First thoughts on relativity in the Peri Ideon
After seeing me talk about relatives (ta pros ti) in Aristotle’s Categories 7, James Warren suggested that I look again at the so-called ‘relativity argument’ in Alexander’s testimony on the lost treatise Peri Ideon. Many of you will know the argument from Owen’s classic 1957 paper A Proof in the Peri Ideon and the industrial-scale debate it generated. But here, I’m just going to offer one preliminary idea.
Alexander (In Met. 82, 11-83,16) reports Aristotle’s (type of) argument that reconstructs a Platonic argument for Forms. Most doubt Alexander quotes the Peri Ideon verbatim, but scholars take Alexander to be a good witness to Aristotle’s argument. But I wonder whether Alexander (and others) have misunderstood Aristotle’s intentions with the argument, even if Alexander’s report is accurate.
The lemma under which Alexander introduces the argument is the following lines (Met. A9 990b15-17 cf. Met. M 4 1079b4-13):
Ἔτι δὲ οἱ ἀκριβέστατοι τῶν λόγων οἱ μὲν τῶν πρός τι ποιοῦσιν ἰδέας, ὧν οὔ φαμεν εἶναι καθ’ αὑτὸ γένος, οἱ δὲ τὸν τρίτον ἄνθρωπον λέγουσιν.
Next, of the more accurate of the arguments, some make ideas of relatives, of which we say there is no independent genus, while others mention the third man.
Alexander aims to record the first sort of ‘more accurate’ argument, and gives the argument from relatives. But what precisely was Aristotle’s attitude to the argument, in the quoted lines? Clearly, Aristotle doesn’t like the argument, but it is a bit unclear why. This isn’t helped by the fact that Aristotle expresses his dislike ambiguously. The relative pronoun, ὧν, could correlate with either (i) ‘τῶν πρός τι … ἰδέας’ or with (ii) ‘τῶν πρός τι’, depending on whether ὧν is feminine or neuter. In case you think I’m going to contort Aristotle, I’ll say now that I think (i) is better Greek. But Alexander, and others, seems to have read Aristotle as meaning (ii).
What is the philosophical difference? On reading (ii) Aristotle objects because, contrary to the argument, there are no Forms for relatives. ‘Independent genus (καθ’ αὑτὸ γένος)’ would have to mean ‘Form’ (not crazy, given καθ’ αὑτὸ is form-talk. γένος less so…). For example, there is no Form for equal, because Forms are unique, while relatives, like equal, must be pluralities. Alexander, I think, understood Aristotle this way. When Alexander resumes his remarks on the argument (cf. μὲν οὖν οὗτος λόγος at 83, 17), he says that the argument establishes Ideas ‘also of relatives’ (καὶ τῶν πρός τι). The argument establishes Ideas for lots of items, but it is the Ideas of relatives that Alexander, and Alexander’s Aristotle, worries about.
On reading (i), Aristotle’s objection is not to Ideas for relatives, but rather to Ideas of an independent relatives. On this view, καθ’ αὑτὸ γένος does not mean ‘Form’, but rather just what it says, an independent genus. The point would be that relative genera come together, in pairs. Generic ‘knowledge’ comes with generic ‘knowable’, ‘parent’ with ‘child’, ‘equal’ with ‘equal’. There is no independent genus ‘Knowledge’, only knowledge that correlates with knowable. However, the relativity argument generates them. That is Aristotle’s problem, on this reading.
So why would we take reading (i), except for the fact that it makes a nicer piece of Greek? Well, for one thing, a Platonist might be persuaded! An argument for the Forms that generates singleton Ideas for relatives will be problematic for the Platonist in her own terms. Parmenides 133c-134c is clear that relatives, including relatives of Ideas (and ‘Idea’ is the term Plato actually uses in that argument), are kinds that come in pairs. The kinds correlate with each other. Topics VI 4, in fact, also aims a similar argument at the Platonist, based on the endoxon that Forms relate to Forms (Top. 147a5-10). Assuming that the Platonist accepts that Forms correlate with Forms, on (i) the relativity argument is a reductio correctly aimed at a Platonist, because it would generate a Form for a relatives, but no Form for its correlative.
(In fact, Aristotle agrees with the Platonist on the point that kinds of relative come in pairs. Aristotle’s official discussion in Cat. 7 stresses this repeatedly. Relatives come with correlatives that reciprocate. Knowledge relates to knowable, larger to smaller, parent to child (Cat. 6b35ff). It may be, then, that the ‘we’ who say that there is no independent genus of relatives are both Aristotle and his Platonist opponents.)
Clearly, the conclusion of the relativity argument should be the result that Aristotle, on my suggestion, complains about. I have some thoughts on this, but I’d like yours! I’d also like to know if you have any objections or comments. Is there some obvious reason that the ὧν must be neuter? Or do you think that the ambiguity does not exist?