54 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] |
| 17774 | Definitions make our intuitions mathematically useful [Mayberry] |
| 17773 | Proof shows that it is true, but also why it must be true [Mayberry] |
| 17795 | Set theory can't be axiomatic, because it is needed to express the very notion of axiomatisation [Mayberry] |
| 17796 | There is a semi-categorical axiomatisation of set-theory [Mayberry] |
| 17800 | The misnamed Axiom of Infinity says the natural numbers are finite in size [Mayberry] |
| 17801 | The set hierarchy doesn't rely on the dubious notion of 'generating' them [Mayberry] |
| 17803 | Limitation of size is part of the very conception of a set [Mayberry] |
| 17786 | The mainstream of modern logic sees it as a branch of mathematics [Mayberry] |
| 17788 | First-order logic only has its main theorems because it is so weak [Mayberry] |
| 17791 | Only second-order logic can capture mathematical structure up to isomorphism [Mayberry] |
| 17787 | Big logic has one fixed domain, but standard logic has a domain for each interpretation [Mayberry] |
| 17790 | No Löwenheim-Skolem logic can axiomatise real analysis [Mayberry] |
| 17778 | Axiomatiation relies on isomorphic structures being essentially the same [Mayberry] |
| 17779 | 'Classificatory' axioms aim at revealing similarity in morphology of structures [Mayberry] |
| 17780 | 'Eliminatory' axioms get rid of traditional ideal and abstract objects [Mayberry] |
| 17789 | No logic which can axiomatise arithmetic can be compact or complete [Mayberry] |
| 21838 | Before we seek solutions, it is important to invent problems [Deleuze] |
| 17784 | Real numbers can be eliminated, by axiom systems for complete ordered fields [Mayberry] |
| 17781 | Real numbers were invented, as objects, to simplify and generalise 'quantity' [Mayberry] |
| 17782 | Greek quantities were concrete, and ratio and proportion were their science [Mayberry] |
| 17799 | Cantor's infinite is an absolute, of all the sets or all the ordinal numbers [Mayberry] |
| 17797 | Cantor extended the finite (rather than 'taming the infinite') [Mayberry] |
| 17775 | If proof and definition are central, then mathematics needs and possesses foundations [Mayberry] |
| 17776 | The ultimate principles and concepts of mathematics are presumed, or grasped directly [Mayberry] |
| 17777 | Foundations need concepts, definition rules, premises, and proof rules [Mayberry] |
| 17804 | Axiom theories can't give foundations for mathematics - that's using axioms to explain axioms [Mayberry] |
| 17792 | 1st-order PA is only interesting because of results which use 2nd-order PA [Mayberry] |
| 17793 | It is only 2nd-order isomorphism which suggested first-order PA completeness [Mayberry] |
| 17794 | Set theory is not just first-order ZF, because that is inadequate for mathematics [Mayberry] |
| 17802 | We don't translate mathematics into set theory, because it comes embodied in that way [Mayberry] |
| 17805 | Set theory is not just another axiomatised part of mathematics [Mayberry] |
| 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] |
| 17785 | Real numbers as abstracted objects are now treated as complete ordered fields [Mayberry] |
| 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] |
| 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] |
| 1513 | The Egyptians were the first to say the soul is immortal and reincarnated [Herodotus] |