JB: Reuben, sounds like you're about to push some political agenda here, and it's not the Republican platform.

HERSH: You're saying my philosophy may be biased by my politics. Well, it's true! This is one of the many novel things in my book-- looking into the correlation between political belief and belief about the nature of mathematics.

JB: Do you have a name for this solution?

HERSH: I call it humanistic philosophy of mathematics. It's not really a school; no one else has jumped on the bandwagon with that name, but there are other people who think in a similar way, who gave it different names. I'm not completely a lone wolf here, I'm one of the mavericks, as we call them. The wolves baying outside the corral of philosophy.

Anyhow, back to your other question. The second half of my book is about the history of the philosophy of mathematics. I found that this was best explained by separating philosophers of mathematics into two groups. One group I call Mainstream and the other I call Humanists and Mavericks. The Humanists and Mavericks see mathematics as a human activity, and the Mainstream see it as inhuman or superhuman. By the way, there have been humanists way back; Aristotle was one. I wondered whether there was any connection with politics. So I tried to classify each of these guys as either right-wing or left-wing, in relation to their own times. Plato was far right; Aristotle was somewhat liberal. Spinoza was a revolutionary; Descartes was a royalist, and so on. These are well known facts. There are some guys that you can't classify. It came out just as you are intimating, The humanists are predominantly left-wing and the mainstream predominantly right wing. Any explanation would be speculative, but intuitively it makes sense. For instance, one main version of mainstream philosophy of mathematics is Platonism. It says that all mathematical objects, entities, or whatever, including the ones we haven't discovered yet and the ones we never will discover-all of have always existed. There's no change in the realm of mathematics. We discover things, so our knowledge increases, but the actual mathematical universe is completely static. Always was, always will be. Well that's kind of conservative, you know? Fits in with someone who thinks that social institutions mustn't change.

So this parallel exists. But there are exceptions. For instance, Bertrand Russell was a Platonist and a socialist. One of my favorite philosophers, Imre Lakatos, was a right- winger politically, but very radical philosophically. These correlations are loose and statistical, not binding. You can't tell somebody's philosophy from his politics, or vice versa.

I searched for a suitable label for my ideas. There were several others that had been used for similar points of view--social constructivism, fallibilism, quasi-empiricism, naturalism. I didn't want to take anybody else's label, because I was blazing my own trail, and I didn't want to label myself with someone else's school. The name that would have been most accurate was social conceptualism. Mathematics consists of concepts, but not individually held concepts; socially held concepts. Maybe I thought of humanism because I belong to a group called the Humanistic Mathematics Network. Humanism is appropriate, because it's saying that math is something human. There's no math without people. Many people think that ellipses and numbers and so on are there whether or not any people know about them; I think that's a confusion.