And what, then, is belief? It is the demi-cadence which closes a musical phrase in the symphony of our intellectual life.

And what, then, is belief? It is the demi-cadence which closes a musical phrase in the symphony of our intellectual life.

The opinion which is fated to be ultimately agreed to by all who investigate, is what we mean by the truth, and the object represented in this opinion is the real. That is the way I would explain reality.

The woof and warp of all thought and all research is symbols, and the life of thought and science is the life inherent in symbols; so that it is wrong to say that a good language is important to good thought, merely; for it is the essence of it.

This branch of mathematics [Probability] is the only one, I believe, in which good writers frequently get results which are entirely erroneous.

If man were immortal he could be perfectly sure of seeing the day when everything in which he had trusted should betray his trust, and, in short, of coming eventually to hopeless misery. He would break down, at last, as every good fortune, as every dynasty, as every civilization does. In place of this we have death.

Another characteristic of mathematical thought is that it can have no success where it cannot generalize.