Triton

“Wait a second: Part of the Taj Mahal is white, and part of the Taj Mahal is brown, and part of the Taj Mahal is—”

“The solution’s even simpler than that. You see, just like ‘white,’ the words ‘Taj Mahal’ have a range of significance that extends, on one side, at least as far as the gates around the grounds, so that once you enter them you can say, truthfully, ‘I am at the Taj Mahal,’ and extend, on another side, at least down to the individual tiles on the wall, and even further to the grotte between them, so that, as you go through the Taj’s door and touch only your fingernail to the strip of no-colored plaster between two tiles, you can say, equally truthfully, T have touched the Taj Mahal.’ But notice also that the grounds of the Taj Mahal have faded

(until they are one with) the area of significance of the ‘surface of India,’ much of which is not the grounds of the Taj at all. And the grotte between the tiles has faded into (until it is one with) Vriamin Grotte—grotte mined from the Vriamin Clay-pits thirty miles to the south, some of which went into the Taj and some of which went into other buildings entirely. Language is parametal, not perimetal. Areas of significance space intermesh and fade into one another like color-clouds in a three-dimensional spectrum. They don’t fit together like hard-edged bricks in a box. What makes ‘logical’ bounding so risky is that the assertion of the formal logician that a boundary can be placed around an area of significance space gives you, in such a cloudy situation, no way to say where to set the boundary, how to set it, or if, once set, it will turn out in the least useful. Nor does it allow any way for two people to be sure they have set their boundaries around the same area. Treating soft-edged interpenetrating clouds as though they were hard-edged bricks does not offer much help if you want to build a real discussion of how to build a real house. Ordinary, informal, nonrigorous language overcomes all these problems, however, with a bravura, panache and elegance that leave the formal logician panting and applauding.” Bron rocked on his desk once. “Visualize an area of significance space—which is hard to do at the best of times, because the simplest model we’ve come up with has to represent it in seven coordinates (one for each sense organ): and the one we use currently employs twenty-one, some of which are fractional—which isn’t any harder than working with fractional exponents, really—and several of which are polar, because the resultant, nondefinable lines between bipolar coordinates nicely model some significance discontinuities we haven’t yet been able to bridge coherently: things like the slippage between the denotative and the co

To outline the parametal model of language, he used the fanciful analogy of “meanings” like colored clouds filling up significance space, and words as homing balloons which, when strung together in a sentence, were tugged to various specific areas in their meaning clouds by the resultant syntax vectors but, when released, would drift back more or less to where, in their cloudy ranges, they’d started out. He wasn’t sure whether he’d gotten the analogy from something he’d browsed over in the office library—perhaps one of the feyer passages in the second volume of Slade’s Summa?—or if it were something from back in his training course. Possibly it had been both.

“I think I’m actually with you,” Miriamne said at one point. “Only, a little while ago, you mentioned things-in-the-Universe. Okay: where in real space is this significance space? And what in real space are these seven-to-twenty-one dimensional fuzzy-edged meaning clouds, or ranges, made of?”

Bron smiled. “You’ve got to remember that all these visualizations, even n-dimensional ones, are in themselves just abstract models to—well, explain how what-there-is manages to accomplish what-it-does. What there is, in this case, is the highly complex organic matrix of the micro-circuitry of the human brain in interface with a lot of wave fronts distorted by objects and energies scattered about the cosmos. And what it does, in this case, is to help the brain to learn languages, produce arguments in those languages, and analyse those arguments in formal logical terms as well as metalogical ones. If you’ll allow me to run some syntax vectors among some balloons that will shunt them all off over wildly metaphoric slippages: The space is in the brain circuitry, and the clouds are composed of the same thing the words are once they pass through the eardrum, the same thing the image of this coffee bulb is composed of once it passes the retina, the same thing the taste of a bar of Protyyn is composed of once it passes the taste buds, the same thing as the vectors that bind the balloons together, or the homing forces that anchor them within their clouds more or less where learning first set them: a series of routed, electrochemical wave fronts.” Miriamne smiled. “And I still think I’m with you/’”Good. Then throw out all the visualizations you’ve been forming up till now, first because there just isn’t any way to visualize a directed wave-front mapping of seven-to-twenty-one dimensional space full of spectrally related meaning ranges that is less than—to put it mildly—oversimplified. And because, second, we’re going to start all over with ‘To affirm P is to deny not-P’ and go ru

“Off you go,” Miriamne said. “Right behind you.”

“All right: the two goals of metalogics are, one) the delimitation of the problem and, two) an exploration of the interpenetration among the problem elements in significance space. In old Boolean terms (Did you see the public-cha