10 ideas
13418 | The old problems with the axiom of choice are probably better ascribed to the law of excluded middle [Parsons,C] |
17611 | We want the essence of continuity, by showing its origin in arithmetic [Dedekind] |
10572 | A cut between rational numbers creates and defines an irrational number [Dedekind] |
17612 | Arithmetic is just the consequence of counting, which is the successor operation [Dedekind] |
18087 | If x changes by less and less, it must approach a limit [Dedekind] |
13419 | If functions are transfinite objects, finitists can have no conception of them [Parsons,C] |
13417 | If a mathematical structure is rejected from a physical theory, it retains its mathematical status [Parsons,C] |
335 | Do the gods also hold different opinions about what is right and honourable? [Plato] |
336 | Is what is pious loved by the gods because it is pious, or is it pious because they love it? (the 'Euthyphro Question') [Plato] |
337 | It seems that the gods love things because they are pious, rather than making them pious by loving them [Plato] |