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):

  1. Nothing is a relative and a substance                                [Assume]
  2. Parts of (secondary) substances are substances          [Premise]
  3. Hand is part of a secondary substance (body)              [Premise]
  4. Hand is a substance                                                                   [From 2 and 3]
  5. Relatives are all things that are (said to be what they are) of something [D1]
  6. Hand is said to be hand of a body                                        [Premise]
  7. Hand is a relative                                                                        [From 5 and 6]
  8. Hand is a relative and a substance                                       [Conjunction of 4 and 7]
  9. 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.[1] 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.

[1] Sedley, D. (2002) ‘Aristotelian Relativities’. In La Style de la Pensee; Harari O. (2011) ‘The unity of Aristotle’s Category of Relatives’. Classical Quarterly.

    • Dhananjay
    • February 3rd, 2014

    This is great, Matt. I’m looking forward to the rest of this line of thought.

    One quick observation: if Aristotle takes as a basic principle that substance and relative (and any other pair of categories, I take it) are mutually exclusive, why does he countenance the expression ‘substance of something’ in Metaphysics, Zeta 3? I think this is the very notion that leads him down the garden path in Zeta, but given the twists and turns of the middle books, it doesn’t seem plausible to me that this thought about the categories is meant to be the savior of the account of substance, though it would have headed off this (to my mind) wrong-headed line of thought. In fact, the way he seems to me to solve this issue within Zeta is to develop a notion of substance of something that is non-relational (much as the notions of the ‘being of something’ or the ‘identity of something’ is non-relational) – by focusing on the ‘something else’ condition in D1. If the substance of X just is what it is to be X (if substance is essence, i.e., form), then there’s nothing over and above X that is the substance of X, and so the something else condition fails, even though we might have thought it didn’t.

      • mbduncombe
      • February 7th, 2014

      Hello! Thanks for raising the point about Met. Z.3. I think in a wide range of contexts, Aristotle take the ‘is said of something’ to be a test for whether something is a relative. And as you say, later he begins to bring in other condition, the irreflexivity condition, because it can do the work of distinguishing substances from relatives. Just two further points:

      In the context of the Categories, with primary and secondary substances, it seems that he cannot get out of the problem that way, since if Cat. 2 is to be believed, secondary substances are said of things.

      Aristotle is a bit inconsistent, in Cat 7, over whether the irreflxivitiy condition holds. He gives similar as a relative (6b), and looks reflexive (everything is simialr to itself). There are ways to deal with such examples, I suppose, but maybe, at the time he wrote Cat. 7 A hadn’t fully grasped the force of the irreflexivity condition, so wouldn’t want to use it to rule out substances being relatives the way you suggest he does in Met. Z.

    • djr
    • February 3rd, 2014

    Two more puzzles about substances that seem to be essentially ‘of’ something else, this time from the Politics:

    1. A slave is a possession of its master, and in fact is like a part insofar as the possession and the part are both “wholly of another”: “That’s why the master is only a master of the slave, but is not of that man, but the slave is not only a slave of a master, but is wholly of that man.” (1.4 1254a11-13)

    2. A free human being is a part of the city: “one should not think that any of the citizens is of himself, but that all are of the city, for each is a part of the city” (8.2 1337a27-29; cf. 1.3 1253a18-29)

    In the slavery case, it would be nice if we could say just that the master and slave are relatives qua master and slave (the Categories uses this example of relatives), but substances qua human beings. But the distinction between the master being merely the master of the slave and the slave being “wholly of that man” seems to claim that the slave is not just essentially related to his master insofar as he is a slave, but that he is essentially related to his master, period. Similarly, the passages about citizens as parts of the city suggest that human beings are not just ‘of’ the city insofar as they are citizens, but that they are ‘of’ the city qua human beings.

    But besides the insistence in the Categories that nothing is both a substance and a relative, but passages from the Metaphysics seem to show that substances cannot be parts of other substances (or so Robert Mayhew, ‘Part and Whole in Aristotle’s Political Philosophy’, Journal of Ethics 1.4 (1997), 325-40).

    In other words, if you have a solution to these difficulties for me, I’ll be in your debt!

    • mbduncombe
    • February 7th, 2014


    I don’t know whether I have a solution to these cases. (1) has puzzled me for a while, since Aristotle wants to change tack and introduce a hierarchy between master and slave (a relative-correlative pair) that is not really present in the formal features of relatives in Cat. 7. Could it be to do with the idea that there are two relations between the master and the slave: the master-slave relation and the possessor-possession relation? Thus, a is master of b and b is slave of a BUT ALSO a possesses b and b is possesed by a. So, in an actual political situation it is the possessor-possession relation that drives the analogy with the whole and the part?

      • djr
      • February 7th, 2014

      I don’t think so, because a slave is a possession; the master-slave relation is just a special case of the possession relation. One way to read the passage I quoted above is to see the propositions “the master is master of the slave” and “the slave is slave of the master” as stating that mastery and slavery are relations and that these are the relata, while “the slave is wholly of that man” tells us that being a slave is not simply a relation in which one person stands to another (as being a master is), but one in which the slave is wholly subordinated to the master in the manner of a possession. So long as ‘slave’ picks out a substance qua one of its relations, I think that’s perfectly consistent with the no-substance-is-a-relative doctrine. ‘Natural’ slaves will not be substances who are also relatives, but substances that necessarily bear a certain relation. But part of what is so strange about the part/whole language applied to slave/master and human/polis is that Aristotle is very clear that lots of human beings don’t live in poleis and that lots of natural slaves don’t have masters. Being a natural slave and being naturally political are both best understood in terms of the relations in which different sorts of people need to stand to others in order to actualize their capacities as human beings, but it isn’t apparent why that should get expressed in the language of parthood. In the human:polis case, it’s possible to treat the part:whole talk as a mere analogy, but Aristotle doesn’t say that slaves are like possessions; he just says that they are possessions, and he seems to want that account to apply to non-natural slaves as well, so that it can explain what is unjust about their enslavement.

  1. February 16th, 2014

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