On Language, Representation, Knowledge Chapter One (draft)

 

Before we can begin to talk about faith or God or really anything at all we have to talk about the instruments we use to talk about such things.

What does it mean to know something, anything? How do we know what we know, and how do we know that we know what we know? We seem to be already getting into the territory of nonsense or nursery rhyme or a missed opportunity for Abbot and Costello. But, however stated, these are essential questions. We can’t go forward until we have addressed them. I won’t say “answered them” because immediately we see a problem with the hope of an answer: if we decide that language is itself a problem an impediment to understanding, then the fact that we are discovering that in language means that our discovery is problematic, suspect. If we decide, as I think we will, that language is both an avenue and a roadblock, what then? The most common image I’ve seen for this is the problem of an infinite glance down the avenue created by facing mirrors. The reflection goes on forever, but you can only see so far because your head gets in the way.

Language is a tool we use to represent knowledge. It may be the tool, but that’s only if we decide—as we have the justification to do within the logic of language—to declare that whatever we represent as knowledge is language, whether that be words, sentences, propositions or music (the universal language) or mathematics (the other universal language) or art. We don’t have to make that determination now; and if we ever do, we will have to see that there will always be an element of arbitrariness in making it. (This responds to perhaps the most fundamental point we will be making: that however we determine the answer to the question “what is knowledge” we could as legitimately have determined it on other ways.)

The nature of the tool determines what is possible. It’s acknowledged, I think, by anyone who has looked at the history of math, that it is not the nature of the universe but possibilities inherent in the numbering system that makes the discipline possible. There are many numbering systems in the world. Virtually every culture has come up with one. But few are of much use in mathematics. You can’t do long division, let alone differential calculus, using Roman Numerals. You can if you start with Arabic numerals, providing you accept the concept of “0” as a number (a hard won provision). It seems that the Arabs did not solve the problem of calculation by inventing their number system. They created a number system, innocently enough I assume, and that system created the problem—created problems that its creators never could have conceived of at the time of creation—and provided a solution. Calculus became possible, though it was centuries before anyone knew this, the moment the numerals were enumerated.

It seems so, as I have just said. But it’s conceivable that the problem that the numbering system solved also, in a sense, preceded the invention of that system, put pressure on the creation of that system. I am not saying it is inevitable that that system would have been created. I’m saying only that the creation of Arabic numerals may not have been entirely arbitrary, that if the Arabs had not come up with that system, someone else might not have, eventually. It is not provable that this is not true. And there is some reason to think it may be true.

Numbers have proven their value. They reveal a lot. They represent the part of reality they are capable of representing with provable effectiveness. Numbers led Einstein to posit blackholes, against his non-numerical inclinations, if I have the story right, and the curvature of space, and the matter of photons, all of which have been confirmed by observation and experiment. This does not prove that numbers don’t also hide from us everything blocked by the intervention of our head in the hallway of mirrors. It does not prove to us the numbers don’t also mislead us as they reveal what they reveal. Can we know that there isn’t possibly a yet-better system of enumerating that would reveal more? And if there isn’t doesn’t everything else we know suggest that numbers hide as they reveal. I can’t say “as much,” because we don’t know what, of theoretically calculable things, they miss. I’m not talking about the cliché notion that poetry and love and so-called emotional knowledge isn’t subject to calculation—things that can perhaps be known by non-mathematical means. I’m talking about things a different mathematical regime may have revealed, as that which calculus existed unrevealed before the invention of calculus, but which, unlike calculus, is not subject to discovery within the current representational possibilities of the now-existing regime of mathematics.