display all the ideas for this combination of philosophers
3 ideas
9605 | If a proposition is false, then its negation is true [Brown,JR] |
Full Idea: The law of excluded middle says if a proposition is false, then its negation is true | |
From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 1) | |
A reaction: Surely that is the best statement of the law? How do you write that down? ¬(P)→¬P? No, because it is a semantic claim, not a syntactic claim, so a truth table captures it. Semantic claims are bigger than syntactic claims. |
9649 | Axioms are either self-evident, or stipulations, or fallible attempts [Brown,JR] |
Full Idea: The three views one could adopt concerning axioms are that they are self-evident truths, or that they are arbitrary stipulations, or that they are fallible attempts to describe how things are. | |
From: James Robert Brown (Philosophy of Mathematics [1999], Ch.10) | |
A reaction: Presumably modern platonists like the third version, with others choosing the second, and hardly anyone now having the confidence to embrace the first. |
9638 | Berry's Paradox finds a contradiction in the naming of huge numbers [Brown,JR] |
Full Idea: Berry's Paradox refers to 'the least integer not namable in fewer than nineteen syllables' - a paradox because it has just been named in eighteen syllables. | |
From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 5) | |
A reaction: Apparently George Boolos used this quirky idea as a basis for a new and more streamlined proof of Gödel's Theorem. Don't tell me you don't find that impressive. |