"In a strict usage the same symbol should never represent the act of sincerely asserting something and the content of what is asserted. For the symbolic distinction between the two, Frege has introduced the 'signpost' symbol. ... \vdash p is to signify the actual assertion of p, while the bare symbol p must henceforth be used only as part of a sentence. ... It should be clear from the modality of a sentence whether it is a question, a command, an invective, a complaint or an allegation of fact."

“Whitehead and Russell ... translate \vdash p imples q into the words 'it is asserted that p implies q. But the phrase 'it is asserted' suggests an impersonal happening of assertions: 'it is asserted' as 'it is raining' or 'it happens'. The value of the assertion sign is lost if we allow ourselves to revert in our verbal translation of it to the muddle of a declaratory sentence which asserts itself or is impersonally asserted by nobody in particular.”

“When order is achieved among human beings by allowing them to interact with each other on their own initiative — subject only to the laws which uniformly apply to all of them — we have a system of spontaneous order in society.”

“The term 'simplicity' functions then merely as a disguise for another meaning than its own. It is used for smuggling an essential quality into our appreciation of a scientific theory, which a mistaken conception of objectivity forbids us to openly acknowledge.”

“To learn by example is to submit to authority. ...By watching the master and emulating his efforts in the presence of his example, the apprentice unconsciously picks up the rules of the art, including those which are not explicitly known to the master himself. These hidden rules can be assimilated only by a person who surrenders himself to that extent uncritically to the imitation of another. A society which wants to preserve a fund of personal knowledge must submit to tradition. ...Common Law ...is the most important system of strictly traditional activities.”

“Comprehension is neither an arbitrary act nor a passive experience, but a responsible act claiming universal validity. Such knowing is indeed objective in the sense of establishing contact with a hidden reality; a contact that is defined as the condition for anticipating an indeterminate range of yet unknown true implications. It seems reasonable to describe this fusion of the personal and the objective as Personal Knowledge. Personal knowledge is an intellectual commitment, and as such inherently hazardous. Only affirmations that could be false can be said to convey objective knowledge of this kind.”

“While the articulate contents of science are successfully taught all over the world in hundreds of universities, the unspecifiable art of scientific research has not yet penetrated to many of these.”