But as the work proceeded I was continually reminded of the fable about the elephant and the tortoise. Having constructed an elephant upon which the mathematical world could rest, I found the elephant tottering, and proceeded to construct a tortoise to keep the elephant from falling. But the tortois
... mathematical knowledge ... is, in fact, merely verbal knowledge. "3" means "2+1", and "4" means "3+1". Hence it follows (though the proof is long) that "4" means the same as "2+2". Thus mathematical knowledge ceases to be mysterious.
... the word "theory" ... was originally an Orphic word, which Cornford interprets as "passionate sympathetic contemplation" ... For Pythagoras, the "passionate sympathetic contemplation" was intellectual, and issued in mathematical knowledge ... To those who have reluctantly learnt a little mathema
I am allowed to use plain English because everybody knows that I could use mathematical logic if I chose.
In all affairs it's a healthy thing now and then to hang a question mark on the things you have long taken for granted.
Men who are unhappy, like men who sleep badly, are always proud of the fact.
Mathematics takes us into the region of absolute necessity, to which not only the actual word, but every possible word, must conform.
I like mathematics because it is not human and has nothing particular to do with this planet or with the whole accidental universe - because, like Spinoza's God, it won't love us in return.
Aristotle maintained that women have fewer teeth than men; although he was twice married, it never occurred to him to verify this statement by examining his wives' mouths.
Physics is mathematical not because we know so much about the physical world, but because we know so little; it is only its mathematical properties that we can discover.
Only mathematics and mathematical logic can say as little as the physicist means to say.
Ordinary language is totally unsuited for expressing what physics really asserts, since the words of everyday life are not sufficiently abstract. Only mathematics and mathematical logic can say as little as the physicist means to say.
To create a good philosophy you should renounce metaphysics but be a good mathematician.
We have nothing to fear but fear itself.
Democracy alone, of all forms of government, enlists the full force of men's enlightened will.
Freedom to learn is the first necessity of guaranteeing that man himself shall be self reliant enough to be free.
We know that equality of individual ability has never existed and never will, but we do insist that equality of opportunity still must be sought.
It is time to provide a smashing answer for those cynical men who say that a democracy cannot be honest, cannot be efficient.... We have in the darkest moments of our national trials retained our faith in our own ability to master our own destiny.
Every man has a right to life. That means that he also has a right to make a comfortable living.
We have always known that heedless self-interest was bad morals; we know now that it is bad economics. Out of the collapse of a prosperity whose builders boasted their practicality has come the conviction that in the long run economic morality pays.
Economic diseases are highly communicable. It follows therefore that the economic health of every country is a proper matter of concern to all its neighbors, near or distant.
Men are not prisoners of fate, but only prisoners of their own minds.
For out of this modern civilization economic royalists carved new dynasties. New kingdoms were built upon concentration of control over material things. Through new uses of corporations, banks and securities, new machinery of industry and agriculture, of labor and capital - all undreamed of by the F
Be sincere; be brief; be seated. Franklin D. Roose
It has always seemed to me that the best symbol of common sense was a bridge.
The people of America are in agreement in defending their liberties at any cost, and the first line of that defense lies in the protection of economic security.
Self-interest is the enemy of all true affection. Franklin D. Roose
We can see now that we Americans were caught unprepared, because we were ordinary human beings, following the best advice we had at the time. No one would have guessed in 1941 that we would be attacked in such an unsportsmanlike manner as we were. No one could have visualized Pearl Harbor, either ou
Freedom of conscience, of education, of speech, of assembly are among the very fundamentals of democracy and all of them would be nullified should freedom of the press ever be successfully challenged.
No business is above Government; and Government must be empowered to deal adequately with any business that tries to rise above Government.
In our personal ambitions we are individualists. But in our seeking for economic and political progress as a nation, we all go up or else all go down as one people.
One reason--perhaps the chief--of the virility of the Roosevelts is [their] very democratic spirit. They have never felt that because they were born in a good position they could put their hands in their pockets and succeed. They have felt, rather, that being born in a good position, there is no exc
There is one front and one battle where everyone in the United States-every man, woman, and child-is in action, and will be privileged to remain in action throughout this war. That front is right here at home, in our daily lives, and in our daily tasks.