Per se and per accidens multiplication of causes

Can there be an infinite sequence of efficient causes? Famously, Aquinas says both “No” and “Yes”, and makes a distinction between a per se ordering (“No”) and an accidental ordering (“Yes”). But it is difficult to reconstruct how the distinction goes, and whether there is good reason to maintain given modern physics.

Here is the central passage from Summa Theologiae I.46.2 reply 7, in Freddoso’s translation:

It is impossible to proceed to infinity per se among efficient causes, i.e., it is impossible for causes that are required per se for a given effect to be multiplied to infinity—as, for instance, if a rock were being moved with a stick, and the stick were being moved by a hand, and so on ad infinitum.

By contrast, it is not impossible to proceed to infinity per accidens among agent causes, i.e., it is not impossible if all the causes that are multiplied to infinity belong to a single order (ordinem) of causes and if their multiplication is incidental (per accidens)—as, for instance, if a craftsman were to use many hammers incidentally, because one after another kept breaking. In such a case, it is incidental to any given hammer that it acts after the action of a given one of the other hammers. In the same way, it is incidental to this man, insofar as he generates, that he himself was generated by another. For he generates insofar as he is a man and not insofar as he is the son of some other man, since all the men who generate belong to the same order (gradum) of efficient causality, viz., the order of a particular generating cause. In this sense, it is not impossible for man to be generated by man ad infinitum.

However, it would indeed be impossible for the generation of this man to depend upon that man, and upon an elemental body [a corpore elementari], and upon the sun, and so on ad infinitum.

What’s going on here? Re-reading the text (and double-checking against the Latin) I notice that per se and per accidens are introduced not as modifying the causal relations, but the infinite multiplication of causes. No indication is given initially that the causation functions differently in the two cases. Further, it is striking that both of the examples of per accidens multiplication of causes involve causes of the same type: hammers and humans (Freddoso’s “man” translates homo throughout the text).

To a first approximation, it seems then that what is forbidden is a regress of infinitely many types of causes, whereas a regress of infinitely many tokens is permitted. But that is too simple. After all, if an infinite causal sequence of humans generating humans were possible, it would surely also be possible for each of these humans to be qualitatively different from the others—say, in exact shade of eye color—and hence for there to be infinitely many types among them. In other words, not just any type will do.

Let’s focus in on two other ingredients in the text, the observation that the humans all “belong to the same order of efficient causality”, and the sun–elementary body–human example. Both of these rang a bell to me, because I had recently been writing on the Principle of Proportionate Causality. At Summa Theologiae I.4.2, St Thomas makes a different distinction that distinguishes between the human–human and the sun–body–human cases:

whatever perfection exists in an effect must be found in the effective cause: either in the same formality, if it is a univocal agent—as when man reproduces man; or in a more eminent degree [eminentiori modo], if it is an equivocal agent—thus in the sun is the likeness of whatever is generated by the sun’s power.

Here is a suggestion. In distinguishing per se and per accidens infinite multiplication of causes, Aquinas is indeed distinguishing counting types and tokens. But the types he is counting are what one might call “causal types” or “perfections”. The idea is that we have the same causal type when we have univocal agency, “as when man reproduces man”, and different causal type when we have equivocal agency, as when the sun generates something, since on Aquinas’ astronomical theory the sun is sui generis and hence when the sun generates, the sun is quite different from what it generates. In other words, I am tentatively suggesting that we identify the gradus of efficient causality of I.46.2 with the modus of perfection of I.4.2.

The picture of efficient causation that arises from I.4.2 is that in a finite or infinite causal regress we have two types of moves between effect and cause: a lateral move to a cause with the same perfection as the effect and an ascending vertical move to a cause that has the perfection more eminently.

The lateral moves only accidentally multiply the explanations, because the lateral moves do not really explain the perfection. If I got my humanity from another human, there is a sense in which this is not really an explanation of where my humanity comes from. The human I got my humanity from was just passing that humanity on. I need to move upwards, attributing my humanity to a higher cause. On this reading, Aquinas is claiming that there can only be finitely many upwards moves in a causal regress. Why? Maybe because infinite passing-on of more to less eminent perfections is just as unexplanatory as finite passing on of the same perfection. We need an ultimate origin of the perfections, a highest cause.

I like this approach, but it fits better with the sun–elemenatary body–human example than the hand–stick–rock example. It seems, after all, that in the hand–stick–rock example we have the same relevant perfection in all three items—locomotion, which is passed from hand to stick and then from stick to rock. This would thus seem like a per accidens multiplication rather than a per se one. If so, then it is tempting to say that Aquinas’ hand–stick–rock example is inapt. But perhaps we can say this. Hand-motion is probably meant to be a voluntary human activity. Plausibly, this is different in causal type from stick-motion: going from stick to hand is indeed an explanatory ascent. But it’s harder to see the progression from rock to stick as an explanatory ascent. After all, a rock can move a stick just as much as a stick can move a rock. But perhaps we can still think we have an ascent from rock-moving to stick-moved-by-hand, since a stick-moved-by-hand maybe has more of the perfection of the voluntary hand motion to it? That sounds iffy, but it’s the best I can do.

I wish Aquinas discussed a case of stick–stick–stick, where each stick moves the next? Would he make this be a per se multiplication of causes like the hand–stick–rock case? If so, that’s a count against my reading. Or would he say that it’s an accidental multiplication? If so, then my tentative reading might be right.

It’s also possible that Aquinas’ examples of hand–stick–rock and sun–elementary body–human are in fact more unlike than he noticed, and that it is the latter that is a better example of per se multiplication of causes.

A Thomistic argument for the Principle of Proportional Causality

The Principle of Proportionate Causality (PPC) defended by Aquinas and other scholastics says that a perfection P can only be caused by something that has P either formally or eminently. To have P formally is to have P. Roughly, to have P eminently is to have a perfection greater than P.

(Some add: “has P virtually” to the list of options. But to have P virtually is just to have the power to produce P, and as our student Colin Causey has noted, this trivializes PPC.)

There are obvious apparent counterexamples to PPC:

• Two parents who are bad at mathematics can have a mathematical genius as a child.

• Ugly monkeys typing at random can produce a beautiful poem.

• A robot putting together parts at random can make a stronger and smarter robot.

It’s tempting to throw PPC out. But there are also cases where one feels a pull towards PPC:

• How can things that represent come from non-representing stuff?

• How can the conscious come from the non-conscious?

• How can something with dignity come from something without any?

• How can the active come from the inactive?

• How can an “ought” come from a mere “is”, i.e., something with normativity from something without any?

Many contemporary philosophers think there is no impossibility even in these cases, but I think most will agree that there is something puzzling about these kinds of causation—that we have some sort of an intuition towards PPC in these cases, of a sort we do not have in the cases of the “obvious apparent counterexamples”. What is the difference between the cases?

Well, in the counterexamples, the differences between the cause and the effect are, arguably, a matter of degree. The two parents have a much lower degree of mathematical ability. The monkeys have a certain beauty to them—being productive of beauty is a kind of beauty—albeit perhaps a lesser one than their lucky output. The robot’s output is just a more sophisticated bunch of moving parts than the robot itself.

But in the examples where one feels pulled to PPC, the differences appear to be differences in kind. Indeed, I think we can all agree that the most plausible way to resist the implied claim in the “How can…?” questions that the thing is impossible is to show how to reduce the seemingly more perfect thing to something of the same sort as the alleged cause.

But “differences in kind” doesn’t seem quite sharp enough. After all, pretty much everyone (even, I assume, young earth creationists) will agree that dogs can come from wolves.

I’ve been puzzled by how one might understand and argue for PPC for a long time, without much progress. This morning I had an inspiration from Nicholas Rescher’s article on Aquinas’ “Principle of Epistemic Disparity”, that lesser minds cannot comprehend the ways of greater ones.

Suppose we order the types of good by a comprehensibility relation ≤ where G ≤ H means that it is possible to understand G by understanding H. Then ≤ is a partial preorder, i.e., a reflexive and transitive relation. It generates a strict partial preorder < where G < H provided that G ≤ H but not H ≤ G.

Next, say that good types G₁ and G₂ are cases of the same perfection provided that G₁ ≤ G₂ and G₂ ≤ G₁, i.e., that each can be understood by the other. Basically, we are taking perfections to be equivalence classes of types of good, under the relation ∼ such that G₁ ∼ G₂ if and only if G₁ ≤ G₂ and G₂ ≤ G₁. The relation ≤ extends in a natural way to the perfections: P ≤ Q if and only if whenever G is a case of P and H is a case of Q then G ≤ H. Note that ≤ is a partial order on the perfections. In particular, it is antisymmetric: if we have P ≤ Q and Q ≤ P, then we have P ≠ Q. Write P < Q provided that P ≤ Q and P ≠ Q.

Now on to a Thomistic argument for the PPC.

Being, truth and goodness are transcendentals. The cognitively more impressive perfection Q is thus also axiologically more impressive. Thus:

Axiological Thesis: If P < Q for perfections P and Q, then Q is a better kind of perfection than P.

The following is plausible on the kind of Aristotelian intrinsic notion of causation that Thomas works with:

Causal Thesis: By understanding the cause one understands the effect.

Thomistic ideas about transcendentals also yield:

Understandability Lemma: To understand a thing one only needs to understand the goods instantiated by the thing.

Finally, let’s add this technical assumption:

Conjunction Lemma: The conjunction of co-instantiable goods is a good.

And now on to the PPC. Suppose x causes y to have a good G and y has a type of good G that is a case of a perfection P. By the Causal Thesis, we understand G by understanding x. By the Conjunction Lemma, let H be the conjunction of all the good of x. By the Understandability Lemma, we understand x by understanding H. Thus, G ≤ H. Let Q be the perfection that H is a case of. Then P ≤ Q and x has Q. Then either P = Q or P < Q. In the former case, the cause has P formally. In the latter case, by the Axiological Thesis, the cause has P eminently.

Of course, the Axiological and Causal Theses, together with the Understandability Lemma, all depend on large and controversial parts of Aquinas’ system. But I think we are making some progress.

I am also toying with an interesting concept. Say that a perfection Q is irreducible provided that it cannot be understood by understanding any conjunction of perfections P such that P < Q. It’s not obvious that there are irreducible perfections, but I think it is plausible that there are. If so, one might have a weaker PPC restricted to irreducible perfections. I have yet to think through the pluses and minuses here.

Proportionate causality

Let’s assume for the sake of argument:

Aquinas’ Principle of Proportionate Causality: Anything that causes something to have a perfection F must either have F or some more perfect perfection G.

And let’s think about what follows.

The Compatibility Thesis: If F is a perfection, then F is compatible with every perfection.

Argument: If F is incompatible with a perfection G, then having F rules out having perfection G. And that’s limitive rather than perfect. Perhaps the case where G = F needs to be argued separately. But we can do that. If F is incompatible with F, then F rules out all other perfections as well, and as long as there is more than one perfection (as is plausible) that violates the first part of the argument.

The Entailment Thesis: If F and G are perfections, and G is more perfect than F, then G entails F.

Argument: If F and G are perfections, and it is both possible to have F without having G and to have F while having G, it is better to have both F and G than to have just G. But if it is better to have both F and G than to have just G, then F contributes something good that G does not, and hence we cannot say that G is more perfect than F—rather, in one respect F is more perfect and in another G is more perfect.

From the Entailment Thesis and Aquinas’ Principle of Proportionate Causality, we get:

The Strong Principle of Proportionate Causality: Anything that causes something to have a perfection F must have F.

Interesting.

The pursuit of perfection and the great chain of being

Consider the following two plausible Aristotelian theses:

1. A substance naturally pursues each of its own perfections.

2. Every natural activity of a substance is a perfection of it.

This threatens an infinite regress of pursuits. Reproduction is a perfection of an oak tree. So by 1, the oak naturally pursues reproduction. But by 2, this natural pursuit of reproduction is itself a perfection of the oak. So, by 1, the oak naturally pursues the pursuit of reproduction. And so on, ad infinitum.

So, 1 and 2, though plausible, are problematic. I suggest that we reject 1. Perhaps the oak tree pursues reproduction but does not pursue the pursuit of reproduction. Or perhaps it pursues the pursuit of reproduction, but doesn’t pursue the pursuit of the pursuit of reproduction. How many levels of pursuit are found in the substance is likely to differ from substance to substance: it is one of those things that the substance’s form determines.

We might say that there are more levels of pursuit in a more sophisticated substance. Thus, perhaps, non-living things only have first order pursuits. To use Aristotle’s physics as an example, the stone pursues being in the center of the universe. But the stone does not pursue the pursuit of being in the center of the universe. But in living things, there are multiple levels. The oak tree grows reproductive organs with which it will pursue reproduction, and in growing the organs it pursues the pursuit of reproduction.

Here is an intriguing hypothesis: in human beings, 1 and 2 are both true. Thus there is thus a kind of (potential?) infinity at the heart of our pursuits. For we are capable of forming a mental conception of our perfection as such, which enables us to pursue our perfections as perfections. If an angel offers a dog food, the dog will take it, since it can conceive of food, and thereby become perfected. But even an angel cannot offer a dog perfection as such, since the dog cannot conceive of a perfection as such. However, we can: if an angel says: “If you ask for it, I will make you perfect in some respect or other, without any loss of perfection in any other respect”, that’s a deal we can understand, and it is a deal that is attractive to us, because we pursue perfection as such.

If the above is right, then we have a kind of deep teleological differentiation between three levels of being:

1. Non-living substances pursue first order perfections only.

2. Living substances have at least one meta-level of pursuit: they pursue the pursuit of some or all of their first order perfections.

3. Rational substances have infinitely many meta-levels of pursuit, at least potentially.

Why the Five Ways don't prove the existence of five (or more!) deities

Here is a potential problem for Aquinas’ Five Ways. Each of them proves the existence of a very special being. But do they each prove the existence of the same being?

After giving the Five Ways in Summa Theologica I, Aquinas goes on to argue that the being he proved the existence of has the attributes that are needed for it to be the God of Western monotheism. But the problem now is this: What if the attributes are not all the attributes of the same being? What if, say, the being proved with the Fourth Way is good but not simple, while the being proved with the First Way is simple but not good?

I now think I see how Aquinas avoids the multiplicity problem. He does this by not relying on Ways 3–5 in his arguments for the attributes of God, even when doing so would make the argument much simpler. An excellent example is Question 6, Article 1, “Whether God is good?” Since the conclusion of the Fourth Way is that there is a maximally good being, it would have been trivial for Aquinas to just give a back-reference to the Fourth Way. But instead Thomas gives a compressed but complex argument that “the first effective cause of all things” must be desirable and hence good. In doing so, Aquinas is working not with the Fourth Way, but the Second Way, the argument from efficient causes.

Admittedly, at other times, as in his arguments for simplicity, St. Thomas relies on God not having any potentiality, something that comes directly from the First Way’s prime mover argument.

This reduces the specter of the attributes being scattered between five beings, corresponding to the Five Ways, to a worry about the attributes being scattered between two beings, corresponding to the First and Second Ways. But the First and Second Ways are probably too closely logically connected for the latter to be a serious worry. The First Way shows that there is a being that is first in the order of the actualizing of the potentiality for change, an unchanged changer, a prime mover. The Second Way shows that there is a being that is first in the order of efficient causation. But to actualize the potentiality for change is a form of efficient causation. Thus, the first being in the order of efficient causation will also be a prime mover. So there is a simple—so simple that I don’t recall Aquinas stating it in the Summa Theologica—argument from the conclusion of the Second Way to the same being satisfying the conclusion of the First Way.

Consequently, in the arguments for the attributes of God, Aquinas needs to only work with the conclusion of the Second Way, and all the attributes he establishes, he establishes as present in any being of the sort the Second Way talks about.

That still leaves a multiplicity problem within the scope of a single Way. What if there are multiple first efficient causes (one for earth, one for the moon, and so on, say)? Here Thomas has three solutions: any first being has to be utterly simple, and only one being can be that on metaphysical grounds; any being that is pure actuality has to be perfect, and only one being can be that; and the world has a unity and harmony that requires a unified first cause rather than a plurality of first causes.

Finally, when all the attributes of God have been established, we can—though Aquinas apparently does not, perhaps because he thinks it’s too easy?—come back to Ways Three through Five and ask whether the being established by these ways is that same one God? The ultimate orderers of the world in the Fifth Way are surely to be identified with the first cause of the Second Way once that first cause is shown to be one, perfect, intelligent, and cause of all other than himself. Plausibly, the maximally good being of the Fourth Way has to be perfect, and Aquinas has given us an argument that there is only one perfect being. Finally, the being in the conclusion of the Third Way is also a first cause, and hence all that has been said about the conclusion of the Second Way applies there. So, Aquinas has the resources to solve the multiplicity problem.

All this leaves an interesting question. As I read the text, the Second Way is central, and Aquinas’ subsequent natural theology in the Summa Theologica tries to show that every being that can satisfy the conclusion of the Second Way has the standard attributes of God and there is only one such being. But could Aquinas have started with the Third Way, or the Fourth, or the Fifth, instead of the First and Second, in the arguments for the divine attributes? Would doing so be easier or harder?

Mereological perfection

1. Every part of God is perfect.

2. Only God is perfect.

3. So, every part of God is God.

4. So, God has no proper parts (parts that aren’t himself).

5. So, divine (mereological) simplicity is true.

A problem for Goedelian ontological arguments

Goedelian ontological arguments (e.g., mine) depend on axioms of positivity. Crucially to the argument, these axioms entail that any two positive properties are compatible (i.e., something can have both).

But I now worry whether it is true that any two positive properties are compatible. Let w₀ be our world—where worlds encompass all contingent reality. Then, plausibly, actualizing w₀ is a positive property that God actually has. But now consider another world, w₁, which is no worse than ours. Then actualizing w₁ is a positive property, albeit one that God does not actually have. But it is impossible that a being actualize both w₀ and w₁, since worlds encompass all contingent reality and hence it is impossible for two of them to be actual. (Of course, God can create two or more universes, but then a universe won’t encompass all contingent reality.) Thus, we have two positive properties that are incompatible.

Another example. Let E be the ovum and S₁ the sperm from which Socrates originated. There is another possible world, w₂, at which E and a different sperm, S₂, results in Kassandra, a philosopher every bit as good and virtuous as Socrates. Plausibly, being friends with Socrates is a positive property. And being friends with Kassandra is a positive property. But also plausibly there is no possible world where both Socrates and Kassandra exist, and you can’t be friends with someone who doesn’t exist (we can make that stipulative). So, being friends with Socrates and being friends with Kassandra are incompatible and yet positive.

I am not completely confident of the counterexamples. But if they do work, then the best fix I know for the Goedelian arguments is to restrict the relevant axioms to strongly positive properties, where a property is strongly positive just in case having the property essentially is positive. (One may need some further tweaks.) Essentially actualizing w₀ limits one from being able to actualize anything else, and hence isn’t positive. Likewise, essentially being friends with Socrates limits one to existing only in worlds where Socrates does, and hence isn’t positive. But, alas, the argument becomes more complicated and hence less plausible with the modification.

Another fix might be to restrict attention to positive non-relational properties, but I am less confident that that will work.

From particular perfections to necessary existence

This argument is valid:

1. Necessarily, any morally perfect being can morally perfectly deal with any possible situation.

2. Necessarily, one can only morally deal with a situation one would exist in.

3. So, necessarily, any morally perfect being is a necessary being.

That said, (1) sounds a bit fishy to me. One may want to say instead:

4. Necessarily, any morally perfect being can morally perfectly deal with any possible situation in which it exists.

But that’s actually a bit weaker than we want. Imagine a being that can deal with one situation and only with it: the case where it has promised to eat a delicious cookie that is being offered to it. But imagine, too, that the being can only exist in that one situation. Then (4) is satisfied, but surely being able to fulfill a promise to eat a cookie isn’t enough for moral perfection. So we do actually want to strengthen (4). Maybe there is something in between (1) and (4) that works. Maybe there isn’t.

There are other arguments of the above sort that one can run, based on premises like:

5. A maximally powerful being can weakly actualize any possibility.

6. An epistemically perfect being can know any possible proposition.

7. A rationally perfect being can rationally deal with any possible situation.

It is looking like moral perfection, maximal power, epistemic perfection and rational perfection each individually imply necessary existence.

If this is right, then we have an ontological argument:

8. Possibly, there is a morally perfect or a maximally powerful or an epistemically perfect or a rationally perfect being.

9. So, possibly there is a necessary being. (By arguments like above.)

10. So, there is a necessary being.

I am not saying that this a super-convincing argument. But it does provide some evidence for its conclusion.

More on omniscience

In an earlier post, I argued that the definition of omniscience as knowing every truth and believing nothing but truths is insufficient for omniscience because an omniscient being would also be certain, and knowledge of every truth does not guarantee certainty of every truth.

Here’s another thing that the definition leaves out. Normally, when we say that someone knows or believes p, we are talking about non-occurrent knowledge. We say things like: “Alice knows the atomic number of carbon”, even while Alice is not thinking about carbon. However, I think an omniscient being—one that enjoys the perfection of knowledge—will need to have occurrent knowledge of all truths. Moreover, the omniscient being will need to always be attending to every piece of that knowledge to a maximal degree. (It is not a perfection in us to attend to everything we think maximally, because for us attending to one thing often excludes attending to another. But that’s due to our imperfection.)

Omniscience, omnipotence and perfection

Recently, I’ve been worried about arguments like this:

1. It is always more perfect to be able to do more things.

2. Being able to do impossible things is a way of being able to do more things.

3. So, a perfect being can do impossible things.

But I really don’t want to embrace 3.

It’s just occurred to me, though, that the argument 1-3 is parallel to the clearly silly argument:

4. It is always more perfect to know more things.

5. Knowing falsehoods is a way of knowing more things.

6. So, a perfect being knows falsehoods.

Once we realize that among “more things” there could be falsehoods, it becomes clear that 4 as it stands is false, but needs to be restricted to the truths. But arguably what truths are to knowledge, that possibles are to power (I think this may be a Jon Kvanvig point, actually). So we should restrict 1 to the possibles.

Perfect rationality and omniscience

1. A perfectly rational agent who is not omniscient can find itself in lottery situations, i.e., situations where it is clear that there are many options, exactly one of which can be true, with each option having approximately the same epistemic probability as any other.

2. A perfectly rational agent must believe anything there is overwhelming evidence for.

3. A perfectly rational agent must have consistent beliefs.

4. In lottery situations, there is overwhelming evidence for each of a set of inconsistent claims, namely for the claims that one of options 1,2,3,… is the case, but that option 1 is not the case, that option 2 is not the case, that option 3 is not the case, etc.

5. So, in lottery situations, a perfectly rational agent has inconsistent beliefs. (2,4)

6. So, a perfectly rational agent is never in a lottery situation. (3,5)

7. So, a perfectly rational agent is omniscient. (1,6)

The standard thing people like to say about arguments like this is that they are a reductio of the conjunction of the premises 2 through 4. But I think it might be interesting to take it as a straightforward argument for the conclusion 7. Maybe one cannot separate out procedural epistemic perfection (perfect rationality) from substantive epistemic perfection (omniscience).

That said, I am inclined to deny 3.

It’s worth noting that this yields another variant on an argument against open theism. For even though I am inclined to think that inconsistency in beliefs is not an imperfection of rationality, it is surely an imperfection simpliciter, and hence a perfect being will not have inconsistent beliefs.

Love and happiness

Could perfect happiness consist of perfect love?

Here’s a line of argument that it couldn’t. Constitutively central to love are the desire for the beloved’s good and for union with the beloved. A love is no less perfect when its constitutive desires are unfulfilled. But perfect happiness surely cannot be even partly constituted by unfulfilled desires. If perfect happiness consistent of perfect love, then one could have a perfect happiness constituted at least partly by unfulfilled desires.

When this argument first occurred to me a couple of hours ago, I thought it settled the question. But it doesn’t quite. For there is a special case where a perfect love’s constitutive desires are always fulfilled, namely when the object of the love is necessarily in a perfectly good state, so that the desire for the beloved’s good is necessarily fulfilled, and when the union proper to the love is of such a sort that it exists whenever the love does. Both of these conditions might be thought to be satisfied when the object of love is God. Certainly, a desire for God’s good is always fulfilled. Moreover, although perfect love is compatible with imperfect union in the case of finite objects of love, perfect love of God may itself be a perfect union with God. If so, then our happiness could consist in perfect love for God.

I am not sure the response to the argument works but I am also not sure it doesn’t work. But at least, I think, my initial argument does establish this thesis:

• If perfect happiness consists of perfect love, it consists of perfect love for God.

Of course none of the above poses any difficulty for someone who thinks that perfect happiness consists of fulfilled perfect love.

If only God is perfect, then God has no proper parts

This argument is valid:

1. Only God is perfect.
2. Every part of God is perfect.
3. So, every part of God is identical with God.
4. So, God has no proper parts.

Premise (2) seems obviously true. So, we learn from the argument that if only God is perfect, then God has no proper parts.

Determinism and moral imperfection

If determinism is true, then I always do the best I can do. If I always do the best I can do, I lack moral imperfection. So if determinism is true, I lack moral imperfection. But I am morally imperfect. So determinism is not true.

Ex nihilo nihil

Nothing comes from nothing. Take that as a given. But a mountain's coming from molehill[note 1], while not literally a case of something from nothing, would be just as bad. There is a Polish proverb that even Solomon cannot pour a drink from an empty container. But, likewise, even Solomon cannot pour wine from a container of water (at least without help from something greater than Solomon). The more doesn't come from the less.

What doesn't have something cannot give it.

Now, obviously, this principle needs to be limited. You can get a headache from playing a videogame for too long, but the videogame doesn't have a headache. The principle applies to positive being, to perfections.

So our causes must have all the perfections we have. It is plain, then, that the cause of humanity must have all the perfections of thought and will that humanity has. The First Cause cannot simply be a bunch of energy or matter. This is obviously important for the second part of the Cosmological Argument, the move from a First Cause to God. And of course, this is a very familiar line of thought. It's very forcefully there in Samuel Clarke, and it was already there in the medievals (whom Clarke amusingly criticizes while recapitulating their arguments).

But I don't want to dwell on the consequences of the principle that nothing can give what it doesn't have. Rather, I want to say something about the line of thought, if one may call it that, that leads me to it this morning. There is nothing really new here. The line of thought is one I had been thinking about for years, partly under the influence of Richard Sisca. But suddenly this morning it becomes very plausible. One is told that on big things people aren't convinced by argument, but rather have something like a conversion. But one can also have something like a conversion with regard to an argument. Suddenly it becomes clear that the line of thought is just right, and that the objections to it are mere technicalities. Sometimes one even has the experience of thinking that one knew this all along—or at least that one should have. This is a very interesting experience.

Better than perfect

A necessary and sufficient condition for a student to have perfect performance on a calculus exam is to correctly, perfectly clearly and with perfect elegance answer every question within the time allotted. But what if the student also includes her proof of the Riemann Zeta Conjecture on the last page? Hasn't the student done better than perfect?

Well, the student hasn't done something more perfect. But the student has taken her answers above and beyond the nature of a calculus exam. So, yes, while one cannot be more than perfect, one can go above nature. Perfection is not the same as maximality of value.

Yet another account of omnipotence

The following account of omnipotence runs into the McEar objection:

1. x is omnipotent iff x can do anything whose doing is consistent with the nature of x.

For suppose McEar has the essential property of doing nothing other than scratching his ear, and suppose he can scratch his ear. Then (1) counts McEar as omnipotent. That's no good.

The Pearce-Pruss account of omnipotence escapes this. But so does this minor twist on (1):

2. x is omnipotent iff x can do anything whose doing is consistent with the nature of a perfect being.

There are things consistent with the nature of a perfect being that McEar can't do, say create a pebble.

Perhaps, though, there is a circularity problem. For a perfect being has all perfections. And one of the perfections is omnipotence. However, I do not know that this is fatal. Compare:

3. a fully self-knowledgeable person is one who knows all her mental attributes.

This seems a perfectly reasonable definition, even if one of the mental attributes of such a person is being fully self-knowledgeable.

Asymptotic approach to moral perfection

Consider the following Kantian (nevermind whether it's actually Kant's) reason for believing in eternal life: In a finite amount of time, we cannot achieve moral perfection, but moral perfection is a basic aim of ours, and basic aims of ours are achievable. Actually, it doesn't work. For if moral perfection cannot be achieved in a finite amount of time, then moral perfection cannot be achieved by us, at least not without seriously fooling with the metric structure of time (could one have a temporal structure where an infinite life is followed by a further time of life?) For at any given time, the life we have lived is only finite.

So, perhaps apart from weird metric structures on time, the only way the Kantian argument can work is if our aim not moral perfection, but asymptotic approach to moral perfection. But there are two objections to taking that to be our basic aim. The first is implausibility. "Be perfect!" is, to my mind, a very plausible moral goal. But "Approach perfection asymptotically!" seems much less compeling. Suppose one asks "Why?" In regard to "Be perfect!" the answer is easy: as long as you're imperfect, you are doing something immoral, and you have overwhelming reason not to do that. In regard to "Approach perfection!" one can give the same answer—but this answer supports not "Approach perfection asymptotically!" but "Be perfect!" (And if "Be perfect!" is impossible, then we have a refutation of ought implies can. I myself think "Be perfect!" is achievable with God's grace in this life, though rarely achieved and not required for eventual salvation.)

The second problem with "Approach perfection asymptotically!" is that it seems to be a goal that one can rationally put off to another day—and do so forever, thereby ensuring that one does not approach perfection asymptotically. Here is another way to put this. "Approach perfection asymptotically!" has very little to say about what I should do right now. I should not do anything that would set in me a character that would make asymptotic approach not likely. (It does not even follow from "Approach perfection asymptotically!" that I should at any given time try to maximize the probability of eventual asymptotic approach.)

What if, instead, we make the goal be: "Constantly improve morally!" But that goal is too weak. It is satisfied by the following life. Today, George causes pain to a bunny for one hour. Tomorrow, he does so for 3/4 of an hour. The day after tomorrow, he does this for 4/6 of an hour. The day after that he does this for 5/8 of an hour. The day after that, he does it for 6/10 of an hour. And so on. There is constant moral improvement, but no asymptotic approach. Nor will it help to combine "Approach perfection asymptotically!" with "Constantly improve morally!"

So, if I'm right, the moral perfection goal is "Be perfect!" And not just "Be perfect eventually, some day during an infinite life!" For that could always be put off. (Think of someone who would live an infinite life and whose goal was to do a pilgrimage to the Holy Land at some time or other. That goal could always be put off rationally, while acting compatibly with it.) Rather, the goal has to be "Be perfect in this finite life!" Or maybe even "Be perfect now!"

I should note that the perfection I am talking about here is moral perfection, which is the mere absence of vice, rather than the evangelical perfection that calls for, e.g., celibacy and selling all one's possessions. This evangelical perfection is a supererogatory perfection. Being viceless is not supererogatory.

Perfection and purgatory

Our Department's (unofficial) weekly Bible study is on 1 John. We meet for about 55 minutes every week. The last three weeks, we've been struggling through 1 John 2:28-3:10 (last week we "covered" only two verses). The dilemma is that the text seems to be telling us that if we are children of God, then we do what is right and love our brother, and if we do not do what is right or fail to love our brother, then we are not children of God. This makes it seem that unless we are perfect, we have no hope of salvation. But we are not perfect (or at least, I am not, and none of my colleagues wanted to claim perfection)—and, besides, 1 John begins by warning us against claiming we are perfect.

I am beginning to wonder if this isn't the right place to bring in the notion of purgatory.

Latin trinitarianism and the perfection of love

Oddly enough, some social trinitarians have argued that perfect being theology supports their view (see Dale's discussion). I shall argue that perfect being theology supports Latin trinitarianism very nicely.

Perfection strongly suggests the presence of perfect interpersonal love.[note 1] Therefore, perfection considerations make it plausible that there is more than one divine person exhibiting perfect interpersonal love. Moreover, love has two kinds of perfections.

The first perfection of love is that of generous giving and receiving—this is the perfection of beneficence. There, the perfection is the greater the greater the gift. The gift of divine existence seems the greatest gift possible. So, at least one divine person has an existence that is a gift of the other, and this person receives this existence gratefully. Note that in generous love, there is no need for any quid pro quo and so the love can be made mutual by gratitude. Moreover, it might be stretching our ability to know about perfection with much confidence, but it is at least plausible that for every pair x and y of divine persons, x and y are related by such giving and receiving, so that either y receives divine existence from x or vice versa (but not both at pain of vicious circularity). Interestingly, this condition is only satisfied by Christian Trinitarianism if the Catholic doctrine of the double procession of the Holy Spirit holds (otherwise, there is no such giving and receiving relation between the the Son and the Holy Spirit).

The second perfection of love is the unitive. All love involves a certain minimal union of mind and will (we try to see things from our beloved's point of view, and we are apt to particularly pursue those goods that our beloved particularly wills), and all love is directed at a union that is more than minimal, a union that is a consummation of the love. The perfection of love will be a consummated love, a love that achieves a perfect union. An absolutely perfect union of love will be one where there is the maximum of unity that still allows for the most perfect kind of love. The most perfect kind of love is interpersonal, so the union of love must maintain a distinction of persons. But, it is plausible (assuming this is at all possible), that everything else but the relations distinguishing the persons, will be in common in the perfect union of love.

In particular, the perfect union of love will, plausibly, involve one mind and one will. Not just in the extended sense in which we talk of two human beings being one mind and one will, but in the literal sense of having in common a mind that is numerically one and a will that is numerically one. (Maybe we can even get the divine simplicity claim that the mind will be identical with the will, but I don't want to insist on that at this point.) This one mind and one will is essentially indivisible, for perfect love will seek an indivisible unity.

We thus get numerically one divine ousia, including numerically one mind and numerically one will, and yet more than one person.

Interestingly, while above I took the route of perfection of union, the route of perfection of generosity can also be used here. Generosity can be perfected in at least two ways. One is with the value of the gift—a better gift is one that perfects generosity more. The other is with the intimacy of the gift-giving—with how close the gift is to the giver. Thus to give money is ceteris paribus less generous than to give an heirloom, and to give an heirloom is ceteris paribus less generous than to give a kidney. The most perfect gift will be one that is both of maximum value and of maximum intimacy on the part of the giver. The divine nature is of maximum value. There are now prima facie two ways for perfect generosity to be exhibited. One way is for the divine giver to make another God, another person with another, qualitatively identical, divine mind and will (or ousia). But this does not exhibit perfect intimacy in the generosity. That intimacy will be perfectly exhibited when the divine mind and will given are the very same divine mind and will that the giver has, when the very same life that the giver has is given to the receiver.

And it is only in a perfectly intimate generosity that reciprocation by gratitude is perfected. For the closer the gift to the heart of the giver, the more the recipient's generosity means to the giver, and when the gift is the giver's own mind and will, the giver's own life to be shared, the generosity can be a deep affirmation of the giver, and indeed is a recognition that one prefers to have one's life as gift than to have it on one's own, and that recognition is a willingness to share that is in principle generous. It is, indeed, a kind of giving back.

Objection: Social trinitarians claim to believe in the unity of God and hence will claim that their doctrine of the Trinity is compatible with everything I said above.

Response: If social trinitarianism is to be distinct as a doctrine from Latin trinitarianism, it, I think, has to claim that Latin trinitarianism posits too much unity in God. But if this claim is made, then the above argument works—for the above account posits the maximum of unity in God apart from the distinction of persons, which is precisely what Latin trinitarianism gives. Of course, if social trinitarianism (which, in general, is kind of hard to define) turns out to be compatible with Latin trinitarianism, then there might be no disagreement here at all.