Cognitivism and the Critic 2: Symbol Processing

It has long been obvious to me that the so-called cognitive revolution is what happened when computation – both the idea and the digital technology – hit the human sciences. But I’ve seen little reflection of that in the literary cognitivism of the last decade and a half. And that, I fear, is a mistake.

Thus, when I set out to write a long programmatic essay, Literary Morphology: Nine Propositions in a Naturalist Theory of Form, I argued that we think of literary text as a computational form. I submitted the essay and found that both reviewers were puzzled about what I meant by computation. While publication was not conditioned on providing such satisfaction, I did make some efforts to satisfy them, though I’d be surprised if they were completely satisfied by those efforts.

That was a few years ago.

Ever since then I pondered the issue: how do I talk about computation to a literary audience? You see, some of my graduate training was in computational linguistics, so I find it natural to think about language processing as entailing computation. As literature is constituted by language it too must involve computation. But without some background in computational linguistics or artificial intelligence, I’m not sure the notion is much more than a buzzword that’s been trendy for the last few decades – and that’s an awful long time for being trendy.

I’ve already written one post specifically on this issue: Cognitivism for the Critic, in Four & a Parable, where I write abstracts of four texts which, taken together, give a good feel for the computational side of cognitive science. Here’s another crack at it, from a different angle: symbol processing.

Operations on Symbols

I take it that ordinary arithmetic is most people’s ‘default’ case for what computation is. Not only have we all learned it, it’s fundamental to our knowledge, like reading and writing. Whatever we know, think, or intuit about computation is built on our practical knowledge of arithmetic.

As far as I can tell, we think of arithmetic as being about numbers. Numbers are different from words. And they’re different from literary texts. And not merely different. Some of us – many of whom study literature professionally – have learned that numbers and literature are deeply and utterly different to the point of being fundamentally in opposition to one another. From that point of view the notion that literary texts be understood computationally is little short of blasphemy.

Not so. Not quite.

The question of just what numbers are – metaphysically, ontologically – is well beyond the scope of this post. But what they are in arithmetic, that’s simple; they’re symbols. Words too are symbols; and literary texts are constituted of words. In this sense, perhaps superficial, but nonetheless real, the reading of literary texts and making arithmetic calculations are the same thing, operations on symbols.

Arithmetic as Symbol Processing

I take it that learning arithmetic calculation has two aspects: 1) learning the relationship between primitive symbols, such as numerals, and the world, and 2) learning rules for manipulating those symbols. Whatever is natural to the human nervous system, arithmetic is not. Children get a good grip on their native tongue little or no explicit teaching; it just comes ‘naturally.’ But it takes children hundreds if not thousands of hours to become fluent in arithmetic. It is not natural in the sense the language, natural language, is.

In what is known as the Arabic notation, we have ten primitive symbols for quantities: 1, 2, 3, 4, 5, 6, 7, 8, 9, 0. That last is a real puzzler and has been regarded as evil at various times and places: How can something, even a mere mark, represent nothing? Children learn the meaning of these symbols by learning to count collections of objects, both real objects (e.g. blocks, pebbles, buttons, whatever), but also objects represented by pictures on a page.

And we have four primitive symbols for operations (+ – × ÷) of which the first two, for addition and subtraction, are the most basic. Children learn their meaning both through manipulating collections of objects (or their visual representations) and through rules of inference.

To be sure that’s not what we call them, but that’s what they are. We call them the addition and subtraction and multiplication and division tables. Each entry in these tables contains a single atomic fact of the form: string1 = string2. String1 always consists of an operator (+ – × ÷) between two numbers. String2 always consists of a single number. To solve an arithmetic problem we must use these atomic facts to make simple inferences. For example:

1 + 1 = 2
5 – 3 = 2
3 × 4 = 12
8 ÷ 2 = 4

And then there are procedures for every more complex cases. My point is simply that arithmetic calculation is symbol processing. Always. Through and through.

Computation: Selection and Combination

The Structuralists talked about the axis of combination and the axis of selection. They were talking about language and, by implication, things that could be analogized to language. But their inspiration is mathematical, as we can see with a bit of elementary algebra. Here’s a simple equation:

x + y = z

The horizontal IS the axis of combination. Here we’re combining three variables, x, y and z, and two operators, + and =. The value of z depends on the value of x and y; it is thus a dependent variable. The values of x and y are not dependent on the values of anything else in this form, and so they are independent variables. The purpose of the form is to tell us just how the value of the dependent variable is related to the values of the independent variables.

The axis of selection is, in effect, the source of values for those variables. Let us say that it is the positive integers plus zero: 0, 1, 2, 3, 4 . . . Now we can select values for x and y along that axis and come up with values for z by using the various rules and procedures of elementary arithmetic. So:

7 + 4 = z: z must be 11
13 + 9 = z: z must 22
4 + 8 = z: z must be 12

And so forth.

Now, consider these expressions from linguistics, where we can use → instead of =, but to a similar effect:

S → NP + VP
NP → N
NP → det + N
VP → V + NP

Those are rules of combination and they are defined in terms of variables: S = sentence, N = noun, NP = noun phrase, V = verb, VP = verb phrase, and det = determiner. Given just those rules, we can generate these forms, among others, for proper sentences:

1) N + V + N
2) N + V + det + N
3) det + N + V + N

To have actual sentences we need to put words into those variables. For example, we can select from these words, among many others:

Nouns: John, boy, Mary, girl, candy, ball
Verbs: like, hit
Determiners: a, the

Buy choosing from the appropriate selection sets we get these sentences, which I’ve indexed to our forms, 1, 2, and 3:

1a) John likes candy.
1b) Mary likes John.
2a) Mary hit the ball.
2b) John hit a girl.
3a) The boy likes candy.
3b) A girl hit John.

For the past half-century linguists have studied syntax from this point of view, broadly speaking — though some will no doubt tell you that I’m now speaking too broadly. There are, in fact, various schools of thinking about syntax and related topics, and they are not mutually consistent. Differences between these schools are deep and, when contested at all, are fiercely contested. But mostly the different schools ignore one another.

And What of Meaning?

Ah, yes, what of it?

Here I would make a distinction between semantics and meaning. Meaning, it seems to me, is fundamentally subjective; that is, it arises only in the interaction of a subject and, in this case, a text (whether written or spoken). Of course, people can communicate with one another and thereby share meanings; and so meaning can be intersubjective as well.

Semantics, on the other hand, is not subjective. To be sure, I’m tempted to say that semantics has to do with the meaning of words, but that would sink me, would it not? If I’ve already said that meaning is subjective, then why would I attempt to assert that semantics IS NOT subjective?

Because it isn’t. Semantics, properly done, is as dumb as rocks. I am thinking of semantics as a domain of study, a topic within linguistics, psychology, philosophy, and computer science. In those contexts it is not subjective. Those investigations may not be fully satisfactory, indeed, they are not; but they are not subjective. Each line of thought, in its own way, objectifies semantics, that is, roughly speaking, the relationship between words and the things and situations to which they (can) refer.

And various computer models of language are among the richest attempts at objectified semantics we’ve got. It is one thing to observe that existing objectifications are inadequate. But one should not infer from that that better, indeed much better, objectifications are impossible in principle. That may be so, but that principle has not, to my knowledge, been demonstrated.

So, semantics is not understood nearly so well as syntax and – as I’ve already indicated – we have major disagreements about syntax. But I don’t think we need to understand semantics deeply and fully in order to assent to the weaker statement that, however it works, it involves symbol processing. That does not, as far as I’m concerned, imply that semantic processing is nothing but symbol processing.

Not at all. It is clear to me that the meaning of symbols is ultimately grounded in non-symbolic schemas, an idea that’s become associated with the notion of embodied cognition. David Hays and his research group (of which I was a member) pursued that line at SUNY Buffalo in the mid-1970s.* And computational investigations of non-processing have been on-going for years, with computer vision being the most richly developed.

And that makes my larger point, for if computation can encompass non-symbolic processing as well as symbolic processing, what else is there? I saying this I do not mean to imply that it’s all smooth sailing from here on out – just hop on the computational bus, weigh anchor, fire the jets, and bombs away hot diggity dawg!! Not at all. There’s still much to learn. In fact over the last half century it’s as though the more we’ve learned, the more we’ve come face to face with our ignorance. That’s how it goes when you’re exploring a new world.

And the only way you can explore this particular new world, is to think in terms of computation. Just how you do that thinking, that depends on your taste, inclination, imagination, and the problems you’re investigating. But, as far as I can tell, computation’s the only game in town.

* * * * *

* See, for example:

William Benzon, Cognitive Science and Literary Semantics, MLN, Vol. 91, pp. 952-982, 1976.

David Hays, Cognitive Structures, HRAF Press 1981.

William Benzon, Cognitive Science and Literary Theory, Dissertation, Department of English, SUNY Buffalo, 1978.