1. Universals, Properties, Kinds
The distinction between universals and particulars.
Start with a basic observation: the world consists of lots of genuinely distinct individuals, i.e., particulars.
But, as we saw in the last class, there is a Fregean notion that, for a to be an individual, a must fall under a concept: a is F.
What is F? A concept for a property, a quality, … a universal. I.e. something that can be multiply instantiated in the world.

2. Particulars exist at unique spatiotemporal locations.
Universals do not. (Either they are multiply instantiated or they exist in some other realm – Plato’s heaven.)
Two views: Realism vs. Nominalism
Particulars are “reducible” to universals. (Each particular is merely a “bundle” of universals. E.g. “a is FGH” means that there exists somewhere this amalgam of properties: F, G, and H.)
Universals are “reducible” to particulars. (Each universal or property is merely a “name” that suggests some commonality between individuals.)

3. Class Nominalism: Properties are classes of particulars
Class Nominalism: Properties are classes of particulars. So, F-ness is simply the name for the class of all things that are F.
(This is advocated by Lewis in The Plurality of Worlds. And the classes can include individuals in different possible worlds.)
Resemblance nominalism: Start with a paradigm for some property, F. All things that resemble this paradigm are members of the class of F things.
Note that classes are not universals because classes are not multiply instantiatable.

4. Trope Theory
Each particular thing possesses its own property of F-ness, which is itself a particular. In other words, this chair is blue. But its blueness is unique; it is not merely one instance of many instances of blueness. The particular, individual blueness of this chair is a trope.
“Blue” is used of many different particulars, presumably because there is some resemblance.

5. Armstrong, “Universals as Attributes”
§1 Uninstantiated Universals
One key question: Should we, or should we not, accept a Principle of Instantiation for universals?
Three possible views:
Universalia ante res (“universals before things”): Platonic, transcendent universals that can exist without being instantiated in the world. Armstrong: this is unacceptable to naturalists.
Universalia in rebus (“universals in things”): rejects uninstantiated universals. Armstrong’s view.
Universalia post res (“universals after things”): nominalism.

6. §2 Disjunctive, Negative, and Conjunctive Universals
Disjunctive properties (i.e. universals) are not to be allowed.
N.b.: “There is some very close link between universals and causality.”
Negative properties (universals) are also not to be allowed.
But conjunctive properties are OK.

7. §3 Predicates and Universals
“[T]here is no automatic passage from predicates (linguistic entities) to universals.” (202a)
Universals are not going to be simply equivalent to the predicates that we use in our language. Rather, universals are discoverable by natural science. In other words, Armstrong advocates a posteriori realism.

8. §4 States of Affairs
State of affairs are primitive.
Truthmaker principle: For every contingent truth at least (and perhaps for all truths contingent or necessary) there must be something the in the world that makes it true.
In other words, there is something in the world in virtue of which a proposition is true.

9. §5 A World of States of Affairs?
“[W]e should think of the world as a world of states of affairs, with particulars and universals only having existence within states of affairs.” (205b)
In other words, particulars and universals can only be said to exist insofar as they constitute facts. No a, no F, except as part of the state of affairs: <a is F>.
“A particular that existed outside states of affairs would not be clothed in any properties or relations. It may be called a bare particular.” Armstrong rejects such bare particulars.

10. §6 The Thin and the Thick Particular
The antinomy of bare particulars:
When we say “a is F” what is the “is”? It is not the “is” of identity (a = a). It is the “is” of instantiation – “of a fundamental tie between particular and property.” a and F are different kinds of things. But, then, that would seem to mean that a really is a bare particular, that it can exist without F and that F can exist without being instantiated.
Thin particular: a abstracted from its properties.
Thick particular: the state of affairs which enfolds thin particulars and properties (a’s being F).

11. §7 Universals as Ways
“My contention is that once properties and relations are thought of not as things, but as ways, it is profoundly unnatural to think of these ways as floating free from things.” (207a)

12. §8 Multiple Location
“To talk of locating universals in space-time then emerges as a crude way of speaking. Space-time is not a box into which universals are put. Universals are constituents of states of affairs. Space-time is a conjunction of states of affairs. In that sense universals are “in” space-time. But they are in it as helping to constitute it. I think that this is a reasonable understanding of universalia in rebus, and I hope that it meets Plato’s objection.” (208ab)