The formalists neglected the content altogether and made mathematics meaningless, the logicians neglected the form and made mathematics consist of any true generalizations; only by taking account of both sides and regarding it as composed of tautologous generalizations can we obtain an adequate theory.
Frank P. RamseyRelated topics
account content form mathematics takingRelated quotes
We had principles in mathematics that were granted to be absolute in mathematics for over 800 years, but new science has gotten rid of those absolutism, gotten forward other different logics of looking at mathematics, and sort of turned the way we look at it as a science altogether after 800 years.
Mahmoud Ahmadinejad
We must consider not only why the classical theory of democracy appears to be in contradiction with the observed practice, but also why the many different responses to this observation, though mutually incompatible, all share the belief that democracy is the best form of political organization.
Moses I. Finley
Impressionism was the name given to a certain form of observation when Monet, not content with using his eyes to see what things were or what they looked like as everybody had done before him, turned his attention to noting what took place on his own retina (as an oculist would test his own vision).
John Singer Sargent
I believe what really happens in history is this: the old man is always wrong; and the young people are always wrong about what is wrong with him. The practical form it takes is this: that, while the old man may stand by some stupid custom, the young man always attacks it with some theory that turns out to be equally stupid.
G. K. Chesterton