37 ideas
| 17925 | Showing a disproof is impossible is not a proof, so don't eliminate double negation [Colyvan] |
| 17926 | Rejecting double negation elimination undermines reductio proofs [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] |
| 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] |
| 22858 | There is collective action, where a trend is manifest, but is not attributable to individuals [Lukes] |
| 22854 | Power is a capacity, which may never need to be exercised [Lukes] |
| 22850 | Hidden powers are the most effective [Lukes] |
| 22852 | The pluralist view says that power is restrained by group rivalry [Lukes] |
| 22855 | One-dimensionsal power is behaviour in observable conflicts of interests [Lukes] |
| 22856 | Political organisation brings some conflicts to the fore, and suppresses others [Lukes] |
| 22857 | The two-dimensional view of power recognises the importance of controlling the agenda [Lukes] |
| 22859 | Power can be exercised to determine a person's desires [Lukes] |
| 22863 | Power is the capacity of a social class to realise its interests [Lukes] |
| 22860 | The evidence for the exertion of power need not involve a grievance of the powerless [Lukes] |
| 22861 | Power is affecting a person in a way contrary to their interests [Lukes] |
| 21133 | Supreme power is getting people to have thoughts and desires chosen by you [Lukes] |
| 22851 | In the 1950s they said ideology is finished, and expertise takes over [Lukes] |
| 22862 | Liberals take people as they are, and take their preferences to be their interests [Lukes] |
| 22853 | Anyone who thinks capitalism can improve their lives is endorsing capitalism [Lukes] |
| 16745 | No one even knows the nature and properties of a fly - why it has that colour, or so many feet [Bacon,R] |