1. Particulars and Properties. Lecture four: Tropes.
Henry Taylor

2. Recap
We have been trying to build an ontology, and we’ve been looking at the nature of properties.
We started off with the problem of resemblance: how is it that two things are alike?
We ended up with a range of options on the table.

3. Positions: realism and nominalism
Universal realists: Armstrong, Moreland, Lewis (on some days).
Nominalists:
Set nominalism (Lewis on other days, Rodriguez-Pereya)
Ostrich nominalism (Quine and Devitt)

4. Universals We then looked at what happens if you accept universals.
Are they concrete or abstract?
Concrete: Armstrong.
Abstract: J. P. Moreland.

5. Universals Are universals all there are?
Yes: A bundle theory of universals.
No: Armstrong. There are thin particulars as well.

6. States of affairs
We ended up with states of affairs: properties are concrete universals, that are wholly present at each instance.
They are instantiated by particulars: things which have universals.

7. Tropes Today we will be looking at another ontology: tropes
Tropes are properties of objects (like universals).
But they are not ‘wholly present’ at each instance.
Each trope is a particular.
This means that each instance of a trope is non-identical with each other instance of the same ‘kind’ of trope.
(We will cash out ‘kind’ soon enough).

8. Some trope folk Keith Campbell
Abstract Particulars (1990) is still the seminal book.
See also the paper ‘The metaphysics of abstract particulars’ (in the Mellor and Oliver collection).
Also: Douglas Ehring and Peter Simons
John Heil’s From an Ontological Point of View has some excellent stuff in it on tropes.

9. Back to the apples.
Universalist says: These two apples each instantiate REDNESS, and the REDNESS of apple 1 is identical with the redness of apple 2.
Trope theorist says: These two apples each instantiate a property. Apple 1 instantiates REDNESS1, and apple 2 instantiates REDNESS2.
These two REDNESS tropes are not identical: each is different from the other.

10. Tropes But how does this explain resemblance between objects?
The universalist explanation is clear:
The two apples each instantiate REDNESS.
The redness of one is identical to the redness of the other.
Everything resembles itself.
So that’s resemblance: explained in terms of identity.
Trope folk clearly can’t embrace that, because they don’t think tropes are identical.

11. Tropes How they do it: exact similarity.
So, REDNESS1 is not identical to REDNESS2.
But they are exactly similar to one another: they are non-identical but exactly alike.
So REDNESS1 and REDNESS2 are exactly similar, and in virtue of this exact similarity, the two apples resemble each other.

12. Tropes Think of it like this:
‘Bill and Ben have the same car’ is ambiguous.
It could mean that Bill has one car, and Ben another car: and each one is a red ford focus.
Or it could mean that there is one car, and Bill and Ben take turns driving it.
The first one is the trope theory (different but exactly similar)
The second is universalist theory (identity, in the philosopher’s sense).

13. Tropes and exact similarity.
So, each trope has some buddies that are exactly similar to it.
REDNESS1, REDNESS2, REDNESS3 etc. all bound by the relation of exact similarity.
These all form a set of exactly resembling tropes.
Any object instantiating any trope in the set resembles all of the objects that instantiate any other trope in the same set.
So, what universalists do with one universal, trope theorists do with sets of exactly resembling tropes.

14. Exact similarity The exact similarity relation is primitive.
So what are objects?
They are bundles of tropes.
So, a ball is the bundle of REDNESS1, SPHERICITY1, MASS1, etc.
These are bound together by another primitive relation of compresence.
So, objects are bundles of compresent tropes.

15. Compresence vs instantiation
States of affairs folk: objects are thin particulars that instantiate universals.
Trope folk: objects are bundles of tropes bound by compresence.

16. Questions/comments?

17. Terminological hell!
1) Tropes are sometimes called ‘modes’ by John Heil, C. B. Martin and E. J. Lowe. That’s the older Lockean word for them.
They’re called tropes by folk like Keith Campbell and Douglas Ehring.
2) Tropes are sometimes called ‘abstract particulars’ (by Keith Campbell) but that’s not because they’re non-spatiotemporal, but because they’re abstract as in they depend for their existence on the object that instantiates them.
3) Trope theory is sometimes called ‘nominalism’ because trope folk don’t believe in universals. But they do believe in properties.

18. Why believe this? Bundle theories
Well, look at the bundle theory of universals.
That got in trouble because it had to say that two objects with the same universals were identical.
This is because all the universals in both bundles were identical, and the identity of the bundle was determined the identity of the universals in it.
Trope theory doesn’t have to say this, because each trope is a particular, so the two bundles have non-identical properties.
So the two bundles are not identical.

19. Why believe this? Thin particulars
Also, remember that Armstrong needed thin particulars, and these are (supposedly) mysterious.
He needed these to explain how each object can be a particular (universals can’t do this).
The trope folk don’t need thin particulars: the tropes themselves show how objects can be particulars (because the tropes are themselves particulars).

20. Why believe this? Whole presence
Also, remember the problems we had with saying that a universal is ’wholly present’ at each of its instances.
Trope theorists don’t believe this, so they dodge these issues straight away.

21. A possible reaction
‘Look, the whole reason we got interested in properties was to explain how two objects can resemble. Universals explain that in terms of each having an identical universal. The trope theorist has to explain it in terms of this primitive relation of exact similarity.
But if you have to take that as primitive, why not just take resemblance between objects as primitive? Why accept tropes or universals at all? Why not just say ‘objects resemble, end of story?’

22. Questions/comments?

23. Another argument (Armstrong).
1) Suppose apple 1 has REDNESS1, and apple 2 has REDNESS2.
2) It is possible for REDNESS1 to ‘switch’ with REDNESS2 so that REDNESS2 is had by apple 1 and REDNESS1 is had by apple 2 (by the combinatoral principle of possibility).
3) The trope theorist says that the world has now changed.
4) But the supposed difference is: undetectable and makes no difference to the causal structure of the world.
5) In order for something to be real, it must make a difference to the causal powers of something (Eleatic principle).
6) (Therefore) this change is not real.
7) (Therefore) the theory that predicts it is real should be rejected (this means trope theory).

24. Replies Deny that ‘trope swapping’ is possible.
Could deny the combinatorial theory of possibility: that elements of reality can be ‘freely recombined’ to create new possibilities.
But is there any reason to deny this other than protecting trope theory?
Deny the Eleatic principle
Again, what principled reason do we have to deny this, independent of commitment to tropes?

25. 5 positions. We now have 5 positions on the table: 1) Set nominalism
2) Ostrich nominalism
3) Universal bundle theory
4) States of affairs
5) Trope bundle theory
Let’s do a poll.

26. Final thoughts: parsimony.
Over the course of these lectures, philosophers have often been really worried about parsimony.
That’s one of the main attractions of nominalism over property realism
AND bundle theories over states of affairs.
AND, concrete theories over concrete-and-abstract.

27. Parsimony But what about not taking parsimony quite so seriously?
John Heil and C. B. Martin:
They accept tropes (they call them modes), and so (technically) they don’t have to accept substance to explain particularity (they could go for bundle theory).
But they do anyway because they think it’s plausible.
They’re not that worried about parsimony.

28. Parsimony More extreme example: E. J. Lowe’s Aristotelian ontology.
He has four categories:
1) Modes: particular properties, tropes.
2) Universals: the universals of which a trope is an instance.
3) Individual substances: Objects.
4) Kinds: The ‘sorts’ that particular objects fall into.

29. Parsimony Take a tomato:
The tomato is an object instantiating a mode or trope: a particular redness, and that mode falls within the property universal ‘redness in general’. The particular tomato also falls within the kind ‘tomato’.
He even thinks that universals and kinds are abstract so he has concrete and abstract stuff in there!

30. Parsimony
Each of these categories does something in his ontology (they’re not postulated for the hell of it)
But clearly he doesn’t lie awake at night worrying about parsimony.
What do we think of this approach?

31. Final thought You now have the basic resources to build an ontology:
Universals
Particulars
Sets
Quantification
Abstract/Concrete
Tropes
Thin/Thick Particulars

32. Thank you!
Final order of business: Lecture evaluations.