1. Particulars and Properties Lecture one: Universalism and Nominalism.
Henry Taylor

2. Preliminaries: Books
Properties edited by D. H. Mellor and Alex Oliver (OUP). This is the most important.
Universals: an opinionated Introduction (Boulder) and
A World of States of Affairs (CUP) by David Armstrong.
From an Ontological Point of View by John Heil (OUP). Very good for an alternative point of view.

3. The project.
Our focus: properties and particulars, concrete and abstract.
We’re going to be looking at this from the point of view of ontology.
Ontology: a systematic account of the most fundamental constituents of reality.
What??? Don’t worry, it will become (somewhat) clearer…
Word of warning: these four lectures will be heavily intertwined, so come to all of them.

4. A simple argument: two apples.

5. A simple argument. There are two apples on the table.
They are alike in certain ways (for example, they are both red).
What explains this likeness?
Well, there are not just two apples, there is also a third thing: redness.
Both apples ‘share’ in this redness.
So, there are (at least) three things here: apple 1, apple 2 and redness, a property.

6. A simple argument made a bit more complex
We have two objects, A1 and A2.
They resemble each other.
This resemblance should be explained somehow.
We should accept the existence of a property universal.
Each one ‘partakes’ of the same property universal: redness.

7. The argument continued.
The universal of A1 is identical to the universal of A2. This is strict, literal identity.
Everything resembles itself.
So the universal of A1 resembles the universal of A2.
A1 and A2 both instantiate redness, and so the similarity between A1 and A2 is explained by them.

8. Summary. We start with a problem (resemblance between objects)
We accept a new kind of entity (universals)
Then we explain resemblance in terms of two claims:
1) that each object has the same (i.e. identical) universal.
2) that identical things always resemble themselves.

9. What do we think of that argument?

10. Universals.
On one side of the divide: Realists: folk who believe that there are universals.
David Malet Armstrong.
Recent loss ( )
One of 20th century’s greatest metaphysicians

11. Universals. On the other: nominalism. There are no universals.
W. V. O. Quine

12. Terminology warning.
Sometimes folk who believe in universals are called ‘property realists’.
This is because some folk take ‘property’ to be synonymous with ‘universal’.
But sometimes nominalists say they believe in properties (it’s just that they don’t think they’re universals).

13. Nominalism: there are no universals.
Some quick objections:
1) Universals are mysterious
2) The relation between an object and its universals is mysterious.
3) All other things being equal, we should postulate as few kinds of entity as we can get away with (parsimony).

14. Nominalism and resemblance
So, how do nominalists explain resemblance?
Several options:
1) Resemblance is just primitive: it cannot be explained.
2) Two objects resemble each other if they fall under the same predicate or concept.
3) Class nominalism: properties do exist, but they are not universals, they are sets.
4) Ostrich nominalism: bit different.
We will be looking at (3) and (4)

15. Class or set nominalism
Properties like ‘redness’ do exist.
But they are just sets of objects.
So, redness is the set containing stuff like British postboxes, London buses, the apples etc. the set of objects is the property.
Two objects resemble with respect to redness iff. they fall into this set.
We don’t need universals. We need sets, but we needed them anyway (everyone loves sets).

16. Problems for set nominalism.
Coextensive properties.
Some exciting words for you: Renate means ‘creature with a kidney’ and cordate means ‘creature with a heart’.
The set of ‘renates’ has the same members as the set ‘cordates’.
If any two sets have the same members, then they are the same set (axiom of extensionality).
So the two sets are the same.
So (assuming that the set is the property) then the property of being a renate is the property of being a cordate.
But clearly they’re different properties!
So set nominalism is wrong.

17. A solution? David Lewis (1941-2001)
‘The greatest philosopher since Leibniz’
Don’t be fooled: he did defend universals in some places, but here he’s defending set nominalism.
Properties are identical with sets of actual and possible entities
So in some possible world there is an animal with a heart and no kidney.
So the sets don’t have the same members at all.

18. More on set nominalism. But this doesn’t work in all cases.
Consider triangularity and trilinearity: having three internal angles, and being bounded by three lines.
The set of triangular objects and trilinear objects is the same in all possible worlds.
So set nominalism predicts that they’re the same property.
But clearly they’re not!

19. Lewis’ reply
Look, we can use the word ‘property’ in all sorts of ways.
On some meanings, ‘triangularity’ and ‘trilinearity’ would be the same property.
And set nominalism gives you a perfect account of this usage.
There may be other uses, but that’s beyond the theory.
What do we think of this? Is it bluster? Or is it a good point?

20. Causation and set nominalism.
Causal efficacy: properties cause stuff.
The weight and velocity of this brick causes the window to smash.
But sets do not have any causal powers.
So properties aren’t sets.

21. Another nominalism: ostrich nominalism.
Ostrich nominalism and mirage realism.

22. Ostrich nominalism. We have two apples, and they resemble each other.
They resemble because they’re each red.
But nonetheless, I don’t have to say that the property universal exists!
I can talk the talk of the realist, but I don’t pay the price.

23. How does this work?
Start with the Quinean concept of ontological commitment.
We should read our commitments off the bound variables of our best theories.
So, we write out our best theory (in first order predicate logic), and look at the bound variables, and that dictates our ontology.
And if we want to say ‘there are two red things’ we can say:
∃x ^∃y (Rx^Ry)
The ‘R’ stands for ‘is red’ But the ‘R’ (the ‘redness’) is not a variable (it’s a predicate).
So we’re not committed to redness (we’re only committed to x and y).

24. Quine.
‘The words ‘houses’, ‘roses’, ‘sunsets’ are true of sundry individual entities… and the word ‘red’ or ‘red object’ is true of each of sundry individual entities which are red houses, red roses, red sunsets; but there is not, in addition, any entity... which is named by the word ‘redness’, nor, for that matter, by the word ‘househood’, ‘rosehood’, ‘sunsethood’. That the houses and roses and sunsets are all of them red may be taken as ultimate and irreducible and it may be held that [the universalist] is no better off... For all the occult entities which he posits under such names as ‘redness’.’
-On what there is, 1948.

25. Reply Armstrong calls this ‘cloak and dagger nominalism’
Quine is stacking the deck in his favour!
Why should we take variables to be more committing than predicates?
Why not take predicates to commit us as well, so that if we say ‘Ra’ then we should be committed to a and to R.
So when we say ‘there is a red apple’ we should accept the existence of the apple and the redness.
To favour the variables over the predicates is ontologically dishonest.

26. What do we think of ostrich nominalism?
Any further questions and comments?
Next time: the concrete and the abstract.