Mathematics may be defined as the economy of counting. There is no problem in the whole of mathematics which cannot be solved by direct counting.

A colour is a physical object as soon as we consider its dependence, for instance, upon its luminous source, upon other colours, upon temperatures, upon spaces, and so forth.

The presentations and conceptions of the average man of the world are formed and dominated, not by the full and pure desire for knowledge as an end in itself, but by the struggle to adapt himself favourably to the conditions of life.

In reality, the law always contains less than the fact itself, because it does not reproduce the fact as a whole but only in that aspect of it which is important for us, the rest being intentionally or from necessity omitted.

Ordinarily pleasure and pain are regarded as different from sensations.

Everyone is free to set up an opinion and to adduce proofs in support of it. Whether, though, a scientist shall find it worth his while to enter into serious investigations of opinions so advanced is a question which his reason and instinct alone can decide. If these things, in the end, should turn out to be true, I shall not be ashamed of being the last to believe them.

The task which we have set ourselves is simply to show why and for what purpose we hold that standpoint during most of our lives, and why and for what purpose we are provisionally obliged to abandon it.