1. Metaphysics Seminar 5: Ontology (2)
Henry Taylor

2. Concrete and Abstract.
The aim: to understand the concrete/abstract distinction as best we can.
Then apply it to our discussion of universals.
Recall: universals are properties that are shared across objects.
Objects instantiate universals.
Each instance of a universal is identical with each other instance of a universal.

3. ’Concrete’ and ‘abstract’
What do they mean?

4. First attempt: examples.
Concrete stuff is like shoes and ships and sealing wax.
Abstract stuff is like numbers, sets, etc.
No good: doesn’t really tell us what the distinction consists in.
Also: not everyone agrees that numbers are ‘abstract’.
What good is examples when it comes to a specific case where we’re not sure? Like universals, are they more like shoes or numbers?
We’re at a loss.

5. Two meanings of ‘abstract’.
1) Something is ‘abstract’ if it depends on something else for its existence (we will encounter this meaning in seminar 7).
2) Something is concrete if it is spatiotemporal, it is abstract if it is non-spatiotemporal.
We will focus on the second for this lecture.

6. Spatiotemporal
There are some vague cases: Cartesian souls exist in time but not space.
So are they concrete or abstract?
E. J. Lowe: we should define ’concrete’ as ‘exists at least in time’, so Cartesian souls count as concrete.
I won’t discuss these vague cases any more.

7. The abstract Abstract means ‘non-spatiotemporal’.
It doesn’t mean ‘spooky’ or ‘exists in heaven’ or ‘is made of magic’ or anything else like that.

8. Are there any abstract objects?
One candidate: numbers.
Quine and Putnam: we should believe in abstract objects because science can’t do without numbers, and numbers are abstract.
Discussion:
What is the problem of knowledge of abstract objects (372-3)? Is Lowe’s reply to it a good one?
What do you think of the indispensability argument for the existence of numbers?

9. Universals Recall: property universals.
For this lecture, let’s assume that they exist.
Then we can ask: are they abstract or concrete?

10. Abstract/Platonic vs Concrete/Aristotelian Universalism
One view: universals are abstract (i.e. non-spatiotemporal).
View held by Plato and J. P. Moreland.
Another: universals are concrete: they’re spatiotemporal.
Sometimes called ‘imminent universalism’ or ‘imminent realism’.
View held by David Armstrong and (maybe) Aristotle.

11. Terminology Warning.
‘Concrete Universalism’, ‘Aristolenian Universalism’ and ‘Immanent Universalism’ all mean the same thing.
‘Abstract Universalism’, ‘Platonic Universalism’ and ‘Transcendent Universalism’ all mean the same thing.

12. Start with Concrete universalism
How does this work?
Well, it claims universals are spatiotemporal.
They exist where they are instantiated.
So, return to our apples:

13. Concrete universalism
The universal ‘red’ is a concrete entity.
It exists where the apples do.
It also exists where other stuff is: postboxes and so on.

14. Concrete Universals
Crucial point: it is not that universals have parts and that one part exists in each place the universal is instantiated.
So, say you have three red apples.
It is not that the universal is made of three parts, and that part 1 exists where Apple 1 exists, and part 2 exists where Apple 2 exists, and part 3 exists where Apple 3 exists.

15. Concrete Universals Why not parts?
Well, consider how universalism explains resemblance.
It does so in terms of identity: apple 1 resembles apple 2 because they have the same universal, and those universals are identical.
What if the redness of apple 1, and the redness of apple 2 were just parts of a universal?
That wouldn’t explain resemblance, because parts of something do not always resemble each other.

16. Parts.
Think of the parts of a car.
They’re nothing like each other.

17. Concrete Universals
No, the relation that the redness of apple 1 bears to the redness of apples 2 and 3 cannot be that they are all parts of a universal, they all have to be identical entirely.
This is what universalists mean when they say that universals are ‘wholly present’ at each of their instances.
The entire universal is present in apple 1, and it is also present in apple 2 entirely and also entirely present in apple 3.
It is ‘wholly present’ and ‘multiply located’.

18. Concrete Universals
Objects aren’t like this: they cannot be wholly located in more than one location.
Parts of them can: your head can be on your pillow, while your feet are at the foot of the bed.
But you are not wholly present both at the pillow and at the foot of the bed.
By comparison, universals are entirely present in more than one place.
Or so say the concrete universal folk.

19. Wholly present? What? Some folk just can’t take this:
‘Even those willing to suspend judgement on what they regard as loony philosophical theses typically baulk at the idea of universals; this is so even when universals are presented (as I try to present them) in a most favourable light’ (John Heil 2003, p.139).

20. What do we think? Is it crazy?

21. Objects.
E. J. Lowe’s argument against multiply instantiated universals.
Philosopher at University of Durham
Recent loss to philosophy.

22. Lowe’s argument.
1) A and B are blue chairs. So, the universal BLUE is located where A is, and where B is.
2) Furthermore: all of the universal is where A is , and all of it is where B is.
3) But if all of BLUE is co-located with A, then A is co-located with BLUE (by symmetry of co-location).
4) And if all of BLUE is co-located with B, then B is co-located with BLUE (by symmetry of co-location).
5) So, A and B are both co-located with BLUE.
6) But co-location is transitive, so A and B (the chairs) are co-located.
7) But A and B are not co-located (clearly)
(Therefore) Contradiction.

23. Questions/comments?

24. Abstract Universalism: J. P. Moreland
These are all problems if we say that universals are concrete, because then you have to say they exist where they are instantiated.
Then you say they’re multiply instantiated, and then you’re in trouble.
So we shouldn’t say they’re spatiotemporal at all.
They are abstract.

25. Abstract universals So, universals exist abstractly.
But normal concrete objects like apples: they instantiate universals.
The redness of the apple is an instantiation of the universal ‘red’, which is abstract.

26. Plato This is very similar to Plato’s view:
Plato accepted a world of ‘the Forms’
The Forms are a non-spatiotemporal realm which explain resemblance.
So, imagine we have two beds, and the question is ‘what makes them both beds?’
Answer: they both partake in the Form ‘bed’: they are unified in that respect.
Notice that this is very similar to the argument from resemblance.

27. Abstract Universals
One reason to accept abstract universals: uninstantiated properties.
Some properties have never come along in the concrete world.
For example: in this world, travelling faster than light is not something anything has ever done.
The person who accepts abstract universals can say that those properties exist, but they just aren’t instantiated.
So you can believe in far more properties than the conrete universalist can.

28. Discussion What do you think of the ‘indispensability’ argument?
Is it crazy to say that a universal can be wholly present in more than one place at once?
What do you think of Lowe’s argument against concrete universals?
What do you think of the ‘theory of meaning’ and ‘uninstantiated universals’ arguments for abstract views (64-66)? Is Armstrong right to dismiss them?
Armstrong complains about the relation between a Form and a particular. What is this complaint? Is it a good one?
Is Armstrong’s answer to the question of how a particular and a universal are related any better than the abstract universalist’s?
Do you prefer concrete or abstract universals?