The Problem of Universals

Put a tomato, a post box and a London bus in a row. Each is red. The question that has occupied philosophers for two and a half thousand years is what, if anything, the three of them share. Not what they look like (that is settled by looking) but whether there is something, redness, which each of them has, and which would still be there if every red thing in the universe were destroyed tomorrow.

Plato's answer was yes, and emphatically so. The Forms are not in the world; they are what the world imitates. A particular red thing is red by participating in Redness, which exists outside space and time and does not change when the tomato rots. The theory does a great deal of work: it explains why different things can be genuinely the same in a respect, why mathematics describes things it never touches, and why definitions can be got wrong. It also asks you to believe in a second realm, and to accept a relation called participation which nobody has ever been able to describe without metaphor.

Aristotle kept the realism and moved the address. Forms are real and they are in things: the form of a horse is present in each horse, not in a separate world that horses somehow resemble. This is immanent realism, and it saves an entire ontological storey. You no longer owe an account of a second realm or of participation. What you owe instead is an explanation of how one and the same form can be wholly present in each of ten thousand horses at once, which is not obviously easier.

The third option is to deny that there is anything to explain. Nominalism holds that only particulars exist. There are red things, and 'red' is a word we apply to them because they resemble one another, and that is the end of the story. The attraction is economy (you believe in the furniture you can bump into and nothing else) and the debt comes due immediately at the word 'resemble'. Two things resemble each other in a respect, and naming the respect looks exactly like naming a universal. Nominalists have spent a great deal of ingenuity on this, with resemblance classes, tropes and primitive predication, and every solution is a little strained.

The most striking moment in the whole argument is in Plato's Parmenides, where the young Socrates is taken apart by an old man using an objection now called the third man. If several men are men because they resemble the Form of Man, then the men and the Form now have something in common, and by the same reasoning a further Form is needed to explain that, and so on for ever. Plato puts the strongest objection to his own theory in his own text and does not answer it. Anyone tempted to treat philosophical positions as camps should sit with that for a while.

It would be easy to dismiss all this as an argument about words. It is worth noticing where it turns up. Any database designer choosing whether 'customer tier' is a string on each customer row or a table that customers point at is settling, for that system, whether the tier is a thing or a label. A separate table gives the tier an identity: it can have properties of its own, be renamed without touching a customer, and exist with nobody in it. A column gives it none of these. Engineers argue this in the vocabulary of normalisation and they are arguing about universals, with storage costs standing where parsimony used to stand.

Science pushes in the realist direction and does not settle it. Physical law quantifies over properties (mass, charge, spin) and treats them as the same property wherever it appears, which is hard to state without universals and hard to justify without them. But the properties physics needs are few, precise and mathematically characterised, and nothing in that vindicates redness. It is quite possible that some universals are real and most of the ones in ordinary speech are conveniences, which is an unsatisfying position and may well be the true one.