48 ideas
| 14018 | Is Sufficient Reason self-refuting (no reason to accept it!), or is it a legitimate explanatory tool? [Bourne] |
| 17774 | Definitions make our intuitions mathematically useful [Mayberry] |
| 17773 | Proof shows that it is true, but also why it must be true [Mayberry] |
| 14008 | The redundancy theory conflates metalinguistic bivalence with object-language excluded middle [Bourne] |
| 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] |
| 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] |
| 16664 | Everything that exists is either a substance or an accident [Albert of Saxony] |
| 14010 | All relations between spatio-temporal objects are either spatio-temporal, or causal [Bourne] |
| 14009 | It is a necessary condition for the existence of relations that both of the relata exist [Bourne] |
| 17785 | Real numbers as abstracted objects are now treated as complete ordered fields [Mayberry] |
| 16703 | God could make a successive thing so that previous parts cease to exist [Albert of Saxony] |
| 16699 | Successive entities just need parts to succeed one another, without their existence [Albert of Saxony] |
| 14016 | The idea of simultaneity in Special Relativity is full of verificationist assumptions [Bourne] |
| 14019 | Relativity denies simultaneity, so it needs past, present and future (unlike Presentism) [Bourne] |
| 14013 | Special Relativity allows an absolute past, future, elsewhere and simultaneity [Bourne] |
| 14015 | No-Futurists believe in past and present, but not future, and say the world grows as facts increase [Bourne] |
| 14007 | How can presentists talk of 'earlier than', and distinguish past from future? [Bourne] |
| 14011 | Presentism seems to deny causation, because the cause and the effect can never coexist [Bourne] |
| 14017 | Since presentists treat the presentness of events as basic, simultaneity should be define by that means [Bourne] |
| 14003 | Time is tensed or tenseless; the latter says all times and objects are real, and there is no passage of time [Bourne] |
| 14005 | B-series objects relate to each other; A-series objects relate to the present [Bourne] |
| 14006 | Time flows, past is fixed, future is open, future is feared but not past, we remember past, we plan future [Bourne] |