64 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] |
| 21901 | 'Difference' refers to that which eludes capture [Deleuze, by May] |
| 21841 | We must create new words, and treat them as normal, and as if designating real things. [Deleuze] |
| 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] |
| 8721 | An 'impredicative' definition seems circular, because it uses the term being defined [Friend] |
| 8680 | Classical definitions attempt to refer, but intuitionist/constructivist definitions actually create objects [Friend] |
| 3678 | Reductio ad absurdum proves an idea by showing that its denial produces contradiction [Friend] |
| 8705 | Anti-realists see truth as our servant, and epistemically contrained [Friend] |
| 8713 | In classical/realist logic the connectives are defined by truth-tables [Friend] |
| 8708 | Double negation elimination is not valid in intuitionist logic [Friend] |
| 8694 | Free logic was developed for fictional or non-existent objects [Friend] |
| 8665 | A 'proper subset' of A contains only members of A, but not all of them [Friend] |
| 8672 | A 'powerset' is all the subsets of a set [Friend] |
| 8677 | Set theory makes a minimum ontological claim, that the empty set exists [Friend] |
| 8666 | Infinite sets correspond one-to-one with a subset [Friend] |
| 8682 | Major set theories differ in their axioms, and also over the additional axioms of choice and infinity [Friend] |
| 8709 | The law of excluded middle is syntactic; it just says A or not-A, not whether they are true or false [Friend] |
| 8711 | Intuitionists read the universal quantifier as "we have a procedure for checking every..." [Friend] |
| 21838 | Before we seek solutions, it is important to invent problems [Deleuze] |
| 8675 | Paradoxes can be solved by talking more loosely of 'classes' instead of 'sets' [Friend] |
| 8674 | The Burali-Forti paradox asks whether the set of all ordinals is itself an ordinal [Friend] |
| 8667 | The 'integers' are the positive and negative natural numbers, plus zero [Friend] |
| 8668 | The 'rational' numbers are those representable as fractions [Friend] |
| 8670 | A number is 'irrational' if it cannot be represented as a fraction [Friend] |
| 8661 | The natural numbers are primitive, and the ordinals are up one level of abstraction [Friend] |
| 8664 | Cardinal numbers answer 'how many?', with the order being irrelevant [Friend] |
| 8671 | The 'real' numbers (rationals and irrationals combined) is the Continuum, which has no gaps [Friend] |
| 8663 | Raising omega to successive powers of omega reveal an infinity of infinities [Friend] |
| 8662 | The first limit ordinal is omega (greater, but without predecessor), and the second is twice-omega [Friend] |
| 8669 | Between any two rational numbers there is an infinite number of rational numbers [Friend] |
| 8676 | Is mathematics based on sets, types, categories, models or topology? [Friend] |
| 8678 | Most mathematical theories can be translated into the language of set theory [Friend] |
| 8701 | The number 8 in isolation from the other numbers is of no interest [Friend] |
| 8702 | In structuralism the number 8 is not quite the same in different structures, only equivalent [Friend] |
| 8699 | Are structures 'ante rem' (before reality), or are they 'in re' (grounded in physics)? [Friend] |
| 8696 | Structuralist says maths concerns concepts about base objects, not base objects themselves [Friend] |
| 8695 | Structuralism focuses on relations, predicates and functions, with objects being inessential [Friend] |
| 8700 | 'In re' structuralism says that the process of abstraction is pattern-spotting [Friend] |
| 8681 | The big problem for platonists is epistemic: how do we perceive, intuit, know or detect mathematical facts? [Friend] |
| 8712 | Mathematics should be treated as true whenever it is indispensable to our best physical theory [Friend] |
| 8716 | Formalism is unconstrained, so cannot indicate importance, or directions for research [Friend] |
| 8706 | Constructivism rejects too much mathematics [Friend] |
| 8707 | Intuitionists typically retain bivalence but reject the law of excluded middle [Friend] |
| 21902 | 'Being' is univocal, but its subject matter is actually 'difference' [Deleuze] |
| 21908 | Ontology can be continual creation, not to know being, but to probe the unknowable [Deleuze] |
| 21899 | There is no being beyond becoming [Deleuze] |
| 21847 | Before Being there is politics [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] |
| 21907 | We don't want another new set of categories; we want a variety of flexible categories [Deleuze, by May] |
| 8704 | Structuralists call a mathematical 'object' simply a 'place in a structure' [Friend] |
| 12887 | A whole must have one characteristic, an internal relation, and a structure [Rescher/Oppenheim] |
| 21840 | A meeting of man and animal can be deterritorialization (like a wasp with an orchid) [Deleuze] |
| 21843 | People consist of many undetermined lines, some rigid, some supple, some 'lines of flight' [Deleuze] |
| 8685 | Studying biology presumes the laws of chemistry, and it could never contradict them [Friend] |
| 8688 | Concepts can be presented extensionally (as objects) or intensionally (as a characterization) [Friend] |
| 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] |