Open theism and the Incarnation

Here is a very plausible pair of claims:

1. The Son could have become incarnate as a different human being.

2. God foreknew many centuries ahead of time which human being the Son would become incarnate as.

Regarding 1, of course, the Son could not have been a different person—the person the Son is and was and ever shall be is the second person of the Trinity. But Son could have been a different human being.

Here is a sketch of an argument for 1:

1. If the identity of a human being depends on the body, then if the Son became incarnate as a 3rd century BC woman in India, this would be a different human being from Jesus (albeit the same person).

2. If the identity of a human being depends on the soul, then God could have created a different soul for the Son’s incarnation.

3. The identity of a human being depends on either the body or the soul.

I don’t have as good an argument for 2 as I do for 1, but I think 2 is quite plausible given what Scripture says about God’s having planned out the mission of Jesus from of old.

Now add:

3. If the Son could have become incarnate as a different human being, which human being he became incarnate as depends on a number of free human choices in the century preceding the incarnation.

Now, 1, 2 and 3 leads to an immediate problem for an open theist Christian (my thinking on this is inspired by a paper of David Alexander, though his argument is different) who thinks God doesn’t foreknow human free choices.

Why is 3 true? Well, if the identity of a human being even partly depends on the body (as is plausible), given that (plausibly) Mary was truly a biological mother of Jesus, then if Mary’s parents had not had any children, the body that Jesus actually had would not have existed, and an incarnation would have happened with a different body and hence a different human being.

Objection: God could have created Mary—or the body for the incarnation—directly ex nihilo in such a case, or God could have overridden human free will if some human were about to make a decision that would lead to Mary not existing.

Response: If essentiality of origins is true, then it is logically impossible for the same body to be created ex nihilo as actually had a partial non-divine cause. But I don’t want the argument to depend on essentiality of origins. Instead, I want to argue as follows. Both of the solutions in the objection require God to foreknow that he would in fact engage in such intervention if human free choices didn’t cooperate with his plan. God’s own interventions would be free choices, and so on open theism God wouldn’t know that he would thus intervene. One might respond that God could resolve to ensure that a certain body would become available, and a morally perfect being always keeps his resolutions. But while perhaps a morally perfect being always keeps his promises, I think it is false that a morally perfect being always keeps his resolutions. Unless one is resolving to do something that one is already obligated to do, it is not wrong to change one’s mind in a revolution. I suppose God could have promised someone that he would ensure the existence of a certain specific body, but we have no evidence of such a specific promise in Scripture, and it seems an odd maneouver for God to have to make in order to know ahead of time who the human that would save the world is.

What if the identity of a human depends solely on the soul? But then the identity of the human being that the Son would become incarnate as would depend on God’s free decision which soul to create for that human being, and the same remarks as I made about resolutions in the previous paragraph would apply.

Reducing de re to de dicto modality

In my previous post, I gave an initial defense of a theory of qualitative haecceities in terms of qualitative origins: qualitative haecceities encapsulate complete qualitative descriptions of an entity’s initial state and causal history. I noted that among the advantages of the theory is that it can allow for a reduction of de re modality to de dicto modality, without “the mystery of non-qualitative haecceities”.

I want to expand on this, and why qualitative-origin haecceities are superior to non-qualitative haecceities here. A haecceitistic account of de re modality proceeds in something like the following vein. First, introduce the predicate H(Q,x) which says that Q is a haecceity of x. Then we reduce de re claims as follows:

• x is essentially F ↔︎ ∀Q(H(Q,x)→□(∀y(Qy→Fx)))

• x is accidentally F ↔︎ ∃Q(H(Q,x)∧◊(∃y(Qy∧Fx))).

Granted, this involves de re modality for second-order variables like Q. But this de re modality is less problematic because we can suppose the Barcan and converse Barcan formulas to hold as axioms for the second-order quantifiers, and we can treat the second-order entities as necessary beings. De re modality is particularly difficult for contingent beings, so if we can reduce to a modal logic where only necessary beings are subject to de re modal claims, we have made genuine progress.

We will also need some axioms. Here are two that come to mind:

• ∀x∀Q(H(Q,x)→Qx) (things have their haecceities)

• ∀x∃Q(H(Q,x)) (everything has a haecceity).

Now, here is why I think that qualitative-origin haecceities are superior to non-qualitative haecceities. Given qualitative-origin haecceities, we can give an account of what H(Q,x) means without using de re modality. It just means that Qy attributes to y all of the actual qualitative causal origins of x, including x’s initial qualitative state. On the other hand, if we go for non-qualitative haecceities, we seem to have two options. We could take H(Q,x) to be primitive, which always should be a last resort, or we could try to define in some way like:

• H(Q,x) ↔︎ (□(Ex→Qx) ∧ □∀y(Qy→y=x))

where Ex says that x exists (it might be a primitive in a non-free logic, or it might just be an abbreviation for ∃y(y=x)). But this definition uses de re modality with respect to x, so it is not satisfactory in this context, and I can’t think of any way to do it without de re modality with respect to potentially contingent individuals like x.

Qualitative haecceities

A haecceity H of x is a property of an entity such that necessarily x exists if and only if x instantiates H.

Haecceities are normally thought of as non-qualitative properties. But one could also have qualitative haecceities. Of course, if an entity has a qualitative haecceity then it cannot be duplicated, so one can only suppose that everything has a qualitative haecceity provided one is willing to agree with Leibniz’s Identity of Indiscernibles.

I am personally drawn to the idea that everything does have a qualitative haecceity, and specifically that the qualitative haecceity of x encapsulates x’s qualitative causal history: a complete qualitative description of x’s explanatorily initial state and of all of its causal antecedents. One might call such properties “qualitative origins”. The view that every entity has a qualitative origin is a haecceity is a particularly strong version of the essentiality of origins: everything in an entity’s causal history is essential to it, and the causal history is sufficient for the entity’s existence.

I suppose the main reason not to accept this view is that it implies that two distinct objects couldn’t have the same qualitative origin, but it seems possible that God could create two objects ex nihilo with the same qualitative initial state Q. I am not so sure, though. How would God do that? “Let there be two things satisfying Q?” But this is too indeterminate (I disagree with van Inwagen’s idea that God can issue indeterminate decrees). If there can be two, there can be three, so God would have to specify which two things satisfying Q to create. But that would require a way of securing numerical reference to specific individuals prior to their creation, and that in turn would require haecceities, in this case non-qualitative haecceities. So the objection to the view requires non-qualitative haecceities.

But what started us on this objection was the thought that God could say “Let there be two things satisfying Q.” But if God could say that, why couldn’t he say “Let there be two things satisfying H”, where H is a non-qualitative haecceity? I suppose one will say that this is nonsense, because it is nonsense to suppose two things share a non-qualitative haecceity. But isn’t there a double-standard here? If it is nonsense to suppose two things share a non-qualitative haecceity, why can’t it be nonsense to suppose two things share a qualitative haecceity? It seems that “what does the explaining” of why two things can’t share a non-qualitative haecceity is the obscurity of non-qualitative haecceities, and that’s not really an explanation.

So perhaps we can just say: Having a distinct qualitative origin is what it is to be a thing, and it is impossible for two things to share one. This does indeed restrict the space of possible worlds. No exactly similar iron spheres or anything like that. That’s admittedly a little counterintuitive. But on the other hand, we have a lovely explanation of intra- and inter-world identity of objects, as well as a reduction of de re modality to de dicto, all without the mystery of non-qualitative haecceities. Plus we have Leibniz’s zero/one picture of the world on which all of reality is described by zeroes and ones: we put a zero beside an uninstantiated qualitative haecceity and a one besides an initiated one, and then that tells us everything that exists. This is all very appealing to me.

Why did Alice make this lectern?

Converse essentiality of qualitative origins holds that if possible objects x and y have the same qualitative causal history—i.e., their initial state is qualitatively the same and the causes of that are qualitatively the same, etc.—then x = y. Kripke’s lectern argument basically makes it plausible to think that if converse essentiality of qualitative origins holds, so does essentiality of origins—the thesis that an object couldn’t have had a different qualitative causal history than it did.

If we reject converse essentiality of origins, then we have a thorny explanatory problem: When Alice took piece of wood W and shaped it into a lectern with shape S, what explains why lectern L₁ rather than, say, lectern L₂ resulted?

One way out of this explanatory problem is a partial occasionalism: Whenever an object comes into existence, while creatures may decide what the qualities of the object are, God causes the specific haecceity.

Another way out is to replace converse essentiality of qualitative origins with a converse essentiality of full origins thesis: if possible objects have the qualitatively and numerically (apart possibly from their own identity) causal history, then they are the same. Then when Alice takes W and shapes it into a lectern with shape S, only L₁ (say) can result. But if Alice’s identical twin Barbara did it, it would have been (say) L₂.

We thus seem to have three options as to the explanation of why Alice produced L₁ rather than L₂.

1. converse essentiality of qualitative origins

2. converse essentiality of full origins

3. partially occasionalistic haecceitism.

Maybe there are other good ones.

Haecceity and esse

I wonder if the haecceity of a thing isn't identical with its esse.

Presentism and haecceities

Suppose that times are maximal consistent present-tense propositions. Then if we are to make sense of eternal recurrence—reality being exactly alike at two different times—it seems we need haecceities for events or tropes. Thus, a certain kind of presentist needs haecceities.

From bundles to bare particulars and back again

Here's a compelling narrative. Start with the bundle theory of substance: substances are nothing but bundles of properties. Then observe that this suffers from serious problems. If a substance is nothing but a bundle of properties, it is unclear how a substance could have had other properties than it does. Further, intuitively it should be possible to have two indiscernible substances--ones with all the same properties. This motivates a move to bare particular theory. According to bundle theory, substances were constituted by one kind of thing: properties. Bare particular theory makes substances be constituted by both properties and a special entity, the bare particular. Introducing the bare particular solves the modal problem, since we can say that the identity of substances is grounded in the identity of the bare particulars, so you can have a substance in one world with different properties than the very same substance in another world, as long as the same bare particular is found in both. Further, there is no difficulty with indiscernibles, as long as you have two bare particulars.

Note that this narrative isn't quite the standard narrative about bare particulars. The standard narrative introduces bare particulars to solve the problem of predication, by making the bare particular be the subject of predication. That standard narrative, however, falls prey to a problem that Andrew Bailey points out: we don't want to say that the bare particular has the ordinary properties of the host substance (for then we get reduplication), but if it does not, then it's not the subject of predication.

So let's stick to my from-bundles-to-bare-particulars narrative. But at this point there is a really interesting move possible, one that was pointed out in my undergraduate metaphysics class by a brilliant freshman, Rose Brugger. According to bare particular theory, substances are constituted by two kinds of things: properties and a bare particular. But Brugger suggested that we take the bare particular to just be an individuating property. Namely, a haecceity.

The result is a really interesting theory. It is a kind of bundle theory. However, first, the motivations for bare particular theory continue to be satisfied: we can ground identity between substances in identity of the haecceity. Second, we solve the puzzle of the mysterious "bareness" of the bare particular: the haecceity isn't some weird propertyless individual, but just a property, albeit a special one. Third, the resulting theory is more parsimonious, because it posits one fewer fundamental category: all it needs are substances and their constituent properties, without a separate category of bare particulars.

The resulting theory is superior to both standard bundle theory and standard bare particular theory, being only slightly more complex than standard bundle theory but solving a number of problems.

Presentism and referring to past individuals

It seems to me that the presentist can only de re refer to past (or future—but that's less of a problem) individuals if there are haecceities or the identity of indiscernibles is true.

Particularizers instead of haecceities

A haecceity of x is a property that, necessarily, x and only x has. For instance, it might be the property of being identical with x. If a particularly strong converse to the essentiality of origins holds, a good choice for a haecceity would be a complete history of the coming-into-existence of x. Haecceities are a useful tool. For instance, they let one replace de re modality with de dicto. For another, they help explain what God deliberates about when he deliberates which individuals to create.

There is a different tool that can do some of the same work: a particularizer. We can think of an x-particularizer as equivalent to the second order property of being instantiated by x. Thus, if A is an x-particularizer, then necessarily a property Q has A if and only if x has Q. I will occasionally read "Q has A" as "A particularizes Q". The main trick to using particularizers is to note that, necessarily, x exists if and only if x instantiates some property. Thus, if A is an x-particularizer, then, necessarily, x exists if and only if some property has A.

Suppose that any two distinct things differ in some property and that particularizers exist necessarily.

Then we can use particularizers for de re modals. Suppose A is an x-particularizer. Then, Q is an essential property of x if and only if necessarily: if any property has A, then Q has A. If we have an abundant account of properties, we can then account for more complex modals. And we can likewise account for God's creative deliberation about individuals: God deliberates about which particularizers should be instantiated.

A particularly neat thing about particularizers is that with some generalization they allow us to reduce quantification over particulars to quantification over properties. We need the primitive predicate P where P(A) if and only if A is a particularizer. If A is a property, I will use A(y) to abbreviate: y has A. Use E(A) to abbreviate ∃B(A(B)). If A is a particularizer of x, then E(A) holds if and only if x exists. Use A~B to abbreviate ∀C(A(C) iff B(C)). If A and B are particularizers, then A~B means that they are co-particularizers—i.e., there is an x such that they are both x-particularizers. Suppose now we want to say that there are exactly two dogs. Let D be the property of being a dog. We say:

• ∃A∃B(P(A)&P(B)&A(D)&B(D)&~(A~B)&∀C((P(C)&C(D))→(A~C or B~C)).

I.e., there are particularizers that (a) particularize doghood, (b) are not co-particularizers, and (c) any particularizer that particularizes doghood is a co-particularizer of one of them.

If we want to deal with relations, and not just unary properties, then we need to generalize the notion of particularizers. One way to do this would to be suppose a primitive "multiplication" operation that forms an n-ary particularizer A₁A₂...A_n out of a sequence A₁,A₂,...,A_n, where an n-ary relation B has A₁A₂...A_n if and only if x₁,x₂,...,x_n stand in B, where A_i is an x_i-particularizer.

Instead of names of particulars, we will then work with names of their particularizers. Note that if in a Fregean way we think of quantifiers as corresponding to second-order properties, then particularizers will correspond to quantifiers (and remember the Montague way of thinking of names as quantifiers—this all fits neatly together).

Abundant Platonists who think that for every predicate there is a corresponding property should not balk at the existence of particularizers. We can define a particularizer either in terms of an entity x, as the property of being instantiated by x, or in terms of a haecceity H, as the property of having an instantiator in common with H. Likewise, we can define a haecceity in terms of a particularizer. If A is a particularizer, then the property of having all the properties that are particularized by A will make a fine haecceity. Or we can take particularizers to be primitive, whether we have abundant or sparse Platonism.

The above shows that we could do without first-order quantification and without talking of particulars. Now I think that nobody should simplify their ontology by getting rid of objects. Yet the above shows that we can do so. How to resist this simplifying reduction? I think the best way is to say that it does not sit well with the fundamentality of claims such as "I exist" and "I am conscious." For on the above reduction, these claims end up being reducible to E(A) and A(consciousness), where A is a me-particularizer. But only someone with an ontology on which "I exist" or "I am conscious" can resist the reduction in this way.

Can presentists say someone will have infinitely many descendants?

In an earlier post, I showed that presentists can count infinities—i.e., that presentists can give a paraphrase for sentences like "There have ever been aleph-0 horses." I did this by an ersatzist construction. I then left it open whether some such construction could work in general to give presentist paraphrase.

The problem is basically the problem of transtemporal quantification. If haecceitism is true, then it's easy. The presentist just replaces talk transtemporal talk of individuals with talk of haecceities. Likewise, if the presentist accepts the impossibility of exact intrinsic duplicates—for then one can replace talk of individuals with talk of individual-types. The interesting question is whether this can be done if you're a presentist who is not a haecceitist and who thinks there can be exact intrinsic duplicates.

I have a sentence that a non-haecceitist presentist who accepts intrinsic duplicates may have difficulty giving finite truth conditions for:

1. Somebody will have infinitely many descendants.

I don't know if presentist truth conditions for (1) are possible.

If we allow infinite sentences, it can be done. But that's cheating. :-) Or is it?

Haecceities and presentism

The following argument is valid:

1. (Premise) If there are no haecceities, then there are no propositions de re about non-existent individuals.
2. (Premise) If presentism is true, then Seabiscuit is a non-existent individual.
3. (Premise) That Seabiscuit was essentially a horse is a proposition de re about Seabiscuit.
4. Therefore, if presentism is true, there are haecceities.

If we add that there are no haecceities, we can conclude that presentism is false.

However, I think (1) is false, because I think contingent entities are wholly individuated by the histories of their origins, where their histories are described in wholly general terms (i.e., without de re reference to any individuals). Consequently, if H is such a history of Seabiscuit, the proposition in (3) can be expressed: "Necessarily, if H is instantiated, it is instantiated by a horse."

Determinism and identity

Consider this argument against determinism: Determinism requires that all future facts follow from the laws and the present state. But the laws of nature make no reference to particular individuals or to haecceities. Thus, the laws underdetermine which particular individuals will come into existence in the future. The laws can only determine what these individuals will be like, cannot determine their numerical identities.

We could use modus tollens on this kind of argument. It is possible that determinism holds and yet individuals come into existence. Therefore, the identity of individuals must be determined by their causal history, if determinism holds. But the only plausible reason to think that the identity of individuals could ever be determined by their causal history is if we think that, in an appropriate sense, identity is constituted by causal history.

How many zebras lived in the 19th century?

Here is a puzzle for a presentist. There seems to be a determinate answer to the question "How many zebras lived (at least in part) in the 19th century?" or at least it is quite possible there is a determinate answer.[note 1] But can the presentist make any sense of the question?

This puzzle is somewhat different from the general puzzle about truths about the past. I am willing to grant for the sake of argument that the presentist can make sense of questions like: "Did Napoleon win at Waterloo?" For the presentist can take the proposition p that Napoleon wins at Waterloo, and say that p was false at the relevant time, and hence the answer is negative.

But the question how many zebras lived in the 19th century is much tougher. Given any time t in the 19th century, the presentist can make sense of the question how many zebras there were alive at t.[note 2] That question is the question of what number z(t) is such that it was true at t that there are z(t) zebras. But the answer to the question of how many zebras lived in the 19th century does not supervene on the values of z(t) as t ranges over the 19th century.

If the presentist has haecceities in her ontology, she can probably make sense of the question. For then the question is: "How many haecceities h are there such that h is a haecceity of a zebra, and h was instantiated in the 19th century?" So the haecceitist presentist seems to be out of trouble.

Can a non-haecceitist presentist do the job? Yes, if she is a closed-future presentist. (A closed-future presentist accepts bivalence for claims about the future.) But it is surprisingly tricky (at least if we want to take into account the possibility that a zebra might have a temporally gappy existence). Here is the simplest way I have. Let T be the set of times in the 19th century. Let S be a non-empty subset of T. Let z(S) be defined as follows. Choose any t in S. Let z(S) be the unique number n such that it was true at t that there exist exactly n zebras z such that P_S(z). Here, P_S(z) is the claim that for every time t' in S, z exists, existed or will exist at t', and for no time t' in T−S is it the case that z exists, existed or will exist at t'. (A−B is the set of all members of A that are not members of B.) (This a definition apparently compatible with presentism, but since P_S(z) partly concerns the then-future, only a closed-future presentist will have no qualms about it.) Then the number of zebras that lived in the 19th century is equal to the sum of z(S) as S ranges over all non-empty subsets of T.

Maybe there is a simpler way of counting 19th century zebras on presentism. But I can't think of one. More obvious solutions fail (thus one might keep track of when zebras come into existence, and count the comings into existence, but this doesn't work very well on presentist grounds for zebras that come into existence on an interval of times open at the bottom end).

There may be a clever way to do this within the confines of open-future presentism. But it's going to be tricky and messy. If it can't be done, then we have an argument why an open-future presentist should be a haecceitist.

I wonder if how complicated the answer to the question is does not give an argument against presentism. For, intuitively, the claim that there were exactly n₁ zebras at noon on January 18, 1855 should be made true similarly to the way the claim that there were n₂ zebras in the 19th cenutry is made true. But the non-haecceitist presentist will have to use very different counting methods for the two cases.

Transworld identity without haecceities

Haecceities are individual essences, even of non-existent beings. Necessarily, entity exists iff its haecceity is instantiated. Some folks think we need haecceities to make sense of alien individuals—i.e., individuals that exist in other worlds but not in ours. We don't, as long as we are willing to be Leibnizian in denying the identity of indiscernibles. Here, then, is a simple theory of identity across worlds that entails the essentiality of origins. The theory applies both to substance-like and event-like individuals.

I will give the simplest version of the theory, for beings in an absolute time who do not engage in any time travel and without backwards causation. A general version of the theory requires the replacement of times by "causal (or maybe even explanatory) points"—points in the causal history of an entity. This is a bit tricky, and so I won't bother with it.

Let e be an entity and w a world. Say that H is a qualitative history of e up to t in w provided that e exists at t in w and H is a proposition giving an at least partial description of w such that:

1. H is purely qualitative except respect of e and t: i.e., the only particulars that are de re involved in H are e and t;
2. H states that e exists at t and gives a complete description of the intrinsic properties of e at t, subject to the restriction in (1);
3. For any state of affairs reported in H, any and all the causes in w of that state of affairs are also reported in H;
4. H reports that e exists at t;
5. H is a minimal proposition satisfying (1)-(4).

Now, let w₁ and w₂ be two worlds such that e₁ exists in w₁ and e₂ exists in w₂. Then e₁=e₂ if and only if there are times t₁ and t₂ and histories H₁ of e₁ up to t₁ in w₁ and H₂ of e₂ up to t₂ in w₂, such that H₁'s description of e₁ and t₁ coincides exactly with H₂'s description of e₂ and t₂.

To put it roughly, e₁ and e₂ are identical if and only if there are points in the existence of each one, such that their respective histories up to these points are the same.

This view entails essentiality of origins. It also implies that there cannot be two entities which, along with their causal histories, have been indiscernible up to some time. Thus, there cannot be completely identical twins. This consequence is counterintuitive, but may be but a small price to pay for avoiding haecceities.

Given this view, we can form something like a haecceity from the disjunction of all the histories of an entity in a world.

The view can be varied by relaxing or tightening the conditions (1)-(5) on histories. I do not yet know which is the optimal version.