On Philosophy

May 28, 2007

Group Predication

Filed under: Logic — Peter @ 12:00 am

There is a doctrine that only individuals are subjects or substances. What exactly this means is never perfectly clear, but those who hold it seem to mean that there is something it is to be an individual thing which aggregate things do not have (perhaps haecceity?). For example, some might claim that individual things have essential properties, while collections of things do not. Once upon a time this used to distinguish people and animals from things like table and chairs. But of course we realize now that the bodies of people and animals are as much collections of parts as anything else, so if such a doctrine is held now it must apply only to the fundamental and indivisible constituents of nature, and possibly immaterial minds if you are a dualist.

But how could such a doctrine possibly be argued for? Well some say that it follows from logic. Now this seems like the cart pulling the horse, as logic is supposed to describe truth, and thus it would seem impossible to deduce facts from logic, only to deduce logic from facts. However let us examine the argument itself. Those who hold this doctrine claim that to be a subject or a substance is to be the proper object of prediction. Thus since I can have the property of going to the store I could be said to be an object of prediction. And, in addition to this they claim that groups and aggregates are not proper objects of prediction, and that to ascribe some property to a group is really only to say something about each of its members. Thus to say that my body goes to the store is really only to say that each of its parts goes to the store, and thus that the body isn’t a proper object of prediction. Now, to return to my initial point, this is a bad argument, because all it might show is that our logic is flawed, that groups and aggregates really are proper objects of prediction and that there is something wrong with our logic if it prevents us from ascribing properties to them as a whole and not to each of their parts. Properly speaking we must decide by some other means whether groups are proper objects of prediction, and then evaluate our logic in light of that.

But fortunately for our logic groups are already proper objects of prediction, if we consider the right predicates. Admittedly some of the time when we make a claim about a group we might only be doing so as a kind of abbreviated way of talking about each of its members individually. But there are predicates that apply only to the group, and which make no sense to apply to individual members. For example, an army can be disbanded, but it doesn’t make any sense to say of an individual soldier that he or she was disbanded, unless we are trying to say that he or she was removed from the army. But to say that he or she was removed from the army is to say that there is a certain relation between him or her and the army, which again makes the army an object of prediction (and isn’t really what we meant to say when we said that the army was disbanded). Or we might say that the army was divided into two equal groups. Although we could try to translate this into a claim about individual soldiers, such as their being placed into group A or group B, it doesn’t capture the full meaning of the group predication, since it says nothing about the relative size of those two groups. Finally, leaving the army behind for a moment, we might wish to say of a collection of particles that their center of mass is at a certain location, but this doesn’t translate at all into a claim about individual particles.

Now to say that a group can be a proper object of prediction is not to say that the group can have properties that don’t depend on, or are not determined by, the properties of its members. It is not that by being a group totally new properties emerge. What is happening is that a group property can express relationships between members of the group, possibly relationships that involve all the members. Although these relationships depend on the properties of the individual objects they don’t depend on those properties independently of each other. Thus they can only be said of the group, and not of members of the group, without making reference to the group. This is a break from the simplistic approach to the states of groups, which says that if A can be in state y or z and B can be in state y or z then the group formed by A+B can be in four states. What this approach misses is that there are things you can say about A+B that are not captured by saying something about the state of A in isolation and the state of B in isolation. For example, you could say of A+B that its members were in the same state, or were in different states.*

Now this is an interesting line of thought in its own right, and I am sure there is plenty more to say about what can be predicated of groups, how it differs from what can be predicated of its members, and the implications of these differences. But to elaborate on those ideas would be to stray too far from the initial topic. So, to return to the initial topic, how does this have an impact on what a substance is? What I think it shows is not that groups have substances, but rather that substance is an empty term. If you define substance as the proper object of predication, as many do, then what substances are depend on how you define predication. Now I have shown here that as we usually understand it we can predicate things of groups. But there is no ultimate fact about what predication is, predication is one of those words that reflects not something about the word, but is defined arbitrarily so as to be useful to us. If it was useful to restrict predication to individuals then we would. Thus substance appears to be equally arbitrary in meaning. Now, like predication, we might say that substance is defined in such a way as to be useful. Certainly that is possible, but philosophers who use the term refuse to use it in that way; they like to make claims about what substances are, and then derive conclusions about the world from the nature of substance. Which is about as methodologically backwards as deriving facts about the world from your logic.

* How many things can you meaningfully say of A+B? I think the answer is 14 (24 – 2).

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