In the Land of Invented Languages - Arika Okrent [71]
Loglan, however, was doing a different kind of thing. Scientific detachment was only one part of the appeal of Loglan (the part that convinced people not to dismiss it immediately). What really got people interested was its new kind of design principle—the calibrated alignment of language with logic. Actually, the principle wasn't new at all. It stretched all the way back to Leibniz and Wilkins and the seventeenth-century idea that we could somehow speak in pure logic. It was new in that great strides had been made in the field of logic since then, so the idea of “speaking logic” now meant something a bit different.
In the early twentieth century, philosophers such as Gottlob Frege, Bertrand Russell, and Rudolf Carnap had developed a preliminary mathematics of language, but it was not a mathematics of concepts—no breaking down the concept dog into the basic elements that defined its dogness. It was instead a mathematics of statements. It was a method of breaking down propositions like “The dog bit the man” or “All dogs are blue” into logical formulas. These formulas were not expressed in terms of nouns, verbs, and adjectives. Instead, like mathematical formulas, they were expressed in terms of functions and arguments. Much like x(x + 5) is a function waiting for you to tell it what the argument x is, dog(x) is a function, “is a dog,” waiting for you to tell it what particular x is a dog. Blue(x) is a function, “is blue,” waiting to find out “what” is blue. Bite(x, y) is a function waiting for two arguments, the biter and the bitten. Give(x, y, z) is a function waiting for three arguments—x gives y to z.
The power of such a notation, both the mathematical and the logical, is that you can do a whole lot without ever knowing what x is. The formula x(x + 5) can itself become an argument in a larger formula; it can participate in the solving of equations and proofs. It may never return a specific number, but it can help you assess the general validity of the statements in which it plays a part. Logical formulas can do the same. “All dogs are blue” is represented by the logical statement x dog(x) → blue(x). Translated back into English, this means, “For every x, if x is a dog, then x is blue.” This logical breakdown can't tell you whether or not the statement is true out there in the real world (we know it's not true, but the logic doesn't), but it can tell you, more precisely than the original English can, what conditions need to be met in order for it to be true. This type of logical notation is even more abstract, and more powerful, than the most complex formulas of arithmetic. Not only do you not need to know what specific x's are dogs or are blue; you don't need to know exactly what “dog” and “blue” are, only that they are functions that take one argument (in logical terms, they are “one-place predicates”). This is very useful. It made whole new branches of theoretical mathematics possible, and it also gave rise to computer programming languages.
Brown's idea was to make logical forms speakable. Then he could test whether this had a Whorfian effect on people who learned it. Would speaking in logic make people more logical? Would it facilitate thought? Of course logical forms already were speakable in the sense that you could give a long-winded paraphrase like “For every x, if x is a dog, then x is blue.” But in Loglan the translation would be compact and independent of the grammar of English (or any other language).
“All dogs are blue.”
Brown's article generated a great deal of excitement in the Scientific American audience.