Ontology as a contingent science

Consider major dividing lines in ontology, such as between trope theory and Platonism. Assume theism. Then all possibilities for everything other than God are grounded in God.

If God is ontologically like us, and in particular not simple, then it is reasonable to think that the correct ontological theory is necessarily determined by God’s nature. For instance, if God has tropes, then necessarily trope theory holds for creatures. If God participates in distinct Platonic forms like Divinity and Wisdom, then necessarily Platonism holds for creatures.

But the orthodox view (at least in Christianity and Judaism) is that God is absolutely simple, and predication works for God very differently from how it works for us. In light of this, why should we think that God had to create a tropist world rather than a Platonic one, or a Platonic one rather than a tropist one? Neither seems more or less suited to being created by God. It seems natural, in light of the radical difference between God and creatures, to think that God could create either kind of world.

If so, then many ontological questions seem to become contingent. And that’s surprising and counterintuitive.

Well, maybe. But I think there is still a way—perhaps not fully satisfactory—of bringing some of these questions back to the realm of necessity. Our language is tied to our reality. Suppose that we live in a tropist world. It seems that the correct account of predication is then a tropist one: A creature is wise if and only if it has a wisdom trope. A Platonic world has no wisdom tropes, and hence no wise creatures. Indeed, nothing can be predicated of any creature in it. What might be going on in the Platonic world is that there are things there that are structurally analogous wise things, or to predication. We can now understand our words “wise” and “predicated” narrowly, in the way they apply to creatures in our world, or we can understand them broadly as including anything structurally analogous to these meanings. If we understand them narrowly, then it is correct to say that “Nothing in the Platonist world is wise” and “Nothing is correctly predicated of anything in the Platonist world.” But in the wide, analogical sense, there are wise things and there is predication in the Platonist world. Note, too, that even in our world it is correct to say “God is wise” and “Something is correctly predicated of God” only in the wide senses of the terms.

On this account, necessity returns to ontology—when we understand things narrowly. But the pretensions of ontology should be chastened by realizing that God could have made a radically different world.

And maybe there is an advantage to this contingentism. Our reasoning in ontology is always somewhat driven by principles of parsimony. But while one can understand why parsimony is appropriately pursued in study of the contingent—for God can be expected to create the contingent parsimoniously, both for aesthetic reasons and to fit reality to our understanding—I have always been mystified why it is appropriately pursued in the study of the necessary. But if ontology is largely a matter of divine creative choice, then parsimony is to be sought in ontological theories just as in physical ones, and with the same theological justification.

The above sounds plausible. But I have a hard time believing in ontology as a contingent science.

An analogy for divine infinity

Here’s an analogy I’ve been thinking about. God’s value is related to other infinities like (except with a reversal of order) zero is related other infinitesimals. Just as zero is infinitely many times smaller than any other infinitesimal (technically, zero is an infinitesimal—an infinitesimal being a quantity x such that |x| < 1/n for every natural number n), and in an important sense is radically different from them, so too the infinity of God’s value is infinitely many times greater than any other infinity, and in an important sense is radically different from them.

Suppose we think with the medievals that value and being are correlative. Then zero value corresponds to complete non-being. There isn’t anything that has that. Between ordinary non-divine things like people and oak trees and non-being we have a radical ontological difference: there are people and oak trees, but there is no non-being. Suppose we push the analogy on the side of God. Then between ordinary non-divine things like people and oak trees and God we will have a radical ontological difference, too. Some theologians have infamously tried to mark this difference by saying that people and oak trees are but God is not. That way of marking the difference is misleading by making God seem like non-being instead of like its opposite. A better way to mark the difference is to say that in an important sense God is and people and oak trees are not (compare what Jesus is said to have have said to St Catherine of Siena: “I am who I am and you are she who is not”). In any case, the gap between God’s “is” and our “is” is at least as radical as the gap between our “is” and the “is not” of non-being.

In fact, I think the gap is more radical: we and all other creatures are closer to non-being than to God. So the analogy I’ve been thinking about, that God’s value is related to other infinities like zero to other infinitesimals (but in reverse order) is misleading: God’s value is in a sense further from other infinities than zero is from other infinitesimals. (And not just because all infinitesimals are infinitesimally close to zero. The relevant scale should not be arithmetic but logarithmic, so that the gap between zero and anything—even an infinitesimal—bigger than zero is in an important sense infinite.)

Don’t take this too seriously. Remember this.

More on the privation theory of evil

Back in April, I suggested that there are two possible privation theories concerning evil:

1. every evil is a privation

2. for every evil, what makes it be evil is a privation.

Well, Aquinas essentially scooped me, in the first article of the De Malo, by distinguishing two senses of evil in the statement “evil is a privation”. If “evil” means the evil thing, the claim is false. But by “evil” we could mean the evilness of the evil thing, and then Aquinas holds the claim to be true. And it seems to me that the evilness of the evil thing is basically that which makes it evil, so Aquinas’ theory is basically my theory (2).

I think too much of our current literature on the privation theory of evil suffers from a failure to explicitly make the distinction between the evil thing and the evilness of the evil thing. As a result, some of the counterexamples in the literature are only counterexamples to (1). And indeed it’s not hard to find uncontroversial counterexamples to the claim that every evil entity is a privation. Josef Stalin was an evil entity (I hope he has repented since), but he was never a privation; an act of adultery is an evil thing, but it is not a privation.

Consider, for instance, the most discussed example in the literature: pain. It gets pointed out that pain is not a lack of pleasure or any other kind of privation. That is very likely true. But Aquinas’ version of the privation theory does not require him to hold that pain is a privation. He can just say that pain is an evil thing, but evil things don’t have to be privations. Rather, what makes the pain be an evil is a privation. Of course that still requires a privative theory as to what makes pain be an evil. But there are such theories. For instance, one might hold a modification of Mark Murphy’s theory about pain and say that what makes pain in paradigmatic cases bad is a privation of a correspondence between our mental states and our desires, given that in paradigmatic cases we desire not to be in pain (and it’s not much of a bullet to bite to say that pain isn’t bad when it doesn’t go against our desires).

The story about pain doesn’t end here. One might, and I think should, question whether the correct ontology of the world includes such entities as “matches” between mental states and desires for pain to be a privation of. I think what Aquinas would likely say is that because being is said analogically, “matches” do exist in an analogical sense, and hence we can correctly talk of their privation. I think this is problematic. For once we allow that “matches” exist analogically, we should equally allow for privations and other lacks to exist analogically—and Aquinas indeed does. And then we run into the problem that even positive things can count as lacks: for instance, sight could count as a lack of the lack of sight. And once we have gone this far, the privation theory becomes trivial.

But the point remains: once we have seen Aquinas’s distinction between the evil being a privation and the evilness of the evil being a privation, the critiques of the privation theory are apt to get a lot more complex.

"On the same grounds"

Each of Alice and Seabiscuit is a human or a horse. But Alice is a human or a horse “on other grounds” than Seabiscuit is a human or a horse. In Alice’s case, it’s because she is a human and in Seabiscuit’s it’s because he’s a horse.

The concept of satisfying a predicate “on other grounds” is a difficult one to make precise, but I think it is potentially a useful one. For instance, one way to formulate a doctrine of analogical predication is to say that whenever the same positive predicate applies to God and a creature, the predicate applies on other grounds in the two cases.

The “on other/same grounds” operator can be used in two different ways. To see the difference, consider:

1. Alice is Alice or a human.

2. Bob is Alice or a human.

In one sense, these hold on the same grounds: (1) is grounded in Alice being human and (2) is grounded in Bob being human. In another sense, they hold on different grounds: for the grounds of (1) also include Alice’s being Alice while the grounds of (2) do not include Bob’s being Alice (or even Bob’s being Bob).

Stipulatively, I’ll go for the weaker sense of “on the same grounds” and the stronger sense of “on different grounds”: as long as there is at least one way of grounding “in the same way”, I will count two claims as grounded the same way. This lets me say that Christ knows that 2 + 2 = 4 on the same grounds as the Father does, namely by the divine nature, even though there is another way in which Christ knows it, which the Father does not share, namely by humanity.

Even with this clarification, it is still kind of difficult to come up with a precise account of “on other/same grounds”. For it’s not the case that the grounds are literally the same. We want to say that the claims that Bob is human and that Carl is human hold on the same grounds. But the grounding is literally different. The grounds of the former is Bob’s possession of a human nature while the grounds of the latter is Carl’s possession of a human nature. Moreover, if trope theory is correct, then the two human natures are numerically different. What we want to say is something like this: the grounds are qualitatively the same. But how exactly to account for the “qualitatively sameness” is something I don’t know.

There is a lot of room for interesting research here.

God and analogy

According to Aquinas, whenever we correctly say something non-negative of God, we speak analogically.

It is correct to say that Socrates is wise and God is wise. But being humanly wise and divinely wise are different—the most fundamental difference being that, by divine simplicity, God doesn’t have his wisdom, but is his wisdom. But this leads to:

1. The predicate “is humanly wise or is divinely wise” applies literally to both Socrates and God.

And yet this disjunctive predicate is not negative, so (1) seems to provide a counterexample to Aquinas’ theory.

But this is too fast. Claim (1) only provides a counterexample to Aquinas’ theory if:

2. Applying analogically and applying literally are incompatible.

But I think Aquinas can, and should, say that (2) is false. If he does that, then he can affirm both (1) and:

3. The predicate “is humanly wise or is divinely wise” applies analogically to both Socrates and God.

In fact, I think Aquinas can say that the relevant kind of analogical application of predicates is a special case of literal predication.

I think that Aquinas is not really making a claim about literal and non-literal use of words when he is talking of analogical predication. Instead, I think he is making a claim about grounding, somewhat like:

4. The predicate “is F” is used analogically between entities x and y just in case the propositions that x is F and that y is F have a relevantly different grounding structure.

On this account, disjunctive predicates like “is a human or a dog” are used analogically: for the grounding structure of the proposition that Alice is a human or a dog is that it’s grounded in Alice being a human, while the grounding structure of the proposition that Fido is a human or a dog is that it’s grounded in Fido being a dog. And similarly, “is humanly wise or is divinely wise” is used analogically, since in the case of Socrates the grounds of applicability are Socrates having wisdom and in the case of God the grounds are God being (his) wisdom.

Notice that on this story, Aquinas’ claim about analogical predication is not so much a linguistic claim as a metaphysical claim about the truth grounds.

The story makes clear why negative predicates are not used analogically: for the grounding structure of the truth that God is not a bicycle and the truth that Alice is not a bicycle is relevantly the same—both are grounded in not being arranged bicycle-wise.

So far, our reconstruction of Aquinas’ theory of predication is:

5. A predicate that applies to God is negative or is used analogically.

But that’s not quite right. Here is one counterexample: “is not a bicycle or is both a bicycle and a non-bicycle.” This predicate is not negative but disjunctive. But it applies to God and to Socrates in the same way—by both not being bicycles.

I think the issue here is this. Just as analogical predication is a metaphysical and not linguistic notion, so negative predication is a metaphysical and not linguistic notion. We might say something like this:

6. The predicate “is F” is used negatively of entity x just in case what grounds x being F is the non-obtaining of some state of affairs.

Thus, “is not a bicycle or is both a bicycle and non-bicycle” is used negatively of both God and Socrates, because what grounds its application in both cases are respectively the non-obtaining of the states of affairs of God being arranged bicycle-wise and of Socrates beng arranged bicycle-wise. On the other hand, the disjunctive predicate “is Athenian or not Greek” is used negatively of God and non-negatively of Socrates. Interestingly, this case shows that the disjunction in (5) is not exclusive. For “is Athenian or not Greek” is used both negatively of God and is used analogically between Socrates and God, since the structure of the grounds of application is relevantly different.

The problems haven’t all gone away. A necessary condition for “is F” to be used analogically of God and a creature is that “is F” applies to God and a creature, and hence a predicate that applies only to God cannot be used analogically. But suppose that in fact no one other than God knows whether the Continuum Hypothesis is true. Then the predicate “knows whether the Continuum Hypothesis is true” is not used analogically, since it only applies to God. But then we have a counterexample to (5).

We could try to modalize (4): a predicate is used analogically provided that it could have one ground as applied to God and another as applied to something other than God. But, again, it’s not hard to come up with a counterexample: “knows that 2 + 2 and is not a creature.” For that predicate can only apply to God.

We could also weaken (5) to merely apply to those predicates that apply (or could apply) to both God and a creature. This may seem to be an undue weakening: now one can escape from Aquinas’ doctrine of analogical predication simply by saying things that only apply (or could only apply) to God. But perhaps one can supplement the weakened (5) with:

7. Any predicate that applies to God is built out of predicates that apply both to God and to a creature.

I am not too happy about this.

The analogy of being and the moving spotlight theory of time

On moving spotlight theories, eternalism is true: past, present and future things all exist. But the present is metaphysically special: you have not said all that is to be said about temporal reality if you just said what happens at which times, and how the times are related by relations like earlier-than and simultaneous-with, without having said which time is objectively present. The puzzle for moving spotlight theories is to say what makes the present special.

Here is a start of a moving spotlight theory. Start with the Thomistic insight that there are multiple ways of existing. For instance, God doesn’t exist in the same way in which we do. Now add that temporal beings have three ways of existing: existing pastly, existing presently and existing futurely. Thus, we have at least four ways of existing: divine existence as pure act, past existence, present existence and future existence. These are genuinely different forms of existence, but they are all analogous. And we further subdivide the three temporal ways of existing into substantial and accidental existence.

Moreover, interestingly, these ways of existing can occur in various combinations. For instance, I exist pastly, presently and futurely. An object in the last moment of its existence exists pastly and presently. An object in the first moment of its existence exists presently and futurely. At the first moment of the Incarnation, the Second Person of the Trinity existed as pure act, as well as both presently and futurely. Right now, the Second Person of the Trinity exists in each of these four ways of being.

So what sets out the present as special is this: an event is present provided that the substances and accidents making up the event exist in present ways of existing.

This is eternalism and not presentism, but it captures one central insight of presentism: that to exist presently is different in kind from existing pastly or futurely. It escapes the three horse argument against presentism by saying that the real horses exist analogously to each other but the unreal one does not exist at all.

Of course, this is only a start. It would be nice to be able to say something substantive about how the three temporal ways of existing differ from one another. I don’t know that this can be done, and I don’t particularly want to pursue this, since I much prefer the elegance of the B-theory of time.

Group "belief"

Even though nobody thinks Strong AI has been achieved, we attribute beliefs to computer systems and software:

• Microsoft Word thinks that I mistyped that word.

• Google knows where I’ve been shopping.

The attribution is communicatively useful and natural, but is not literal.

It seems to me, however, that the difference in kind between the beliefs of computers and the beliefs of persons is no greater than the difference in kind between the beliefs of groups and the beliefs of persons.

Given this, the attribution of beliefs to groups should also not be taken to be literal.

Eternalism and presentism

Here is an argument against eternalism:

1. If eternalism is true, times are like places.
2. Times are not like places.
3. So, eternalism is false.

There are a number of arguments for (2). Many, though not all, of them have something to do with the directionality of time, given that space lacks such directionality. Now consider this parallel argument against presentism, and hence for eternalism:

4. If presentism is true, times are like worlds.
5. Times are not like worlds.
6. So, presentism is false.

There are a number of arguments for (5). Here's a fun one. If I am happy now and miserable at all other times, I'm really unfortunate. If I am happy in the actual world and miserable at all other worlds, I'm really lucky one. In general, misery at other times matters in a way in which misery at other worlds does not.

So how to break this impasse? One way would be to opt for a theory other than eternalism and presentism, say growing block. Another way is to keep on adding disanalogies between times and places or between times and worlds until one of the disanalogies ends up being much stronger. Yet another way, and I think the most promising, is to embrace both (2) and (5), but explain the disanalogy in a way that is compatible with presentism or eternalism (whichever is one's preference).

One should also note that arguments from analogy tend not to be the strongest.

Grounding inhomogeneity and analogy

I ought to respect innocent human life. So I ought not feed cyanide to the innocent. I ought to respect the legitimate intellectual autonomy of others. So I ought not force my students to believe all my metaphysical views.

So, some ought claims are grounded, in part or whole, in other ought claims, and sometimes in further non-normative claims (such as that cyanide kills). This is familiar in many other cases. Thus, it's a standard libertarian view about freedom that some exercises of freedom are only derivately free: they are free insofar as they flow from a character that was formed by other free actions.

It would generate a vicious regress to suppose that all free actions are derivatively free. (In this case, the impossibility of the regress is obvious from the fact that we've only performed finitely many actions in our history.) Likewise, it would be a vicious regress to suppose all ought claims are grounded in further ought claims.

So there are some thing that are derivatively obligatory and some that are non-derivatively obligatory. (The two categories might overlap. For if I promise to fulfill a non-derivative obligation, then that obligation is both non-derivatively obligatory and obligatory by derivation from the duty to keep promises.) Likewise for freedom and many other properties. The non-derivative cases may be brute and ungrounded, or they may be grounded in a different kind of fact (e.g., maybe non-derivative freedom is grounded in alternate possibilities or non-derivative ought is grounded in divine commands—I am not advocating either option as it stands).

Here is a maxim I find plausible: Properties that exhibit this kind of grounding inhomogeneity—sometimes being grounded in one kind of fact and sometimes either ungrounded or grounded in a different kind of fact—are in fact non-fundamental.

This may lead one to say that properties that exhibit this kind of inhomogeneity are really disjunctive. That (or the related suggestion that they are existentially quantified) may be true, but I think it isn't the whole truth. Maybe freedom just is the disjunction of non-derivative and derivative freedom. But it's not a mere disjunction, in the way that being red or cubical is. It's a disjunction between related properties. In the cases of freedom and obligation, the relationship here seems to me to be precisely that of Aristotelian analogy: there is a focal sense of freedom and obligation—the non-derivative case—and there is a non-focal sense as well.

Conjecture: When we are dealing with a somewhat natural property that exhibits grounding inhomogeneity, we are precisely dealing with a disjunction (or quantificational combination) between analogous more fundamental properties.

Aquinas' thinking on divine names fits well here. St Thomas thinks that when we predicate wisdom of God and Socrates, we do so analogically, because God's wisdom is God and Socrates' wisdom is accidental to him. But this difference is precisely a grounding inhomogeneity in the property wisdom, with God being the focal case.

Analogy and properties

Spot is a cat and Tob is a table. Spot has four legs and Tob has four legs. But "has four legs" in these two claims is analogical. The two claims are ultimately grounded in similar sorts of facts, but not in exactly similar sorts of facts. What makes Spot have four legs is that he has certain organs of locomotion, four in number. What makes Tob have four legs is that it has certain supporting parts, four in number.

Suppose we start talking about legs with people and cats, and only later move on to tables. Then we are analogically extending the concept of quadruple leggedness to pick out that feature that in tables is similar to what quadruple leggedness is or would be like in people and cats.

We could (in the sense corresponding to metaphysical possibility) use a very well trained cat that has particularly rigid ears and tail as a three legged table, by standing it up on on the ears and tail and putting a dish on the tummy. That cat/table would have four legs in the cat sense and three legs in the table sense. We would then say that this object has four legs qua cat and three legs qua table. On my adverbial ontology, the clear way to express this is to say that the object is a cat four-leggedly and a table three-leggedly.

But if this is right, then we should say similar things about Spot and Tob. Spot is a cat four-leggedly while Tob is a table four-leggedly. And these adverbs do different, albeit analogous, things to being a cat and being a table.

The predicate "has four legs" is adverbial. Something satisfies it in virtue of being something or other in a four-legged manner.

There had better be some non-adverbial predicates. Otherwise, we will have a vicious regress or circularity.

I conjecture that all accidental predication ("accidental" in the medieval, not the modal, sense) is adverbial and analogical in this way. One needs to, as it were, fill in an underlying predicate, the "G" in "is a G Fly", in order to make sense of "is F".

The line of thought is inductive: all the accidental predicates that I can think of are analogical in this way.

The incarnation and adverbial ontology

Christ is God and Christ is a human. God is unchanging and humans are changing. God is omnipresent and humans are spatiotemporally delimited. God is all powerful and the power of humans is limited. All praise be to Christ on this Christmas day!

Yet such theological claims appear to lead to contradiction: is Christ unchanging or change? is he limited or unlimited? Since we have excellent reason to think the claims are all true, we have excellent reason to think the claims are not contradictory. A traditional way to resolve the apparent contradiction is to introduce a qua or as qualifier:

1. Christ is unchanging, omnipresent and omnipotent as God, but as human he changes, and is limited in presence and power.

Such answers do work logically speaking, but it would be good to have a little bit more to say about what the "as" does.

I want to suggest something that may not be original[note 1] but that I found enlightening. Start with the observation that there is no contradiction at all in this sentence:

2. Sam is quick as a reader and slow as a runner.

And there is an obvious and easy way to understand (2) that removes all appearance of contradiction:

3. Sam reads quickly and runs slowly.

No contradiction results from contradictory adverbs being attached to different predicates. From Sam reading quickly we can deduce that Sam does something quickly, but that does not contradict his doing something else slowly.

Now we can make the same move in regard to (1). We will need two base predicates which are then adverbially modified. The ones that come to mind are "is God" and "is human". Then (1) becomes:

4. Christ is God unchangingly, omnipresently and omnipotently, but he is human changingly and limitedly in presence and power.

So far that's just words. But now make it into ontology. The ontology takes a cue from Spinoza's nesting of modes. (Other philosophers have nested modes, but I think it is only in Spinoza that the nesting is really central.) When Sam reads quickly, there is Sam, who reads, and Sam's reading, which is quick. If Sam reads excessively quickly, there is Sam, who reads, and Sam's reading, which is quick, and the quickness of Sam's reading, which is excessive. All of these, other than Sam himself, are modes (Spinoza wrongly thinks Sam is a mode, too). We can now talk of a mode being directly or indirectly a mode of something. Thus, the quickness of Sam's reading is directly a mode of Sam's reading and indirectly a mode of Sam. The excessiveness of Sam's quickness of reading is directly a mode of Sam's quickness of reading and indirectly a mode of Sam's reading as well as of Sam.

Next theorize that a mode m is an essence of an individual x if and only if m is directly a mode of x. This could simply be a necessary "if and only if" or, more ambitiously, it could be an account of what it is to be an essence, essences being nothing but direct modes. Observe that this is a non-modal account of essence—here we are talking of essence in the ancient and medieval sense, not in the modern modal sense (such a distinction was pointed out by Fine, but the best account in print is by Michael Gorman).

Thus all our accidental modes are indirectly modes of us, through our essence. My present typing of this post is a mode of my humanity: I am human typingly. And Christ, unlike us, has (at least[note 2]) two essences: humanity and divinity. Thus any mode of his is one of his essences or is a mode of one of his essences. (Sometimes our words will be ambiguous. Thus when we say that "Christ is wise", that is ambiguous whether he is divine in a wise manner or is human in a wise manner or both.)

This account makes it plausible that analogy will be a central concept. Adverbs apply analogically across predicates. The "quickly" in "Sarah runs quickly" and "Sarah thinks quickly" is to be understood analogically. In general, I suspect cross-essence predications are to be understood analogically. That is a Thomistic aspect in the theory.

Another Aristotelian aspect is that we can make sense of "necessary accidents". Thus, Aristotle thinks it is an accident of a human that the human have a capacity for laughter, but he also thinks this is a necessary accident—every human necessarily has a capacity for laughter. It is insufficient for a mode to be an essence that the mode is necessary: it must be directly a mode of the individual. But just as it is indirectly a mode of me that I be laughing—I am human laughingly when I laugh (which differs from, say, being an alien or angel laughingly)—it indirectly but necessarily a mode of me that I have a capacity for laughter—I am a human with a capacity for laughter ("with..." is one of the many ways of indicating adverbial modifiers).

There is a serious theological difficulty. Does not the account contradict divine simplicity? After all, does not (4) posit a mode of God, namely divinity, and modes of a mode of God, namely omnipresence of divinity, omnipotence of divinity and unchangingness of divinity? Yes, but that only contradicts divine simplicity if these modes are all distinct. But they aren't distinct. Divinity, omnipresence of divinity and all the others are all just God. Thus God is his own mode in this technical vocabulary. But since predication of God is analogical, what this means it that God is related to himself in a way analogical to our relationship to our modes. (Compare: the person who loves herself is related to herself in a way analogical to the way someone who loves another is related to that other.) It's important not to take "mode" to mean "accident", but that was already something necessary from the fact that essences are modes.

Of course, this is not a complete account of divine simplicity yet. Something needs to be said about apparently contingent modes of God, such as creating Adam. (I think claims like "God creates Adam" should not be taken as predicating a mode of God. Why not, with the medievals, take the claim as predicating a mode of Adam? Or as predicating being creator of all contingent beings of God and contigency of Adam?)

This reconciliation with divine simplicity does, however, mean that I cannot simply define a substance as something that isn't a mode. For God on this reconciliation is a substance and a mode. (And that is Thomistic, too, though the vocabulary of "mode" is not. God is both substance and that substance's pure act.) We might define a substance as something that isn't a mode of anything else. Or we might say that x is a substance if and only if the proposition that x exists has a truthmaker which is x and has no other truthmaker.

Finally, I leave it as an exercise to the reader to extend my "metaphysically Aristotelian quantification" to this context. At the same time, some of my cross-level uses of "is" in this post will need some charitable analogical reading.

Two questions about identity

Here is an interesting line of thought.

Consider these two questions:

1. What is it for x and y to be identical?
2. What necessary and sufficient conditions can be given for a person to be identical with a person?

These two questions seem respectively exactly parallel to:

3. What is it for an action to be permissible?
4. What necessary and sufficient conditions can be given for a killing of a person to be permissible?

Here, (3) is a metaethics question while (4) is an applied ethics question.

One way to notice the difference I'd like to highlight between (3) and (4) is to consider the kinds of answers one might get. For instance, on a fairly standard natural law theory, the answer to (3) is that an action is permissible if and only if it does not conflict with one's nature, while the answer to (4) is, perhaps, that the killing be a proportionate act of justice or self-defense and not otherwise impermissible. On a Kantian theory, the answer to (3) is that an action is permissible if and only if it treats no person as a mere means. But the answer to (4) may be exactly like the natural law answer. On a divine command theory, the answer to (3) is that what makes an action permissible is its not being forbidden by God, but again the answer to (4) might just like on the other theories.

Observe, thus, what we are very unlikely to get from standard answers to (4): we are very unlikely to find out what the permissibility of a killing consists in. If we want an answer to that question, the natural lawyer will say that the permissibility of a killing consists in its comformability to our nature, the Kantian that it consists in its not treating anyone as a mere means, and the divine command theorists that it consists in its not being forbidden by God. None of these answers will answer the applied ethics question we want, as these answers are at too high a level of generality: we can replace "killing" by any other action type, and they remain applicable.

Now go back to the metaphysics. I have no idea how to answer (1). It's hard to think of anything more fundamental than identity to answer it in terms of. But I think the analogy with the ethics question suggests this. If we can get a substantive answer to (2), it's not going to be an answer to the question of what identity of persons consists in. It's simply going to be an answer as to what interesting necessary and sufficient conditions for identity are in the special case where it is given that the relata are persons.

If we want to know what the identity of persons (or at least finite persons) consists in, the correct answer will not be so informative: what makes person a be identical with person b is that (i) a is a person, (ii) b is a person, and (iii) Iab, where "Iab" is a stand-in for whatever identity in general consists in. I have no idea what "Iab" will say, but I know that it won't say anything about memories, gradual replacement of cells, etc. For, "Iab" is the general account of identity, and that is beyond the details of particular kinds of beings.

This line of thought is attractive, but resistable. One might instead insist that identity is something different in different types of beings. (This may or may not involve the further step of accepting a relative identity theory.) Here, the "types" could be categories—substances, accidents, relations, etc. Or they could be kinds—dogs, persons, photons, electromagnetic fields, etc. I prefer the first option, but what I say applies in both cases. One way to flesh out such views is with a theory of analogy. There is no one thing that identity consists in: there is a relation between a substance and substance, and a relation between an accident and an accident, and so on, and these are all analogous (maybe one of them is focal?). Or if one prefers the second type of "type", one might say: there is a relation between a dog and a dog, and a relation between a person and a person, and so on, and these are all analogous.

On this kind of view, we might well have something substantive to say about what identity between, say, a person and a person consists in, which does not reduce simply to saying: this is a person, and this is a person, and this equals this. I think very naturally such a view will call for a typed logic. (Query to self: In a typed logic of this sort, should there be a quantification over types of quantification?)

I wonder if the argument of my recent AJP paper on diachronic identity is vulnerable to this sort of view. Quite possibly. But I still think the reduction of diachronic to synchronic identity that I perform in that paper is plausible.

Do Aquinas and Scotus disagree on univocal predication of God?

Duns Scotus defines univocal predication as follows: P is univocal provided that Px&~Px is always a contradiction, and hence P can be used in multiple lines of a syllogism. Famously, Aquinas says that no positive term can be univocally predicated of a creature and of God, while Scotus says that some can be univocally predicated, for instance "being". I suggest, however, that the disagreement could be merely verbal, due to the two philosophers using the word "univocal" differently.

For here is a way of developing Aquinas' position. When I attribute wisdom to God and when I attribute wisdom to Socrates, the truth grounds of my attribution are different but related. In the case of God, the truth ground of my attribution is the simple God, who is identical with wisdom. In the case of Socrates, the ground is Socrates' accident of wisdom inhering in Socrates. We have a ground or truthmaker heterogeneity here: the same claim is true for different reasons. If the grounds were completely different, the word "wisdom" would be equivocal. However, the grounds are not different but analogically related, and hence "wisdom" is analogical.

Now, let us plug this into Scotus' definition. "Wisdom" will be univocal in Scotus' sense if and only if it is a contradiction to suppose of x that x is wise and that x is not wise. But on Aquinas' view, as I read him, this is a contradiction. For either x is God or x is not God. If x is God, then "x is wise" and "x is not wise" are claims that are true if and only if, respectively, x is or is not identical with wisdom, and hence x cannot both be wise and non-wise. If x is not God, then "x is wise" and "x is not wise" are claims that are true if and only if, respectively, x has or does not have wisdom, and hence x cannot both be wise and non-wise. In either case, a contradiction ensues from supposing that x is wise and not wise.

The analogy thesis on my reading is about the grounds of the predication. What grounds there must be for the predication to be true differs depending on whether the subject of predication is divine. But this does not allow for a contradiction.

Consider the following predicate H: "if ___ is an animal, then it is a healthy animal, and if it is urine, then it is indicative of health, and if it is food then it is productive of health, and ..." This is meant to be an expansion of Aquinas' and Aristotle's favorite example of an analogical predicate, "is healthy". But now notice that while the grounds of "x is H" differ depending on what x is, nonetheless no x can both satisfy H and not satisfy H. That a horse is healthy and that its urine is healthy tell us different things about the horse and urine, respectively, but in the case of the horse, only one thing is said by attribution of H, and in the case of urine, only one thing is said by attribution of H.

Granted, we might expand the example and allow that there are two senses of "The horse is healthy". In the primary sense, it means that the horse is in good physical condition, while in the secondary sense, it means that if the horse were made into food, that food would be healthy. I am not aware of Aquinas allowing such a case, however. So it is quite possible that Aquinas thinks that in analogical predication, only one kind of ground is allowed for each particular subject of predication. And if so, then the predicate satisfies Scotus' definition of univocity, and can be used as the middle term in a syllogism.

Kind relative predication

It is a broadly Aristotelian doctrine that many predicates apply to individuals in a kind-relative way. Call such predicates k-predicates. (We can stipulatively say that God is the sole member of a kind membership in which is identical with himself, or something like that.) For a k-predicate F, what exactly it is for an x to be F depends on what kind of an entity x is. If it is the same thing for x to be such that Fx as for y to be such that Fy, then kinds of x and y are either the same or have something in common (e.g., a higher genus).

Examples of k-predicates are easy to find. To determine whether a given individual "has legs", we first have to see what counts as legs for an individual of that kind. Thus, Peter has legs in virtue of a particular pair of limbs. Which limbs count as legs? That is defined in part by his human nature, or maybe more generally his nature as a member of Tetrapoda. What it would be for an amoeba to have legs is a different, and more poorly defined, question. What it is for a table is fairly well defined in terms of the nature of the table (we could imagine a table with four upward projecting horns at the corners; the nature of a table being to stand on solid ground on its legs, if it has any, would prevent these from counting as legs).

Whether an entity is n inches tall is even more clearly kind-relative. It depends on which axis counts as the "vertical" axis—remember that the entity might be lying on its side for much of the day.

Another kind of predicate is an r-predicate. An r-predicate is a predicate that can only be had by members of one particular (perhaps higher level) kind. Thus, "is a mammal" is an r-predicate, since it can only be had by mammals. And "is Socrates" is also an r-predicate, since it can only be had by a human.

We can perhaps form complex predicates that are neither k- nor r-predicates. Thus, "is not Socrates" is not an r-predicate (all horses and chairs, and most humans satisfy it) and may not be a k-predicate either. Though on the other hand, it may a k-predicate: maybe for non-humans, it holds in virtue of kind difference, while for humans, it holds in virtue of numerical difference within a kind.

There are also some non-contentful predicates, like "is a substance" or "is self-identical" that are neither k- nor r-predicates.

Thesis: All simple, contentful predicates are either k- or r-predicates.

I don't know if the thesis is true. There seem to be counterexamples. Having a particular shape does not seem to be a k- or r-predicate. Likewise, having a certain mass does not seem to be such, either. I suspect such apparent counterexamples can be overcome—but that may be matter for another post.

Commonality of nature and the Incarnation

St. Athanasius insists that it was crucial for Christ's redemption of us that Christ both share in the divine nature and in the human nature: in the divine nature to unite us with God, and in the human nature in order to unite us with God. The bond of a common nature with us made his redemptive work applicable to us.

The idea that the common human nature is a genuine bond is a fruitful one. (A lot of science-fiction from the middle of the last century takes this bond to be important. Yes, the aliens of the stories are persons, but there is a special bond that human persons share. However, a number of science-fiction writers confused this special bond with some kind of human superiority to the aliens they populated their stories with. But that is mistaken, a mistake which we will avoid if we remember C. S. Lewis's discussion of two kinds of patriotism--the bad kind where one likes one's country because one thinks one's country is better and the good kind where one simply has affection for one's country and its institutions and culture.)

It is, however, tempting after Kant to see what is significant about us as not our humanity which integrally includes both the personal and the animal aspects of our existence, but just the personal aspects. If we see what is significant about us as just personhood, then Athanasius' account of why the Incarnation was needed loses some of its force. For if what is significant about us is personhood, then the second person of the Trinity already had personhood prior to the Incarnation. Admittedly that personhood was not precisely like ours--if St. Thomas is right, we can term the Logos and ourselves "persons" only by analogy. But nonetheless there is an analogy there, and the fleshly nature of the Incarnation becomes less clearly needed.

It is theologically important to hold on to the idea that we are not just persons. We are also animals. We are human beings with all that this entails. That is one reason why accounts that attempt to reconcile evolution with the divine plan by insisting that God only cared about producing persons, and left it to a chance he did not control whether these persons should be mammals or reptiles, biped or quadrapeds, and so on, are theologically mistaken. A part of the significance of the Incarnation is that our concrete enfleshment matters. The kind of persons we are is defined in large part by our flesh, and the kind of flesh we have is defined in large part by its aptness towards personal activity. Ignoring the concrete enfleshment is apt to lead us to philosophical error, such as the error of those who think that there are two co-located beings in front of this computer, one a person and the other an animal, an error that leads to moral mistakes on issues like abortion and euthanasia.

What is this commonality of nature that all of humans have and which St. Athanasius thought so important? Platonists will say it is our common participation in a single thing, the Form of Humanity. Aristotelians will say that it is our possession of numerically distinct essences, which are, nonetheless, qualitatively the same. The Platonic story fits somewhat better with St. Athanasius' account, but both accounts provide an ontological basis for the commonality of nature.

Christ, having reconciled us human beings with God will also re-integrate our nature, bringing the animal and the personal together, when he transforms us in the resurrection, completing his new creation in us. Blessed be his name!

The Word became flesh. Let us bend the knees of our body and of our soul before him as we celebrate with joy this jarring truth.