Proof Quotes - page 8
The priesthood have, in all ancient nations, nearly monopolized learning. Read over again all the accounts we have of Hindoos, Chaldeans, Persians, Greeks, Romans, Celts, Teutons, we shall find that priests had all the knowledge, and really governed mankind. Examine Mahometanism, trace Christianity from its first promulgation; knowledge has been almost exclusively confined to the clergy. And, even since the Reformation, when or where has existed a Protestant or dissenting sect who would tolerate [a free inquiry]? The blackest billingsgate, most ungentlemanly insolence, the most yahooish brutality is patiently endured, countenanced, propagated and applauded. But touch a solemn truth in collision with a dogma of a sect, though capable of the clearest proof, and you will soon find you have disturbed a nest, and the hornets will swarm about your legs and hands, and fly into your face and eyes.
John Adams
I, too, have made a wee-little book from the same materials, which I call the Philosophy of Jesus; it is a paradigma of his doctrines, made by cutting the texts out of the book, and arranging them on the pages of a blank book, in a certain order of time or subject. A more beautiful or precious morsel of ethics I have never seen; it is a document in proof that I am a real Christian, that is to say, a disciple of the doctrines of Jesus, very different from the Platonists, who call me infidel and themselves Christians and preachers of the gospel, while they draw all their characteristic dogmas from what its author never said nor saw. They have compounded from the heathen mysteries a system beyond the comprehension of man, of which the great reformer of the vicious ethics and deism of the Jews, were he to return on earth, would not recognize one feature.
Thomas Jefferson
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