## Sunday, February 7, 2016

### Is Two Plus Two Really Four?

We have each other’s blood on our hands.

And in our veins.

Husserl apparently marveled that “2+2=4” is true, everywhere and always, whether beings exist who are capable of comprehending it or not. It’s an ineluctably true statement.

If so, then “2+2=4 is true everywhere and always, whether beings exist who are capable of understanding it or not” is also an ineluctably true statement. And that one isn’t about math. This leads me to suspect a problem.

Has Husserl made a distinction between the statement as statement and the “fact” to which the statement is a pointer? I don’t know. The statement is not true in itself. The statement becomes true in reference to a system of language that defines the meaning of its terms. In mathematics, in the base ten system (and obviously others, but not all), the statement 2+2=4 is true—by definition. There is no requirement for the concepts marked by “2,” “4,” “+,” or “=” to have any extension in material reality. And in other contexts the statement may either be false or nonsense, even where those five concepts have meaning.

So what Husserl is (presumably) noticing is that the concepts in question are such at that other beings elsewhere in the universe would, in theory, with time identify them, would come up with a mathematics which recognized number precisely as we do and also combination and equality. And it is because of the nature or facts of the universe that this would (or always in theory could) happen. Our math has done such a good job helping us understand and control our world that it must correspond in an essential way to what the world is so that any intelligent beings given time would also discover the same math. (Or if not, and we found them, we could teach them our math and they would understand it and acknowledge its truth.)

Maybe.

But it seems to me the claim is highly homocentric. It implies that the rightness of our math exists independent of the perspective of the people who invented/discovered and deploy it on the world. Question: If you did not (and for some imaginable reason could not) see the world in terms of numbers, would our math from your perspective be true? Might you be able to describe and control the world using some system of knowledge that is not mathematical? We don’t know what that would be. It might be something like direct apprehension and what we would have to call intuition, as a bird creates a nest without math, but a bird that could explain what he’s doing.

There is reason to believe that the concept of number is not natural. Humans everywhere seem to develop some sort of number system for their own use, with obvious similarities (and real differences). But they are all humans. We humans tend to invent the borders between things and then to believe that those borders are real borders. We count the number of mushrooms in the circle without realizing that they are no more distinct mushrooms than the individual feet of a centipede are distinct creatures.

There are times when it is useful to count them and to limit them, but there is always something false in that act.

That statement “2+2=4” and the statement “2+2=4 is true everywhere and always, whether beings exist who are capable of understanding it or not” may be useful anywhere in the universe under certain conditions. But neither one is simply ineluctably true.