What the use of P [the significance level] implies, therefore, is that a hypothesis that may be true may be rejected because it has not predicted observable results that have not occurred.
A formal and consistent theory of inductive processes cannot represent the operation of every human mind in detail; it will represent an ideal mind, but it will help the actual mind to approximate that ideal.
The real difficulty about volcanism is not to see how it can start, but how it can stop.
Variation must be taken as random until there is positive evidence to the contrary.
There are some current 'theories' that, when divested of begged questions, reduce to the non-controversial statement, 'Here are some facts and there may be some relation between them.'
An observation, strictly, is only a sensation. Nobody means that we should reject everything but sensations. But as soon as we go beyond sensations we are making inferences.
All suggested accounts of the origin of the solar system are subject to serious objections. The conclusion in the present state of the subject would be that the system cannot exist.
We have to come back to something like ordinary language after all when we
want to talk "about" mathematics!
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