A Quote by Gian-Carlo Rota
Are mathematical ideas invented or discovered? This question has been repeatedly posed by philosophers through the ages and will probably be with us forever.
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Simon Critchley's 'The Book of Dead Philosophers' - it's a quick thumbnail sketches of philosophers through the ages.
It seems to me there's this grand mathematical world out there, and I am wandering through it and discovering fascinating phenomena that often totally suprise me. I do not think of mathemaatics as invented but rather discovered.
I believe everything learned in college is an answer to a question that someone has posed. Questions get posed differently and the answers that come back transport us to places we never knew existed.
Will we fight or will we retreat? That is the question that is posed to us. Some of my friends on the other side of the aisle often refer to Iraq as a distraction.
Mathematics may be the only exception in the sciences that leaves no room for skepicism. But, if mathematical results are exact as no empirical law can ever be, philosophers have discovered that they are not absolutely novel - instead, they are tautological.
It would have been the easiest thing in the world for us to build those emplacements under the guise of something totally different and they would have never been discovered. The amazing thing was that they weren't discovered earlier. It was a question of carelessness, lack of foresight.
The constructs of the mathematical mind are at the same time free and necessary. The individual mathematician feels free to define his notions and set up his axioms as he pleases. But the question is will he get his fellow mathematician interested in the constructs of his imagination. We cannot help the feeling that certain mathematical structures which have evolved through the combined efforts of the mathematical community bear the stamp of a necessity not affected by the accidents of their historical birth.
A couple of hundred years from now, maybe [science fiction writers] Isaac Asimov and Fred Pohl will be considered the important philosophers of the twentieth century, and the professional philosophers will almost all be forgotten, because they're just shallow and wrong, and their ideas aren't very powerful.
The question at hand is the danger posed to truth by computer-manipulated photographic imagery. How do we approach this question in a period in which the veracity of even the straight, unmanipulated photograph has been under attack for a couple of decades.
Foolishness is doing ignorantly something forbidden repeatedly by sages since ages, and Madness is doing the very same prohibited thing repeatedly but intentionally.
During the Middle Ages there were all kinds of crazy ideas, such as that a piece of rhinoceros horn would increase potency. Then a method was discovered for separating the ideas - which was to try one to see if it worked, and if it didn't work, to eliminate it. This method became organized, of course, into science.
Tonight, I ask for your prayers for all those who grieve, for the children whose worlds have been shattered, for all whose sense of safety and security has been threatened. And I pray they will be comforted by a power greater than any of us, spoken through the ages in Psalm 23: "Even though I walk through the valley of the shadow of death, I fear no evil, for You are with me."
The thing with the question of oneness or non-oneness is that you can literally discuss it forever. You can go into the philosophy section of any library and you'll see people have been discussing it forever and will continue to do so.
The tendency to gather and to breed philosophers in universities does not belong to ages of free and humane reflection: it is scholastic and proper to the Middle Ages and to Germany.
Our wise old church...has discovered that if you will act as if you believed belief will be given to you; if you pray with doubt, but pray with sincerity, your doubt will be dispelled; if you will surrender yourself to the beauty of that liturgy the power of which over the human spirit has been proved by the experience of the ages, peace will descend upon you.
...they discovered only a small asteroid inhabited by a solitary old man who claimed repeatedly that nothing was true, though he was later discovered to be lying.
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