Trudeau's confusion seems to stem from the nominalism of W. V. Quine, which in turn stems from Quine's appalling ignorance of the nature of geometry. Each of these geometries is a model , a pattern of ideas, and is to be judged by the interest and beauty of its particular pattern. But the point which is important to us now is this, that there is one thing at any rate of which pure geometries are not pictures, and that is the spatio-temporal reality of the physical world. It is obvious, surely, that they cannot be, since earthquakes and eclipses are not mathematical concepts. Keats's ode itself, while denying this by precept, bears it out by example.
Truth occupies the alethic pole of the intellectual sphere and beauty the aesthetic pole.
Each is admirable in its way. The aesthetic pole is the focus of belles lettres , music, art for art's sake. Mathematics is actually an aesthetic subject almost entirely. There are almost as many different constructions of M 24 as there have been mathematicians interested in that most remarkable of all finite groups . At one point while working on this book we even considered adopting a special abbreviation for 'It is a remarkable fact that,' since this phrase seemed to occur so often.