We say that a sentence is factually significant to any given person, if, and only if, he knows how to verify the proposition which it purports to express.

While moral rules may be propounded by authority the fact that these were so propounded would not validate them.

The fact that people have religious experiences is interesting from the psychological point of view, but it does not in any way imply that there is such a thing as religious knowledge...Unless he can formulate this 'knowledge' in propositions that are empirically verifiable, we may be sure that he is deceiving himself.

The principles of logic and mathematics are true simply because we never allow them to be anything else. And the reason for this is that we cannot abandon them without contradicting ourselves, without sinning against the rules which govern the use of language, and so making our utterances self-stultifying. In other words, the truths of logic and mathematics are analytic propositions or tautologies.

We say that a sentence is factually significant to any given person, if, and only if, he knows how to verify the proposition which it purports to express.

But if science may be said to be blind without philosophy, it is true also that philosophy is virtually empty without science.

The ground for taking ignorance to be restrictive of freedom is that it causes people to make choices which they would not have made if they had seen what the realization of their choices involved.