1. Particulars and Properties Lecture two: The concrete and the abstract.
Henry Taylor

2. Lectures All lectures (as well as other materials) available at:
jhenrytaylor.wordpress.com

3. 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.

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

5. 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.

6. Two meanings of ‘abstract’.
1) Something is ‘abstract’ if it depends on something else for its existence (we will encounter this meaning in lecture 4).
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.

7. 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.

8. 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.

9. 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.
What do we think?
I’d like to link this with what we’ve been looking at so far: universals.

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

11. Abstract/Platonic vs Concrete/Aristotelian Universalism
One view: universals are abstract (i.e. non-spatiotemporal).
View held by Plato (maybe) 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.

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. Troubles
Suppose we have two red apples, A1 and A2, and I throw A1 out the window.
Then it means that the universal RED is in motion (A1) and also not in motion (A2).
But this violates the law of non-contradiction.

22. Possible replies
Of course, it could be said that these are only really problems when we are thinking of objects.
Objects cannot both be in motion and be at rest, but universals can.
But:
1) Why should we think it is less of a problem when it comes to universals?
2) We can make this a problem for objects as well.

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

24. 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.

25. Lowe’s argument What do we think of that argument?
What will the concrete universalist say?
They will probably deny that co-location is symmetrical, or transitive in the case of concrete universals.
Is that satisfactory?

26. 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.

27. Plato’s heaven?
One problem: If you say they’re not spatiotemporal, you need to find somewhere (outside of spacetime) to put them! You need to postulate a Platonic heaven or something.
Reply: no, you don’t need to put them somewhere because they do not exist anywhere at all: they’re none spatiotemporal.

28. Abstract Universals
Another objection: These things are so spooky. We know what the redness of this apple is, I can see it, but when you tell me it’s non- spatiotemporal, I lose any grip on what it is.
It’s mystery mongering.
Is that a really damaging objection?

29. More problems
The basic issue is that if you say universals are abstract, all sorts of problems pop up explaining how they interact with concrete reality.
For example:
1) Properties have causal powers (remember the brick’s mass and velocity, causing the window to smash).
2) Only spatiotemporal entities have causal powers.
3) Therefore, properties are spatiotemporal.

30. Instantiation Another problem: on this view, objects are concrete.
But they instantiate properties, which are abstract.
‘Instantiation’ of an abstract property: what does that mean and how does it work?

31. Instantiation? The Concrete person might say this:
‘Look, I accept concrete universals that are wholly present in multiple locations. That has problems, fair enough. But YOU (the Platonist) accept abstract properties and ‘instantiations’ of those properties. But what precisely is an instantiation and (crucially) don’t all of the problems associated with concrete universals apply to instantiations of abstract universals?
So you have all the same problems as me and you also accept this spooky Platonic heaven’

32. Concrete vs Abstract Universalism.
What do we think of the two views?

33. Next Week: Bundles and thin and thick particulars.