Monday, October 3, 2011

Harman, Wittgenstein, Math&Logic, Compositionism, Biology

Once I’d posted my previous Wittgenstein → OOO piece I realized that I’d pretty much glossed over the middle of the Tractatus. What’s in there? I wondered, and how would that affect my proto-OOO reading of the opening section?

Well, what’s in there seems to be a form of correlationism, as it’s about the relationship between language and the world, moving toward the self and the world:
5.63 I am my world. (The microcosm.)

5.64 Here it can be seen that solipsism, when its implications are followed out strictly, coincides with pure realism. The self of solipsism shrinks to a point without extension, and there remains the reality coordinated with it.
Wittgenstein’s interest in (Newtonian) mechanics, which I glossed in the previous piece, stems in part from the peculiar conception of language he advances, namely language as logical form. In classical mechanics Wittgenstein found a robust physical theory that was so constrained that one could plausibly argue that it can be characterized by math&logic.

Of course, Wittgenstein would subsequently abandon this approach to language. Perhaps that was because he came to realize that, if THAT’s how language works, then not only must we pass over aesthetics and ethics in silence (6.421), but, in the end, pretty much everything else as well. Thus his great final proposition (Wovon man nicht sprechen kann, darüber muß man schweigen. / What we cannot speak we must pass over in silence.) becomes something of a demonstration of the world’s status as ever withdrawing object/objects. If you will, Wittgenstein has taken the via negativa to demonstrate reality.

Composition as Math&Logic

At the same time, I submit, Wittgenstein managed a brush with what Latour has recently called compositionism (PDF). Sorta’. When you look DOWN a composition in the direction of particles, it’s reductionism. When you look UP, you’re composing, arranging objects within other objects, each with its own appropriate order. Wittgenstein’s concern with logic is basically a concern with a certain mode of composition.

Here’s how Wittgenstein begins his argument:
1 The world is all that is the case.

1.1 The world is the totality of facts, not of things....

1.13 The facts in logical space are the world.
Here it’s not clear whether he’s talking about the world, or about logic. But it makes no difference, does it, if language is somehow the limit of the world?

Wittgenstein begins introducing formal notation here and there in section 4. For example:
4.127 The propositional variable signifies the formal concept, and its values signify objects that fall under the concept.

4.127 Every variable is the sign for a formal concept....

4.1272 Thus the variable name ‘x’ is the proper sign for the pseudo-concept object.

Wherever the world ‘object’ (‘thing’, etc.) is correctly used, it is expressed in conceptual notation by a variable name.
And now he begins to deal with composition:
4.22 An elementary composition consists of names. It is a nexus, a concatenation of names.

4.221 It is obvious that the analysis of propositions must bring us to elementary propositions which consist of names in immediate combination.

This raises the question of how such combination into propositions comes about.

And we’re off to the races. There’s much more I could bring into play, I suppose, that indeed, I could attempt to reconstruct Wittgenstein’s argument. But that’s not what I’m after.

What I’m after is traces of compositionism. Latour has introduced it as something new, and I DO believe that (I think). But we can agree, can we not? that everything has antecedents, an admission which does not, in my view, condemn us to footnoting Plato. So I’m thinking that mathematics and logic are tools of pure composition, composition unencumbered by anything beyond their own symbology. Here are the axioms and postulates, and this is how we compose them into new formal objects. Wittgenstein’s project in the Tractatus was to encumber math&logic with world and see what comes out. Answer: silence.

Composition as Visual Rhetoric

With that in mind, let me turn to my own French hero, Claude Lévi-Strauss, whose work I’ve discussed in Lévi-Strauss on Myth: Some Informal Notes. He was quite fond of math, or pseudo-math, and his works often feature interesting diagrams and formal-appearing notation. His great work on myth, Mythologiques, is peppered with such things. I dare say Lévi-Strauss couldn’t have done his work without them. We would be wrong to dismiss them because they don’t really have the formal mathematical content which the terminology and notation conventions seem to imply.

These are rhetorical devices, and they are used to express the compositionist aspect of Lévi-Strauss’s thought. And legitimately so. One cannot understand his argument without carefully attending to them.

Language, as is so often said, is linear, one thing after another. One can, and one often does, reread and skip ahead, thereby side-stepping linearity. But it’s a stop-gap. It is so much easier to let one’s eye play over a diagram, a set of signs and symbols arranged in two dimensions on a flat surface. What Lévi-Strauss has to say about the logic of mythic thought is best understood though such free-form scanning of those conceptual objects he created for that purpose, the diagrams, propositional forms, lists and so forth.

Then we have Greimas, from whom Latour has his term, actant. Greimas is known for one such diagram, a rectangle with inscribed diagonals, which he puts though its conceptual paces time and again.

And that brings us to Harman and The Quadruple Object, which has diagrams similar to those of Greimas. The four corners are always there, variously labeled (e.g. Earth, Gods, Mortals, Sky, p. 89; Real Object, Real Qualities, Sensual Object, Sensual Qualities, p. 79), but the sides and the diagonals may not always be there. So there is variation on a limited and tightly constrained theme.

I've not read through to those sections of the book, word by careful word, but I've looked at the diagrams and dipped into the associated prose. While Harman makes no formal claims for those diagrams that I can see (for example, there is no talk of transformation groups, as in Lévi-Strauss), I don't think these diagrams are MERE illustrations either. They may not be absolutely necessary to grasp Harman’s thought, but I'm thinking that the penultimate chapter on ontography, which itself has no diagrams, probably goes better if you have studied—studied not merely looked at—the earlier diagrams and can look back at them as necessary.

So I'm tentatively scoring those diagrams for compositionism. They are not mere illustrations, but rhetorical devices for conveying the compositionist facet of Harman’s thinking.

Biology and Reductionism

Finally, and by way of clarification, I do not regard math and logic as the only fountain of compositionist conceptual technique, nor even a particularly privileged one. I believe that biology is a deeply compositionist discipline, but it is not a particularly mathematical one, though mathematics does show up here and there (e.g. genetics).

Biology is a descriptive discipline, with much of the descriptive burden being carried by pictures and diagrams. It is very much concerned with design—though the word has unfortunate resonances—and design, after all, is about composition. And it is biology that has mounted the most sustained assault on the reductionism implicit in Wittgenstein’s early valorization of classical mechanics.

But that’s another story.

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