Abstract
On Malcolm Schofield’s highly influential reading of the Similarity Regress in Part I of the Parmenides, the problem that the Regress poses is explanatory. Socrates posited the Similarity Form in order to explain why similar things are similar: similar things are similar because they participate in the Form Similarity as copies of the same original. Yet, the Similarity Regress generates an infinite series of Similarity Forms such that explanation is deferred ad infinitum. Schofield provides a philosophical incentive for adopting his reading. He argues that the treatment of similarity in Part II of the dialogue yields a complete explanation of similarity. If we adopt this account, we can avoid the Similarity Regress altogether since a Form of Similarity is not needed in order to explain why similar things are similar. Thus, his interpretation has a hugely important philosophical pay-off.
However, there is a different way to read the argument. Socrates claims that each Form is only one. Yet, the Similarity Regress is an argument that generates an infinite series of Similarity Forms. This results in a violation of the principle of non-contradiction: there is both only one Similarity Form and infinitely many Similarity Forms. Yet, anything that is incompatible with the principle of non-contradiction is surely absurd. Nobody, as far as I am aware, has explored whether this reading also has philosophical pay-off if we look at it together with similarity in Part II. However, should this interpretation pay off, it would be a viable alternative to Schofield’s.
In this paper, I explore both views in the context of the treatment of similarity in Part II of the Parmenides. I argue for an account of similarity that differs from Schofield’s. Although my account is not wholly dismissive of Schofield’s, it renders the pay-off of Schofield’s account less appealing than he suggests. Furthermore, I show that the account of similarity in Part II also yields important lessons for the proponent of the alternative reading of the Similarity Regress: similarity as treated in Part II simply leads to further infinite regresses, thereby pushing us to consider rejecting the account of similarity in Part II too and to look for some other account intead.
On Malcolm Schofield’s (1996) highly influential reading of the Similarity Regress in Part I of the Parmenides[1] (henceforth SV, for ‘Schofield’s version’), the argument generates an infinite series of Similarity Forms. It thereby postpones the explanation of similarity ad infinitum. However, Schofield argues that with similarity as conceived of in Part II, we find a way of understanding similarity that does not require Forms and on which we have a complete explanation of similarity. Armed with this, we can solve the Similarity Regress. This is one important reason why SV seems attractive and credible; if Schofield is right about the treatment of similarity in Part II and its connection with the Similarity Regress on SV, it has hugely important philosophical pay-off.
However, there is a different way to read the argument. On this view (henceforth AV (the alternative version)), the Similarity Regress is an argument that generates an infinite series which results in a violation of the principle of non-contradiction: there is both only one Similarity Form and infinitely many Similarity Forms. Yet, anything that is incompatible with the principle of non-contradiction is surely absurd.[2] Nobody, as far as I am aware, has explored whether AV also has philosophical pay-off if we look at it together with similarity in Part II. Yet, if it does, this would lend it credibility and appeal as an alternative to SV.
In this paper, I uncover and compare the philosophical pay-off of SV and AV in the context of the treatment of ὅμοιον (similar) and ἀνόμοιον (dissimilar) in Part II of the Parmenides. I begin by making some assumptions about the dialogue and explaining SV and AV. Next, I offer an analysis of similarity in Part II which differs from Schofield’s. In doing so, unlike Schofield, I look at the connection between ὅμοιον (similar) and ἀνόμοιον (dissimilar), ταὐτό (same) and ἕτερον (different). I proceed to show that we can use this connection to construct arguments that generate infinite series of similarity and dissimilarity properties. For the proponent of SV, this has interesting consequences. She might think it provides a solution to the Similarity Regress. However, this solution is less appealing than Schofield suggests because it comes at a high ontological cost. Having considered this, she might come to think that the cost is too high to make it a viable solution. As a consequence, she might even re-evaluate SV, perhaps instead maintaining that both postponement of explanation and ontological cost make the Similarity Regress troubling. My treatment of similarity in Part II also yields significant results for the proponent of AV: it shows that adopting similarity as it is treated in Part II instead of in Part I yields the very same problem as in Part I: infinite regress. Thus, contra Schofield’s claim, it does not provide a solution to the Similarity Regress; rather, it pushes us to consider rejecting the account of similarity in Part II too and look for some other account.
Some assumptions
Part II of the Parmenides is initially presented as a demonstration of a training method that will help the young Socrates.[3] This seems to give the reader a good idea of what Part II will be: preliminary exercises for a novice philosopher. However, interpretations of Part II are plagued by disagreements about even very basic features. Some of these are relevant to my approach to the text here: whether or not Parts I and II are parts of the same dialogue and should be read together;[4] what the purpose of Part II is (e. g., just a training exercise,[5] a joke,[6] something more substantive?[7]) and what consequences this has for how the reader should approach Part II; what exactly the one (ἕν) and the others (τἆλλα) are;[8] how the deductions are related. I cannot hope to resolve these issues here. Consequently, I begin by making some basic assumptions:
Parts I and II are parts of one, unified dialogue. Thus, a reader is entitled to look to Part I when reflecting on arguments in Part II and vice versa.[9]
Part II is a training exercise but not mere intellectual gymnastics. It prompts the reader to examine the arguments as they appear in the text and to reflect and tease out implications of the arguments, e. g. by constructing further arguments that are not explicitly stated but which Plato lays the ground for, both in connection with other parts of the text and independently of it.[10]
I take it that the metaphysics in Part II excludes Forms. Thus, the one (ἕν) and the others (τἆλλα) are not Forms. I also assume that the others are any of the things that are not the one. However, I avoid any further commitments about their metaphysical status.[11]
In the first deduction, Parmenides examines what follows from the first hypothesis, ‘if the one is’, where the focus is on ‘one’; in the second deduction, he sees what follows from the same hypothesis, where the focus is on ‘is’.[12] In the first deduction, he argues that if the one is, then for the pair of properties, F and not-F, neither F nor not-F can be ascribed to the one. Then, in the second deduction, he argues that if the one is, the pair of properties, F and not-F, then both F and not-F must be ascribed to the one.[13]
We are entitled to look at passages from different deductions together in exploring similarity, dissimilarity identity and non-identity in Part II.[14]
Two competing interpretations: Explaining SV and AV
On SV, the Similarity Regress runs as follows:
Similar things are similar in virtue of being copies modelled on the same original, Similarity.
Copies and their models are similar.
Nothing can be similar in virtue of being modelled on itself.
Similarity and other similar things are similar in virtue of being copies modelled on the same original, Similarity2.
Therefore, Similarity2 and other things are similar in virtue of being copies modelled on the same original, Similarity3 – and so on ad infinitum.[15]
Why is this argument problematic according to Schofield? Similarity was supposed to explain the participation relation on an original-copy model according to which instantiations stand to Forms like copies to a paradigmatic original. On this model, to participate in a Form is to be similar to the Form as a copy is similar to the original. Thus, in order to explain why similar things are similar, we must posit a Form of Similarity in which they participate as copies relate to an original. Thus, Barry the drunk whale and Iqbal the drunk aardvark are similar because they both participate in Similarity as copies of the same model. However, Similarity, Barry and Iqbal are all similar. On this explanation, then, they are all similar because they participate in a further Form, Similarity2, as copies to an original. But since Similarity2, Barry and Iqbal are all similar, they participate in a further Form, Similarity 3 as copies to an original – and so on ad infinitum. Consequently, on this original-copy model, the explanation of why Barry and Iqbal are similar is deferred ad infinitum – and the same goes for all other cases of similarity. The problem that the Regress results in, then, is that Similarity, on the copy-original model, cannot perform the explanatory function it was supposed to.
Alternatively, we can read the argument as an infinite regress on AV:
Similar things are similar in virtue of being copies modelled on the same original, Similarity.
Copies and their models are similar.
Nothing can be similar in virtue of being modelled on itself.
Similarity and other similar things are similar in virtue of being copies modelled on the same original, Similarity2.
Therefore, Similarity2 and other things are similar in virtue of being copies modelled on the same original, Similarity3 – and so on ad infinitum.
For any property, F, there is exactly one Form of Fness.
Therefore, there is both only one Similarity Form and infinitely many Similarity Forms.
On this reading, the problem that the Similarity Regress poses is logical. Socrates has been quite clear that there is only one Form Fness for each predicate, F;[16] Forms are one over many, hence 6. Socrates’ attempt to explain the participation relation on the copy-original model, however, generates an infinite number of Similarity Forms. Socrates’ claim that there is only one Form Fness for each predicate F (6) and the infinite number of Similarity Forms create a contradiction: there is both only one Similarity Form and infinitely many Similarity Forms (7).[17]
Sameness, difference, similarity and dissimilarity as distinct
In this section, I begin investigating similarity and its correlate, dissimilarity, in Part II, giving some preliminary reasons for taking ὅμοιον (similar) and ἀνόμοιον (dissimilar) and the closely related ταὐτό (same) and ἕτερον (different)[18] to be terms that have precise and distinct meanings.
In Greek, ὅμοιον often means ‘sameness’. Therefore, one might think that there is reason to suppose that, in Part II, ὅμοιον and ταὐτό are equivalent. If so, one might also suppose that ἀνόμοιον and ἕτερον are used interchangeably.
However, cases where ὅμοιον is used to indicate sameness in Plato tend to occur in conversational passages where philosophically precise language is less important. Moreover, in these cases, ὅμοιον tends to feature with ἀεί. For example:
ἀεὶ ὅμοιον εἶ, ὦ Ἀπολλόδωρε· ἀεὶ γὰρ σαυτόν τε κακηγορεῖς καὶ τοὺς ἄλλους
You are always the same, Apollodorus – always bad mouthing yourself and others.
Symposium 173d4–5
ἀλλ' ἐγὼ κινδυνεύω ἀεὶ ὅμοιον εἶναι·
But I am likely always the same.
Charmides 170a2
In these passages, ἀεί is what gives ὅμοιον the sense of sameness (identity here) rather than similarity. Thus, Plato is not in the habit of using ὅμοιον alone to mean ‘sameness’.
Furthermore, it is clear that in the first deduction, Parmenides offers us a set of arguments for the conjunctive conclusion that the one is not ταὐτό to itself or something else, or ἕτερον to itself or something else. This is separate from the set of arguments that conclude that the one is neither ὅμοιον nor ἀνόμοιον to itself or to anything else. Likewise, in the second deduction, we find two distinct sets of arguments. One purportedly shows that the one is both ταὐτό and ἕτερον to itself and to something else (if it is). The other supposedly shows that the one is ὅμοιον and ἀνόμοιον to itself and to something else (if it is). Plato is also very careful to avoid using ὅμοιον and ἀνόμοιον in the arguments about ταὐτό and ἕτερον. This separation between ταὐτό, ἕτερον, ὅμοιον and ἀνόμοιον continues throughout Part II; in fact, in the fourth, fifth, sixth, seventh and eighth deductions, ὅμοιον (similar), ἀνόμοιον (dissimilar), ταὐτό (same) and ἕτερον (different) all appear and each is treated separately. Thus, Plato must have mutually distinct things in mind with the two pairs of opposites, ταὐτό and ἕτερον, ὅμοιον and ἀνόμοιον.
An analysis of similarity, dissimilarity, identity and non-identity
My next task is to uncover distinct semantic criteria for each of the terms: ὅμοιον (similar) and ἀνόμοιον (dissimilar) and the closely related ταὐτό (same) and ἕτερον (different). In doing so, I look at the first and second deductions. In the passages I explore, there are two important phrases that are difficult to translate and interpret: ταὐτό + πέπονθεναι (lit. to have suffered the same) and ἕτερον + πέπονθεναι (lit. to have suffered the different). In this section, I assume that ταὐτό + πέπονθεναι means ‘to have some property in common with’ and that ἕτερον + πέπονθεναι means ‘to have some discrepancy in properties with respect to’; I postpone the justification of this until the next section. I also assume from the outset that ταὐτό (same) means identical and that ἕτερον (different) means non-identical. Whilst I take it that this is independently plausible, the criteria I find for ταὐτό and ἕτερον support this, as I show below.
The argument in the first deduction that shows that the one is neither similar to itself nor to something else[19] begins with a general claim: that which has suffered the same as something is similar to it (τὸ ταὐτόν που πεπονθὸς ὅμοιον[20]).[21] This gives us the first important feature of similarity, the sufficient conditions for similarity:
For any x and any y, if there is some property that x and y has, then x is similar to y.
I turn now to establish the necessary conditions for similarity. I use the following argument from the second deduction:
Argument A (147c2–8):[22]
A1. Since (the one) was different from the others, the others would also be different from it.
ἐπειδὴ γοῦν ἕτερον τῶν ἄλλων ἐφάν καὶ τἆλλά που ἕτερα ἂν ἐκείνου εἴη – τί μήν; (147c2–3)
A2. Thus, as (the one) is different from the others, so the others are also different from it, neither more nor less.
οὐκοῦν οὕτως ἕτερον τῶν ἄλλων, ὥσπερ καὶ τἆλλα ἐκείνου, καὶ οὔτε μᾶλλον οὔτε ἧττον; – τί γὰρ ἄν; (147c3–5)
A3. So, if the one and the others are neither more nor less (different from one another), they are in a similar manner.
εἰ ἄρα μήτε μᾶλλον μήτε ἧττον, ὁμοίως. – ναί. (147c5–6)
A4. Since the one is different from the one and the others are different from the one, the one has suffered the different from the others and the others have suffered the different from the one.
Tacit.
A5. Since the one and the others are in a similar manner, the one has suffered the same as the others and the others have suffered the different from the one.
Tacit.
A6. Therefore, by having suffered being different from the others and the others just so [having suffered being different from (the one), the one has suffered the same as the others and the others have suffered the same as the one.
οὐκοῦν ᾗ ἕτερον εἶναι πέπονθεν τῶν ἄλλων καὶ τἆλλα ἐκείνου ὡσαύτως, ταύτῃ ταὐτὸν ἂν πεπονθότα εἶεν τό τε ἓν τοῖς ἄλλοις καὶ τἆλλα τῷ ἑνί. (147c6–8).
According to A1, the one is non-identical to the others and the others are non-identical to the one. Parmenides then claims that the one is non-identical to the others and vice versa in exactly the same way, ‘neither more nor less’ in A2. I take it that the claim here is not that the one is non-identical to the others to the same degree that the others are non-identical to it since non-identity does not come in degrees. Instead, this indicates that both the others and the one have something in common: they are non-identical and, therefore, according to A3, ‘are in a similar manner’.
Consider A3. Plato here uses ὁμοίως (in a similar manner), not ὅμοιον (similar). Thus, we cannot straightforwardly read the inference to be: since the one and the others share something (being non-identical), they are similar. Nevertheless, ὁμοίως must be closely related to ὅμοιον. Thus, I take it to mean that they are similar to one another in respect of something specific (being non-identical). Since, if something is non-identical, it has the property of non-identity, they have some property in common (in respect of being non-identical), as in A5. From this, we can infer a more general claim: for any x and any y, if x is similar to y in respect of some feature, x has some property in common with y in respect of that feature. It follows from this that:
For any x and any y, if x is similar to y, there is some property that x and y have.
From I and II together, we can infer the following criteria for similarity: for any x and any y, x is similar to y if and only if there is some property that x and y have.
I now provide criteria for dissimilarity. In the second deduction, we find an argument that shows that the one, if it is, is in no way dissimilar to itself or something else.[23] It also begins with a general claim: ‘that which has suffered the different either from itself or something else would be dissimilar from itself or from something else, if that which has suffered the same as something is similar to it’ (τὸ γε μὴν ἕτερον πεπονθὸς ἢ ἑαυτοῦ ἢ ἄλλου ἀνόμοιον ἂν εἴη ἢ ἑαυτῷ ἢ ἄλλῳ, εἴπερ τὸ ταὐτὸν πεπονθὸς ὅμοιον)[24] I take it that ‘itself’ and ‘something else’ are exhaustive, hence the first feature of dissimilarity is:
For any x and any y, if x there is some property that x has and y does not or y has and x does, then x is dissimilar to y.
Given that similarity and dissimilarity are opposites, I take it that there is a second feature of dissimilarity which corresponds to feature II of similarity:
For any x and any y, x is dissimilar to y, if there is some property that x has and y does not or that y has and x does not.
Thus, the criteria for dissimilarity I adopt are: for any x and any y, x is dissimilar to y if and only if there is some property that x has and y does not or that y has and x does not.
I turn now to uncover definitions of ταὐτό (identical) and ἕτερον (non-identical). Consider the following argument:
Argument B (148c4–d5):
B1. Insofar as something has suffered the same, it would not have suffered something of another sort.
ᾗι ταὐτὸν πέπονθε, μὴ ἀλλοῖον πεπονθέναι (148c4).
B2. In not having suffered something of another sort, it would not be dissimilar.
μὴ ἀλλοῖον δὲ πεπονθὸς μὴ ἀνόμοιον (148c4–5).
B3. In not being dissimilar, it would be similar.
μὴ ἀνόμοιον δὲ ὅμοιον εἶναι (148c5–6).
B4. Insofar as something has suffered the other, it would be of another sort.
ᾗ δ' ἄλλο πέπονθεν, ἀλλοῖον (148c6).
B5. In being of another sort, it would be dissimilar.
ἀλλοῖον δὲ ὂν ἀνόμοιον εἶναι – ἀληθῆ λέγεις. (148c6–7)
B6. Since the one is the same as the others and because it is different (to the others), for both or either of these reasons, it is similar and dissimilar to the others.
ταὐτόν τε ἄρα ὂν τὸ ἓν τοῖς ἄλλοις καὶ ὅτι ἕτερόν ἐστι, κατ' ἀμφότερα καὶ κατὰ ἑκάτερον, ὅμοιόν τε ἂν εἴη καὶ ἀνόμοιον τοῖς ἄλλοις – πάνυ γε (148c7–d1)
B7. And likewise, since it seemed different from itself and the same as itself,[25] for both or either of these reasons, it is similar and dissimilar (to itself).
οὐκοῦν καὶ ἑαυτῷ ὡσαύτως, ἐπείπερ ἕτερόν τε ἑαυτοῦ καὶ ταὐτὸν ἑαυτῷ ἐφάνη, κατ' ἀμφότερα καὶ κατὰ ἑκάτερον ὅμοιόν τε καὶ ἀνόμοιον φανήσεται; – ἀνάγκη (148d1–4)
B1, I take it, tells us that insofar as something has the same property as something, it does not have any other property, irrespective of the sort of property it is. Thus, if Barry and Harry are both drunk, then, there is no property that one has and the other does not in respect of their shared property, drunk. According to B2, insofar as there is no property whatsoever that one thing has and the other does not, insofar as there is some property that they both have, then they are not dissimilar (in any respect). Thus, if Barry and Harry are both drunk, there is no property that one has and the other does not in respect of their shared property, drunk. Insofar as there is no property whatsoever that one has and the other does not in this specific way, they are not dissimilar in any respect.
Consider this in the context of identity. Common sense dictates that if something shares all and only its properties with something, they are one, self-identical thing. This together with 1 and 2 gives us the first feature of identity:
For any x and any y, if for any property that x has, y has it and for any property that y has, x has it, then x is identical to y.
Since, I take it, identity and non-identity are exclusive:
For any x and any y, if there is some property that x has and y does not or that y has and x does not, x is non-identical to y.
Consider B4. I take it that ἄλλο + πεπονθέναι (to have suffered the other) is not used interchangeably with ἕτερον + πεπονθέναι (to have suffered the different). However, it must be related closely enough to enable us to explain why πεπονθέναι features at all. I read it as meaning: having the property of being another thing; for, ἄλλο is so closely and consistently aligned with ‘the others’, and having a property fits with the meaning of πεπονθέναι (to have suffered) + ταὐτόν and ἕτερόν. Presumably, something has the property of being another thing than something if and only if it is non-identical to it. This, together with B5 gives us:
For any x and any y, if x is non-identical to y, there is some property that x has and y does not or that y has and x does not.
Since, I take it, identity and non-identity are exclusive:
For any x and any y, if x is identical to y, then for any property that x has, y has it and for any property that y has, x has it.
I–IV together with the treatment of similarity and dissimilarity give us the criteria for identity and non-identity:
For any x and any y, x is identical to y if and only if x is similar to y in every respect and there is no respect in which x is dissimilar to y.
For any x and any y, x is non-identical to y if and only if there is some respect in which x is dissimilar to y and it is not the case that x is similar to y in every respect.
To have suffered the same and to have suffered the different
Recall that I assumed that ταὐτό and ἕτερον mean ‘identical’ and ‘non-identical’. The criteria I have uncovered provide ample justification for this; after all, they are in effect Leibnizian criteria for strict numerical identity.
I have also taken the rather opaque ‘to have suffered the same’ (ταὐτό + πεπονθέναι) and ‘to have suffered the different’ (ἕτερον + πεπονθέναι) to mean ‘to have some property in common with’ and ‘to have some discrepancy in properties’.[26] However, justifying this is less straightforward. There is an existing detailed analysis of ταὐτό + πεπονθέναι that differs from mine: Schofield’s.[27] He reads ταὐτό + πεπονθέναι as ‘being qualified in the same way’. On this analysis, I take it, Barry the drunk whale and Iqbal the drunk aardvark are similar because they are qualified in the same way, i. e. they both share the predicate ‘drunk’.
If Schofield’s reading is right, it has hugely important consequences which make it very appealing for a proponent of SV: it allows her to block the infinite series of Forms generated by the Similarity Regress. Reconsider the Regress on SV:
Similar things are similar in virtue of being copies modelled on the same original, Similarity.
Copies and their models are similar.
Nothing can be similar in virtue of being modelled on itself.
Similarity and other similar things are similar in virtue of being copies modelled on the same original, Similarity2.
Therefore, Similarity2 and other things are similar in virtue of being copies modelled on the same original, Similarity3 – and so on ad infinitum.
If we accept the account of similarity in Part II as Schofield understands it, the Regress is not sound and no infinite series of Forms is generated. 1 is false because things are in fact similar in virtue of sharing the same predicate. The explanation of their similarity ends here; there is no need to posit a Form (or indeed anything further). This blocks the move to 4 and 5. For example, suppose Barry the whale and Iqbal the aardvark are both drunk. They are similar because they are qualified in the same way: ‘drunk’ is predicated of both. This provides us with a perfectly good explanation of their similarity; we do not need to appeal to anything further.
However, Schofield argues that in the passages about similarity, not only is the ontology of Forms absent but there are no ontological assumptions or commitments whatsoever.[28] Consequently, his reading is incompatible with my criteria, which do require ontological commitments: for any x and any y, x has the property of being similar to y (x is similar to y) if and only if there is some property that x has and y has; for any x and any y, x has the property of being dissimilar to y (x is dissimilar to y) if and only if there is some property that x has and y does not have or that y has and x does not have.
Schofield’s reason for this is that Plato does not use ‘similarity’ as an abstract noun in passages about similarity in Part II.[29] (Although Schofield himself is not concerned with dissimilarity and therefore does not discuss the meaning of ἕτερον + πεπονθέναι (to have suffered the different) we might argue that it means ‘being qualified in a different way’, where this does not imply any ontological commitments either. The justification here would be that Plato does not use ‘dissimilarity’ as an abstract noun in passages about dissimilarity.)
I agree that Plato does not use language that we would expect him to if the ontology of Forms were assumed in the passages about similarity and dissimilarity in Part II. However, predication is naturally taken to imply properties. Furthermore, in the first and second deductions, I take it, what characterises the majority of the conclusions is denials of and ascriptions to the one of property-parts – and Plato does not use any special language to indicate this.[30] This is a pattern that continues throughout Part II. This supports my view that similarity and dissimilarity properties are denied of and ascribed to the one.
So why my interpretation? It has several advantages. Firstly, I take it that ‘to have suffered the same’ (ταὐτό + πεπονθέναι) and ‘to have suffered the different’ (ἕτερον + πεπονθέναι) cannot simply mean having the properties of identity and non-identity since, as I have already shown, Plato is careful to change his language in the similarity and dissimilarity arguments; ταὐτό (same) and ἕτερον (different) never occur with πεπονθέναι (to have suffered) in the sameness and difference arguments. My interpretation fits with this. Secondly, I can explain why Plato uses ταὐτό and ἕτερον with πεπονθέναι (to have suffered) in the similarity and dissimilarity arguments but not in the sameness and difference arguments: the criteria for the opposites, identity and non-identity, are not the same as for the opposites, similarity and dissimilarity. Thirdly, my reading fits well with the argument at 147c2–8. There, Parmenides suggests that because the one and the others share a property, non-identity, they are similar in that respect (147c3–6). This is compatible with my reading of ταὐτό + πεπονθέναι (to have suffered the same), on which sharing one property is sufficient for similarity. Fourthly, together with the criteria for identity and non-identity, my interpretation yields Leibnizian criteria for identity and non-identity that are worth taking seriously, as demonstrated by the wealth of scholarship on Leibniz’ Law. Finally, as I show below, my reading yields interesting philosophical lessons when looked at in conjunction with the Similarity Regress, whether on SV or AV.
First, though, I deal with an objection to the way I read ταὐτό + πεπονθέναι (to have suffered the same) and ἕτερον + πεπονθέναι (to have suffered the different). It might be argued that πεπονθέναι has a causal sense.[31] This is not accommodated on my interpretation. Moreover, there are two readings of ταὐτό + πεπονθέναι and ἕτερον + πεπονθέναι that do capture this causal sense, making them more plausible. We could understand ταὐτό + πεπονθέναι and ἕτερον + πεπονθέναι as being caused to be identical and being caused to be non-identical or we could think that ταὐτό + πεπονθέναι and ἕτερον + πεπονθέναι mean being affected by identity and non-identity themselves. However, whilst πεπονθέναι (to have suffered) can have a causal sense, it does not have to.[32] In addition, neither of the two alternative readings is satisfactory. On the former, we are left asking why being caused to be identical or non-identical is especially relevant for similarity and dissimilarity. The latter is also problematic since Plato does not give us any strong linguistic signs that suggest we should have identity and non-identity themselves in mind throughout; indeed, Plato seems to use ‘the F itself’ or ‘nature’ (φύσις) when indicating some property itself.[33]
Similarity, dissimilarity and properties
I assume the criteria for similarity, dissimilarity, identity and non-identity above for the rest of the paper and turn now to briefly make some further comments on them. I take it that things can be similar and dissimilar in different respects (as assumed by the criteria for identity and non-identity). I suggest that the respects in which things are similar are determined by shared properties. For example, my red sock is similar to my black sock and vice versa in respect of material in virtue of a shared property: being woollen. Likewise, my red sock is similar to my black sock and vice versa in respect of size in virtue of their shared property: being a size small. This suggestion is supported by Argument C:
C1. Since (the one) was different from the others, the others would also be different from it.
ἐπειδὴ γοῦν ἕτερον τῶν ἄλλων ἐφάν καὶ τἆλλά που ἕτερα ἂν ἐκείνου εἴη. – τί μήν; (147c2–3)
C2. So, in this way, just as (the one) is different from the others, so the others are also different from it, neither more nor less.
οὐκοῦν οὕτως ἕτερον τῶν ἄλλων, ὥσπερ καὶ τἆλλα ἐκείνου, καὶ οὔτε μᾶλλον οὔτε ἧττον; – τί γὰρ ἄν; (147c3–5)
C3. Since the one and the others are (different from one another) neither more nor less, they are in a similar manner.
εἰ ἄρα μήτε μᾶλλον μήτε ἧττον, ὁμοίως. – ναί. (147c5–6)
C4. Since the one is different from the one and the others are different from the one, the one suffers the different from the others and the others suffer the different from the one.
Tacit.
C5. Since the one and the others are in a similar manner, the one has suffered the same as the others and the others have suffered the different from the one.
Tacit.
C6. Therefore, by having suffered being different from the others and the others just so [having suffered being different from] (the one), the one has suffered the same as the others and the others have suffered the same as the one.
οὐκοῦν ᾗ ἕτερον εἶναι πέπονθεν τῶν ἄλλων καὶ τἆλλα ἐκείνου ὡσαύτως, ταύτῃ ταὐτὸν ἂν πεπονθότα εἶεν τό τε ἓν τοῖς ἄλλοις καὶ τἆλλα τῷ ἑνί. (147c6–8).
According to C1, the one is non-identical to the others and vice versa. In C2, Parmenides takes it to follow from C1 that the one and the others are both non-identical; it is clear from C5 that this amounts to both having the property: non-identity. In C3, he moves from the claim that they are non-identical to the claim that they are similar to one another in respect of being non-identical. This suggests that things are similar in particular respects in virtue of particular (correlative) shared properties. Given that dissimilarity mirrors similarity, I take it that dissimilarity works like this too, so that my black sock and red sock are dissimilar to one another in respect of colour in virtue of a discrepancy in properties, i. e. because my black sock is black but my red sock is not and my red sock is red but my black sock is not.
Argument C tells us more about the relationship between similarity and dissimilarity and properties. If things have similarity and dissimilarity properties in respect of shared properties and discrepancies in properties, it seems that if similarity and dissimilarity are themselves properties, they are higher-order properties; it is in virtue of my red sock and my black sock both having the property of being a size small that my red sock has the property of being similar to my black sock in respect of size. Likewise, it is in virtue of my red sock’s being handmade and my black sock’s not being handmade and my black sock’s being machine-made and my red sock’s not being machine-made that my red sock is dissimilar to my black sock in texture.
We might, of course, deny that similarity and dissimilarity are properties themselves and instead maintain that similarity just is having a property in common and dissimilarity just is having a discrepancy in properties. However, this does not fit with the pattern of arguments in Part II. In the first deduction, pairs of opposed properties are denied of the one, and, in the second, pairs of opposed properties are ascribed to the one. Likewise, in the third deduction, pairs of opposites are ascribed to the one, and, in the fourth deduction, pairs of opposites are denied of the one. Yet, in all these deductions, one of the pairs of opposites is similarity and dissimilarity. Consequently, similarity and dissimilarity cannot simply be having a property in common and having a discrepancy in properties. Rather, they should be taken as higher-order properties themselves.
Another question is how widely we are entitled to take the scope of similarity and dissimilarity properties. Given that the pattern in the second deduction (and all other positive deductions) seems to be to attribute as many properties to the one and the others as possible, I think we are entitled to think that similarity and dissimilarity properties occur at more than one higher-order. For example, suppose Barry the whale is similar to Slothocles the sloth in respect of activity. This is in virtue of Barry and Slothocles both sharing the property of swimming. Barry will also be similar to Slothocles in a further respect and at an even higher-order. This is in virtue of another shared property: similar to something in virtue of sharing the property of swimming.[34] Likewise, Barry the whale is dissimilar to Slothocles the sloth in respect of species. This is in virtue of a property that Barry has and Slothocles does not have (whale) and a property that Slothocles has and Barry does not (sloth). But notice that Barry has the property of being dissimilar to Slothocles. According to the criteria for identity, Slothocles cannot be dissimilar to himself in any way. Thus, this is a property that Barry has but which Slothocles does not. Barry then will have a further higher-order property: dissimilar to Slothocles in virtue of a further discrepancy in properties, i. e. being dissimilar to Slothocles and not being dissimilar to Slothocles.
I argued in this section that similarity and dissimilarity are widely construed such that things have similarity properties in virtue of other similarity properties and dissimilarity properties in virtue of other dissimilar properties. In the next section, I use what I have established so far about similarity and dissimilarity in Part II to reflect on possible regress arguments that Plato lays the ground for.
The return of the regress?
Part of the reflective role of the reader of Part II, I have claimed, is to construct arguments that are not explicitly stated in the text but which Plato lays the ground for. By the time the reader reaches the end of Part I, she will already have encountered the Largeness and the Similarity Regresses. In the transition between the two Parts, Zeno, many of whose arguments are plausible infinite regresses, is connected to the content of Part II.[35] When the reader progresses to the second deduction, she finds another infinite regress argument: the One and Being argument. Consequently, the careful reader will be particularly aware of infinite regresses when reflecting on Part II in general, especially in the second deduction (and the first, which mirrors it). Moreover, regress has also been explicitly connected with similarity with the Similarity Regress. Thus, the reader has been primed to think about infinite regress in the context of similarity (and its correlate, dissimilarity). Consequently, I take it that the reader of the first and second deductions ought to think about infinite regress arguments together with the treatment of similarity and dissimilarity. One way to do this is to construct arguments based on their treatment in the text. In what follows, I do just this, using my suggested criteria for similarity, dissimilarity, identity and non-identity.
I begin by constructing an argument that generates infinite series of similarity properties, Argument D. The similarity criteria yield the first premise:
D1. For any x and any y, x is similar to y if and only if there is some property that x and y has.
I argued in the previous section that:
D2. If something is similar to something in some respect, it is similar to it in virtue of sharing a relevant property, e. g. my red sock is similar to my black sock in respect of size in virtue of sharing the property of being a size small.
From my earlier discussion, it is evident that:
D3. If some particular thing is similar to some particular thing, it has a further and different property: similar to something (in the same respect and in virtue of the same shared properties). For example, since my red sock has the property of being similar to my black sock (in respect of size and in virtue of sharing the property of being a size small), it also has a different property: being similar to something (also in respect of size and in virtue of sharing the property of being a size small with something). Call this similarity1.
It follows that:
D4. Therefore, if something is similar to something in virtue of similarity1, then it will have a further similarity property (in virtue of sharing the property similarity1), similarity2. For example, if my red sock and black sock both have the property similarity1, then they also have the property similarity2 (in virtue of similarity1).
D5. Therefore, if something is similar to something in virtue of similarity2, then it will have a further similarity property (in virtue of sharing the property similarity2), similarity 3 – and so on ad infinitum. For example, if my red sock and black sock both have the property similarity2, then they also have the property similarity 3 (in virtue of similarity2) – and so on.
This argument generates an infinite series of similarity properties – but there will be many more infinite series of similarity properties. Recall that, on the criteria for identity, for any x and any y, x is identical to y if and only if x is similar to y in every respect. Therefore, everything will have an infinite series of this sort for every property it shares with itself, as well as for every property it shares with something else. In addition, everything is non-identical to everything else. I take it that it is impossible for two (or more) things to be non-identical to the same thing in virtue of the very same discrepancy in properties. Consequently, for every pair of things that are non-identical, they will share the property of being non-identical to something in virtue of some discrepancy in properties. They are thereby similar and similar in virtue of this similarity – and so on.
Nevertheless, explanation is not postponed ad infinitum. After all, we have criteria for similarity. This allows us to give a perfectly good explanation of why things are similar, even if there are infinitely many such explanations: my red sock is similar to the black sock and vice versa because they both have the property of being a size small because they both have the property of similar1 etc.
We can create a correlate dissimilarity argument which generates infinite series of dissimilarity properties, Argument E. The first premise is the criteria for dissimilarity:
E1. For any x and any y, x is dissimilar to y and y is dissimilar to x (in some respect) if and only if there is some property that x has and y does not or that y has and x does not.
I previously established that:
E2. If something is dissimilar to something in some respect, it is dissimilar to it in virtue of some relevant discrepancy in properties. For example, Barry is dissimilar to Slothocles in respect of species in virtue of a particular discrepancy in properties: Barry is a whale and a Slothocles is not and Slothocles is a sloth and Barry is not.
It follows that:
E3. If something is dissimilar to something in some respect, it has the property of being dissimilar to it (in that respect and in virtue of a relevant discrepancy in properties). For example, Barry has the property of being dissimilar to Slothocles (in respect of species and in virtue of a discrepancy of properties: whale and not whale and sloth and not sloth). Call this dissimilar1. Slothocles has the property of being dissimilar to Barry (in respect of species and in virtue of a discrepancy of properties, whale and not whale and sloth and not sloth). Call this dissimilarity 2.
E4. Therefore, if one thing is dissimilar to another in virtue of the discrepancy in properties (dissimilarity1 and not dissimilarity1, dissimilarity2 and not dissimilarity2), then it has a further property: dissimilarity3. For example, Barry has the property of dissimilarity1 but Slothocles does not and Slothocles has the property of dissimilarity2 but Barry does not. Therefore, Barry has a further property of dissimilarity to Slothocles in virtue of this discrepancy, dissimilarity3. Likewise, in virtue of the same discrepancy, Slothocles will have a further property of dissimilarity of to Barry, dissimilarity 4 – and these pairs of dissimilarity properties will go on so on ad infinitum.
This argument generates an infinite series of dissimilarity properties – but there will be many more infinite series of dissimilarity properties. After all, on the non-identity criteria, for any x and any y, x is non-identical to y if and only if x is dissimilar to y in some respect and not similar to y in every respect. Therefore, there will be infinite series of this kind for every discrepancy in properties, where each thing has at least one discrepancy with respect to every other thing. However, it does not postpone explanation ad infinitum since we have criteria for dissimilarity. This allows us to give a perfectly good explanation of why things are dissimilar, even if there are infinitely many such explanations: Barry is dissimilar to Slothocles and vice versa because they do not both have the property whale, because they do not share the property sloth etc.
We might think then that despite these infinite series, the treatment of similarity (which involves an explanation of the closely related dissimilarity, identity and non-identity) in Part II has the exact same philosophical pay-off as Schofield’s analysis for the proponent of SV: it solves the Similarity Regress. According to Schofield’s reading of the Similarity Regress, Barry the drunk whale and Iqbal the aardvark are similar because they share a Similarity Form. This is what gets the regress going; we then need to posit a further Form to explain this similarity – and so on ad infinitum. On Schofield’s analysis of similarity in Part II, Barry and Iqbal are similar because they are qualified in the same way i. e., they share the same predicate, drunk, not because they share in a Form. This gives us a perfectly good explanation of similarity; we need not posit anything further. Thus, if we adopt the analysis of similarity in Part II, the Similarity Regress is a non-starter.
On my reading, Part II also provides the proponent of SV with an explanation of similarity that allows her to avoid the Similarity Regress. Barry the drunk whale and Iqbal the drunk aardvark are similar in virtue of sharing a property: drunk. If we adopt the Part II account of similarity then, we need not posit Forms to explain similarity at all. We can therefore avoid the Similarity Regress altogether.
Of course, on my interpretation of the account of similarity, multiple infinite series of similarity and dissimilarity properties are generated. There are three ways a proponent of SV might respond to this. Firstly, she might think that the account of similarity in Part II provides a solution to the Similarity Regress but comes at a steep ontological price; explanation is not deferred ad infinitum but we must accept infinitely many similarity and dissimilarity properties. Thus, it provides us with a solution, but not one as neat as Schofield’s reading. Secondly, she might think the account of similarity in Part II does not provide a solution to the Similarity Regress at all in light of this ontology. She might consequently re-evaluate SV altogether; perhaps what this shows is that it was ontology and not just explanation that made the Similarity Regress troubling in the first place.
Nevertheless, on all responses, reading the Similarity Regress with the treatment of similarity and dissimilarity has a philosophical pay-off. On the first, we have a solution, albeit one that is more problematic than Schofield suggests. The account of similarity in Part II also has advantages; it is much fuller than the one in Part I. For example, its correlate, dissimilarity, and relationships with identity and non-identity receive extensive attention. On the second, we are prompted to consider rejecting the alternative and the more fleshed out account of similarity in Part II if we want to use an analysis of similarity to block the Similarity Regress. We might even re-evaluate why the Similarity Regress was problematic in the first place.
Seeing Arguments D and E as infinite regresses is not compatible with AV; the infinite series are not used to reach any contradictions. However, we can extend them to do just this. One of the principles that underlie both the first and second deductions is that properties are parts, where, if something has infinitely many parts, it is infinitely many.[36] However, as Parmenides makes clear in the Being and One Regress, if something is, it must be one.[37] We can therefore add to Argument D:
D6. Everything is similar to something.
D7. If something has infinitely many properties, it is infinitely many.
D8. Each thing is one.
D9. Therefore, everything is both one and infinitely many.
We can also extend Argument E to reach the same conclusion:
E5. Each thing is dissimilar to every other thing.
E6. If something has infinitely many properties, it is infinitely many.
E7. Each thing is one.
E7. Therefore, everything is both one and infinitely many.
On AV, these arguments do nothing to block the Similarity Regress; they are just different regresses – and ones that have been generated from an alternative account of similarity. Nevertheless, they are important; they show that Plato lays the ground for more infinite regresses in the Parmenides than is commonly supposed. Moreover, in doing so, he points to challenges for the reader hoping to block the Similarity Regress in Part I by looking to the treatment of similarity and dissimilarity in Part II; here, we find an alternative explanation of similarity that is more fleshed-out but also generative of infinite regresses and ontologically costly. This pushes us to reject a second analysis of similarity. Consequently, I maintain that AV is worth taking seriously in respect of the philosophical pay-off it has when we look to Part II. It, therefore, deserves further exploration as a plausible reading of the Similarity Regress.
*
I have examined the philosophical pay-off of two different views of the Similarity Regress in Part II of the Parmenides. On the first, SV, the Similarity Regress is an argument that is troubling because it postpones explanation ad infinitum. I have argued against Schofield that in Part II, similarity is sharing a property. This, together with other features of the treatment of similarity in Part II, yields an interesting lesson regarding the Similarity Regress: we find a different and more fleshed-out account of similarity in Part II from the one that is assumed by the Similarity Regress. This leads to what a proponent of SV might think of as a solution to the Similarity Regress (as Schofield argues) but one with a steep ontological cost (contra Schofield) or as a strategy to block the Regress that fails, and perhaps this prompts her to re-evaluate SV. On AV, I argued, we find an account of similarity in Part II that is different from and more fleshed out than the one in Part I but which leads to the very same problem: infinite regress.[38]
References
Allen, R. E. (1997): Plato’s Parmenides. New Haven: Yale University Press.Search in Google Scholar
Cherniss, H. (1944): Aristotle’s Criticism of Plato and the Academy. Baltimore: Johns Hopkins University Press.Search in Google Scholar
Cornford, F. M. (1939): Plato and Parmenides: Parmenides’ Way of Truth and Plato’s Parmenides. London: Kegan Paul.Search in Google Scholar
Frye, P. H. (1938): Plato. Lincoln: University Studies of the University of Nebraska.Search in Google Scholar
Gardner, D. (2018): ‘The Ambiguity of the “One” in Plato’s Parmenides’, Méthexis 30, pp. 36–59.10.1163/24680974-03001003Search in Google Scholar
Gill, C. & McCabe, M. M., eds. (1996): Form and Argument in Late Plato. Oxford: Oxford University Press.10.1093/oso/9780198240129.001.0001Search in Google Scholar
Gill, M.L., and Ryan, P. (1996): Plato: Parmenides. Indianapolis: Hackett Publishing Company.Search in Google Scholar
Harte, V. (2002): Plato on Parts and Wholes: The Metaphysics of Structure. Oxford, Oxford University Press.10.1093/0198236751.001.0001Search in Google Scholar
Hermann, A., Hedley, D. & Chrysakopoulou, S. (2010): Plato’s Parmenides: Text, Translation & Introductory Essay. Las Vegas: Parmenides Publishing.Search in Google Scholar
Kahn, C. H. (2013): Plato and the Post-Socratic Dialogue: The Return to the Philosophy of Nature. Cambridge: Cambridge University Press.10.1017/CBO9781139381734Search in Google Scholar
Ledger, G. (1989): Re-Counting Plato: A Computer Analysis of Plato’s Style. Oxford: Clarendon Press.Search in Google Scholar
McCabe, M. M. (1994): Plato’s Individuals. Princeton: Princeton University Press.Search in Google Scholar
McCabe, M.M. (1996): ‘Unity in the Parmenides: The Unity of the Parmenides’. In: Gill & McCabe, eds. (1996), pp. 1–47.10.1093/acprof:oso/9780198732884.003.0008Search in Google Scholar
Meinwald, C. (1991): Plato’s Parmenides. Oxford, Oxford University Press.10.1093/oso/9780195064452.001.0001Search in Google Scholar
Owen, G. E. L. (1953): ‘The Place of the Timaeus in Plato’s Dialogues’, Classical Quarterly 3, pp. 79–95.10.1017/S0009838800002652Search in Google Scholar
Prior, W. J. (1985): Unity and Development in Plato’s Metaphysics. London: Croom Helm.Search in Google Scholar
Rickless, S. C. (2007): Plato’s Forms in Transition: A Reading of the Parmenides. Cambridge, Cambridge University Press.10.1017/CBO9780511482618Search in Google Scholar
Rickless, S. C. (2016): Plato’s ‘Parmenides’ (Metaphysics Research Lab, Stanford University), https://plato.stanford.edu/archives/spr2016/entries/plato-parmenides/.Search in Google Scholar
Ryle, G. (1966): Plato’s Progress. Cambridge, Cambridge University Press.Search in Google Scholar
Sayre, K. (1985): ‘Plato’s Late Ontology: A Riddle Resolved’, Philosophical Review 94, pp. 395–399.10.2307/2185006Search in Google Scholar
Sayre, K. (1996): Parmenides’ Lesson: Translation and Explication of Plato’s Parmenides. Notre Dame, IN: University of Notre Dame Press.Search in Google Scholar
Schofield, M. (1996): ‘Likeness and Likenesses in the Parmenides’. In: Gill & McCabe, eds. (1996), pp. 49–77Search in Google Scholar
Scolnicov, S. (2003): Plato’s Parmenides. Los Angeles: University of California Press.10.1525/9780520925113Search in Google Scholar
Shorey, P. (1903): The Unity of Plato’s Thought. Chicago: The University of Chicago Press.Search in Google Scholar
Taylor, A. E. (1926): Plato: The Man and His Work. London: Methuen and Co. Limited.Search in Google Scholar
Taylor, A. E. (1934): The Parmenides of Plato. Oxford: Clarendon Press.Search in Google Scholar
Vlastos, G. (1954): ‘The Third Man Argument in the Parmenides’, Philosophical Review 64, pp. 319–349.10.2307/j.ctv24rgc46.18Search in Google Scholar
© 2023 the author(s), published by De Gruyter.
This work is licensed under the Creative Commons Attribution 4.0 International License.
