Friday


Last August I wrote about the possibly apocryphal quote from Paul Valéry: to see is to forget the name of the thing one sees. I mentioned then that I am fascinated by this quote and often return to it. I found myself thinking about it again recently and find that I have more to say on it. A good aphorism is pregnant with meaning and can always be the point of departure for another meditation, as a text of scripture can always be the point of departure for another sermon.

To see is to forget the name of the thing one sees. What is meant by “seeing” in this context?

Seeing — true seeing, genuine seeing — is seeing that transcends the ordinary experience of seeing. The ordinary experience of seeing gets lost in conventions. People scarcely notice the things around them. As soon as a thing is seen, it is immediately assigned to some familiar category and no more attention is paid to. In this way, seeing becomes an exercise in identification, and identification draws upon a familiar conceptual scheme, a Weltanschauung in which there is a place for everything and everything is to be found in its place. Such “seeing” is little more than an excuse to dismiss things with a glance, to ignore the world.

To see is to forget the name of the thing one sees. This encapsulation of an extraordinary kind of seeing immediately suggests another kind of seeing, the kind of seeing that is ordinary seeing. What is ordinary experience? What defines the mundane? There is a passage from a posthumously published fragment of Wittgenstein that comes to mind:

“Nothing could be more remarkable than seeing a man who thinks he is unobserved performing some quite simple everyday activity. Let us imagine a theatre; the curtain goes up and we see a man alone in a room, walking up and down, lighting a cigarette, sitting down, etc. so that suddenly we are observing a human being from outside in a way that ordinarily we can never observe ourselves; it would be like watching a chapter of biography with our own eyes, — surely this would be uncanny and wonderful at the same time. We should be observing something more wonderful than anything a playwright could arrange to be acted or spoken on the stage: life itself. — But then we do see this every day without its making the slightest impression on us! True enough, but we do not see it from that point of view.”

Ludwig Wittgenstein, Culture and Value, p. 4e

Wittgenstein here observes an unexpected coincidence of ordinary and extraordinary experience. For Wittgenstein, extraordinary seeing is simply a shift in perspective away from ordinary seeing. And ordinary seeing is not an excuse to ignore the world, as I wrote above, but is an immersion in the world. The Wittgensteinian conception of extraordinary experience is immanent; Wittgenstein rejects the transcendent as a source of the extraordinary.

I can imagine someone not getting the point of Wittgenstein’s example; it is more in the nature of a parable than an argument. And like most parables, it is inherently ambiguous. Wittgenstein was, after all, from Vienna: a crucible of modernity in which thoroughly modern ideas were no sooner given their initial formulation than they were dialectically confronted with their opposite number. As I have noted elsewhere, reflexivity is of the essence of modernity.

Should we seek the extraordinary variety of seeing invoked in the possibly apocryphal Valéry quote in ordinary experience? Is there a dialectic of ordinary and the extraordinary experience that would reveal seeing as the seeing the forgets itself as seeing? For Wittgenstein, it is a change of one’s point of view that renders the ordinary extraordinary. Presumably, also, there is a change in point of view that would render the extraordinary ordinary.

Is there a changed point of view that would give us extraordinary experience from our ordinary experience? Can we find an unexpected coincidence of the two through a shift in perspective? Can a change within oneself make one see as one has not seen before? What is true seeing, genuine seeing? Vision. Thus the seeing with which the quote is concerned is visionary seeing. How does one attain a vision?

The ordinary might converge upon the extraordinary through repetition. Repetitive rituals — essentially, iterations of ordinary experience — have long been employed to induce altered states of consciousness, that is to say, extraordinary experience. I wrote about this in Algorithms of Ecstasy.

But Valéry would not likely have been sympathetic to this. In his famous essay, “Man and the Sea Shell,” Valéry wrote, “…it is the nature of the intelligence to do away with the infinite and to abolish repetitions.” It is perhaps unreasonable to take this line from Valéry out of context, for it is a line that means something in its context. But it is not entirely unreasonable. Elsewhere Valéry makes explicit criticisms of Cantorianism and the Cantorian conception of the infinite, and the simplest way to the infinite is the endless iteration of anything.

There is also, in Valéry, an implicit criticism of the extraordinary, and this criticism could well be of a piece with his rejection of Cantor. If the quote that concerns us is indeed from Valéry, it is not a paean to outlandishness for the sake of outlandishness. For Valéry, Cantor is too outlandish. For Valéry, even extraordinary vision would be ordinary in a sense, finite to be sure, not the excrescence of an altered state of mind. And thus we find ourselves back at the coincidence and convertibility of ordinary and extraordinary experience, of mundane seeing and visionary seeing.

In the difference between the approaches to the extraordinary by way of the transcendent or the immanent, Valéry and Wittgenstein represent the immanent. Cantor perhaps represents the transcendent, though he had little to say regarding experience, whether ordinary or extraordinary. But perhaps a theory of extraordinary experience, hence visionary seeing, might be derived from Cantor, and, once derived, placed in transcendental contrast to the immanence of Valéry and Wittgenstein.

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A Formulation of Naturalism

16 November 2009

Monday


Hallett Cantorian Set Theory

One of my favorite books on set theory is Michael Hallett’s Cantorian Set Theory and Limitation of Size. While I have read some rather critical notices of the book, I am not the only one who appreciates it. I found a customer review at Amazon by William D. Fusfield that reads, “This is BY FAR the best and most INTERESTING book available on how Cantor developed his key ideas about transfinite sets, large cardinals, ordinals etc.”

Since Cantor is remembered for legitimizing the infinite as a mathematical concept, it might be a little surprising to hear that Hallett attributes “finitism” to Cantor, but by finitism Hallett does not mean any of the range of constructivist or strict finitist positions staked out by those who deny the legitimacy of the actual infinite and set theory, but rather it describes what we may call the methodological finitism of Cantor’s approach to the transfinite numbers he defined by way of set theory.

Finite mathematics is largely uncontroversial and commands the consensus of almost all who take an interest in the matter, however much they disagree on other parts of mathematics. Thus Hallett formulates what he calls Cantor’s principle of finitism thus:

“The transfinite is on a par with the finite and mathematically is to be treated as far as possible like the finite.” (p. 7)

This I would call methodological finitism. A little further on, on page 32, Hallett quotes Weyl thus:

“…for set theory, there is no difference in principle between the finite and the infinite.”

Hallett then comments:

“…the unity which Weyl points to is so much a fundamental part of Cantorianism (at least when we substitute ‘transfinite’ for ‘infinite’) that I have called it Cantor’s principle of finitism.”

A week ago I was musing about naturalism while making a longish drive and it occurred to me that something parallel to this approach could be used in a formulation of naturalism. “Parallel” is the key term here as were are talking about very different things with naturalism and the transfinite. What strikes me about Hallett’s formulation is the innate good sense of “as far as possible.” This stands in contrast to polarizing and absolutist definitions that employ formulations like “nothing but” or some equivalent of an extremal clause.

In contemporary science, scientific materialism is largely uncontroversial and commands the consensus of almost all interested parties. But from a philosophical standpoint materialism is as dissatisfying as finitism. If you can focus on the science and not think much about the materialism, you’ll be fine. But if the whole object of your interest in science is to illuminate the world and to come to a better understanding of it over all (as is my own interest), then one cannot only not avoid thinking about scientific materialism, one is obligated to think about it carefully.

At this point, then, I would suggest a methodological naturalism parallel to Hallett’s formulation of methodological finitism in Cantor: “Naturalism is on a par with materialism, and philosophically is to be treated as far as possible like materialism.” Or one could formulate it thus: “The natural is on a par with the material and scientifically is to be treated as far as possible like the material.”

Such a formulation would acknowledge both the success and the limitations of classical materialism that views the world entire as “nothing but” matter in motion — Democritean atoms whirling in the void — a classically reductionist formulation. Methodological naturalism as I have formulated it above, parallel to Hallett, would follow classical materialism as far as possible, and would only depart from materialism when that materialism was unsustainable in light of the evidence. And at this point I do not mean to suggest that one makes a transition from matter in motion to a non-naturalistic account of the world. On the contrary, it is at this point that naturalism shows itself to be as distinct from materialism as the infinite is distinct from the finite. Naturalism takes the spirit of materialistic explanation forward into areas that patently cannot be treated in terms of matter in motion.

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Naturalism: a Series

1. A Formulation of Naturalism

2. Two Thoughts on Naturalism

3. Naturalism: Yet Another Formulation

4. Joseph Campbell and Kenneth Clark: Bifurcating Naturalisms

5. Naturalism and Object Oriented Ontology

6. Naturalism and Suffering

7. Transcendental Non-Naturalism

8. Methodological Naturalism and the Eerie Silence

9. Some Formulations of Methodological Naturalism

10. Darwin’s Cosmology: A Naturalistic World

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