Wittgensteinian Magisteria

13 September 2011


One of the most memorable and enduring aspects of Wittgenstein’s later work is his conception of family resemblance. Wittgenstein in his Philosophical Investigations formulates an essentially anti-essentialist position, and his account of family resemblances is an attempt to state how things resemble each other without sharing some single “essence.” He wanted to get away from the idea there there must be something in common, and to this end he urged his readers to look for themselves and see if there is anything in common — say, for example, among all games.

I have been thinking about family resemblances in Wittgenstein because I mention the idea in passing in my paper, The Moral Imperative of Human Spaceflight, which I am to present at the upcoming 100 Year Starship Symposium. (I hope you’ll show up to be in my cheering section.)

Wittgenstein described family resemblances as, “…a complicated net of similarities which overlap and intersect.” This translation is due to Walter Kaufmann (Critique of Religion and Philosophy, Princeton: Princeton University Press, 1978, p. 55), which is a rather more felicitous rendering than the familiar Anscombe translation: “a complicated network of similarities overlapping and criss-crossing,” (Ludwig Wittgenstein, Philosophical Investigations, The German Text, with a Revised English Translation, Third Edition, Malden, Oxford, and Victoria: Blackwell Publishing, 2003, section 66, p. 27e).

When I was thinking about this use of “overlapping” (“übergreifen” in the original German) I happened to watch a video by Richard Dawkins, and I thought about Dawkins’ criticism of Gould’s exposition of “non-overlapping magisteria” or NOMA for short. S. J. Gould wrote an essay on the topic which is fairly well know. Here are a few quotes taken from it:

“…each subject has a legitimate magisterium, or domain of teaching authority—and these magisteria do not overlap (the principle that I would like to designate as NOMA, or ‘nonoverlapping magisteria’).”

“The net of science covers the empirical universe: what is it made of (fact) and why does it work this way (theory). The net of religion extends over questions of moral meaning and value. These two magisteria do not overlap, nor do they encompass all inquiry (consider, for starters, the magisterium of art and the meaning of beauty). To cite the arch cliches, we get the age of rocks, and religion retains the rock of ages; we study how the heavens go, and they determine how to go to heaven.”

“This resolution might remain all neat and clean if the nonoverlapping magisteria (NOMA) of science and religion were separated by an extensive no man’s land. But, in fact, the two magisteria bump right up against each other, interdigitating in wondrously complex ways along their joint border. Many of our deepest questions call upon aspects of both for different parts of a full answer—and the sorting of legitimate domains can become quite complex and difficult. To cite just two broad questions involving both evolutionary facts and moral arguments: Since evolution made us the only earthly creatures with advanced consciousness, what responsibilities are so entailed for our relations with other species? What do our genealogical ties with other organisms imply about the meaning of human life?”

“I believe, with all my heart, in a respectful, even loving concordat between our magisteria—the NOMA solution. NOMA represents a principled position on moral and intellectua] grounds, not a mere diplomatic stance. NOMA also cuts both ways. If religion can no longer dictate the nature of factual conclusions properly under the magisterium of science, then scientists cannot claim higher insight into moral truth from any superior knowledge of the world’s empirical constitution. This mutual humility has important practical consequences in a world of such diverse passions.”

Stephen Jay Gould, “Nonoverlapping Magisteria,” Natural History 106 (March 1997): 16-22; Reprinted here with permission from Leonardo’s Mountain of Clams and the Diet of Worms, New York: Harmony Books, 1998, pp. 269-283.

Dawkins will have none of this. He devotes a section of Chapter 2 of The God delusion to criticizing the very idea of NOMA. Here is a typically Dawkinsian passage:

“The very idea is a joke. You can bet your boots that the scientific evidence, if any were to turn up, would be seized upon and trumpeted to the skies. NOMA is popular only because there is no
evidence to favour the God Hypothesis. The moment there was the smallest suggestion of any evidence in favour of religious belief,
religious apologists would lose no time in throwing NOMA out of the window. Sophisticated theologians aside (and even they are
happy to tell miracle stories to the unsophisticated in order to swell congregations), I suspect that alleged miracles provide the
strongest reason many believers have for their faith; and miracles, by definition, violate the principles of science.”

Richard Dawkins, The God Delusion, Chapter 2

Dawkins goes on for several pages in this vein, but the only reason I cite Dawkins here is that he represents the antithesis of the NOMA position outlined by Gould. What interests me in this debate between Gould and Dawkins is that the NOMA and anti-NOMA positions do not exhaustively divide the field of opinion.

In fact, however heretical to the orthodox, I think that one of the most prevalent views held today in industrialized Western nation-states is the antithesis of both Gould and Dawkins. I propose to call this position COMA, which should be understood to stand for COinciding MAgisteria.

It is difficult for me to give a good formulation of COMA, partly because the idea, while ancient, is new to me, and it is not my own position. So I have no definitive formulation. I will rely upon my reader’s sympathy and indulgence to provide what I leave out in my account of COMA.

COMA is simply this: that religion and science are simply alternative formulations of one and the same truth. The dogmatically religious insist upon putting everything in religious terms and denying the contributions of science, while the dogmatically scientific insist upon putting everything in scientific terms and denying the contributions of religion, but ultimately there is only one truth of the world, which is studied from the varying perspectives of science and religion (inter alia).

I have had many people say things like this to me personally. While I can’t cite any locus classicus, but I’m sure that someone, somewhere, has written down this obvious point of view.

I will go further, however, and state that even among NOMA, anti-NOMA, COMA, and whatever anti-COMA might be, that these positions still do not exhaust the field of opinion. What lies beyond NOMA and COMA? Wittgenstein.

Wittgenstein’s conception of family resemblances takes another step with possible magisteria, which is that step beyond either wholly overlapping (as with COMA) or being mutually exclusive (as with NOMA), such that that magisteria may intersect (which Anscombe translates as “criss-cross”). I’m sure you get the idea. Gould and Dawkins, NOMA and SOMA, present regions of thought as spatial areas (much as Frege does in his exposition of tertium non datur in the Foundations of Arithmetic). Well, concepts as we usually find them in the real world only present these kind of ideal boundaries in the abstract. In actual fact, the boundaries of a given concept interpenetrate related concepts, often to the point that it is difficult to distinguish them. This, I think — family resemblances that overlap and intersect — is the proper way to understand the relationship between religious and scientific concepts.

Though I will, again, go one step further. I mention in my “The Moral Imperative of Human Spaceflight” paper that Wittgenstein has left an item off the relationships of family resemblance: conflict. The individual variation that both lies at the basis of natural selection and which gives each of us our unique features, is that element of conflict in family resemblance, which is never total or absolute.

Despite all the talk about so-called “militant atheists” like Dawkins (and Dennett, and others), it has in fact become quite trendy to downplay the conflict between science and religion. I listened to a set of lectures from The Teaching Company, Science and Religion — a pure exemplification of the spirit of revisionist history — in which the lecturer, Professor Lawrence M. Principe, Ph.D., ridicules what he calls the “The Warfare Thesis” and attempts to show that, because many eminent scientists were in fact deeply pious and religious, there really hasn’t been any conflict between science and religion. While I enjoyed the lectures, I didn’t agree with them, and this was one of those clear-cut cases in which historical revisionism seems to be carried to its own self-fulfilling prophecy.

But this is merely an aside in the point I wish to make today, and that point is that NOMA is really not all that common a view, that COMA is probably more prevalent, but that neither NOMA or COMA sufficiently capture the relations between science and religion, which might better be described in terms of Wittgensteinian family resemblances. Not that science and religion resemble each other, but that their relations are like the relations that hold between things that do resemble each other. This is an obviously imperfect exposition. Perhaps with time I can frame my point with greater clarity.

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The Doors of Intellection

23 February 2009

“If the doors of perception were cleansed every thing would appear to man as it is, infinite. For man has closed himself up, till he sees all things through narrow chinks of his cavern.”

William Blake, The Marriage of Heaven and Hell

William Blake, The Marriage of Heaven and Hell, Plate 14

William Blake, The Marriage of Heaven and Hell, Plate 14

William Blake is the source of the famous phrase “the doors of perception” — it is from his wonderfully Faustian The Marriage of Heaven and Hell — though most readers will connect the phrase to the novel by Huxley. Huxley, of course, took his title from Blake. Since in yesterday’s Algorithms of Ecstasy I mentioned religious experiences induced, at least in part, by chemical means, it is appropriate to mention in this connection Huxley’s drug-addled visions of “Love as the primary and fundamental cosmic fact” (in a letter to Humphry Osmond). Huxley represents a dead end in the scientific pursuit of the absolute; Huxley represents science that has lost its objectivity and has ceased to operate according to methodological naturalism, and therefore ceased to be science.

What Blake has observed about the doors of perception holds good also for the doors of intellection: if the doors of intellection were cleansed every thing would appear to man as it is, infinite. For man has closed himself up, till he understands all things through narrow chinks of his cavern.

I have just finished listening to Richard Dawkins’ The God Delusion on CD. From a philosophical perspective, the book is highly problematic, but Dawkins is quite explicitly coming from a scientific perspective, and he knows it. He often has difficulty concealing his contempt for philosophical argumentation, and this makes the book problematic as he takes on many paradigmatically philosophical questions and does so from a scientific standpoint. Thus much of the book is at cross purposes with its intended subject matter.


I mention Dawkins not to criticize him, however — many others have already done so, and I genuinely enjoyed the book — but to take up some of the themes with which he closes. The book has a fine peroration, and I was pleased with this as many authors on such subjects don’t bother to craft a good closing so that the book just lurches to a halt without any sense of climax and resolution. Dawkins delivers nicely on this score.

In the last few pages Dawkins introduces a number of notions, among them the Middle World and the motif of our sense perception being like the slit of light admitted by a burka. The Middle World is the familiar world of things not too large (like the objects of cosmology), not too small (like the objects of quantum mechanics), and not too fast (like objects approaching the speed of light), so that they obey the familiar laws that seem to hold for the greater part of things of our experience. dawkins_spine

The final sentences of Dawkins’ book thus proclaim, “Could we, by training and practice, tear off our black burka, and achieve some kind of intuitive — as well as just mathematical — understanding of the very small, the very large, and the very fast? I genuinely don’t know the answer, but I am thrilled to be alive at a time when humanity is pushing against the limits of understanding. Even better, we may eventually discover that there are no limits.”

Dawkins is here suggesting the equivalent for physical science of opening the doors of intellection, as well as the doors of perception. Prior to this passage the motif of the burka is used to emphasize the narrow range of phenomena to which our senses give us access, and he rightly generalizes to the possibility of understanding that similarly throws off the limits imposed by the anthropocentric origins of our ideas about the world.

However, there are limits. We already know this, and we can prove it. Dawkins’ mention of “just mathematical” in this passage — as though to say “mere mathematical” — provides a clue as to the false hopefulness of this otherwise inspiring conclusion. There is a highly developed branch of mathematical logic that deals explicitly and systematically with what are called the “limitative theorems”, i.e., theorems of formal logic that demonstrate the logical limits of our thinking.  The formal treatment of these limits is daunting, but it has been well-put (intuitively so, no less) by Wittgenstein: “The limits of my language mean the limits of my world.” (Tractatus Logico-Philosophicus, 5.6)

The limitative theorems are especially interesting in relation to Dawkins’ book given an amusing formulation given to the most famous of the limitative theorems, viz. Gödel’s incompleteness theorems:

“Suppose we loosely define a religion as any discipline whose foundations rest on an element of faith, irrespective of any element of reason which may be present. Quantum mechanics for example would be a religion under this definition. But mathematics would hold the unique position of being the only branch of theology possessing a rigorous demonstration of the fact that it should be so classified.”

F. De Sua, “Consistency and completeness — a résumé” American Mathematical Monthly, 63 (1956)

The kind of intuitive mastery of concepts that originate in mathematics and advanced recent work in the physical sciences is difficult, but we have ample evidence that it is achievable. The concept of zero was once advanced mathematics; today it is elementary, and most people experience little difficulty in mastering the concept. The truth table method for semantic decision procedures was advanced logic when Wittgenstein wrote his Tractatus; now it is familiar fare for elementary logic textbooks.

We create intuitions through the labor of the mind, and once an adequate intuition is obtained we can let the labor fall away as though it had never existed, like the scaffolding that held Michelangelo up to the underside of the ceiling of the Sistine Chapel. That is to say, it is possible to transcend the process by which we arrive at our ideas — the ontogeny of cognition, as it were — and to grasp the idea beyond its own history. When we do this in the social context of the idea (as with the examples above of the concept of zero and the truth table method) we even transcend the phylogeny of cognition. To invoke Wittgenstein again: .

My propositions are elucidatory in this way: he who understands me finally recognizes them as senseless, when he has climbed out through them, on them, over them. (He must so to speak throw away the ladder, after he has climbed up on it.)

Wittgenstein, Tractatus Logico-Philosophicus, 6.54

This motif of throwing away the ladder after climbing up it has become widely quoted in philosophical literature. Wittgenstein gives the paradoxical tension between intuitive concept and formal surrogate in its strongest form. Even when the tension does not appear in this radically paradoxical form, it is still present, informing our conceptions of logic, mathematics, and science. Sometimes the intuitive conception comes first, and we struggle to formalize it; sometimes the formal concept comes first, and we struggle to find an intuition adequate to it. In either case, it is a philosophical labor of no mean order (and one rarely appreciated for what it is).

This notion was also given a surprising and equally paradoxical (i.e., counter-intuitive) formulation by Alfred North Whitehead:

“It is a profoundly erroneous truism, repeated by all copy-books and by eminent people when they are making speeches, that we should cultivate the habit of thinking of what we are doing. The precise opposite is the case. Civilization advances by extending the number of operations which we can perform without thinking about them. Operations of thought are like cavalry charges in a battle — they are strictly limited in number, they require fresh horses, and must only be made at decisive moments.”

Alfred North Whitehead, An Introduction to Mathematics, Chapter 5

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