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.
Two definitions of ‘relatives’
In this section, I will outline Aristotle’s two definitions and his reasons for introducing the second definition. Aristotle’s first definition, D1, is formulated as follows:
We call relatives all such things as are said to be just what they are of or than other things in some other way in relation to something else. (Trans. Ackrill) (Cat. 7 6a36-b1).
This account of relatives is capacious. Any term that is said of or than something else will correspond to a relative. The paradigm way of formulating relational statements would be ‘the parent is parent of something’. We learn later that this ‘something’ is should also be specified, at 6b28-36, as ‘offspring’. A paradigmatic relational statement, then, will be of the form ‘the parent is parent of offspring’.
D1 is capacious enough to allow, for example, parts of a whole to be relatives. A hand is part of a body and, a fortiori, a hand is of or than something. This spaciousness could be a problem, when combined with an assumption that nothing can be both a substance and a relative. Here is Aristotle’s worry (8a20-27):
- Nothing is a relative and a substance [Assume]
- Parts of (secondary) substances are substances [Premise]
- Hand is part of a secondary substance (body) [Premise]
- Hand is a substance [From 2 and 3]
- Relatives are all things that are (said to be what they are) of something [D1]
- Hand is said to be hand of a body [Premise]
- Hand is a relative [From 5 and 6]
- Hand is a relative and a substance [Conjunction of 4 and 7]
- Contradiction between 1 and 8.
To avoid the conclusion that ‘hand’ is both a substance and a relative, Aristotle must reject one of 1-8, and in fact targets (5) for rejection. Aristotle says:
Now, if the definition of relative that was given above is adequate it is either exceedingly difficult or impossible to reach the solution that no substance is spoken of as a relative. But if this is not adequate, and if those things are relatives for which being is the same as being somehow related to something, then perhaps an answer may be found. (Cat. 7 8a28-b34).
That is, Aristotle introduces a new account of relatives, and says that this might help avoid the contradiction that threatens. Commentators usually take Aristotle strategy to be to restrict the scope of ‘relatives’ in a principled way, so as to avoid having to include parts of secondary substances as relatives. That is, the second definition (D2) has a narrower extension than the first (D1). But it seems very unclear what D2 actually amounts to. In the next few posts, I will use circumstantial evidence to clarify D2.
 Sedley, D. (2002) ‘Aristotelian Relativities’. In La Style de la Pensee; Harari O. (2011) ‘The unity of Aristotle’s Category of Relatives’. Classical Quarterly.