47 ideas
8220 | Philosophy is in a perpetual state of digression [Deleuze/Guattari] |
8217 | Philosophy is a concept-creating discipline [Deleuze/Guattari] |
8242 | Philosophy aims at what is interesting, remarkable or important - not at knowledge or truth [Deleuze/Guattari] |
8223 | The plague of philosophy is those who criticise without creating, and defend dead concepts [Deleuze/Guattari] |
8247 | Phenomenology needs art as logic needs science [Deleuze/Guattari] |
8224 | 'Eris' is the divinity of conflict, the opposite of Philia, the god of friendship [Deleuze/Guattari] |
17774 | Definitions make our intuitions mathematically useful [Mayberry] |
17773 | Proof shows that it is true, but also why it must be true [Mayberry] |
17796 | There is a semi-categorical axiomatisation of set-theory [Mayberry] |
17795 | Set theory can't be axiomatic, because it is needed to express the very notion of axiomatisation [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] |
8246 | Logic hates philosophy, and wishes to supplant it [Deleuze/Guattari] |
8219 | Logic has an infantile idea of philosophy [Deleuze/Guattari] |
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] |
17779 | 'Classificatory' axioms aim at revealing similarity in morphology of structures [Mayberry] |
17778 | Axiomatiation relies on isomorphic structures being essentially the same [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] |
17784 | Real numbers can be eliminated, by axiom systems for complete ordered fields [Mayberry] |
17782 | Greek quantities were concrete, and ratio and proportion were their science [Mayberry] |
17781 | Real numbers were invented, as objects, to simplify and generalise 'quantity' [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] |
17785 | Real numbers as abstracted objects are now treated as complete ordered fields [Mayberry] |
8221 | We cannot judge the Cogito. Must we begin? Must we start from certainty? Can 'I' relate to thought? [Deleuze/Guattari] |
8222 | Concepts are superior because they make us more aware, and change our thinking [Deleuze/Guattari] |
8218 | Other people completely revise our perceptions, because they are possible worlds [Deleuze/Guattari] |
8248 | Phenomenology says thought is part of the world [Deleuze/Guattari] |
8245 | The logical attitude tries to turn concepts into functions, when they are really forms or forces [Deleuze/Guattari] |
21906 | Political theory should not focus on the state or economy, but on the small scale of power [Deleuze/Guattari, by May] |
6005 | Animals are dangerous and nourishing, and can't form contracts of justice [Hermarchus, by Sedley] |
8243 | Atheism is the philosopher's serenity, and philosophy's achievement [Deleuze/Guattari] |