Posts Tagged ‘ Relations ’

Aristotle on Relatives in Categories 7 (Part 3): Opaque and Transparent Relatives

In the last post, I set up Quine’s distinction between transparent and opaque ways of reading a statement. What I need to do now, is connect this to Aristotle’s two conceptions of relative terms, as he sets them up in Cat. 7. I will first argue that D1 relatives are opaque, on Aristotle’s view, then that D2 relatives are transparent. In the next post, I will explain how this helps Aristotle avoid the conclusion that some substances are relatives. Roughly, when construed opaquely, a proposition involving a relative gives us less information, so the proposition is more ambiguous. It is this ambiguity that means some relatives appear to be substances. When construed transparently, a proposition gives us much more information, so is not ambiguous. At least, not ambiguous enough to allow some relatives to appear to be substances. But I’m getting ahead of myself. First I will argue that D1 relatives are relatives viewed opaquely, while D2 are viewed transparently.

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Aristotle on Relatives in Categories 7 (Part 2): Quine’s Safari

We saw in the first post in this series that  Aristotle gives two definitions of relatives in Categories 7, which I called D1 and D2. Aristotle worries that D1 will allow some substances to be relatives, so introduces D2. Specifically, Aristotle worries that parts of secondary substances, like hand, will turn out to be both substances and relatives. So, what is the difference, according to Aristotle, between D1 and D2?

One way we could understand the difference is as a difference of extension: D2 excludes some items that D1 does not. Hand would have to be one of the relatives excluded from D2, but included in D1. The existing suggestions in the literature are of this kind.[1]

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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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