Only Because We Don't Think Clearly”:
Brian Josephson on Mathematics, Mind,
and the Human World
PREFATORY NOTE: THE PROMINENT ETHICIAN AND PHILOSOPHER OF mind, Thomas Nagel (1979), begins one of his most important essays with the question, What is it like to be a bat? The question may seem a bit strange, but it is deeply consequential. It asks whether, as humans, we are fixed in a particular point of view or instead have access to all aspects of the world, all points of view. One could also think of the issue in Kantian terms. Do we know “things in themselves” or do we know only appearances? More importantly, can we even say anything about things in themselves? One's inclination is to reply, “Yes, surely we can. We do it all the time.” But the matter is not that simple. Certainly we say things that are true and things that are false. But does that mean we are talking about things in themselves?
One might think of the problem this way. The world (everything that is) is like the surface of the earth. Perception and conceptualization are like the grid on a map. We see things a certain way (e.g., with colors) and talk about them in a certain way (e.g., as having colors). This is akin to locating and categorizing places by reference to a cartographic grid. I situate Bengal in, say, row G, column 7. That may be true. But it is not the way Bengal is “in itself.” Similarly, I may characterize the grass as green. That may be true. But is it the way the grass is “in itself”? Or is it just the way grass is “for humans”?
It is relatively easy to accept the human quality of our truths regarding colors. It is more difficult, however, when it comes to light waves. “Okay,” one might say, “Perceived colors are for humans'—and maybe animals with similar eyes—but surely we can say that grass in itself reflects light with a particular wavelength?” Here too things are complicated. Again, there are correct and incorrect claims that one can make about light waves. But perhaps even talking about light in terms of waves is specifically human, so that we cannot really claim that this is