From one divine person to two or more

1. Personhood is teleologically relational in the sense that a person is the kind of being that necessarily can only be fulfilled in relationships with other persons.

2. Necessarily, any person other than God is a creature.

3. So, if God is a single person, this person necessarily can only be fulfilled in relationships with creatures.

4. If a being only finds its fulfillment in relationships with Fs, then the being’s fulfillment depends on Fs.

5. So, if God is a single person, God’s fulfillment depends on creatures.

6. God’s fulfillment does not depend on creatures.

7. Thus, God is not a single person.

8. thus, if God is a person, God is two or more persons.

(I think most non-Christian monotheists these days will say that God is a single person. But I wonder if it wouldn’t be a better view for them to deny that God is a person at all, and to insist that the centrality of personhood to the understanding of God is a mistaken Christian approach.)

Here is another variant on the argument:

9. Necessarily, a person can only flourish in relationship to another equal person.

10. It is possible that God flourishes.

11. If God is a single person, then it is impossible for there to be another person equal to God.

12. So, God is a single person, it is impossible that God flourishes. (9 and 11)

13. So, God is not a single person. (10 and 12)

14. So, if God is a person, God is two or more persons.

Now, granted, it is a standard view in Christianity that one cannot prove the doctrine of the Trinity by reason. If the arguments above are sound, have I contradicted that view? No, for several reasons. First, the arguments don’t establish that God is three persons. Second, the arguments only establish that if God is a person at all, then God is two or more persons—but a further argument is needed that God is a person at all. (Perhaps perfect being theology can yield that.)

A two-sorted logic and the Trinity

For a while this spring I’ve been thinking about ways of avoiding quaternity views of God.

The problem is that, first,

1. Father ≠ Son, Son ≠ Spirit and Father ≠ Spirit

and, second, we seem to have to choose between the following two options:

A. Father = God, Son = God and Spirit = God, or

B. Father ≠ God, Son ≠ God and Spirit ≠ God.

Add:

2. Father is divine, Son is divine, Spirit is divine, and God is divine.

If we accept (1) and (A), then we have a logical contradiction given classical identity.

If on, other hand, we accept (1), (B) and (2), then there are four that are divine, a quaternity!

A now-standard solution to problems like this is to go for a version of a relative identity theory rather than classical identity. Then the (negated) = in (1) and the = in (A)/(B) are different identity relations (e.g., sameness of person versus sameness of essence).

In this post, I want to consider a somewhat different take on non-classical identity. Suppose we take a variant on two-sorted logic. On a many-sorted logic, bound variables and names come with sorts, and predicates have grammatical restrictions on the sorts of terms that can be their arguments. Usually, the restrictions say for each argument place what sort of term can go in that place. But we can have a more complicated kind of sort restriction.

Suppose, then, we have two sorts: essence and hypostasis, and that = has the classical rules of inference, but has the sort restriction that only terms of the same sort can go on the two sides of =. Suppose that “Father”, “Son” and “Spirit” are of the hypostasis sort, and “God” is of the essence sort. Then we can have (1), but neither (A) nor (B) will express a truth, as both (A) and (B) will be ungrammatical. Even if = has the classical rules of inference, I think there will be no way for us to derive that there are four that are divine. Indeed, in the two-sorted logic, the only way to say “there are four that are divine” is:

3. There are four essences that are divine or there are four hypostases that are divine.

For we cannot mix the essence-variables and hypostasis-variables in an “=” formula.

Interestingly, I think we can have an even stronger non-classical logic of identity while avoiding incoherence and quaternity, though I don’t know if this will appeal to anyone. Make the sort restriction on = be that u = v is grammatical if and only if either u and v are both of the same sort or u is a hypostasis term and v is an essence term. Next, specify that the =-elimination says that from the sentence a = b and a formula ϕ(a), we are allowed to infer ϕ(b), but only if “ϕ(b)” is grammatically correct.

In this stronger logic, we can have all three of (1), (A) and (2), apparently without contradiction. The crucial thing is that from Father=God it is impossible to conclude God=Father, because the latter is ungrammatical. It seems to me to be the Holy Grail of Trinitarian logic to be able to affirm all of (1), (A) and (2).

That said, I don’t like the asymmetric sort restriction on =.

A nuanced compatibilism and the problem of heavenly freedom

The problem of heavenly freedom is the apparent tension between these two claims:

1. The blessed in heaven are free

2. The blessed in heaven cannot sin.

One solution is compatibilism, but as Pawl and Timpe note, this undercuts the Free Will Defense.

But there is another move. One can be a compatibilist and say that while one can have freedom without the ability to do otherwise, nonetheless freedom with the ability to do otherwise is better. If one accepts this version of compatibilism, one can affirm (1) and (2) while yet offering a Free Will Defense.

This, however, leads to an obvious riposte: If freedom with the ability to do otherwise is better, why don’t we have that kind of freedom in heaven? Isn’t heaven supposed to be the best state for us?

One can, however, add another nuance. There are some activities that it is good to have done at some point, but repetition significantly diminishes the value. It is of some value to have read The Murder of Roger Ackroyd. To re-read it, not so much. Or for a religious example, think of the Hajj. Suppose freedom with the ability to do otherwise is like that. Perhaps, then, it is valuable to have made the choice for God with the ability to do otherwise. But a repeat of that choice is of rather lesser value. So much lesser, that if on earth one has made the choice for God with the ability to do otherwise, in heaven the value of doing so again is outweighed by the value of making guaranteed righteous choices.

This is not too different from Pawl and Timpe’s preferred solution of allowing for derivative freedom in heaven. But there may be an advantage to the above solution. Pawl and Timpe’s solution doesn’t solve the problem of infants who go to heaven without being able to make a free choice in this life—they don’t seem to have derivative freedom. (One of my undergraduate students has ably pressed this problem.) The nuanced compatibilism I have suggested can help with that: the infants in heaven genuinely have freedom. Granted, their death has denied them one of the goods proper to earthly life—the good of choosing righteousness with the ability to do otherwise. But that they have lost something by their untimely death is indeed rather intuitive.

We might ask: But why wouldn’t God then give them a chance to make a decision with ability to choose otherwise after death? Wouldn’t that be better? In one respect, it would indeed be better: in the respect of choosing with the freedom to choose otherwise. But in another respect, it would be less good: in the respect of having the risk of choosing wrongly. These are incommensurable considerations, and God can reasonably follow either one.

Granted, this move weakens the force of the Free Will Defense. We can no longer say that it’s better all things considered for God to give us the kind of freedom that allows us to reject him. For while that’s a better kind of freedom, it comes with an incommensurable cost—the risk that we will reject him. However, we can still say that God can rightly choose to follow either of the incommensurable considerations. In our case, he has opted to give us the better freedom despite the risk; in the case where he has taken some infants to himself, he opted for the guarantee of freedom being rightly used.

I don’t endorse the above solution. But I think it’s possible.

An argument from wonderful people

1. Person x appears like they are in the image of God.

2. So, probably, x is in the image of God.

3. If God doesn’t exist, no one is in the image of God.

4. So, God exists.

From the imago Dei to God

1. It is not inappropriate to have a level of respect for human beings at least as great as what would be fitting for beings in the image and likeness of God.

2. If naturalism is true about humans and God does not exist, then it is inappropriate to have a level of respect for human being that is at least as great as what would be fitting for beings in the image and likeness of God.

3. So, either naturalism is false about humans or God exists (or both).

Regarding premise 1, think about how problematic it would be to say that someone like Mother Teresa had too much respect for her fellow human beings.

Regarding premise 2, naturalism tells us that innately we’re just an arrangement of atoms, and if we add to that that God doesn’t exist, then this arrangement of atoms doesn’t have a special God-directed significance, so it seems inappropriate to bestow on us the level of respect that a being in the image and likeness of God would have.

I think one can strengthen the argument to provide additional evidence for the existence of God. If God doesn’t exist, then the only plausible way that humans could deserve the imago Dei level of respect is if human beings have a deep and very valuable reality going far beyond the neural networks in our brains, a reality that intrinsically calls for that very high level of respect. (If there is a God, then we don’t need quite as much intrinsic value for us to be worthy of that kind of respect, because we could derive value from our relation to the infinite God.) This is much more than ordinary non-naturalisms about consciousness give.

We thus learn from considerations of respect that if there is no God, humans need to be very non-natural in a god-like way. And beings like that are very hard to explain apart from God. So if we are beings like, this provides significant evidence for theism.

A really big choice

A messy Irenaean world which leaves much to be desired and then grows in value due to our contribution has a great value.

A perfectionistic world where everyone is already perfectly virtuous and everything is good and we just maintain that level of good also has great value.

Quite plausibly the two worlds have incommensurable value.

God could just choose between these incommensurable values. But what God does is something else: he leaves it to the first humans to choose. This seems an especially great gift: we get to choose the basic shape of the value that our world takes.

We sin, and we get the Irenaean world.

Little evils

From time to time I wonder why it is that we focus on big evils in discussing the problem of evil. After all, first consider this argument:

1. As far as we can tell, Alice’s cancer is a gratuitous evil.

2. So, probably, there is a gratuitous evil.

3. If there is a God, there is no gratuitious evil.

4. So, probably, there is no God.

And then this one:

5. As far as we can tell, Bob’s stubbed toe is a gratuitous evil.

6. So, probably, there is a gratuitous evil.

7. If there is a God, there is no gratuitious evil.

8. So, probably, there is no God.

The same kind of backing can be given to (1) and (5). We’ve thought long and hard about Alice’s cancer and its connections to the rest of the world, and can’t find a theodicy. We’ve thought long and hard about BOb’s stubbed toe and its connections to the rest of the world, and can’t find a theodicy. And the rest of the two arguments seems to flow the same way. But as far as I can tell (!), nobody’s become an atheist because of arguments like (5)-(8) while many have become atheists because of arguments like (1)-(4).

What’s going on?

Here is one answer, which at times I’ve felt some pull towards: we shouldn’t take (1)-(4) as seriously as we do.

Here is another answer: we should take (5)-(8) more seriously than we do.

But there may be a good conservative answer, one that maintains our intuition that (1)-(4) should be taken seriously while (5)-(8) shouldn’t. There is a difference in the two arguments, and it lies in the difference between the inference from (1) to (2) and the inference from (5) to (6). In the cancer case, a good that would justify God’s permission of the evil would have to be a very large good. In the stubbed toe case, a justifying good could be pretty small. But it is much easier to overlook a small good than a very large good. Thus, (5) confers much less probability on the existence of gratuitous evil than (1) does.

When I first thought of this conservative answer, I had the image of an elephant: it’s hard to overlook an elephant in the room, but a smaller thing is easier to overlook.

Is that a good image? Are bigger goods easier to see?

Sometimes. A tiny increment in pleasure may be hard to see just as it’s hard to tell the difference in color between two nearby shades of green. If the stubbed toe led to Bob having a slightly greater appreciation of his health the next day, he might not notice.

On the other hand, some really big goods are things we may take for granted, and they need to be pointed out first by some wise person for us to expressly notice them. For instance, the value of human dignity. However, goods that we take for granted are likely irrelevant here—for goods that we take for granted are unlikely to be goods that need Bob’s cancer to exist.

Furthermore, it may not be all about smaller things being harder to see. Consider Rover the dog. How likely is it that there is a cat bigger than Rover? Well, it is more likely when Rover is small than when Rover is big. Similarly, if an evil is smaller, then it is more likely that it is connected to good big enough to justfy it than if the evil is bigger.

So, I think, one can make a case that the inference from a cancer to gratuitous evil is better than the inference from a stubbed toe to a gratuitious evil. But is it much, much better? That I am not sure about. Yet we take (1)-(4) very seriously and we take (5)-(8) not seriously at all. Even if we are right to take (1)-(4) more seriously than (5)-(8), perhaps we make too big a difference between them. Perhaps we shouldn’t take (1)-(4) quite as seriously as we do, and perhaps we should take (5)-(8) more seriously, and perhaps both!

Rowe's argument from evil revisited

In his 1979 classic paper, Rowe says that a necessary condition for an “omniscient, wholly good (OG) being” to fail to prevent an evil s₁ is that at least one of the following three conditions holds:

1. there is some greater good, G, such that G is obtainable by OG only if OG permits s₁, or

2. there is some greater good, G, such that G is obtainable by OG only if OG permits either s₁ or some evil equally bad or worse

3. s₁ is such that it is preventable by OG only if OG permits some evil equally bad or worse.

We might put it this way: Rowe is saying that OG will prevent all gratuitous evils, and an evil is gratuitous if none of (i)–(iii) are satisfied.

First, note that (i) can be omitted, since if we have (i), we have (ii) as well. That’s a nice simplification: we only need (ii) and (iii).

More interestingly, however, note an ambiguity in “there is some greater good”. To see the ambiguity, consider this apparent counterexample to Rowe.

Suppose both theological compatibilism and Molinism are false, and God decides to give Alice a free choice between a great moral good G₁ and a tiny moral evil s₁, in circumstances where Alice is very likely to choose G₁. Absent theological compatibilism and Molinism, God cannot, however, ensure that Alice will choose G₁. Suppose, also, that free choice is not valuable as such, but significantly freely choosing well is very valuable (where significant freedom is freedom to choose between right and wrong), and much more valuable than choosing well without significant freedom. Finally, let’s suppose Alice goes for s₁. It is reasonable to say that s₁ is non-gratuitous, for preventing s₁ would lose the opportunity for the great good of Alice significantly freely choosing G₁. But an opportunity for a good may not count as a good. Condition (iii) is not satisfied—if God didn’t give Alice the choice between G₁ and s₁, no other evil would have to be permitted. But neither is (ii). For the good G of Alice significantly freely choosing G₁ does not exist, since Alice does not in fact choose G₁.

For many years I thought that this was a counterexample to Rowe. Today it hit me that this might be uncharitable. When Rowe says “there is some greater good”, he might mean a greater possible good or a greater type of good. Thus, in my example there is a greater possible good or a greater type of good, that of Alice significantly freely choosing G₁, albeit this is a good that isn’t actually instantiated.

Thus, charitably, let’s take Rowe to be quantifying over possible goods (or, pretty much equivalently, types of goods). A weak support for this is that the “some evil” in (ii) clearly quantifies over possible evils, so it makes the conditions neater to quantify over possible goods and evils.

Here is another problem for Rowe’s account. Suppose (ii) and (iii) are not satisfied, but instead we have:

4. there is a good, G, such that G is obtainable by OG only if OG permits s₁ or something at least as bad while the only way that s₁ is preventable by OG is by permitting some lesser evil s₂ or something at least as bad as s₂, and that G plus s₁ is better than s₂.

It seems that in case like this, s₁ need not be gratuitous. But note that a case like this does not require either G to be a greater good in comparison to the evil s₁ nor does it require s₂ to be at least as bad as s₁. For intance, suppose the value of G is 10, the value of s₁ is  − 11 and the value of s₂ is  − 3. Then G plus s₁ has value  − 1, which is better than the  − 3 we get by preventing s₁ at the cost of s₂ and loss of G. In cases like this, (ii) and (iii) need not be satisfied, and yet the evil need not be gratuitous. In other words, there cases where we have a kind of mix of (ii) and (iii). (It’s hard to think of examples, but it’s also hard to think of examples of (iii). I think the examples would have to involve divine promises.)

I also worry about incommensurability. For simplicity, let’s suppose there is no incommensurability: all values and disvalues are comparable. Also, let’s suppose that there are only finitely many scenarios in play, so we don’t have to worry about infinite sequences of less and less bad options and stuff like that.

Still Rowe’s necessary condition for non-gratuity have become more complicated: (ii) or (iii) or (iv), and with the quantifiers ranging over possible goods and possible evils. And once conditions get so complicated, one starts to worry that we are missing something. It would be nice to simplify the conditions.

Here is my attempt at such a simplification:

1. There is a possible scenario where s₁ is permitted by OG which is at least as good as any possible scenario where s₁ is prevented by OG.

Before continuing, I want to worry a bit about the following. Suppose that by preventing an evil s₁ you lose a good G, where G is not a greater good, but an “equal good”, i.e., the value of G equals exactly the disvalue of s₁. In that case, it seems plausible that a morally perfect being would prevent s₁, since there is a presumption in favor of preventing evils. I will take avoid this worry simply by assuming that it’s better to have neither G nor s₁ than to have both G and s₁ in cases where the value of G equals the disvalue of s₁, i.e., that axiology has a presumption in favor of no-evil. Otherwise, we need to slightly modify (1).

Suppose (1) is true. Let G be the sum total of the goods in the scenario A that’s at least as good as any possible scenario where s₁ is prevented by OG. It follows that any way of preventing s₁ involves either the loss of G or a scenario where the totality of evil is greater than s₁. If G is a greater good compared to s₁, then we thus have (ii). If G is empty, then it seems that there are no goods in the scenario, but we must have greater evils in the s₁-prevention scenarios than in A, and so we have (iii). Finally, if G is non-empty but not greater in comparison to $s_1 then I suspect we are going to have (iv) or something very close, but it’s a bit too complicated for me to think through in detail at the moment.

Moreover, (1) is intuitive as a necessary condition on God’s permitting an evil, in a way in which the triple disjunction (ii) or (iii) or (iv) is probably too complicated to be intuitive. I take it, then, that (1) is a friendly amendment to Rowe’s atheistic argument.

But at this point there is an interesting skeptical theist move. Rowe needs to be able to be epistemically justified in pointing to some evil s₁ and denying (1). But that’s pretty hard. Claim (1) existentially quantifies over all possible scenarios where s₁ is permitted by OG. It’s not that easy to know that one of them has the property indicated in (1), given the vast range of scenarios where s₁ is permitted by OG.

Trinity, quaternity and naming God

One now-classic solution to some of the challenges of the doctrine of the Trinity is relative identity. On relative identity accounts of the Trinity, we do not heretically say, e.g., that the Father is absolutely identical with the Son, but instead we posit a same-essence (or same-God) relative identity relation, and say that the Father is same-essence as the Son. Now, most of the time proponents of relative identity views deny that there is any such thing as absolute identity at all. All identities are relative to a sortal. However, in their famous “Material Constitution and the Trinity”, Brower and Rea offer an account of the Trinity using relative identity within a system where there is such a thing as absolute identity, governed by the standard rules of first-order logic.

Any account of the Trinity that allows for absolute identity governed by classical logic faces an interesting problem. Suppose:

1. There is such a thing as absolute identity, denoted by “=” and governed by its standard first-order logic rules.

2. There is a name for God as such, “G”, and names for the Father, Son and Holy Spirit, respectively, “F”, “S” and “H”.

3. F ≠ S

4. S ≠ H

5. F ≠ H

6. For all x, if x = F or x = S or x = H while y = F or y = S or y = H, and if x = G, then y = G.

7. If x = x, y = y, z = z, w = w, x ≠ y, x ≠ z, y ≠ z, x ≠ w, y ≠ w and z ≠ w, then x, y, z and w are four, counting by absolute identity.

8. Then F, S, H and G are four, counting by absolute identity.

9. Heresy! In no sense is there a divine quaternity!

Premise (6) captures the idea that the persons of the Trinity have equality with respect to divinity, and hence if x and y are persons of the Trinity, then if either of x and y “is God” in some sense of “is” and “God”, then the other “is God” in the same sense.

Proof of 8 from 1–7:

1. If F = G or S = G or H = G, then F = G and S = G and H = G. By 6

2. If F = G and S = G, then F = S. By 1

3. So F ≠ G or S ≠ G. By 3 and ii

4. So F ≠ G and S ≠ G and H ≠ G. By i and iii

5. F = F, S = S, H = H. By 1

6. G = G. By 1

7. So, F, S, H and G are four, counting by absolute identity. By 3–5, iv–vi and 8

There is a way out of this, in van Inwagen’s work on the Trinity. Van Inwagen denies that there are names for the Father, Son, Spirit and God: there are just predicates, like “is divine” and “is a Father”.

This is overkill for getting out of the above. It is difficult for a Christian to completely deny the existence of divine names. After all, you become a Christian by having someone pour water over you while saying: “I baptize you in the name of the Father, and of the Son and of the Holy Spirit.”

I think the quaternity argument leaves Christians who want to uphold classical absolute identity with two options:

1. There is no name for God.

2. There are no names for the Father, Son or Holy Spirit.

Here, “name” means “proper name”, since that’s the kind of name that classical logic talks about.

Accepting both (a) and (b) is not, I think, an option. Of the two, I think (b) is the more problematic. Names are too central to human relationships with persons. Thus, I think, the Christian who wants to uphold classical absolute identity should accept (a). And there is some support in Christian tradition for denying that God has a name.

(This is not what Brower and Rea do. In footnote 7, they talk of “the name ‘God’”, albeit in the context of discussion of a heretical view, but as I read the footnote they have no reservation about “God” being a name.)

While (a) is the less problematic of the two options, I still think (a) is problematic. Grammatically, “God” and “the Trinity” and the tetragrammaton all function as proper names. While there is some precedent in the Christian tradition for denying that God has a name, that still seems a bit of a stretch.

I think that if one is going to adopt a relative-identity account of the Trinity, then one should either deny that there is such a thing as absolute identity or at least one should deny that it is governed by the rules of classical logic.

I tentatively propose the following modification to the classical theory of absolute identity as a way of getting out of the quaternity argument. Restrict the identity-introduction rule that says that for any name N we get to write down N = N to the case of what one might call hypostatic or individual names (or, perhaps, to non-essence names). Thus, we get to write “Father=Father” but not “God=God”. Now everything in the quaternity argument goes through, except we don’t get (vi) and and hence we can’t infer (vii) or (8).

The Sign of the Cross and the Trinity

A principle that both Catholic and Orthodox Christians appreciate is lex orandi, lex credendi: the law of prayer is the law of faith,

Now notice that we cross ourselves with the Trinity in a specific order: “In the name of the Father, and of the Son, and of the Holy Spirit.” This is probably the most common Christian prayer in the world. And it has an order: first, the Father is mentioned, then the Son, and then the Holy Spirit. The same order is found in the baptismal formula. While Eastern Christians tend to cross themselves right-to-left and Western Christians left-to-right, the order of the words is maintained (at least in the Churches where Trinitarian words are used: more details here).

It feels badly off to pray “In the name of the Father, and of the Holy Spirit, and of the Son.” Now, we might say that the feeling of its being “off” has a deflationary psychological explanation—we are just used to a specific order. Or, somewhat better, it is off insofar as it disconnects us from the practices of the community. But the universality of the order in the most common Christian prayer together with the theological methodology of lex orandi, lex credendi and the intuition that other orders aren’t as good should impel us to see theological significance in the order.

We might, of course, see a purely missional order here. First the Father is active in the world, then the Son, and then the Holy Spirit is sent. But I think we want more than just such a temporal ordering in our explanation. After all, while the Holy Spirit is especially sent in New Testament times, it seems right to talk of the Spirit’s activity in Old Testament times. And maybe even some of the explicit mentions of Ruakh Elohim, God’s Spirit, including at the beginning of Genesis, is already an indication of the economic involvement of the Spirit. It is at least better if we can ground what feels like an important feature of a central Christian prayer in something eternal.

One solution would be a subordinationist one: the Son is subordinate to the Father, and the Holy Spirit is subordinate to the Son. But that would be a heresy.

I propose that the filioque, whether formulated in terms of the Holy Spirit proceeding from the Father and the Son or from the Father through the Son, gives an elegant eternity-based account of what makes the order in the prayer appropriate. First, the Father, from whom the Son proceeds, and then the Holy Spirit who proceeds from the Father and/through the Son. The order is not that of subordination but of procession.

The filioque

Suppose we model the Trinity as three vertices with arrows between them representing relations of procession, such that:

1. No two vertices have two arrows between them and arrows only go between distinct vertices.

2. The arrows define the vertices in the sense that there is no way to relabel the vertices while preserving which vertex has an arrow to which vertext (i.e., there is no non-trivial directed graph automorphism).

There are seven different structures possible subject to (a).

Condition (b) is a way of capturing part of the traditional Western idea that the Trinity is relational, so that the distinctions between the persons arise from the processional structure. Four of the graphs violate this condition: in (1) we can rearrange the labels in any way without changing the relational structure; in (4) and (5) we can swap A and C; in (7), we can rotate the whole graph by 120 degrees.

Aquinas captures the relationality idea by the principle that person x is distinguished from person y if and only if there is a (real) processional relation between x and y. I think this principle is too strong in one way and too weak in another way. It is too strong, because (2) would allow the persons to be distinguished, even though there is no processional relation between A and C (or B and C): A would be the unique person from whom someone proceeds; B would be the unique person that proceeds; C would be the unique person unrelated by procession. It is too weak, because in (7) we have a processional relation between each person, but it fails to distinguish the three persons. Of course, (2) and (7) have other flaws.

The following options satisfy condition (b): (2), (3) and (6).

Graph (2) is theologically unacceptable, as it has a person not related to any other. And so while the relationality in (2) would be sufficient to define the persons, because C would be unrelated to A and B, the graph does not represent a fully relational Trinity. Besides which, (2) has two persons, A and C, who do not proceed from another, and the East and West agree that only the Father does not proceed.

Graph (3) is interesting. If we adopted this model of the Trinity, we would have to take A to be the Father, since everyone agrees that the Father does not proceed for anyone. Moreover, since everyone agrees that the Son proceeds from the Father, we would hae to

In graph (3), we would have to take A to be the Father, since the Father does not proceed from any other person, as the East and West agree. Likewise, the East and West agree that the Son comes from the Father. So B would have to be the Son. That would make the Holy Spirit be C, and proceed only from the Son. Neither the East nor the West will like this. And it would violate the principle that the Son eternally has nothing beyond what the Father has, excepting what follows from the Son’s being generated by the Father, since now the Son has the Spirit proceeding from him, but the Father does not. I suppose one might try to reconcile (3) with the Western view by saying that the Spirit proceeds mediately from the Father and immediately from the Son. I don’t like this.

That leaves graph (6), the Western view of the Trinity, with A being the Father, C being the Son and B being the Holy Spirit.

This isn’t really a great argument against the Eastern view of the Trinity, because the East will deny (b), on the grounds that one can distinguish the persons not merely by the directions of the procession, but by the types of processions, with generation and spiration being different types. One can think of this Eastern move as allowing the arrows to have different colors, and then instead of (b) having the condition that there is no way to relabel the vertices while preserving which vertex has an arrow of what color to what vertex.

The point here is rather to allow us to state with some precision what principles force the western view. Namely, we have:

Theorem: Suppose:

1. There are exactly three persons in the Trinity

2. The (binary) procession relation is asymmetric: if y proceeds from x, x does not proceed from y

3. At most most one person does not proceed from another

4. There is one person from whom both of the other persons proceed

5. There is no way to relabel the persons while preserving the procession relations.

Then there is a way of respectively naming the persons “Father”, “Son” and “Holy Spirit” such that it is correct to say: “The Father does not proceed, the Son proceeds from the Father, and the Holy Spirit proceeds from the Father and the Son.”

How has Aquinas not proved the Trinity?

St Thomas holds that we cannot know by natural reason that God is a Trinity. However, he also endorses a version of St Augustine’s account of the Trinity, on which God has a mental Word or concept of himself that he generates mentally, and then there is a Love that is responsive to that Word. Why is this not a proof by natural reason?

On this point, Thomas is sadly brief in the Summa Theologiae: “Again, the similarity with our intellect does not sufficiently prove anything about God, since the intellect is not found univocally in God and in us.”

But Aquinas thinks that we can literally talk about God, even if we do so by means of analogy. He has argued, by reason, that God exists and has all perfections. One of these perfections is knowledge of everything, and thus of himself. Does this not commit Aquinas to being able to say on the basis of natural reason that God generates his self-knowledge, a self-knowledge that, by divine simplicity, must then be God himself rather than a mere creature? And does not God love himself under the description that this knowledge provides?

I think Aquinas would (with perhaps minor cavils) endorse all the claims in my previous paragraph as knowable by natural reason. How is this not a proof of the Trinity? I think the answer is this. Focus on the generation of the Son—the case of the Holy Spirit will presumably be similar. We do not know by reason whether the relation of generating self-knowledge is a real relation in God. If it is a real relation it will individuate the knower from the knowledge, thereby ensuring that there are at least two persons in God. But it needs to be a real relation in God, rather than a merely conceptual one. And here Thomas’s brief remark about univocity seems apposite. Aquinas thinks that what makes our language about God analogical rather than univocal is that the grounding of claims about God is radically different from the grounding of similar claims about creatures. Thus, when we say Socrates is wise, this is grounded by the inherence in Socrates of an accident of wisdom, while when we say God is wise, this is grounded by the identity between God and his wisdom. Because of this, even if it turns out that in us the generation of self-knowledge is a real relation (but not one between persons, since we are not simple, and hence our self-knowledge does not need to be of one essence with us), since the grounding structure of claims about God is radically different, as far as unaided human reason goes, it may not be grounded in a real relation in God—though it might be. We need God’s revelation to know if it is a real relation or not. And indeed God has revealed that it is.

Gale's criticism of Stump and Kretzmann's ET-simultaneity

Stump and Kretzmann give three main concepts of simultaneity in their famous paper:

• T-simultaneity between items in time

• E-simultaneity between items in eternity

• ET-simultaneity between items in time and items in eternity.

Stump and Kretzmann observe that ET-simultaneity is not reflexive: a temporal item is not ET-simultaneous with a temporal item and an eternal item is not ET-simultaneous with an eternal item. My mentor Richard Gale in his book on God argues that this is a serious problem: a relation that is’t reflexive just doesn’t have a hope of counting as a simultaneity relation.

But Gale is wrong. For T-simultaneity and E-simultaneity are clearly simultaneity relations, but neither of them is reflexive either! For an eternal item is not T-simultaneous with itself and a temporal item is not E-simultaneous with itself.

Now, granted, when we talk of reflexivity of a relation, it’s within a relevant domain. Thus, we say that being the same color is reflexive, even though St Michael the Archangel is not the same color as himself, because the relevant domain for sameness of color is things that have color, not immaterial intellects.

So we might say that T-simultaneity and E-simultaneity are reflexive because their respective domains are temporal and eternal things, and they are each reflexive in their domains.

We might, but we shouldn’t. Stump and Kretzmann’s investigation is of a domain of items that may or may not be simultaneous in different senses, a domain that includes both eternal and temporal things. And in that domain, none of the relations they consider are reflexive. And that’s OK.

Proper parts and dependence

Consider this initially plausible thesis:

1. If x has a proper part, and all of x’s proper parts depend on y, then x depends on y.

Add:

2. An effect depends on its cause.

3. Nothing depends on itself.

We conclude:

4. Nothing that has proper parts is a cause of all of them.

This has a nice theological application.

5. God is the cause of everything that is not God.

6. Therefore, if God has proper parts, he is the cause of all of them.

7. So, God has no proper parts.

However, I am dubious of premise 1. I think (1) depends on a story about parthood on which a whole is made of its parts. But if we don’t have that story, we could imagine a simple thing that then goes on to produce a proper part for itself. And so we lose the nice argument for divine simplicity. Which is too bad, but there are others.

An easily patched hole in the First Way

In his First Way, Aquinas argues that as we trace back the sequence of movers from effect to cause, we get to a first unmoved mover, and this is God.

But need the unmoved mover thus reached in the sequence of movers be God? Imagine this scenario. God creates some material beings, as well as an unchanging, timeless and immaterial demiurge that has the power to make the material beings move—and indeed exercises that power. Then if we were to trace back the sequence of movers, the unmoved mover we would get to would be the demiurge, not God. This demiurge would have potentiality, but not a temporal potentiality, so it would not be itself in motion, and hence it would be an unmoved mover.

This doesn’t deeply affect the argument, since Aquinas could do the same thing as he does in the Third Way, where he traces contingent beings to a necessary being, and then considers the possibility of necessary beings that get their necessity from other beings, and traces it back to an absolutely necessary being, namely God. Similarly, God could say that any unmoved mover that has some potentiality or contingency depends on a prior being and so on, and in the end we would get to God anyway.

Indeed, even in this scenario with a demiurge, we might want to say that it is God and not the demiurge who is the first unmoved mover. For God would still be a mover, albeit working through the demiurge who is a secondary cause, and God would be unmoved, and God would be first. So Aquinas would still be correct that the “first mover” is God—it’s just that the scenario suggests that Aquinas does skip a step.

God and growing block

1. On the growing block theory of time, if God is in time, God grows.

2. God doesn’t grow.

3. So, God is not time or the growing block theory is not true.

Divine timelessness

This is probably the simplest argument for the timelessness of God, and somehow I’ve missed out on it in the past:

1. God does not change.

2. Creation has a finite age.

3. There is nothing outside of creation besides God.

4. So, change has a finite age. (1–3)

5. There is no time without change.

6. So, time has a finite age. (4,5)

7. If something is in time, it has an age which is less than or equal to the age of time.

8. God does not have a finite age.

9. God is not in time. (6–8)

Premise (2) is supported by causal finitism and is also a part of Jewish, Christian and Muslim faith.

Some philosophers deny (3): they think abstract things exist besides God and creation. But this theologically problematic view does not affect the argument. For abstract things are either unchanging or they change as a result of change in concrete things (for instance, a presentist will say that sets come into existence when their members do).

The most problematic premise in my view is (5).

Omniscience, timelessness, and A-theory

I’ve been thinking a lot this semester, in connection with my Philosophy of Time seminar, about whether the A-theory of time—the view that there is an objective present—can be made consistent with classical theism. I am now thinking there are two main problems here.

1. God’s vision of reality is a meticulous conscious vision, and hence if reality is different at different times, God’s consciousness is different at different times, contrary to a correct understanding of immutability.

2. One can only know p when p is true; one can only know p when one exists; thus, if p is true only at a time, one can only know p if one is in time. On an A-theory of time, there are propositions that are only true in time (such as that presently I am sitting), and hence an omniscient God has to be in time. Briefly: if all times are the same to God, God can’t know time-variable truths.

I stand by the first argument.

However, there may be a way out of (2).

Start with this. God exists at the actual world. Some classical theists will balk at this, saying that this denies divine transcendence. But there is an argument somewhat parallel to (2) here. If all worlds are the same to God, God can’t know world-variable truths, i.e., contingent truths.

Moreover, we can add something positive about what it is for God to exist at world w: God exists at w just in case God actualizes w. There is clearly nothing contrary to divine transcendence in God’s existing at a world in the sense of actualizing it. And of course it is only the actual world that God actualizes (though it is true at a non-actual world w′ that God actualizes w′; but all sorts of false things are true at non-actual worlds).

But given the A-theory, reality itself includes changing truths, including the truth about what it is now. If worlds are ways that all reality is, then on A-theory worlds are “tensed worlds”. Given a time t, say that a t-world is a world where t is present. Argument (2) requires God to exist at a t-world in order for God to know something that is true only at a t-world (say, to know that t is present).

Now suppose we have an A-theory that isn’t presentism, i.e., we have growing block or moving spotlight. Then one does not need to exist at t in order to exist at a t-world: on both growing block and moving spotlight our 2025-world has dinosaurs existing at it, but not in 2025, of course. But if one does not need to exist at t in order to exist at a t-world, it is not clear that one needs to exist in time at all in order to exist at a t-world. The t-world can have a “locus” (not a place, not a time) that is atemporal, and a being that exists at that atemporal locus can still know that t is present and all the other A-propositions true at that t-world.

Next suppose presentism, perhaps the most popular A-theory. Then everything that exists at a t-world exists at t. But that God exists at the t-world still only consists in God’s actualizing the t-world. This does not seem to threaten divine transcendence, aseity, simplicity, immutability, or anything else the classical theist should care about. It does make God exist at t, and hence makes God in time, but since God’s existing in time consists in God’s actualizing a t-world, this kind of existence in time does not make God dependent on time.

I still have some worries about these models. And we still have (1), which I think is decisive.

Towards a solution to the "God as author of evil" problem for the Thomistic model of meticulous providence

On the Thomistic primary/secondary causation model of meticulous divine providence, when we act wrongly, God fully determines the positive aspects of the action with primary causation, and we in parallel cause the action with secondary causation.

Like many people, I worry that this makes God the author of sin in an objectionable way.

Alice and Bob are studying together for a calculus exam that will be graded on a curve. In order that she may do terribly on the exam, and thus that he might do better, and hence be more likely to get into his dream PhD program in ethics, Bob lies to Alice, who has missed three weeks of class, that the derivative of the logarithm is the exponential.

What does God cause in Bob’s action on the Thomistic model? It seems that all of the following are positive aspects:

1. The physical movements in Bob’s mouth, throat, and lungs.

2. The sounds in the air.

So far we don’t have a serious theological problem. For (1) and (2) are not intrinsically bad, since Bob could virtuously utter the same sounds while playacting on stage. But let’s add some more aspects:

3. Bob’s intention that the speech constitute an assertion of the proposition that the derivative of the logarithm is the exponential.

4. Bob’s intention that the asserted proposition be a falsehood that Alice comes to believe and that leads to her doing terribly on the exam.

Perhaps one can argue that falsity a negative thing—a lack of conformity with reality. However, intending falsity seems to be a positive thing, a positive (but wicked) act of the will. Thus it seems that (3) and (4) are positive things. But once we put together all of (1)–(4), or even just (3) and (4), then it’s hard to deny that what we have is something wicked, and so if God is intending all of (1)–(4), it’s hard to avoid the idea that this makes God responsible for the sin in a highly problematic way.

There may be a way out, however. In both written and spoken language, meaning is normally not constituted just by the positive aspects of reality but also by negative ones. In spoken language, we can think of the positive aspects as the peaks of the soundwaves (considered as pressure waves in the air). But if you remove the troughs from the soundwaves, you lose the communication. In print, on the other hand, the meaning depends not just on the ink that’s there, but on the ink that’s not there. A page wholly covered with ink means nothing. We only have meaningful letters because the inked regions are surrounded by non-inked regions.

It could well turn out that the language of the mind in discursively thinking beings like us is like that as well, so that a thought or intention is constituted not only by ontologically positive but also by ontologically negative aspects. Now you could be responsible for the ink within the print inscription

5. The derivative of the logarithm is the exponential

without being responsible for the inscription. For instance, you and a friend might have had a plan to draw a black rectangle and you divided up the labor as follows: you inked the region of rectangle covered by the letters of “The derivative of the logarithm is the exponential” and then your friend would ink the rest of the containing rectangle—i.e., everything outside the letters. But your friend didn’t do the job. Similarly, then, if intentions are constituted by both positive and negative features, God could intend the positive features of an intention without being responsible for the intention as such.

This does place constraints on the language of the mind, i.e., on the actual mental accidents that constitutes our thoughts, and specifically our intentions. Note, though, that we don’t need that all intentions have a negative constituent. Only intentions to produce negative things, like falsehood, need to have a negative constituent for us to avert the problem of God willing intentional sin. We could imagine a written language where positive phrases are written in two colors of ink, one for the letters and the other for the surrounding rectangle, and their negations are written by omitting the ink for the letters. In such a language, statements involving positive phrases are purely positive, while those involving negative phrases are partly negative.

I am not very happy with this solution. I still worry that being responsible for the ink in (5) makes one responsible for (5) when one chooses not to have the rest of the rectangle filled in.

Perfect vision

One of the major themes in modern philosophy was concerns about the way that our contact with the world is mediated by our “ideas”. Thus, you are looking at a tree. But are you really seeing the tree, or are you just seeing your sense-impression, which doesn’t have much in common with the tree? Even direct realists like Reid who say you are seeing the cat still think that your conscious experience involves qualia that aren’t like a tree.

Thinking about this gives us the impression that an epistemically better way to relate to the tree would be if the tree itself took the place of our sense-impressions or qualia. Berkeley did that, but at the cost of demoting the tree to a mere figment of our perception. But if we could do that without demoting the tree, then we would be better kinds of perceivers.

However, that on some theory we would be better kinds of perceivers is not a strong reason to think that theory is true! After all, we would be better perceivers if we could see far infrared, but we can’t. It’s not my point to question the orthodoxy about our perceptions of trees.

But now think about beatitude, where the blessed see God. If seeing God is like seeing a tree in the sense that there is something like a mediating supersense-impression in us, then something desirable is lacking in the blessed. And that’s not right. Such a mediated vision of God is not as intimate as we could wish for. Would it not be so much more intimate if it were a direct vision of God in the fullest sense, where God himself takes the place of our qualia? We shouldn’t argue from “it would be better that way” to “it is that way” in our earthly lives, but in beatitude it does not seem such a terrible argument.

But where this kind of argument really comes into its own is when we think of what the epistemic life of a perfect being would be like. The above considerations suggest that when God sees the tree (and it is traditional to compare God’s knowledge of creation to vision), the vision is fully direct and intimate, and the tree itself plays the role of sense-impressions in us. We would expect a perfect being’s vision to be like that.

Now notice, however, that this is an account of God’s vision of the world on which God’s vision is partly extrinsically constituted: the tree partly constitutes God’s conscious experience of the tree. This is the extrinsic constitution model of how a simple God can know. We have thus started with us and with considerations of perfection, and have come to something like this model without any considerations of divine simplicity. Thus the model is not an ad hoc defense of divine simplicity. It is, rather, a model of the perfect way to epistemically relate to the world.