Facts have to be discovered by observation, not by reasoning

At all times, except when a monarch could enforce his will, war has been facilitated by the fact that vigorous males, confident of victory, enjoyed it, while their females admired them for their prowess.

Our beliefs are, however, often contrary to fact.

Sir Arthur Eddington deduces religion from the fact that atoms do not obey the laws of mathematics. Sir James Jeans deduces it from the fact that they do.

Thinking you know when in fact you don't is a fatal mistake, to which we are all prone

To modern educated people, it seems obvious that matters of fact are to be ascertained by observation, not by consulting ancient authorities. But this is an entirely modern conception, which hardly existed before the seventeenth century.

The Eugenic Society . . . is perpetually bewailing the fact that wage-earners breed faster than middle-class people.

Formality Thus the absence of all mention of particular things or properties in logic or pure mathematics is a necessary result of the fact that this study is, as we say, "purely formal".