Universals and Instances

Two mugs are both chipped. Three apples are all red. Every electron has the same charge. Facts of this shape are as ordinary as facts get, and stating what they consist in has occupied the subject for two and a half thousand years without a settled result.

The argument that starts everything

Set out plainly:

The conclusion names an entity, and the name it has been given since Plato is the name for whatever is one over many.

The second half of that definition is the job description. The first half is the strange part, and it is where the disagreement begins. A particular cannot be wholly in two places at once. A universal, if there are any, can: the whole of redness is in the apple and the whole of it is in the pillar box, and it is not divided between them the way a rope is divided between two people holding it.

Plato took the shared item to exist independently of its instances, in a way that would leave the Forms untouched if every red thing were destroyed. Aristotle took universals to exist only in the things that have them, so that redness with no red things would be nothing at all. That split, transcendent and immanent realism, is still live, and D. M. Armstrong's defence of the immanent version is the standard modern statement.

Types and tokens

A distinction from a quite different source turns out to be the same distinction, and having it in hand makes the abstract case concrete.

Count the words in the sentence "the cat sat on the mat". The answer is six, and the answer is five, and both are right. C. S. Peirce introduced the vocabulary that separates them, in his 1906 paper "Prolegomena to an Apology for Pragmatism", using exactly this kind of case.

There are six tokens in the sentence and five types, because "the" appears twice. Nothing exotic is needed to see this, and yet a type is repeatable in precisely the way a universal is. This is why the type and token distinction gets used across philosophy well beyond the theory of properties, and why an argument about universals can often be restated as an argument about whether types are anything over and above their tokens.

The alternative

The one over many argument has a premise, and premises can be denied. Everything that opposes universals denies the second one: that sameness in a respect requires a single shared item.

The denial has to say something positive instead, and the leading option takes the shared facts as basic rather than as consequences of something shared.

The proposal is that the apple and the pillar box resemble each other, that this is simply how they are, and that nothing further needs to exist to make it so. Whether that is an explanation or a refusal to explain is exactly the point at issue, and the answer is not obvious in either direction.

Two difficulties are standardly raised. The first is that resemblance is itself a respect in which pairs of things can be alike, so a defender of the view is at risk of needing the very entity the view was designed to avoid. The second is that resemblance comes in degrees and in respects, and saying which respect is in play looks like it requires reference to the properties again. Gonzalo Rodriguez-Pereyra's development of the position treats the resemblance facts as primitive, so that there is strictly no resemblance relation for the first objection to fasten on.

How many properties are there

One further split cuts across the whole debate and is worth naming now, because it decides what any of these views has to account for.

On an abundant conception there is a property corresponding to every meaningful predicate, however gerrymandered: being green or a prime number, being within a mile of a post box, being not a mug. Properties on this conception are cheap, there are enormously many, and they are not expected to explain anything about the causal structure of the world.

On a sparse conception there are relatively few, just the ones responsible for the objective similarities and causal powers of things, and finding out which they are is a job for science rather than for reflection on language. Sparse properties are what carve nature at its joints.

Many philosophers accept both, using the abundant ones for semantics and the sparse ones for metaphysics. The important thing at this stage is to notice which is in play. The one over many argument is much more persuasive when it is run on charge and mass than when it is run on being within a mile of a post box.

What has been fixed

The vocabulary of repeatability, and the argument that has driven the subject since Plato. What has not been fixed is the answer, and nothing later in this tier assumes one.

The next article turns to a requirement that has come up twice already without being made precise: what it takes to tell whether you have one thing or two.