Universals

Traditionally, sentences have subjects and predicates. The subject of a sentence refers to an object, and the predicate predicates a property of the object. In fact, lots of sentences are not of subject-predicate form:

is made up from two simple sentences, and so only basic sentences seem like they should be of subject-predicate form. was usually analyzed as of subject-predicate form, but that is a bad way to do things. In fact there are two "subjects" (Jack, Jill) and a relation (_ loves _) between them.

A predicate is a relation that only relates one thing. In principle one could have $n$-ary relations for any $n$, though we rarely actually go past three or four.

For the most part, we won't really care, all relations will behave like the simplest case, predicates, and so we usually just talk about predicates, but there is often parenthetical mention of relations and the like, and sometimes it does matter, and so you need to be aware of the jargon.

What a predicate predicates is a property. There is no similarly well established terminology for the general case. Sometimes the $n$-ary linguistic thing (the analog of a predicate) is called a relation, but sometimes the $n$-ary semantic thing (the analog of the property) is called a relation, sometimes a property. This is a mess, and philosophers often just move to the predicate-property case when they want to be clear and say it's the same for the general case.

A predicate is a piece of language. If it gets its meaning, as names do, by being suitably associated with something nonlinguistic, the association is predication, and what it is associated with is a property, and it is a matter of dispute whether properties are objects, though often not. After all, properties are had by objects, objects are not had by properties, objects are not had by objects, and properties are not had by properties, and so properties are different from objects.

In,

the patch and the apple are objects, red is a property. However, in red is an object, not a property. If there are objects that are in some way intimately connected with properties, like red is to red, then we need a name for them. They are often called universals. They have also been called attributes, ideas, concepts, properties, and probably other things as well. Those terms are also used in other ways. I'll try to use "universal" as a neutral term for the object that is related in the way explained to a property.

The universal associated with the property of being red is sometimes called, "the red," or "redness."

Are there universals, and what are they like? Once we start talking about words that occur in predicates we naturally find ourselves moving them into subject position, and hence talking about universals. Does that alone show that there are universals? Many philosophers have given exactly that argument, but it is no more convincing than the argument that Pegasus must exist since "Pegasus doesn't exist" is true. It looks like a variant of Plato's beard.

Let's, for now, just suppose that there are universals, and try to work out what they could be like. If things go well, that alone is a reason to think that there are universals.

They have one immediate benefit: they make semantics easy: predicates can be thought of as just disguised names for universals.

Since Plato's beard has been such a tangle, what is the comparable problem for universals? The object version is, "Can there be nonexistent objects?"

The universals version is, "Can there be uninstantiated universals?" That is, since questions about universals will amount to questions about properties, and hence about predication, is there a predicate $P$ such that $P(a)$ is false for every object $a$? "Winged horse" looks like an example. Since there are so many colors compared to objects, it seems likely that there is a color, call it "fred," such that nothing is fred.

There are two possible answers to our question:

Yes. If there are uninstantiated universals, what makes them different from each other, and where are they? They aren't in the actual world, and, it seejms, what makes them different is that there are possible objects on which they differ. Thus, the view that there are uninstantiated universals seems to commit us to

Plato has another argument for existence of universals: nothing is really circular, or straight, or morally good, or beautiful, things only approximate those ideals. Well, in order for anything to approximate an ideal, that ideal must exist, and so there must be the perfect circle, the beautiful, and so on, and those are universals. Plato's heaven, unlike, say, Frege's realm, really is a heaven: it is the residence of all the perfections, the ideals.

This all seems bad to us moderns except that it is still the way we seem to conceive mathematics. In medieval times, a "realist" was someone who believed in universals (as opposed to a nominalist). Today, a "realist" is someone who thinks that there are mathematical objects.

No. So, the only universals are instantiated universals. Thus, while "the red" exists, "the fred" does not.

-- ShaughanLavine - 18 Feb 2008

Once we decide that the only universals are instantiated universals, we are not obligated to let any crazy bunch of things be a universal---we've already granted that not everything is a universal, and so we can make choices.

Armstrong proposes immediately that the disjunction of two universals need not be a universal, thus The Red is a universal, The Feline is universal, but The Red or Feline is not. Why? What does Armstrong think we need universals? His main reason is to solve the problem of the one over the many: When two things are, for example, both red, there is a way in which they are alike. We need to explain, Armstrong thinks, how they are alike. His answer: they both instantiate The Red, they literally have a constituent in common. If there were a universal The Red or Feline, my cat Mosha and that red shirt would both instantiate it, but, it doesn't seem like they have anything in common. Such "disjunctive universals" don't do the job universal are, in Armstrong's opinion, for. So we won't take them to exist. What about the negation of a universal? The UnDead? is not something things that are not dead have in common: rocks and people are not dead, but ... .

On the other hand, Armstrong allows conjunctions of universals to be universals, if they are instantiated. Thus, The Red Truck is a universal, but, presumably, the Red Feline is not. Why allow conjunctions? Well, things that share two properties (red and truck) are more alike than things that share only one.

Lewis says that it might seem like a good idea to have only maximally specific universals, and then to disallow conjunctions. (Thus, Scarlet might be a universal, while Red is not, since it is Scarlet or Maroon or ... .) The problem is that there might not be any maximally specific ones: Within a mile of the North Pole, within an inch of the North Pole, within a micron of the North Pole, ..., but (to make the example work) there is no such thing as being just at the North Pole since no object can have zero size. That's the thought, and so it seems better to allow conjunctions and some universals included in others.

It does seem that similarity is a phenomenon we have to account for, but, for the rest, Armstrong is just making stuff up to accord with his intuitions about what we want to say is the same or different. Those are linguistic, not, or at least not without argument, metaphysical intuitions.

If you don't like universals you can do without them in thousands of ways, but two popular ones we need to discuss that Armstrong mentions are

In class nominalism, we replace the universal, The Red, by the class of all red things. That doesn't work to explain similarity: The Red is in both, and so they are similar, but, though both are in the class of red things, that isn't something that is the same about them.

In similarity nominalism, we accept one special relation, similarity, and try to replace universals with collections of things that are sufficiently similar. The problem is that we seem to need similarity in some respect (same color, …), and "respects" amount to universals, and so the project doesn't work unless we can find a way to make do with similarity alone.

Lewis doesn't think that a solution of the problem of the one over the many requires universals: He thinks it is perfectly reasonable to just take such similarities as a being red and b being red as a brute fact not in need of explanation. After all, using universals leaves the fact that the two instantiate the same universal as a brute fact without explanation, and so it is not clear that there is any significant progress. (Think about the universal Instantiates.)

Nonethless, Lewis says, he too thinks universals are important, though for different reasons.

Lewis distinguishes between universals and properties (this is artificial terminology). Everything that falls under a predicate has a common property---a (one-placed) property just gives us the extension (the things that fall under) a predicate. Lewis says we need those to provide meanings for predicate expressions. Consider the predicate "is red or feline." Its extension is not given by a universal and so we need properties that are not universals. Lewis just takes properties to be classes.

So there are, for Lewis, some good "natural" properties, namely, the ones that are the class of all things that instantiate a universal. (Or, that instantiate one of a group of closely related universals.) Armstrong really really really wants universals. For all that Lewis says that he has use for universals, all he actually uses is that some properties are better ("more natural") than others. Universals provide an "explanation" of naturalness.

Lewis catalogs a frighteningly long and detailed list of uses for natural properties, but (sigh of relief) he really only has one (I think). He needs, and thinks any philosopher needs something like, the notion of duplicates.

Duplicates. Two things are duplicates if they have all the same intrinsic Xproperties.X "Intrinsic because two things can be duplicates even if one is farther north than the other. The "definition" I just gave obviously doesn't work, since for any object, there is the property of being just that object, and so, on my definition, there aren't any duplicates: we've allowed too many crazy properties. We need to only keep good properties, and so the definition uses not "properties," but "natural properties."

The notion of a duplicate is not a familiar one, but Lewis uses it to introduce lots of familiar notions.

What are duplicates good for?

Someone else might have said that a law is a necessary regularity of nature expressed using natural properties. The qualification "necessary" is needed here, because there might be accidental regularities, and they wouldn't be laws. Lewis rejects that attempt at a characterization of a law because he doesn't think we can make sense of the needed notion of necessity except in terms of laws, and so he thinks the attempt is uninformative.

If there is nothing other than the physical, if either there is nothing mental or mental states are all physical states, then the mental supervenes on the physical since whatever is mental just is physical.

Suppose, however, that there are mental state distinct from anything physical. It still might be the case that to understand the world, it is enough to understand the physical part: That would be true if there is never a mental difference without a physical difference. If that works, the development of the mental just follows from the development of the physical.

Definition. The mental supervenes on the physical if any two states of affairs that are physical duplicates are also mental duplicates.

Since our physical theories lay claim to explaining all of our motions, including what we say, there doesn't seem to be any way for the mental to leak into anything we can observe, do, or know about each other. There can, nonetheless, be real mental phenomena if they supervene on the physical.

One simple way for the mental to supervene on the physical would be for mental states to correspond in a simple way with physical states. Then we could deduce psychology from physics. However, it could turn out that the relation between mental and physical states is complex, or even that it is not governed by laws. Then psychology would be a separate science from physics, but the mental could still supervene on the physical.

Given the idea, people have used it for other purposes. For example, some claim that chemistry supervenes on physics but is not reducible to it.

Criticism

Lewis thinks that he can make sense of simplicity using natural properties, and so avoid the uninformative use of physical necessity in characterizing laws. How do we know which properties are natural? When Lewis gives examples, he just takes the ones that actually occur in our theories or the ones that are most easily expressed in our language to be the natural ones. There is no criterion external to those considerations. Thus, simplicity is "explained" in terms of natural properties, but natural properties are identified in terms of simplicity in our theories. The circle is no larger than before.

Lewis wants us to think of natural properties as "carving nature at its joints" of identifying fundamental similarities and relationships. That won't work for the content of language project: the properties we need for that are the ones that are (I'll make up a term) humanly natural—easy for us to identify, not fundamental characteristics of nature. That casts doubt on the other cases as well: are mental natural properties more, less, or as natural as physical natural properties? And so on.

What I said about simplicity raises a more general skeptical worry: Even if there are natural properties, how could we ever know?

-- ShaughanLavine - 20 Feb 2008

Quine on Natural Kinds

Lewis said he had use for universals, but the only use is to pick out "natural properties." He really has no use for universals in themselves.

Quine, like everyone, agrees that some properties are special, but unlike Armstrong or Lewis

Armstrong's primary use for universals is to explain in what way things that share a common natural property genuinely have something in common: they instantiate the same universal. Lewis, by dropping the universal, has no explanation of what things that share a common natural property have in common. He bites the bullet and just takes it as a basic unexplained fact that things that share a common natural property are similar. Quine recognizes that natural kinds are supposed to play a role in explaining how it is that things that are of the same natural kind are similar, but, he notes, it doesn't work: you can't define similarity in terms of natural kinds (though there are attempts at such definitions that look plausible) and you can't define natural kinds in terms of similarity. That means (though Quine doesn't say so outright) that Lewis's idea is seriously problematic and that postulating universals does not explain similarity.

Quine, given the problems about how natural kinds and similarity are related, grants that there is some relation between the two, but keeps both. So, what is similarity? He introduces, not a metaphysical similarity (Armstrong's instantiate the same universal; Lewis's when nature is carved at the joints, things that are in the same piece), but a behavioral similarity that is shared by most people, a biological similarity. Every species of animal, Quine thinks, has such a form of similarity: all animals, not just people, learn by association: Pavlov's dogs, since a bell was rung before they were fed, salivated at the sound of a bell. How does that work? Obviously, it can't unless the dogs perceive different ringings of a bell as similar and different feedings as similar. One could, for example, determine if dogs find the sound of a buzzer similar to the ringing of a bell by measuring whether, and how much, the dogs salivate when a buzzer buzzes.

Different species have different similarity mappings. There are some trivial reasons for that: dogs are color blind. There are other, surprising, differences.

Similarity mappings are "obviously" important in the way in which we acquire our most basic kinds: We learn what red is by being shown a bunch of things and being conditioned to which ones are red. That wouldn't work unless the similarity mapping of the learner and the similarity mapping of the teacher are similar. As Quine notes, in language learning, the kinds are established by humans for humans and intended to be shared among large groups of humans, and so it is no surprise that the similarity relations are close enough and they work: if they didn't, there wouldn't be a word for whatever basic kind is under discussion.

That is pretty different from a metaphysically significant notion of kind. It is entirely an accident of human biology. Phonemes are an informative case. We not only manage to learn how to communicate with each other, we also manage to learn things about the world. If our similarity matched up to an objective notion of similarity or tracked metaphysically basic universals or carved nature at its joints, that would seem expected. As things are (according to Quine), it requires explanation. His explanation is evolutionary: creatures with similarity relations that had no relation to objective similarities would die without reproducing, and so our similarity relation must get some things "right." Of course, what is important is not determined by the character of the world, but by our needs: we need to not eat poisonous things, we need to distinguish friends from foes. Those are notions pretty far removed from the basic physical structure of the world. We might therefore expect to have some kinds that are connected to biology. Color is Quine's example. There are others: we can read faces and stances, even of nonhuman mammals. Babies are cute. These are very far from Armstrong's official universals (though he does use color as an example) and Lewis's natural properties.

Why do we need natural kinds to do science? Because we need to pick out classes of things (kinds) to formulate laws. Given how unrelated our innate kinds are to the physical world, how do we manage? We can invent new kinds as a matter of experience, and we take the kinds that play a role in our most general nonhumancentered theories to be natural properties in some (Lewis, Armstrong) objective senses. Examples: We carve whales and porpoises out of the fish kind for biological purposes. We group marsupials as more similar to each other than to nonmarsupials, even putting marsupial mice with kangaroos instead of with mice. Electric charge.

Thus, there aren't only given kinds, the ones we're born with—we invent/discover new kinds through experience, and value some of them for scientific purposes, namely, the ones that figure in general useful laws. In sufficiently developed sciences, we come to be able to live without kinds, because we can explain similarities and differences completely from fundamental scientific understanding. Quine's example is chemistry: water is no longer an unexplained kind, but H2O? . In the end, kinds are eliminated in favor of structure.

-- ShaughanLavine - 25 Feb 2008