41 ideas
17926 | Rejecting double negation elimination undermines reductio proofs [Colyvan] |
17925 | Showing a disproof is impossible is not a proof, so don't eliminate double negation [Colyvan] |
17924 | Excluded middle says P or not-P; bivalence says P is either true or false [Colyvan] |
17929 | Löwenheim proved his result for a first-order sentence, and Skolem generalised it [Colyvan] |
17930 | Axioms are 'categorical' if all of their models are isomorphic [Colyvan] |
17928 | Ordinal numbers represent order relations [Colyvan] |
17923 | Intuitionists only accept a few safe infinities [Colyvan] |
17941 | Infinitesimals were sometimes zero, and sometimes close to zero [Colyvan] |
17922 | Reducing real numbers to rationals suggested arithmetic as the foundation of maths [Colyvan] |
17936 | Transfinite induction moves from all cases, up to the limit ordinal [Colyvan] |
17940 | Most mathematical proofs are using set theory, but without saying so [Colyvan] |
17931 | Structuralism say only 'up to isomorphism' matters because that is all there is to it [Colyvan] |
17932 | If 'in re' structures relies on the world, does the world contain rich enough structures? [Colyvan] |
12270 | Being is one [Melissus, by Aristotle] |
17943 | Probability supports Bayesianism better as degrees of belief than as ratios of frequencies [Colyvan] |
17939 | Mathematics can reveal structural similarities in diverse systems [Colyvan] |
17938 | Mathematics can show why some surprising events have to occur [Colyvan] |
17934 | Proof by cases (by 'exhaustion') is said to be unexplanatory [Colyvan] |
17933 | Reductio proofs do not seem to be very explanatory [Colyvan] |
17935 | If inductive proofs hold because of the structure of natural numbers, they may explain theorems [Colyvan] |
17942 | Can a proof that no one understands (of the four-colour theorem) really be a proof? [Colyvan] |
17937 | Mathematical generalisation is by extending a system, or by abstracting away from it [Colyvan] |
3847 | Man is nothing else but the sum of his actions [Sartre] |
3846 | Man IS freedom [Sartre] |
3843 | There is no human nature [Sartre] |
20762 | There are no values to justify us, and no excuses [Sartre] |
3852 | If values depend on us, freedom is the foundation of all values [Sartre] |
20764 | In becoming what we want to be we create what we think man ought to be [Sartre] |
3848 | Cowards are responsible for their cowardice [Sartre] |
20763 | When my personal freedom becomes involved, I must want freedom for everyone else [Sartre] |
22229 | Existentialists says that cowards and heroes make themselves [Sartre] |
3842 | Existence before essence (or begin with the subjective) [Sartre] |
6868 | 'Existence precedes essence' means we have no pre-existing self, but create it through existence [Sartre, by Le Poidevin] |
3844 | Existentialism says man is whatever he makes of himself [Sartre] |
20754 | It is dishonest to offer passions as an excuse [Sartre] |
6571 | When a man must choose between his mother and the Resistance, no theory can help [Sartre, by Fogelin] |
3851 | If I do not choose, that is still a choice [Sartre] |
3059 | There is no real motion, only the appearance of it [Melissus, by Diog. Laertius] |
5100 | The void is not required for change, because a plenum can alter in quality [Aristotle on Melissus] |
456 | Nothing could come out of nothing [Melissus] |
3845 | Without God there is no intelligibility or value [Sartre] |