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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