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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.)


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.




  1. This is really about the meaning of 'words'. No matter what number system is used, the fact remains that a singular unit ("one") is distinct from 'zero' (nothingness). You cannot have a fractional part without the definition of a whole.
    A binary existence (something either is, or isn't) is fundamental to, well, everything. If you accept this, then 2+2, or any other mathematical concept, must follow. Acceptance doesn't enter the picture, really. These things exist outside of our judgement of them.
    Denial of these basic concepts just enters gobbledygook into the conversation.
    There is plenty of non-mathematical thinking to be done, and plenty of gradations within that. That is enough to keep the philosophers employed without getting into definitions of 'unity' and 'multiplicity'.
    Also, our language doesn't handle things well. Note the difficulty physicists have with the confusing non-intuitive nature of quantum realities. Even the math tends to fall well short there.
    Damn. Now my brain stem aches.

  2. This is not about the meaning of words but about the ontology of language and the ontology and of concepts and their relation to what would be called "being." You're skirting around the fact, assuming the validity of the thing under consideration. "If you accept this...." then you are already inside language, and therefore outside of the question which is being asked. If you want to do math, then you will always say 2+2=4. But insofar as "2" is a word, a sign, representing a concept, it is not something that exists apart from consciousness. It doesn't exist in the universe outside of language. Hence the statement that it is always and everywhere true is either tautology of nonsense. Nothing to marvel at.

  3. Just an interesting thought here...sometimes it depends on context. Did you know 1+1+1? Yes, if you're talking about one man + one woman = one child, in the context of sexual intercourse. Or what about the context of a man and woman coming to together but losing the baby. Then the conclusion would be 1+1=0. Or triplets? lol I could go on but I think you get the idea. Just a thought, not trying to argue either way. Interesting article by the way!