Archive for October, 2010

The Algebra of Truth

October 4, 2010

Here is a true statement:  ” Liberals did not invent taxes.”

Here is another true statement: “Conservatives did not invent taxes.”

As far as I know, both of these statements are correct and historically accurate. They are both true.

Combined together, by simple addition: “Liberals did not invent taxes and conservatives did not invent taxes.” Another way to say it is “Neither liberals nor conservatives invented taxes.” But these two statements are not quite the same.

Each true statement, taken separately, can be described as a half-truth (½T). The question is how to put them together, by addition or by multiplication. Does a half-truth plus a half-truth yield a whole truth (½T + ½T = T) or does a half-truth times a half-truth yield a quarter truth (½T x ½T = ¼T²), only we also have multiply the units and get square-truth. What??

Multiplication can be thought of as a mathematical metaphor for two different kinds of experience, repeated addition or a blending of properties. So, 3 inches time 2 equals six inches, and 2 inches time 3 also equals 6 inches. But 3 inches times 2 inches yields six square inches. Fortunately, we have a clear physical picture of what a square inch is, so the blending of the two dimensions is not confusing. Square truth??

The power of language lies in its ability to create virtual worlds by the simple manipulation of grammar and vocabulary. That is true of mathematical language as well as cultural language. It is a power that is dangerous if the mind gets too absorbed and intoxicated by the unreal intensity that is easily generated, particular by modern technologies.

Back to square truth. Here is a word combination that flows strictly from the rules of algebra. Is there a way to put ordinary meaning into these words? The second combining statement above, the one that starts with “Neither..”, does this. This statement points to the possibility of something larger than the simple polarity of liberals and conservatives, putting these two contending groups into a larger historical framework. Like √-1, symbolized by i, we know the number exists though we cannot write a numeral for it.

Square truth. It’s just that for which the truth is the square root of! Like many radical ideas, it may not be expressible in numerals. Mathematicians call that irrational. Perhaps it is irrational to think that there is something beyond the polarities of argument about “who’s better than who” (see Seuss:The Big Brag (Yertle the Turtle)).

I have argued elsewhere in the blog that the mominalization of the adjective “true” into the noun “truth” is something that should not be done casually. I would go on and assert that “truth” is always partial, and therefore subject to the multiplication of fractions rules. As a direct consequence, as we learn more and more about the world, the fraction of knowledge we have, compared to the implied whole, gets smaller and smaller! That’s a little scary, and humiliating.