The point is: There is nothing identical in a picture and what it depicts. There is nothing identical in the model and what it is a model of. Nothing, nothing at all! They share not one atom in common! They need not share one measurement! Only the perceptive context imposes commonality on them, for a variety of learned and physiological reasons. (G. Spencer-Brown’s elegant, elegant argument wobbles, ultimately, on the same pivot point.) There are only identical processes some thing else can undergo in response to both — emblematic of their relation. And, presumably, different processes as well — emblem that the two (original and depiction) are distinct and, possibly, hierarchical.
For A to be recognized as a model of B, first a set of internal relations, as A relates to itself, must be read from A, then processed in some way probably similar to a mathematical integration; then another set of internal relations must be read from B (some of the relations may be similar to those read from A; but they need not be) and then integrated (by a similar process; or by a very different one), and the two results compared; if I find the results congruent, then I recognize A as a model of B in the context of the joint integrative process that produced the congruent results. But information about A may come to me via photograph, while I may have to gather information about B, blindfolded, with just my hands, from miniature plastic sculptures. Even so, if I have developed the proper interpretative context, I may well be able to recognize that, say, some small, plastic object B is a model of the photographed object A (checkable against a sight model when the blindfold is removed), while other small plastic objects C, D, and E are not — in terms either of the context I’ve developed, or in terms of the more usual sight context — models of A.
26. About every fragment of reality, an infinite number of different statements can be made. For every fragment of reality, an infinite number of different models can be made.
27. On one side of a paper write: “The statement on the other side of this paper is true.” Now turn the paper over and write: “The statement on the other side of this paper is false.” Now put down your pencil; and turn the paper over several more times, considering the truth and falsity of the statements you have written — till you perceive the paradox.
The young Bertrand Russell noted that the whole of the Principia Mathematica remained shaky because of it; he came up with one resolution that, later, as an older man, he repudiated. Karl Popper has, somewhere, a proof that it cannot be resolved at all.
It can.
But to follow the resolution, fold up the paper and put it in the breast pocket of your Pendleton, as I did on the train platform in South Bernham one May, and come along with me.
Vanessa Harpington had gone off painting in North Africa, but had sweetly left the keys to her country home circulating among various of her Camden Town friends. So I’d come down to pass that summer in a fine old English house with my friend Alfred, himself the long-haired nephew and namesake of a rather infamous Polish Count K.
One rainy afternoon, I was in the sitting room, with a sketch pad, making a drawing of the scene outside the window — rain splashing through the leaves of one of the small sycamores in the yard — when Alfred, smoking a meerschaum carved into a likeness of A. E. Van Vogt, wandered in, looked at my drawing, looked out the window, looked at my drawing again, and nodded. After a moment’s silence, he said: “Would you say you are making a model of the situation outside the window?”
“I suppose you could call it that,” I said, sketching a line in for the drapery’s edge.
“Would you say that it models the fact that it is raining?”
“Well, all those slanted lines are supposed to be raindrops. And the runnels of water on the windows there…” I looked up.
Alfred had stepped forward. The streaming pane silhouetted his hawkish features. He took another pull on his pipe and, expelling small puffs of smoke, intoned: “Truth… Falsity… Model… Reality…” and glanced back.
“I beg your pardon?” I said. There was a sweetish aroma in with the tobacco.
“Has it ever occurred to you,” Alfred said, “that logically speaking, ‘true’ and ‘false’ can only be applied to statements about the real; but that it is nonsense to apply either one directly to the real? I mean — ” He took his pipe and pointed with the stem toward the window; his long hair swung — “if, in here, in the sitting room, you were to make the statement, ‘It is raining outside,’ or some other model of the situation you perceive through the glass — ”
“Like a drawing?”
“—or a sculpture, or a photograph; or a flashing light that, by arrangement, we had both agreed to interpret as, ‘It is raining outside,’ or some abstract mark on a piece of paper, or an arbitrary set of musical notes that we had some such similar agreement — ”
“A sign — ” I said. “An image, a symbol — ”
“I said a model. Do accept my terminology.” The partially silhouetted head cocked. “I’m only trying to save you pages and pages of semiological hair-splitting. Now: As I was saying, suppose I chose to model the situation outside with the statement, ‘It is raining outside,’ rather than the way you are, with a pencil and paper, then you might have come along, observed my model — or, in this case, heard what I said — observed the garden through the window, and commented: ‘That is a true statement.’ Or, if you will, ‘That is a true model.’—”
“I think that’s a rather limited way to look at, say, well any aesthetic model.”
“So do I! So do I!” said Alfred. “But if we had agreed that we were going to use the model in that way, for the purely limited purpose of obtaining information about a limited aspect of reality — say, whether it was or was not raining — then we could.”
“Okay. If we agreed first.”
“But, by the same token, you can see that it would be perfectly ridiculous for you to come along, point out the window and say, ‘The outside is true,’ or ‘The rain is true,’ or even ‘The rain outside is true’.”
“Oh, I could say it. But I do get your point. If I did, I wouldn’t be using ‘true’ in any truly logical way; I’d be using it metaphorically; aesthetically if you will; as a sort of general intensifier.”
“Precisely. Do you see, then, what allows one to put ‘true’ or ‘false’ on a model, such as my statement on your picture?”
“I suppose,” I said, squinting at my paper and considering asking Alfred to step just a little aside beside he was blocking a doffing sycamore branch, “It’s because I’ve been working very hard to get it to look like what… I’m modeling — Alfred, do you think you might move to the left there just a bit — ”
“Oh, really!” Alfred stepped directly in front of the window and jabbed his pipe stem at me. “All Vanessa’s oak paneling, these leather bindings and dusty hangings, seem to have addled your brain. A statement doesn’t look like the thing it models! When I say ‘It is raining,’ neither the ‘it’ nor the ‘is’ refers to anything real in the situation. And the position of the pointer on that barometer dial over there — just as good a model of what’s going on outside as any of the others we’ve mentioned — has no internal structure similar to the situation it’s modeling at all (though it’s attached to something that has an internal structure dependent on it; but that’s a different story)! No, some structural similarity may explain why you choose to use a particular thing for a model, but it is the use you are putting it to — the context you are putting it into, if you will — that, alone, allows you to call it ‘true’ or ‘false.’ Truth and falsity, the potential for being true or false, are not manifestations of the internal structure of the thing that is, potentially, to be so labeled. They are, rather, qualities ascribable to a given thing when, in a particular context, it is functioning in a particular way, i.e., modeling some situation truly (however we choose to interpret that) or modeling it falsely (however we choose, given a particular, modular context, to interpret that)…”