Trope theory and merely numerical differences in pleasures

Suppose I eat a chocolate bar and this causes me to have a trope of pleasure. Given assentiality of origins, if I had eaten a numerically different chocolate bar that caused the same pleasure, I would have had had a numerically different trope of pleasure.

Now, imagine that I eat a chocolate bar in my right hand and it causes me to have a trope of pleasure R, and immediately as I have finished eating that one chocolate bar, I switch to eating the chocolate bar in my left hand, which gives me an exactly similar trope of pleasure, L, with no temporal gap. Nonetheless, by essentiality of origins, trope L is numerically distinct from trope R.

To some (perhaps Armstrong) this will seem absurd. But I think it’s exactly right. In fact, I think it may even an argument for trope theory. For it seems pretty plausible that as I switch chocolate bars, something changes in me: I go from one pleasure to another exactly like it. But on heavy-weight Platonism, there is no change: I instantiated pleasure and now I instantiate pleasure. On non-trope nominalism, likewise there is no change. It’s trope theory that gives us the change here.

Reducing exact similarity

It is a commonplace that while Platonists need to posit a primitive instantiation relation for a tomato to stand in to the universal redness, trope theorists need an exact similarity relation for the tomato’s redness to stand in to another object’s redness, and hence there is no parsimony advantage to Platonism.

This may be mistaken. For the Platonist needs a degreed or comparative similarity relation, too. It seems to be a given that maroon is more similar to burgundy than blue is to pink, and blue is more similar to pink than green is to bored. But given a degreed or comparative similarity relation, there is hope for defining exact similarity in terms of it. For we can say that x and y are exactly similar provided that it is impossible for two distinct objects to be more similar than x and y are.

That said, comparative similarity is perhaps too weird and mysterious. There are clear cases, as above, but then there are cases which are hard to make sense of. Is maroon more or less similar to burgundy than middle C is to middle B? Is green more or less similar to bored than loud is to quiet?

A privation theory of evil without lacks of entities

Taking the privation theory literally, evil is constituted by the non-existence of something that should exist. This leads to a lot of puzzling questions of what that “something” is in cases such as error and pain.

But I am now wondering whether one couldn’t have a privation theory of evil on which evil is a lack of something, but not of an entity. What do I mean? Well, imagine you’re a thoroughgoing nominalist, believing in neither tropes nor universals. Then you think that there is no such thing as red, but of course you can say that sometimes a red sign fades to gray. It is natural to say that the faded sign is lacking the due color red, and the nominalist should be able to say this, too.

Suppose that in addition to being a thoroughgoing nominalist, you are a classical theist. Then you will want to say this: the sign used to participate in God by being red, but now it no longer thusly participates in God (though it still otherwise participates in God). Even though you can’t be a literal privation theorist, and hold that some entity has perished from the sign, you can be a privation theorist of sorts, by saying that the sign has in one respect stopped participating in God.

A lot of what I said in the previous two paragraphs is fishy. The “thusly” seems to refer to redness, and “one respect” seems to involve a quantification over respects. But presumably nominalists say stuff like that in contexts other than God and evil. So they probably think they have a story to tell about such statements. Why not here, then?

Furthermore, imagine that instead of a nominalist we have a Platonist who does not believe in tropes (not even the trope of participating). Then the problems of the “thusly” and “one respect” and the like can be solved. But it is still the case that there is no entity missing from the sign. Yet we still recognizably have a privation theory.

This makes me wonder: could it be that a privation theory that wasn’t committed to missing entities solve some of the problems that more literal privation theories face?

Theism and abundant theories of properties

On abundant theories of properties (whether Platonic universals or tropes), for every predicate, or at least every predicate satisfied by something, there is a corresponding property expressed by the predicate.

Here is a plausible sounding argument:

1. The predicate “is morally evil” is satisfied by someone.

2. So, on an abundant theory of properties, there exists a property of being morally evil.

3. The property of being morally bad, if it exists, is thoroughly evil.

4. So, on an abundant theory of properties, there exists something that is thoroughly evil.

5. If theism is true, nothing that exists is thoroughly evil (since every entity is the perfect God or created by the perfect God).

6. So if theism is true, an abundant theory of properties is false.

If I accepted an abundant theory of properties, I would question (3). For instance, maybe properties are concepts in the mind of God. A concept of something morally evil is not itself an evil concept.

Still, it does seem to me that this argument provides a theist with a little bit of a reason to be suspicious of abundant theories of properties.

Temporary intrinsics and internal time

The main problem the literature presents for eternalist theories is the problem of temporary intrinsics: how an object can have an intrinsic property at one time and lack it at another.

The most common solution is perdurantism: four-dimensional objects have ordinary properties derivatively from their instantaneous temporal parts or slices having them, and since the slices only exist at one time, the properties can be as intrinsic as one likes.

Another solution that has found some purchase is a view on which the properties that we previously thought were intrinsic, such as shape and charge, are in fact fundamentally relational, defined by a relation to a time. Thus, to be square is to be square at some time or other. This results in a more commonsense ontology than perdurantism, but it has the problem of just denying that there are temporary intrinsic properties.

This morning it’s occurred to me that if we say that substances carry with them an internal time sequence that is intrinsic to them, then relationalism can admit temporary intrinsic properties. A property of a substance, after all, can be intrinsic even if the property is relational, as long as the relations that the possession of the property is grounded in are intrinsic to the object, say by being relations between parts or other metaphysical components of that object. After all, shape is seen as the paradigmatic case of an intrinsic property, and yet it is often seen as grounded in the relations between the particles making up an object. But on a view on which substances carry an internal time sequence, the internal times can be taken to be intrinsic aspects of the substance, and then ordinary properties can be seen as relational to the these internal times. Thus, to be square is more fundamentally to be square at some internal time or other.

What kinds of intrinsic aspects of the substance are the internal times? Here, there are multiple options. They could be sui generis aspects of the substance. They could be tropes—for instance, if substances all have beginnings, one could identify a time with the trope of having survived for a temporal duration D.

Internal times could even be time slices of the substance. This last option may seem to take us back to perdurantism, but it does not. For it is one thing to say that I am in pain because my temporal part ARP_t is in pain—it sure seems implausible to say that I am in pain derivatively from something else being in pain—and another to say that my being in pain is constituted by a relation to ARP_t, which part is in no pain at all. (That pain is constituted by a relation between the aspects of a substance is not at all strange and unfamiliar as a view: a materialist may well say that pain is constituted by relations between neuronal activities.)

Note, too, a view on which intrinsics are relational to internal times also solves another problem with views on which ordinary properties are relational to times: if those times are external, then time travel to a time at which one “already” exists is ruled out.

My own preferred view is that a nested trope ontology. I have a trope of being human. That trope then has an infinite number of temporal existence tropes, corresponding to all the different internal times at which I exist. These temporal existence tropes—or maybe even temporal human existence tropes—are then the internal times. And I can even say what the relation that makes a temporary intrinsic obtain at a temporal existence tropes t is: that temporary intrinsic obtains at t provided that it is a trope of t.

Accidents and truthmakers

It is difficult to hold (a) Aquinas’ idea that in transubstantiation the accidents of bread and wine continue existing after the bread and wine have perished together with (b) the idea that accidents are truthmakers for predications.

For if the accident of the whiteness of the bread is a truthmaker for the proposition that the bread is white, then it is (absurdly) true to say that the bread is white even after transubstantiation, since when the truthmaker exists, the proposition it makes true is true.

So, if one wants to hold on to the logical possibility that accidents could outlast their substance, one has to modify the thesis that accidents are truthmakers for predications. Instead, perhaps, one could say that the truthmaker for the proposition that x is F is x’s Fness together with x. This solves the problem of the bread being white after transubstantiation, since after transubstantiation there is no bread, and so if the truthmaker is the accident of whiteness together with the bread, then after transubstantiation the bread part of the truthmaker doesn’t exist. So all is well.

But here is a further puzzle. Intuitively, if God can detach the bread’s accidents from the bread when the bread ceases to exist, why can’t God detach the bread’s accidents from the bread while the bread continues to exist? But if God could detach the bread’s accidents from the bread while the bread continued to exist, then God could detach, say, the whiteness W of a bread from a bread B, and then the bread could be dyed black. Were that possible, it couldn’t be true that W and B are a truthmaker for the proposition that the bread is white, since W and B could continue to exist without the bread being white any more.

So, holding that the substance and its accident is a truthmaker for the predication, while accepting the logical possibility of Aquinas-style transubstantiation, requires one to hold that God can only detach the bread’s accidents from the bread while annihilating the bread. That seems counterintuitive.

Another move is this. Posit an “attachment” trope. Thus, when x is F, there are three particular things: x, x’s accident of Fness, and an attachment trope between x and x’s accident of Fness. Further, posit that in transubstantiation the ordinary accidents continue to exist, but the attachment tropes perish. And now we can say that the truthmaker of “The bread is white” is B, W and the attachment trope between B and W. (There is no infinite regress, since we can suppose that the attachment trope cannot exist detached.) But God can make W exist without the attachment trope, and either with or without B.

But it is an unpleasant thing that the attachment trope is a metaphysical ingredient posited solely to save transubstantiation. Moreover, the attachment trope would be a counterexample to the Thomistic principle that God can supply whatever creatures do. For it is essential to the story that the attachment trope cannot possibly exist in the absence of bread.

Probably, the Thomist’s best move is to deny that accidents (whether with or without the underlying substance) provide truthmakers for predications. If we did that, then a nice bonus is that we can have accidents moving between substances, which would provide a nice metaphysical account of why it is that flamingos turn pink after eating pink stuff.

Presentism, change and ontology

Presentism says that only present things exist. This by itself cannot explain the nature of change.

For assume an ontology on which, necessarily, everything that exists is either a concrete substance or a necessary abstract object. Consider a world w₁ where all the concrete substances exist for all time, but some of them are changing their properties, e.g., shape. Notice that the presentist, the growing blocker and the eternalist all agree about what exists at w₁, since no entity comes into or out of existence on this ontology, and hence the differences between the three theories are irrelevant to w₁. Yet, w₁ is a world with change.

Hence presentism by itself cannot explain change.

Perhaps someone who thinks that presentism is needed to explain change should opt for a trope ontology rather than a substance-and-abstracta or substance-only ontology. For then they can say that at w₁, entities—namely, tropes—come into and out of existence.

Yet another bundle theory of objects

I will offer a bundle theory with one primitive symmetric relationship. Moreover, the primitive relationship is essential to pairs. I don’t like bundle theories, but this one seems to offer a nice and elegant solution to the bundling problem.

Here goes. The fundamental entities are tropes. The primitive symmetric relationship is partnership. As stated above, this is essential to pairs: if x and y are partners in one world, they are partners in all worlds in which both exist. If x and y are tropes that exist and are partners, then we say they are coinstantiated.

Say that two possible tropes, existing in worlds w₁ and w₂ respectively, are immediate partners provided that there is a possible world where they both exist and are partners. Then derivative partnerhood is defined to be the transitive closure of immediate partnerhood.

The bundles in any fixed world are in one-to-one correspondence with the maximal non-empty pluralities of pairwise-partnered tropes, and each bundle is said to have each of the tropes that makes up the corresponding plurality. We have an account of transworld identity: a bundle in w₁ is transworld identical with a bundle in w₂ just in case some trope in the first bundle is a derivative partner of some trope in the second bundle. (This is a four-dimensionalist version. If we want a three dimensionalist one, then replace worlds throughout with world-time pairs instead.) So we have predication (or as good as a trope theorist is going to have) and identity. That seems enough for a reductive story about objects.

We can even have ersatz objects if we have the ability to form large transworld sets of possible tropes: just let an ersatz object be a maximal set of pairwise derivately partnered tropes. An ersatz object then is said to ersatz-exist at a world w iff some trope that is a member of the ersatz object exists at w. We can then count objects by counting the ersatz objects.

This story is compatible with all our standard modal intuitions without any counterpart theoretic cheats.

Of course, the partnership relationship is mysterious. But it is essential to pairs, so at least it doesn’t introduce any contingent brute facts. And every story in the neighborhood has something mysterious about it.

There are two very serious problems, however:

1. On this story we don’t really exist. All that really exist are the tropes.

2. This story is incompatible with transsubstantiation—as we would expect of a story on which there is no substance.

So what’s the point of this post? Well, I think it is nice to develop a really good version of an opposing theory, so as to be able to focus one’s critique on what really matters.

Tropes of tropes

Suppose that x is F if and only if x has a trope of Fness as a part of it.

Here is a cute little problem. Suppose Jim is hurting and has a trope of pain, call it Pin. But Pin is an improper part of Pin. Thus, Pin has a trope of pain—namely itself—as a part of it, and hence Pin is hurting. Thus, wherever someone is hurting, there is something else hurting, too, namely their pain.

The standard move against “two many thinkers” moves is to say that one of them is thinking derivatively. But if we do that, then it looks like the fact that Jim is hurting is more likely to be derivative than the fact that Pin is hurting. For Jim hurts in virtue of having Pin as a part of it, while Pin hurts in virtue of having itself as a part of it, which seems a non-derivative way of hurting. But it seems wrong to say that Jim is hurting merely derivatively, so the real subject of the pain is Pin.

An easy solution is to say that x is F if and only if x has a trope of Fness as a proper part of it.

But this leads to an ugly regress. A trope is a trope, so it must have a trope of tropeness as a proper part of it. The trope of tropeness is also a trope, so it must then have another trope of tropeness as a proper part and so on. (This isn’t a problem if you allow improper parthood, as then you can arrest the regress: the trope of tropeness has itself as an improper part, and that’s it.)

One can, of course, solve the problem by saying that the trope theory only applies to substances: a substance x is F if and only if x has a trope of Fness as a proper part of it, while on the other hand, tropes can have attributes without these attributes being connected with the tropes having tropes. But that seems ad hoc.

As a believer in Aristotelian accidents and forms, which are both basically tropes, I need to face the problem, too. I have two ways out. First, maybe all tropes are causal powers. Then we can say that if “is F” predicates a power, then x is F if and only if x has a trope of Fness as a proper part. But for attribution of non-powers, we have a different story.

Second, maybe the relation between objects and their tropes is not parthood, but some other primitive relation. Some things stand in that relation to themselves (maybe, a trope of tropeness stands in that relation to itself) and others do not (Pin is not so related to itself). This multiplies primitive relations, but only if the relation of parthood is a primitive relation in the system.

The usefulness of having two kinds of quantifiers

A central Aristotelian insight is that substances exist in a primary way and other things—say, accidents—in a derivative way. This insight implies that use of a single existential quantifier ∃x for both substances and forms does not cut nature at the joints as well as it can be cut.

Here are two pieces of terminology that together not only capture the above insight about existence, but do a lot of other (but closely related) ontological work:

1. a fundamental quantifier ∃u over substances.

2. for any y, a quantifier ∃_yx over all the (immediate) modes (tropes) of y.

We can now define:

• a is a substance iff ∃u(u = a)

• b is a (immediate) mode of a iff ∃_ax(x = b)

• f is a substantial form of a substance a iff a is a substance and ∃_ax(x = f): substantial forms are immediate modes of substances

• b is a (first-level) accident of a substance a iff u is a substance ∃_ax∃_xy(y = b & y ≠ x): first-level accidents are immediate modes of substantial forms, distinct from these forms (this qualifier is needed so that God wouldn’t coount as having any accidents

• f is a substantial form iff ∃u∃_ux(x = f)

• b is a (first-level) accident iff ∃u∃_ux∃_xy(y = b).

This is a close variant on the suggestion here.

Grounding accidents in substances

Consider this plausible principle:

1. x partially grounds y if and only if there are cs that fully ground y and x is one of the cs.

But now consider this plausible-sounding Aristotelian claim:

2. The substance (or its form or its essence—the details won’t matter) partially grounds each of its accidents.

Note that the grounding here is not full. For if my substance fully grounded my accident of sleepiness, then my substance would be metaphysically sufficient for my sleepiness, and I would be always sleepy, which is fortunately not the case.

So, by 2, my sleepiness is partly grounded by my substance (i.e., me?), and merely partly. By 1, then, it follows there are other things, beside my substance, such that my sleepiness is fully grounded by my substance and those other things. What are those other things? Is it other accidents of me? If so, then the problem repeats for them. Or is it something beyond my substance or accidents? But what would that be?

I am inclined to think that the solution to this problem is to reject 1. Somehow, 1 is reminiscent to me of the false view that:

3. x indeterministically causes y only if there are cs that deterministically cause y and x is one of the cs.

Compositional and non-compositional trope theories

There are two kinds of trope theories: Those on which the tropes are parts of the particular object—call these “compositional” trope theories—and those on which the relation between the object and its tropes is not a whole-to-part relation. Compositional trope theories have an initial advantage over non-compositional ones: they have no need to introduce a new relation to join objects to their tropes.

But this is only an apparent advantage. Consider this old argument. Assume compositional trope theory. Suppose my toe is blue. Then its blueness trope is a part of the toe, which is in turn a part of me, and so the blueness trope is a part of me. Hence I am blue.

Of course, the compositionalist has an answer to this argument: there are two different kinds of parthood here. The toe is, as the medievals would say, an integral part of me. And the blueness trope is a non-integral part of the toe. Transitivity holds for integral parts. It may or may not hold for non-integral parts, but it certainly doesn’t hold across types of parthood: if y is an integral part of x and z is a non-integral part of y, it does not follow that y is any kind of part of x.

But notice now that the compositionalist has lost the main advantage over the non-compositionalist. The compositionalist’s initial advantage was not having to introduce a new kind of relation over and beyond the familiar composition relation. But the familiar composition relation was the one between wholes and integral parts, and our compositionalist now has to introduce a new relation over and beyond that. Granted, it is a new relation of the same type as the familiar one. But this actually makes the compositionalist’s theory more complicated. For now the compositionalist has two relations, integral composition and non-integral composition, plus a new relation type, composition. But the non-compositionalist need only have two relations, integral composition and the object-to-trope relation. These two relations don’t need to have a new relation type to fall under. In other words, the non-compositionalist has only one mystery in her theory—what is the object-to-trope relation—while the compositionalist has two mysteries—what is the object-to-trope relation and what is the type composition.

The same point applies more generally to compositional ontologies versus relational ontologies.

Accidents outliving their substances

Thomas Aquinas's take on transsubstantiation supposes that the accidents of bread and wine can continue existing even after the bread and wine have perished, something that was heavily criticized by people like Jan Hus.

But here is an argument for the possibility of an accident outliving its substance. Consider a very long rattlesnake, stretching out to maybe ten million kilometers in length. The rattlesnake is rattling for one second. The rattling of the tail is an accident of the rattlesnake, call this accident R. Then the snake is near-instantaneously destroyed, e.g., by a series of synchronized explosive charges.

Well, near-instantaneously in one reference frame! This snake is long enough that there will be another reference frame in which the front half is destroyed 15 seconds before the back half is. In this reference frame, there will be a time when the rattling of the tail occurs even though the front half of the snake doesn't exist. But a snake whose front half has been destroyed is no longer existing. So in this reference frame the accident R exists even though the snake no longer does.

Granted, in the case of the snake it is only true in some reference frames that the snake doesn't exist while R does, while in the Eucharist the persistence of the accidents past the demise of the bread and wine takes place in all reference frames. But once we have seen that the principle that accidents must be contemporaneous with their substance is not generally true, I think some wind is taken out of the objector's sails.

A perdurantism without temporal parts

Standard perdurantism holds that we are four-dimensional worms made up of three-dimensional temporal parts. Many of the changing properties that we think of ourselves as having directly, we actually have derivatively from the temporal parts. Thus, I am typing a post in virtue of having a temporal part typing it up, and I am conscious of the screen in front of me in virtue of a temporal part of me being conscious of it.

Standard perdurantism has many problems, for instance:

1. Perdurantism commits one to proper parts, and implausibly thin and hyperplanar ones.
2. Surely I am that entity which is non-derivatively consciously rather than that entity which is derivatively conscious.
3. Perdurantism normally comes along not just with slices, but thicker temporal parts. But then Merricks argues that we cannot know how old we are. For all I know, I might be the temporal part from five minutes ago until now (in which case I am five minutes old), or from ten minutes ago until now (in which case I am ten minutes ld), and so on. Only a handful of temporal parts containing my present stage have the age I think myself to have, so probably I don't have the age I think myself to have.

There is, however, a perdurantism without any of these problems, if one accepts the right kind of trope theory. Suppose I exist at t. Then my existing at t is a trope of me, call it e_t. At least unless t is the first moment of my existence, e_t is an accidental trope: if I perished before t, then I wouldn't have had e_t. (If essentiality of origins holds, then it is an essential property of me that I exist at the first moment of my existence.) Note that I am not committing myself to the controversial thesis that existence is a property. Even if existence isn't a property, it is plausible that existence in a location—i.e., spatial locatedness at x—is a property. And if so, then why shouldn't temporal locatedness at t be a property?

I now suppose that I am a four-dimensional entity that has (where the "has" is not tensed) all of the e_t tropes (where t is a time during my existence): it is true to say that I exist at all these times. But many of the temporally qualifiable predicates, like "is conscious" and "is bent", that apply to me apply in virtue of e_t itself having certain tropes. Thus, I am now bent or conscious in virtue of e_now having a certain bendedness or consciousness trope.

Strictly speaking, it's not e_now that is bent or conscious, but it has the kind of trope which makes that substance that has the e_now trope be bent or conscious. Compare this: If I am gorging myself, then that happens in virtue of an eating trope itself having a gorging trope. But the eating trope isn't gorging itself. It is I who am gorging myself. So the gorging trope is a trope of eating such that any substance that has the eating trope with the gorging trope gorges itself. The gorging trope, thus, makes me—the substance—be a gorger and makes my eating trope be not a gorger, but gorgingly. This is linguistically tricky.[note 1]

On standard perdurantism, I persist over time in virtue of having temporal parts that exist at various times. On this trope perdurantism, I persist over time in virtue of having temporal locatedness tropes.

On this theory, the temporal locatedness tropes e_t play the role of the temporal parts of standard perdurance. But they aren't parts. So we aren't committed to parts, much less implausibly thin and hyperplanar ones.

We also do not have the problems in (2) and (3). For while I am conscious at t in virtue of e_t having a certain consciousness trope c_t, that consciousness trope doesn't make e_t be conscious. So while I am conscious in virtue of something other than me—namely, e_t—being a certain way, I am not conscious in virtue of something other than me being conscious. Thus, I do not derive my consciousness from the consciousness of anything else, and so I am non-derivatively conscious. I do derive my consciousness from something else being a certain way, but when that something else is a trope of me, that's quite innocent. Thus, (2) is not an issue here.

Nor is (3), for the obvious reason that a fusion of e_t-type tropes, even if there is such a fusion (which I very much doubt), doesn't think. It's substances that think, and they think in virtue of having certain tropes. The tropes don't think, and neither do their fusions.

I don't think this is the whole story. If I were seriously defending this story, I wouldn't say that I have the trope e_t directly. I might say that I have the trope e_t as a trope of my humanity, where my humanity may well be the only trope I have directly (see the paper of mine here).

I don't know if the above story is true. I am a bit sceptical of the thinness and hyperplanarity, as it were, of the e_t tropes—they don't seem to me to be very natural. And I am not 100% sure I want to commit to tropes. But this version of perdurantism might be true.

Note, also, a neat thing. Normally the perdurantist needs to argue why perdurance is preferable to exdurance. But I do not think there is any plausible trope exdurantism paralleling this trope perdurantism.

Objection: The trope e_t is a part of me, so this devolves to a more standard perdurantism.

Response: Maybe in some sense my tropes are parts of me. But they are different sorts of parts from the kinds of parts that standard perdurantism invokes. For tropes depend, at least for their identity, on that which they are tropes of. But the whole is constructed out of the temporal parts on standard perdurantism. So trope perdurantism reverses the order of grounding.

A quick argument for tropes

1. Every thought is a trope of a thinker.
2. There are thoughts.
3. So, there are tropes.

From tropes to the Trinity

Suppose that each cat has its own catness trope, each dog has its own dogness trope, and so on: each thing has its own essence trope. Thus, whenever we have two cats, we have two individuals—understood as bare particulars, bundles, substances, composite wholes, or in some other way—and two catnesses. Now, the question comes: When we say "There are two cats", is the content that

1. There are two individuals each of which is a cat, or that
2. There are two catnesses?

Whenever one is true, so is the other. Moreover, both statements are pretty natural. On a reference magnetism semantics on which the contents of our assertions are determined by charity plus naturalness, the choice between (1) and (2) will be a close one. In fact, it may be so close that it may be indeterminate whether "There are two cats" means (1) or (2). If naturalness favors either reading, it seems to favor (2) slightly, I think. So the choice between (1) and (2) will be a close one, and the answer will be either indeterminate or in favor of (2).

Likewise, does "Felix" refer to the individual or the catness? If the former, then "Felix sits" has the content that this individual has a sitting trope, and if the latter, then "Felix sits" has the content that this catness is coinstantiated with a sitting trope. Again, both candidates are pretty close to as natural. So again, the question whether names refer to individuals or their essence tropes will be a close one on reference magnetism, and maybe the answer will be indeterminate.

Suppose now that by a miracle there came to be two cat individuals that had the very same catness trope. Why not, after all? There doesn't appear to be anything logically contradictory about the supposition. After all, Siamese twins may share a heart. Why can't they share a trope as well?

So now you assign names, Felix and Tiger, and you say: "Felix is not Tiger." While it may have been indeterminate, or at least was close, whether ordinary cat names referred to catnesses or individuals, in the case at hand there is no indeterminacy or closeness. Charity now requires that at least these two names refer to the individuals, not the shared catness, since there is but one shared catness.

But while it is clear that we should say that Felix is not Tiger, it is less clear whether we should say that there are two cats. It is tempting to argue that Felix is a cat, Tiger is a cat, Felix and Tiger are two, so there are two cats. Certainly, there are two each of which is a cat. But are there two cats? Remember that it was indeterminate or close whether in general "There are two cats" referred to a duality of individuals or a duality of catnesses. If it should turn out to have in general referred to a duality of catnesses, then we should say "There is one cat". But even if it was indeterminate whether "There are two cats" refers to a duality of individuals or catnesses, we might reasonably in this very exceptional case settle on duality of catnesses. There is also a significant consideration in favor of describing the case by saying "There is one cat": it lets one say that there is exactly one catness trope per cat.

But now suppose we have three individuals, the Father, the Son and the Holy Spirit, who have one divinity trope. Then charity will make us say that the Father, the Son and the Holy Spirit are three individuals. Should we say that they are three Gods or that they are one God? If in ordinary cases we take counting to go with essence tropes, then we unambiguously have to go for the "one God" reading. If in ordinary cases, counting is indeterminate between individuals and their essence tropes, then we might in the case at hand simply reasonably resolve the ambiguity by speaking in the "one God" way, which then lets us say, as appears right, that there is exactly one divinity trope per God.

I am not defending this exact theory of the Trinity. One needs to be very cautious talking of individuals that have divinity due to divine simplicity. But I think something like the above is Aquinas' story.

A theory of time

This isn't meant to be a very good theory, but it's a start. The primitive notion I want to explicate is this notion of temporal priority between events: A is at least in part earlier than the start of B. I will abbreviate this to "A is earlier than B". And then we say that A is earlier than B if and only if there is a chain of at least partial causation starting at A and ending at B.

A consequence of this theory is that it is not possible to have simultaneous causation: if A causes B, then A is earlier than B. That's a count against it, but perhaps not a fatal one.

Another consequence of this theory is that it gives no account of simultaneity between events. That may not be such a bad thing.

A limitation is that we have no notion of a time, just of temporal ordering of events. That may be fine. But the costs are adding up.

I am more troubled by the fact that this rules out time travel and, more generally, temporally backwards causal influences. This makes me want to reject the theory.

But I can reprise the theory, not as a theory of the temporal priority between events, but of the temporal priority between accidents (or maybe just modes?) of a single substance. Just say that an accident A of a substance S is earlier than an accident B of S if and only if there is a chain of at least partial causation between accidents of S starting at A and ending at B.

We still have to rule the possibility of temporally backwards causation within the life of a single substance. But that's less costly, I think, than ruling out temporally backwards causation between events in general.

We still have the problem of not having simultaneous causation or any account of simultaneity for that matter. And no notion of times.

We can introduce times as follows. In some worlds, it will happen that there are nomic relationships between the accidents of a substance that are simply parametrized in terms of some parameter t such that accident A is earlier than accident B (in the above causal sense) if and only if t(A)<t(B). In such a case, we can call values of this parameter times. In worlds where there is no such neat parametrization, there may be temporal priority, but no times.

We get divine internal atemporality now as a corollary of the claim that God has no accidents.

But there are still a lot of costs. For one, the lack of a notion of simultaneity makes it hard to make sense of the transcendental unity of apperception. Maybe that's just too bad for that unity?

Shifty propositions

Say that a proposition p is shifty provided that there are worlds w₁ and w₂ at which p holds, and a proposition q such that q grounds p at w₁ but q does not ground p at w₂.

A proposition p is non-shifty provided that either it cannot have a ground or there is some proposition q such that p entails that q grounds p.

The proposition that Obama or McCain is president is shifty: in some worlds it is grounded in Obama being president and in others it is instead grounded in McCain being president.

Propositions of the form of the proposition that N exists are non-shifty, if "N" directly rigidly refers to a substance.

Propositions expressed by typical simple subject-predicate sentences are shifty if trope theory is true. For instance, that I am sitting is grounded by the proposition that I have s₁, where s₁ is the trope of sitting that I actually have, but could have been equally well grounded by the proposition that I have s₂, where s₂ is some other trope of sitting. On the other hand, if Platonism is true, then sentences whose subject term directly refers and whose predicate expresses a property are going to be non-shifty, as in every world where they are true, they are grounded by some proposition of the form of the proposition that N exemplifies P.

There is something other than simple substances, I think

I do not see any way to avoid the conclusion that the correct ontology includes more than just simple substances. This is depressing and exhilarating. I think there are modes of substances. Very weird. I entertained the thought that it might come to this, but didn't expect it to be so soon (I didn't disbelieve in modes, but I also didn't believe in them). But I had to either believe in modes of substances, or parts of substances, or regions of spacetime, and modes of substances seem the most innocent. I need either parts or regions to make sense of claims like: "This person is red on his left side and green on his right side." But the kinds of regions I need—thanks to an argument by Josh Rasmussen—are regions that travel with a substance, because the person who is red on his left side and green on his right side doesn't change color as he moves through space. And the only way I see to define such regions is with the parts or powers of substances. So I had to believe in parts or powers. But parts are very mysterious, while I already believed that substances were powerful. So to believe in their powers seems the better move. And powers are modes. This makes Eucharistic theology a touch more straightforward, too.

Platonism

Jerry waltzes. According to the Platonist, this means that Jerry instantiates the universal waltzing. So, where initially we thought we had Jerry alone, we now have Jerry, instantiation and waltzing. But we also, equally, have Jerry, instantiation and waltzing when Jerry is sitting instead of waltzing. After all, instantiation and waltzing are universals, and so they exist necessarily, even when Jerry isn't waltzing. So, what is different between the situation where Jerry instantiates waltzing and the one where he does not? It won't help to say that the ordered pair <Jerry, waltzing> instantiates instantiation. For the same problem reappears. Whether Jerry waltzes or not, Jerry, waltzing, the ordered pair <Jerry, waltzing>, and instantiation necessarily exist. Going to further levels of the regress will get us more entities, but it will not help resolve the problem. For we will simply get more beings that exist even when Jerry isn't waltzing, and those beings don't help to differentiate betweent he case of him waltzing and him not waltzing. (Nor does this depend on time; we can distinguish between the case of Jerry's instantiating waltzing at some time or other and the case of Jerry's not instantiating waltzing at some time or other.)

So what can the Platonist do? Well, she could just say that it's simply a fact, a fact not analyzed in terms of further Platonic entities, that Jerry in fact instantiates waltzing, or that <Jerry, waltzing> instantiate instantiation. But then she says exactly the same sort of thing that the ostrich nominalist does. And if she says it in this case, why bring in instantiation at all? Why not just say that Jerry in fact waltzes, and be done with it? Or maybe the Platonist will say that there is a state of affairs of Jerry's instantiating waltzing or <Jerry, waltzing> instantiating instantiation. Fine, but why do that? Why not just say that there is a state of affairs of Jerry's waltzing, and be done with it? Or perhaps the Platonist will posit a trope of instantiating present in <Jerry, waltzing> or a trope of instantiating-waltzing present in Jerry. But why not, then, just posit a trope of waltzing in Jerry?

I do not think this kills Platonism. It just shows that if Platonism is to do something useful for us, it is something other than helping us understand the nature of predication. For if Platonism is seen as helping with predication, it does this by reducing all predication to predications of the form "x instantiates P" or "<x,P> instantiates instantiation". Now in some cases, it is helpful to ground all instances of a class in terms of a distinguished subclass. Thus, in my dissertation, I argued that all modal claims should be grounded in claims about the powers of things. The latter claims are, of course, modal. However, if such a grounding is to have any usefulness, the distinguished subclass must be somehow preferable, maybe epistemologically, maybe in terms of comprehensibility, or in some other way. But why should, say, the state of affairs of Jerry's instantiating waltzing be preferred to the seemingly simpler state of affairs of Jerry's waltzing?

Now it may well be that Platonism has other uses than helping with problems of predication. It may indeed.