Notion Quotes - page 10
P. Bernays has pointed out on several occasions that, since the consistency of a system cannot be proved using means of proof weaker than those of the system itself, it is necessary to go beyond the framework of what is, in Hilbert's sense, finitary mathematics if one wants to prove the consistency of classical mathematics, or even that of classical number theory. Consequently, since finitary mathematics is defined as the mathematics in which evidence rests on what is intuitive, certain abstract notions are required for the proof of the consistency of number theory.... In the absence of a precise notion of what it means to be evident, either in the intuitive or in the abstract realm, we have no strict proof of Bernays' assertion; practically speaking, however, there can be no doubt that it is correct...
Paul Bernays
The great defect, for Chamfort, consisted in the public's reluctance to submit its thinking to the rigors of rational examination, and its tendency to rely instead on intuition, emotion, and custom. "One can be certain that every generally held idea, every received notion, will be an idiocy, because it has been able to appeal to a majority,” the Frenchman observed, adding that what is flatteringly called common sense is usually little more than common nonsense, suffering as it does from simplification and illogicality, prejudice and shallowness: "The most absurd customs and the most ridiculous ceremonies are everywhere excused by an appeal to the phrase, but that's the tradition.”.
Alain de Botton