Motivating the problem of universals: resemblance relations

The medieval debate regarding the problem of universals grew so fierce that it is said to have spilled out into fistfights on the streets of 1400s Paris.¹ This is a blog post about why that debate remains relevant to basic philosophical questions about perception and the possibility of inquiry.

Say that you entertain some fact about elm trees and beech trees, for example that elm trees are, on average, taller than beech trees.

You are describing some way the world could be. You can set out to find out if that fact is true or false. You can do this even, as Hilary Putnam pointed out, if you have no idea yet how to tell elm trees and beech trees apart. If you became serious about figuring out whether that fact was true you'd probably either need to figure out how to do this, or consult someone who can.

In Plato's Meno, Plato reflects on what kinds of things can be taught and learnt. The Meno is a dialogue between the philosopher Socrates and the dialogue's namesake, a young aristocrat named Meno. At one point in the dialogue Meno turns the tables on Socrates and asks him the following question:

MENO: And how will you enquire, Socrates, into that which you do not know? What will you put forth as the subject of enquiry? And if you find what you want, how will you ever know that this is the thing which you did not know?

SOCRATES: I know, Meno, what you mean; but just see what a tiresome dispute you are introducing. You argue that a man cannot enquire either about that which he knows, or about that which he does not know; for if he knows, he has no need to enquire; and if not, he cannot; for he does not know the very subject about which he is to enquire

For me, one answer to Meno's challenge² is that we can describe things even before we know much about them, by making use of our prior experiences of other similar things. For example, even if I've never seen red leaves before, I can look at (1) a red apple, then (2) a green leaf, and then wonder whether there are such things as red leaves. I don't need to know much more about red leaves other than that they are red (like red apples) and that they would be leaves (like green leaves) in order to then go out and enquire whether they exist (for example by going and surveying different kinds of trees, asking a botanist, etc).

"Abstraction" is a very useful word for describing what is going on here. It shares an etymology with the word "tractor" (a thing which pulls - as in "tractor beam"). The prefix "ab-" implies that the word is about pulling things apart, or separating them. In the example above, you are pulling apart the "redness" from an apple and the "leafiness" from a leaf and then combining these two abstract concepts to form a new one.

The particular version of the problem of universals I am interested in is the question of how we are able to reason about predicates like "red" or "is a leaf" in the first place. In particular - how do we extract these predicates from past experiences, and how are we able to use them to describe the world of future possible experiences?

This is a fairly dry-sounding topic, and so I wanted to write a bit about why I find it interesting, before writing more in future posts about what a good theory might look like. It was not a topic I was at all personally curious about as an undergraduate - except maybe as a historical curiosity (to answer questions like, e.g. why did Plato even think he had to posit a world of the forms?). I didn't even make the link a few months ago when I was writing this post on a closely related topic.

Sometimes the commonest parts of human experience are hard to think about precisely because they are a part of everything around us. This can make it harder to see that something magical is going on right under our noses. In the case of the problem of universals, the magical thing that is going on is our ability to abstract common predicates from particular experiences at all.

Why should this kind of abstraction be problematic? Consider the example of someone wondering about red leaves again. A natural way to explain what is going on is to say that we just remember our previous experiences (of the red apple, and the green leaf) and then imagine that other experiences might resemble them (in colour, in shape, etc) in certain ways.

In On the Relations of Universals and Particulars Bertrand Russell observes that as soon as you rely on some relation like "resemblance" in your account of how predicates work - you are forced to acknowledge that there is something going on that isn't explainable just in terms of our experiences. Russell argues that "resemblance" itself is a mysterious concept, and one which leads to a regress if we try to give an account of it in terms of resemblance to other experiences. This leads him to a fairly radical position: positing that all predicates and relations (he follows historical tradition by terming them universals) have some kind of mind-independent Platonic existence.

The fistfights between philosophy students in medieval Paris I mentioned at the start of this blog post took place between two camps. One camp, the realists, adopted a position similar to Russell's. The other camp, the nominalists, argued that universals have no independent existence, they are just a part of the way we use words.

Russell presents his argument from On the Relations of Universals and Particulars in a slightly more readable form in his book The Problems of Philosophy:

But a difficulty emerges as soon as we ask ourselves how we know that a thing is white or a triangle. If we wish to avoid the universals whiteness and triangularity, we shall choose some particular patch of white or some particular triangle, and say that anything is white or a triangle if it has the right sort of resemblance to our chosen particular. But then the resemblance required will have to be a universal. Since there are many white things, the resemblance must hold between many pairs of particular white things; and this is the characteristic of a universal. It will be useless to say that there is a different resemblance for each pair, for then we shall have to say that these resemblances resemble each other, and thus at last we shall be forced to admit resemblance as a universal. The relation of resemblance, therefore, must be a true universal. And having been forced to admit this universal, we find that it is no longer worth while to invent difficult and unplausible theories to avoid the admission of such universals as whiteness and triangularity.