44 ideas
21852 | Nomads are the basis of history, and yet almost unknowable [Deleuze] |
21844 | The history of philosophy is an agent of power: how can you think if you haven't read the great names? [Deleuze] |
21849 | Thought should be thrown like a stone from a war-machine [Deleuze] |
21845 | Philosophy aims to become the official language, supporting orthodoxy and the state [Deleuze] |
21839 | When I meet objections I just move on; they never contribute anything [Deleuze] |
21841 | We must create new words, and treat them as normal, and as if designating real things. [Deleuze] |
21901 | 'Difference' refers to that which eludes capture [Deleuze, by May] |
21842 | Don't assess ideas for truth or justice; look for another idea, and establish a relationship with it [Deleuze] |
21850 | Dualisms can be undone from within, by tracing connections, and drawing them to a new path [Deleuze] |
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] |
21838 | Before we seek solutions, it is important to invent problems [Deleuze] |
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] |
21908 | Ontology can be continual creation, not to know being, but to probe the unknowable [Deleuze] |
21902 | 'Being' is univocal, but its subject matter is actually 'difference' [Deleuze] |
21899 | There is no being beyond becoming [Deleuze] |
21903 | Ontology does not tell what there is; it is just a strange adventure [Deleuze, by May] |
21904 | Being is a problem to be engaged, not solved, and needs a new mode of thinking [Deleuze, by May] |
21847 | Before Being there is politics [Deleuze] |
21907 | We don't want another new set of categories; we want a variety of flexible categories [Deleuze, by May] |
3061 | Anaxarchus said that he was not even sure that he knew nothing [Anaxarchus, by Diog. Laertius] |
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] |
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] |
17934 | Proof by cases (by 'exhaustion') is said to be unexplanatory [Colyvan] |
21840 | A meeting of man and animal can be deterritorialization (like a wasp with an orchid) [Deleuze] |
17937 | Mathematical generalisation is by extending a system, or by abstracting away from it [Colyvan] |
21843 | People consist of many undetermined lines, some rigid, some supple, some 'lines of flight' [Deleuze] |
21853 | We are currently extending capitalism to the whole of society [Deleuze] |
21848 | Some lines (of flight) are becomings which escape the system [Deleuze] |
21851 | The State requires self-preservation, but the war-machine desires destruction [Deleuze] |