Why are you so sure parallel lines exist? Believe nothing, merely because you have been told it, or because it is traditional, or because you have imagined it.
The sceptic will say, 'It may well be true that this system of equations is reasonable from a logical standpoint, but this does not prove that it corresponds to nature.' You are right, dear sceptic. Experience alone can decide on truth.
At the Egyptian city of Naucratis there was a famous old god whose name was Theuth; the bird which is called the Ibis was sacred to him, and he was the inventor of many arts, such as arithmetic and calculation and geometry and astronomy and draughts and dice, but his great discovery was the use of letters.
Mathematics is an obscure field, an abstruse science, complicated and exact; yet so many have attained perfection in it that we might conclude almost anyone who seriously applied himself would achieve a measure of success.
One should not understand this compulsion to construct concepts, species, forms, purposes, laws ('a world of identical cases') as if they enabled us to fix the real world; but as a compulsion to arrange a world for ourselves in which our existence is made possible:-we thereby create a world which is calculable, simplified, comprehensible, etc., for us.
The great pagan world of which Egypt and Greece were the last living termsonce had a vast and perhaps perfect science of itsown, a science in terms of life. In our era this science crumbled into magic and charlatanry. But even wisdom crumbles.
But in physics I soon learned to scent out the paths that led to the depths, and to disregard everything else, all the many things that clutter up the mind, and divert it from the essential. The hitch in this was, of course, the fact that one had to cram all this stuff into one's mind for the examination, whether one liked it or not.
Widespread intellectual and moral docility may be convenient for leaders in the short term, but it is suicidal for nations in the long term. One of the criteria for national leadership should therefore be a talent for understanding, encouraging, and making constructive use of vigorous criticism.
Scientists constantly get clobbered with the idea that we spent 27 billion dollars on the Apollo programs, and are asked "What more do you want?" We didn't spend it; it was done for political reasons. ... Apollo was a response to the Bay of Pigs fiasco and to the successful orbital flight of Yuri Gagarin. President Kennedy's objective was not to find out the origin of the moon by the end of the decade; rather it was to put a man on the moon and bring him back, and we did that.
All science is methodolgy with regard to the Absolute. Therefore, there need be no fear of the unequivocally methodological. It isa husk, but not more than everything except the One.
Epistemology without contact with science becomes an empty scheme. Science without epistemology is-insofar as it is thinkable at all-primitive and muddled.
It was basic research in the photoelectric field-in the photoelectric effect that would one day lead to solar panels. It was basic research in physics that would eventually produce the CAT scan. The calculations of today's GPS satellites are based on the equations that Einstein put to paper more than a century ago.
The system of Descartes... seemed to give a plausible reason for all those phenomena; and this reason seemed more just, as it is simple and intelligible to all capacities. But in philosophy, a student ought to doubt of the things he fancies he understands too easily, as much as of those he does not understand.
...we are all inclined to ... direct our inquiry not by the matter itself, but by the views of our opponents; and, even when interrogating oneself, one pushes the inquiry only to the point at which one can no longer offer any opposition. Hence a good inquirer will be one who is ready in bringing forward the objections proper to the genus, and that he will be when he has gained an understanding of the differences.