Posts Tagged ‘ Categories ’

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.

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Aristotle on Relatives in Categories 7 (Part 1): Two Definitions

I got a taste of ancient conceptions of relativity pretty much in the first week of my PhD when I read David Sedley’s paper ‘Aristotelian Relativities’. I wrote my dissertation on the  scraps of evidence concerning relatives in Plato but stopped before I got to Aristotle’s feast of ideas. A very nice email from one of Dhananjay’s colleagues asking about relations in Aristotle prompted me to write down some ideas about Cat. 7 that have been cooking for a while. Bon appetit!

Aristotle’s class of relatives (ta pros ti), discussed in Categories 7, excludes some items that we consider relations and includes some that we do not. Aristotle excludes three or more place relations, such as between, but includes some monadic properties: e.g. large (6a36-b10); and virtue and vice (6b15). So what does Aristotle think relatives are? He defines them at Cat. 6a35 (D1) but gives a different definition later in the same chapter at 8a15, (D2).  Traditionally, scholars have thought that D2 is strictly narrower than D1: that is, at least one relative, that falls under D1 does not fall under D2. However, in this and the next few posts, I will argue, using a distinction formulated by Quine, that D1 and D2 give us two different ways to view relatives: the D1 relatives are relatives viewed opaquely, while the D2 relatives are relatives viewed transparently.

In this, the first post, I will discuss in more detail Aristotle’s definitions and explain Aristotle’s motivation for giving D2, roughly, that D1 may lead him into a contradiction. In the next post, I will introduce a distinction between two ways of understanding propositions involving relatives: transparently and opaquely. In the third post, I will argue that D1 relatives are relatives viewed opaquely, while D2 relatives are relatives viewed transparently. To prove my reading, I will show that the distinction I identify allows Aristotle to avoid the contradiction he worries about.

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