A number of years ago I got into a discussion with an acquaintance about what kind of symbol system tells us “the truth” about the world. This is not how my interlocutor expressed the problem; she simply insisted that mathematics gives us the truth. I tried many different approaches to get her to understand that what she was saying made absolutely no sense, because the first thing that must happen (once any collection of symbols is at hand) in order to talk about truth was that those symbols have to be interpreted, and such interpretation is not given in advance. Thus, I have a modest background in some advanced forms of mathematics (mainly formal logic, abstract algebra, and a touch of differential geometry), and I understand that simply having a bunch of squiggles in front of you is not enough to adjudicate whether those squiggles say anything at all, much less anything that is true. Meanings must be assigned to those squiggles such that they hang together to form some kind of model, and that model then must be associated with the world in some form such that the model can be interpreted as making claims about the world which then can be interpreted as to its truth content. And here, “world” can mean either the world of concrete experience or a purely abstract “world” which is itself something of a mathematical construct. Also, my choice of the term “truth content” rather than “truth value” is not an innocent one: I wish to leave open the possibility that truth evaluations can be more complex and multi-dimensional than the mere assignment of values.
It became very clear that while I understood my acquaintance’s position, she in no way understood mine. This was because while I was repeatedly able to paraphrase – that is, interpret – her argument, when asked to do the same for mine she was unable to do anything other than repeat her own position, which addressed none of the points I had made. In later years, she was known to crow a bit about how she “won” the argument. To be fair, in retrospect I realize that there were a number of ways I could have made my own position clearer, as it was burdened by a much greater degree of philosophical nuance than the position she was presenting. And I confess that I do not think quickly on my feet; indeed, I’ve only ever suggested that, given time, I can think thoroughly. (One of the reasons I went into philosophy is because a line like, “Herstein! If we don’t get this metaphysical principle out the door by end of business today, our competition is going to crucify us!” is not something one is ever likely to hear from one’s department head.) Continue reading