charact ers. Each immanent charact er is a unity, in the sense that it does not have different elements, but there are many of them; the likeness in Socrates is different from the likeness in Zeno. Finally, Forms are absolute unities. There is just one form of Likeness and that form is the cause of the many immanent likenesses sensible objects have 5 .
Understood in this way, the use of a plural expression in sentence 1) is not surprising. Although supposed to be freed from the co-presence of opposites, immanent charact ers are numerically many. Socrates' challenge in 1) is, therefore, for someone to show him that immanent charact ers, such as "the likeness I have" and "the likeness you have" are also unlike. But if that is the right interpretation for this sentence, we should expect Parmenides to develop an argument in this direction, i.e. showing that immanent charact ers are subject to the co-presence of opposites.
Well, this is precisely what we find in the argument known as the Whole-Part Dilemma (Prm. 131a-e). According to this argument, a sensible particular that participates in a given Form must get either the whole Form or a part of it. But if the "largeness I have" is just a part of the Largeness itself, then it must be smaller than the whole to which it is a part of. But if that is the case, opposite predication would emerge, and "largeness in us" would be also small. In the same way, the 166 "equal I have" would be unequal, since it cannot be equal to the whole of which it is only a part.
The challenge comprised in sentence 2), in its turn, match the other horn of the Whole-Part Dilemma. By being as a whole in each of the particulars beautiful things, the Beauty itself, being one Form, would also be many, precisely as many as the number of beautiful things. At least, this is a plausible interpretation for Parmenides' conclusion that by being as a whole in each of its participants, a Form would end up "separated from itself " ( Prm. 131b1: Ἓν ἄρα ὂν καὶ ταὐτὸν ἐν πολλοῖς καὶ χωρὶς οὖσιν ὅλον ἅμα ἐνέσται, καὶ οὕτως αὐτὸ αὑτοῦ χωρὶς ἂν εἴη).
In fact, the multiplication of one single Form in indefinitely many others is also the conclusion of other arguments, the Third Man being the most famous. Regardless of the sp ecific interpretation one adopts for this argument, Parmenides explicit conclusion to the Third Man is that according to its premises "each one of the Forms will no longer be one, but unlimited in multitude" (Prm.132b2: καὶ οὐκέτι δὴ ἓν ἕκαστόν σοι τῶν εἰδῶν ἔσται, ἀλλὰ ἄπειρα τὸ πλῆθος). These arguments, along with others arguments in the first part of the dialogue, show exactly what Socrates said to be astonishing in sentence 2), i.e.: that the Forms and Kinds that he hypothesized as a solution to Zeno's paradox have in themselves the opposite properties of being one and many.
With the next challenge (3) we move to the second part of the dialogue. There, we are not talking about Forms in general anymore, but we are talking about one single Form, the One itself. Socrates challenge now is for someone to demonstrate him that "what is one" (a common platonic idiom to designate the Form of the One) is also many, and, conversely, the many to be one. The first clause of this challenge, i.e. to show that the One itself is also many is met by Parmenides' Second Deduction. The second deduction wants to investigate the consequences of the hypothesis that "the one is" or that "the one is one" (Prm. 142b3: ἓν εἰ ἔστιν). At this point of the dialogue, the First Deduction had already concluded that if the One is considered solely in virtue of itself, as a radically austere unity, then it is nothing at all. Now, the Second Deduction wants to investigate the consequences of a One that relates at least with being. And the conclusion it reaches is that if the One is, then it is both in motion and at rest; the same and different; like and unlike; equal and unequal, and so on. But in order to conclude that the One has all these pairs of opposite properties, Parmenides first establishes that the One itself is also many.
In fact, during the Second Deduction, Parmenides demonstrates with two different arguments why "what is one" is also many. The first argument (142d-143a), shows that if the One is, then it is a whole composed of at least two different parts (one and being). Oneness and being are properties of the One of the Second Deduction, and they are here treated as different parts of this subject. Just like in the preceding arguments, a subject with more than one property is here considered a whole composed of parts, each part of it representing one of its properties.
Consider now each part of this whole composed of being and oneness. Is being ever absent from the oneness part, or oneness absent from the being part? No. Actually, the hypothesis of the second deduction mandates that we treat being and oneness always together. Therefore, each part of the "One that is" has two parts (oneness and being); and each of those parts have again two parts, and so on ad infinitum. The "One that is" is, thus, unlimited in multitude.
Another argument on the Second Deduction also demonstrates how "what is one" is many, this time by generating the whole series of numbers from the premise that the One is. But for the sake of brevity I will not treat this argument here.
I want to move, now, to the second clause of sentence (3). This clause states that Socrates would be astonished if someone show him "the many to be one" (Prm.129c.1: τὰ πολλὰ ἕν). Interpreters unanimously understand that "τὰ πολλὰ" here stands for the Form of Many, since that would make the sentence balanced. Socrates challenges someone to show him that the One itself (ὃ ἔστιν ἕν) is also many and, conversely, that the Many itself (τὰ πολλὰ) is also one.
Here, again, we find a very unexpected choice of words. The expression used to supposedly designate the Form of Many (τὰ πολλὰ), besides being plural, does not comes with any of the platonic vocabulary related to the Forms. If Plato's intention was to designate a Form, he certainly could have used the singular expression τὸ πλῆθος to designate the Form of Multitude here, as he did some lines earlier. Or, at the very least, he could have used one of his semi-technical terms to indicate the Forms, such "αυτὸ τὸ"; "τὸ ὃ ἔστιν" etc. Instead of that, what we find in sentence 3) is just "τὰ πολλὰ", an expression used many time during the first part of the dialogue to designate not the Form of Many, as the interpreters suppose, but the multiple sensible things.
Nevertheless, as soon as we realize that the first clause of sentence 3) makes reference to the second part of the dialogue, we envisage another way of making the sentence well balanced, with the advantage of not having to force into it a very strange designation of the Form of Many. According to my interpretation of sentence 3), the expression "τὰ πολλὰ" designates here the "things other than the One" or simply "the others" that appears in the second part of the dialogue. If you remember, Parmenides plan of deductions aims to investigate the consequences for the hypothesis that the One is (or is not) not only for the One itself, but also for the "things other than the One" . Well, these "things others than the One" are exactly "the many things" (τὰ πολλὰ) of sentence 3.
At least, this is what is stablished by the Third Deduction. The third Deduction investigates what are the consequences for "the others" if the One is. The first conclusion Parmenides reaches in the course of this investigation is that "the others" equals "the many things" (τὰ πολλὰ), since they are others than the One. In Parmenides' words: "And the things others than the One would surely be many (πολλὰ); for if things other than the One were neither one nor more than 167 one, they would be nothing" (158b2-3). This is pretty much enough to est ablish that the expression "things others than the One" refers to "the many things" , at least in the context of the third Deduction. But what Socrates challenges his Eleatic companions to demonstrate is that "the many things" , that we now know equals the "things other than the One" , are also one.
Well, that is exactly what the Third Deduction concludes. After est ablishing that "the things other than the One" are not identical to the One, Parmenides quickly remarks that, nonetheless, these things must have some relation to the One. In his words: "And yet the others are not absolutely deprived of the One, but somehow partakes of it. " (157c) In fact, as the deduction will demonstrate, the others (i.e. the many things) partake of the One by being wholes composed of many distinct parts.
It seems, therefore, that the Third Deduction demonstrates what Socrates says to be astonishing on the second clause of sentence 3, i.e.: that the many things are also one. However, you must be asking yourselves why would Socrates be astonished in this case? Socrates proposed his Theory of Forms to Zeno precisely for such kind of things to happen, that the many distinct sensible particulars could also be one. According to my reading of sentence (3), on the contrary, what seems to be Socrates' first intention is now presented as an unwilling surprise. This is the point where Plato geniality as a philosophical writer enters the scene. Sentence (3), as well as all the other challenges outlined above, is an example of a very clever use of the figure of sp eech known as prolepsis or simply "anticipation" . If you read sentences 1 to 4 again, this time taking in consideration the ontology that will emerge in Plato's dialogues after the Parmenides, you will be able to recognize that these sentences pretty much describe the ontological landscape of dialogues such as the Sophist and the Philebus.
Reading the Philebus, we discover that Socrates identify two distinct problems connected to the proposition that "the many are one, and the one many" . The first problem is actually very commonplace, as Socrates explains, and it is related to the fact that a sensible thing, like Protarchus, is one thing although having multiples parts. Nevertheless, the second problem is really amazing because it is not about "the things that come to be and perish" but about the unities that populate the world of Forms. It is remarkable that Socrates uses the same words in both dialogues as if quoting himself here (cf. Phl. 15b-16d).
Similarly, sentence (4) anticipates the metaphysical developments of the Sophist. There, another Eleatic charact er, the Stranger will proposed an Ontology based on the interwoven of Forms (συμπλοκή τῶν ειδῶν). What charact erizes this revised Platonic ontology is precisely the fact that according to it Forms can mix together and separate. Again, it is as if Socrates were here quoting his conversation with the Eleatic Stranger (cf. Sph. 251a-255e).
Socrates' astonishment in all these sentences has, therefore, two different but nevertheless simultaneously correct readings. Each one of these readings correspond to a sp ecific level of access to the Platonic ontology. Readers that do not have access to the development of later dialogues such as the Sophist or the Philebus understand Socrates' astonishment as the negative surprise Socrates would display in the case of the falsification of important tenets of his theory. However, for those acquainted with Plato's later ontology, these sentences anticipate Socrates' marvel with something that will be indeed the case, i.e.: that the Forms themselves are organized through a complex relation of parts and wholes, unities and multiplicities. In the second part of the Parmenides these complex relations come up in the form of paradoxes and antinomies. But in dialogues such as the Sophist, the Philebus, and the Sta teman, these relations will appear in a positive exposition of a renewed ontology, an ontology according to which every Form preserve some type of relationship with any other Form, even its contrary.