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.

Wishful thinking

Start with this observation:

1. Commonly used forms of fallacious reasoning are typically distortions of good forms of reasoning.

For instance, affirming the consequent is a distortion of the probabilistic fact that if we are sure that if p then q, then learning q is some evidence for p (unless q already had probability 1 or p had probability 0 or 1). The ad hominem fallacy of appeal to irrelevant features in an arguer is a distortion of a reasonable questioning of a person’s reliability on the basis of relevant features. Begging the question is, I suspect, a distortion of an appeal to the obviousness of the conclusion: “Murder is wrong. Look: it’s clear that it is!”

Now:

2. Wishful thinking is a commonly used form of fallacious reasoning.

3. So, wishful thinking is probably a distortion of a good form of reasoning.

I suppose one could think that wishful thinking is one of the exceptions to rule (1). But to be honest, I am far from sure there are any exceptions to rule (1), despite my cautious use of “typically”. And we should avoid positing exceptions to generally correct rules unless we have to.

So, if wishful thinking is a distortion of a good form of reasoning, what is that good form of reasoning?

My best answer is that wishful thinking is a distortion of correct probabilistic reasoning on the basis of the true claim that:

4. Typically, things go right.

The distortion consists in the fact that in the fallacy of wishful thinking one is reasoning poorly, likely because one is doing one or more of the following:

1. confusing things going as one wishes them to go with things going right,

2. ignoring defeaters to the particular case, or

3. overestimating the typicality mentioned in (4).

Suppose I am right about (4) being true. Then the truth of (4) calls out for an explanation. I know of four potential explanations of (4):

1. Theism: God creates a good world.

2. Optimalism: everything is for the best.

3. Aristotelianism: rightness is a matter of lining up with the telos, and causal powers normally succeed at getting at what they are aiming at.

4. Statisticalism: norms are defined by what is typically the case.

I think (iv) is untenable, so that leaves (i)-(iii).

Now, optimalism gives strong evidence for theism. First, theism would provide an excellent explanation for optimalism (Leibniz). Second, if optimalism is true, then there is a God, because that’s for the best (Rescher).

Aristotelianism also provides evidence for theism, because it is difficult to explain naturalistically where teleology comes from.

So, thinking through the fallacy of wishful thinking provides some evidence for theism.

Optimalism about necessity

There are many set-theoretic claims that are undecidable from the basic axioms of set theory. Plausibly, the truths of set theory hold of necessity. But it seems to be arbitrary which undecidable set-theoretic claims are true. And if we say that the claims are contingent, then it will be arbitrary which claims are contingent. We don’t want there to be any of the “arbitrary” in the realm of necessity. Or so I say. But can we find a working theory of necessity that eliminates the arbitrary?

Here are two that have a hope. The first is a variant on Leslie-Rescher optimalism. While Leslie and Rescher think that the best (narrowly logically) scenario must obtain, and hence endorse an optimalism about truth, we could instead affirm an optimalism about necessity:

1. Among the collections of propositions, that collection of propositions that would make for the best collection of all the necessary truths is in fact the collection of all the necessary truths.

And just as it arguably follows from Leslie-Rescher optimalism that there is a God, since it is best that there be one, it arguably follows from this optimalism about necessity that there necessarily is a God, since it is best that there necessarily be a God. (By the way, when I once talked with Rescher about free will, he speculatively offered me something that might be close to optimalism about necessity.)

Would that solve the problem? Maybe: maybe the best possible—both practically and aesthetically—set theory is the one that holds of necessary truth.

I am not proposing this theory as a theory of what necessity is, but only of what is in fact necessary. Though, I suppose, one could take the theory to be a theory of what necessity is, too.

Alternately, we could have an optimalist theory about necessity that is theistic from the beginning:

2. A maximally great being is the ground of all necessity.

And among the great-making properties of a maximally great being there are properties like “grounding a beautiful set theory”.

I suspect that (1) and (2) are equivalent.

Nicholas Rescher

Nicholas Rescher was just awarded the Aquinas Medal of the American Catholic Philosophical Association. Here is the introduction I gave for him on this occasion.

Introduction of Nicholas Rescher for the Aquinas Medal

It is my great honor to introduce Professor Nicholas Rescher to receive the highest honor of this Association, the Aquinas Medal. Professor Rescher is University Professor of Philosophy at the University of Pittsburgh. He has been the President of both the American Catholic Philosophical Association as well as of the American Philosophical Association. He is an honorary member of Corpus Christi College, Oxford, and is an elected member of the European Academy of Arts and Sciences, the Royal Society of Canada and the Institut International de Philosophie, and the recipient of eight honorary doctorates.

Nicholas Rescher was born in Germany in 1928, and in 1938 his family emigrated to the United States, after his father’s law practice was ruined by his opposition to Nazis. He did his undergraduate studies at Queens College in Flushing, right after the Second World War, graduating at the age of 21. He immediately enrolled as a graduate student at Princeton, where he completed the first draft of his doctoral dissertation on Leibniz—on whom he had not taken any classes—by spring of the same academic year, and got his Ph.D. a year later, in 1951, at the age of 22. For a year he held an instructorship at Princeton.

Then the Korean War interrupted his academic career. Von Neumann’s attempts to ensure his talents be better utilized by the military notwithstanding, Dr. Rescher was drafted into the Marine Corps. Fortunately, he was able to get work with the Marine Corps Institute’s correspondence education program, among other things grading calculus exams. Next, from 1954 to 1956, Dr. Rescher worked for the RAND Corporation in Santa Monica, and notably was a co-inventor of the Delphi Method of forecasting.

In 1957, at age 28, Dr. Rescher resumed his university career, first teaching at Lehigh University, and then, starting in 1961, at the University of Pittsburgh, which had just begun its legendary project of creating a top philosophy Department, having just hired Adolf Gruenbaum, with Dr. Rescher’s hiring being followed by those of Kurt and Annette Baier, Nuel Belnap and Wilfrid Sellars. Professor Rescher has remained on the faculty of the University of Pittsburgh to this day, though starting in the 1970s, he also began visiting Oxford in the summers.

Professor Rescher’s prodigious academic output is legendary. Indeed, a colleague offered me the following argument to prove that Rescher wrote an infinite number of books: However many of his books you have read, there are some you haven’t.

Actually, the number is finite, though the mistake is easily excused. Between 1955 and 2006, Professor Rescher has published approximately 110 books and over 350 articles, averaging to about 2.3 books and 6.7 articles per year.

Like Leibniz, Rescher believes that we live in the best of all possible worlds. Best in what way, we may ask? Through the optimal balance between diversity and unity. And Professor Rescher’s scholarly work is a microcosm of the world in this regard, unique in contemporary philosophy in regard to both aspects individually and in combination.

First, diversity. Professor Rescher has written books in epistemology, metaphysics, pragmatism, process philosophy, philosophy of science and technology, ethics, social philosophy, logic and metaphilosophy. In the history of philosophy he has published books on figures including Galen, Alexander of Aphrodisias, al Kindi, al Farabi, Leibniz, Kant, Pascal and Peirce.

But what is most noteworthy is not quantity and diversity by itself, but the deep unity underlying the work. The thread joining all of it is an pragmatic world view that places our human concerns at the forefront. However this pragmatism is not technological in nature. For our human concerns are not just to survive, but to live deeply: to know, to feel, to act. The more we know, the more questions we can ask, and so the human task is in principle one that cannot be brought to completion. Nor is the pragmatism dogmatic, but methodological and at one remove from first order epistemic considerations. Truth is not defined by pragmatic concerns, nor do we simply assume something to be true because it is useful to do so, but pragmatic concerns guide our choice of epistemic practices—we engage in those practices of inquiry that in fact are useful for prediction and control.[1] What Rescher has produced is a grand philosophical system, pragmatic in nature, and comprehensive in outlook, like that of his great hero and the subject of a significant portion of his scholarship, Leibniz.

But unlike in Leibniz’s approach, a down-to-earth, humble, bottom-up approach keeps Professor Rescher from invoking God in his philosophical work when this can be avoided. Ultimately, however, Professor Rescher was drawn, in his words, toward the community of the world’s “theistically committed Platos and Plotinuses, its Anselms and Aquinases, its Leibnizes and Hegels [—] those who saw humanity as subject to transcendent aspirations and obligations—and for whom forms of worship and religious styles of thought really mattered.”[2] And so he is not only the most catholic with a lowercase ‘c’ in his interests among his philosophical contemporaries, but he is a Catholic with a capital ‘C’, a man radiating a serenity tied to a loving and diligent search for truth in communion with others, both his contemporaries and the Aquinases and Leibnizes of the past.

His catholicity makes it possible for students and colleagues to discuss anything whatsoever with him. He combines personal warmth with an old-fashioned courtesy that comes naturally to him, both offering and automatically inviting respect. It would not occur to us as graduate students to call him anything but a formal “Dr. or Professor Rescher”. But then, after a successful doctoral defense, we would be told—and here I quote the last line of an email from him which I will always treasure—“P.S. At this point, do please call me Nick.”

I would like to end with a quote from the last section of Nick’s 2002 autobiography, and express my wish and prayer for the continued truth of it in his case:

The ennui of the accustomed explains not only why elderly people like to travel, but also why they incline to live vicariously in the doing of the young. However, this is far less of a problem with someone whose life is dedicated to learning, for there lies before one an endless horizon of more things to learn about. To be sure, it might seem that, very abstractly considered, learning and thinking themselves are "more of the same." But that is altogether false because, concretely considered, the idea at issue is always something new, something fresh.

I give you Nick Rescher, Aquinas Medalist, who will give us something new, something fresh. [1] Rationality in Pragmatic Perspective, pp. 21-22. [2] “In Matters of Religion”, p. 132.

The scholarly life: Two views

The pessimist:

I HAVE, alas! Philosophy,
Medicine, Jurisprudence too,
And to my cost Theology,
With ardent labour, studied through.
And here I stand, with all my lore,
Poor fool, no wiser than before.
Magister, doctor styled, indeed,
Already these ten years I lead,
Up, down, across, and to and fro,
My pupils by the nose,--and learn,
That we in truth can nothing know!
That in my heart like fire doth burn.
'Tis true I've more cunning than all your dull tribe,
Magister and doctor, priest, parson, and scribe;
Scruple or doubt comes not to enthrall me,
Neither can devil nor hell now appal me--
Hence also my heart must all pleasure forego! (Goethe, Faust, Part I)

The optimist:

The ennui of the accustomed explains not only why elderly people like to travel, but also why they incline to live vicariously in the doing of the young. However, this is far less of a problem with someone whose life is dedicated to learning, for there lies before one an endless horizon of more things to learn about. To be sure, it might seem that, very abstractly considered, learning and thinking themselves are "more of the same." But that is altogether false because, concretely considered, the idea at issue is always something new, something fresh." (Nicholas Rescher at age 73, Enlightening Journey, p. 266)

One should also, I think, supplement the quote with Rescher's idea that as one learns more, the knowledge makes possible new questions, and so the quest for knowledge is, in principle, without end for finite knowers.

I think Rescher gets right what Faust gets wrong. It may be true that the more one knows, the more one realizes what a small fraction of the questions there are one knows the answer to. But that is not reason for despair--for one can, after all, know more and more, both more facts and more questions.

I sometimes have suffered from a fear of the ennui of eternity in heaven. I realize that this is an irrational fear--the vision of God, our infinite lover and beloved, can unchangingly satisfy us forever. But it does seem plausible that growth, progress and change are important aspects of human nature (that's one reason I don't like the account of heavenly life as timeless--another reason is the apparent nonsensicality of saying "after this temporal life, there will be a timeless existence"). I was thinking about these ideas from Rescher yesterday, and I think they did much to take away the fear of the ennui of eternity. Here's the argument: I can see the life of ever increasing inquiry, truth leading to questions leading to truth, synoptic view leading to new questions leading to a wider synthesis, as a life worth engaging in for eternity. But what God has prepared for us, which eye has not seen and ear has not heard, either includes that or--quite likely--includes something even more satisfying. So the idea that eternity would produce ennui is mistaken--at least if one loves truth.