5. AN EARLY PHILOSOPHICAL PROBLEM: INFINITY

I have long believed that there are genuine philosophical problems which are not mere puzzles arising out of the misuse of language. Some of these problems are childishly obvious. It so happened that I stumbled upon one of them when I was still a child, probably about eight.

Somehow I had heard about the solar system and the infinity of space (no doubt of Newtonian space) and I was worried: I could neither imagine that space was finite (for what, then, was outside it?) nor that it was infinite. My father suggested that I ask one of his brothers who, he told me, was very good at explaining such things. This uncle asked me first whether I had any trouble about a sequence of numbers going on and on. I had not. Then he asked me to imagine a stack of bricks, and to add to it one brick, and again one brick, and so on without end; it would never fill the space of the universe. I agreed, somewhat reluctantly, that this was a very helpful answer, though I was not completely happy about it. Of course, I was unable to formulate the misgivings I still felt: it was the difference between potential and actual infinity, and the impossibility of reducing the actual infinity to the potential. The problem is, of course, part (the spatial part) of Kant’s first antinomy, and it is (especially if the temporal part is added) a serious and still unsolved6 philosophical problem—especially since Einstein’s hopes of solving it by showing that the universe is a closed Riemannian space of finite radius have been more or less abandoned. It did not, of course, occur to me that what was worrying me might be an open problem. Rather, I thought that this was a question which an intelligent adult like my uncle must understand, while I was still too ignorant, or perhaps too young, or too stupid, to grasp it completely.

I remember a number of similar problems—serious problems, not puzzles—from later, when I was twelve or thirteen; for example, the problems of the origin of life, left open by Darwinian theory, and whether life is simply a chemical process (I opted for the theory that organisms are flames).

These, I think, are almost unavoidable problems for anybody who has ever heard about Darwin, whether child or adult. The fact that experimental work is done in connection with them does not make them nonphilosophical. Least of all should we decree in a high-handed manner that philosophical problems do not exist, or that they are insoluble (though perhaps dissoluble).

My own attitude towards such problems remained the same for a long time. I never thought it possible that any of those which bothered me had not been solved long ago; even less that any of them could be new. I had no doubt that people like the great Wilhelm Ostwald, editor of the journal Das monistische Jahrhundert (i.e. The Century of Monism). would know all the answers. My difficulties, I thought, were entirely due to my limited understanding.