While the articulate contents of science are successfully taught all over the world in hundreds of universities, the unspecifiable art of scientific … - Michael Polanyi

The confidence placed in physical theory owes much to its possessing the same kind of excellence from which pure geometry and pure mathematics in general derive their interest, and for the sake of which they are cultivated. ... We cannot truly account for our acceptance of such theories without endorsing our acknowledgement of a beauty that exhilarates and a profundity that entrances us.

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. ... <math>\vdash</math> 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.

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 (and perhaps yet inconceivable) 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.