79 ideas
| 19648 | Since Kant we think we can only access 'correlations' between thinking and being [Meillassoux] |
| 19674 | The Copernican Revolution decentres the Earth, but also decentres thinking from reality [Meillassoux] |
| 19657 | In Kant the thing-in-itself is unknowable, but for us it has become unthinkable [Meillassoux] |
| 19675 | Since Kant, philosophers have claimed to understand science better than scientists do [Meillassoux] |
| 19649 | Since Kant, objectivity is defined not by the object, but by the statement's potential universality [Meillassoux] |
| 19666 | If we insist on Sufficient Reason the world will always be a mystery to us [Meillassoux] |
| 19656 | Non-contradiction is unjustified, so it only reveals a fact about thinking, not about reality? [Meillassoux] |
| 17774 | Definitions make our intuitions mathematically useful [Mayberry] |
| 17773 | Proof shows that it is true, but also why it must be true [Mayberry] |
| 13252 | Some truths have true negations [Beall/Restall] |
| 13247 | A truthmaker is an object which entails a sentence [Beall/Restall] |
| 13249 | (∀x)(A v B) |- (∀x)A v (∃x)B) is valid in classical logic but invalid intuitionistically [Beall/Restall] |
| 13243 | Excluded middle must be true for some situation, not for all situations [Beall/Restall] |
| 13242 | It's 'relevantly' valid if all those situations make it true [Beall/Restall] |
| 13246 | Relevant logic does not abandon classical logic [Beall/Restall] |
| 13245 | Relevant consequence says invalidity is the conclusion not being 'in' the premises [Beall/Restall] |
| 13254 | A doesn't imply A - that would be circular [Beall/Restall] |
| 13255 | Relevant logic may reject transitivity [Beall/Restall] |
| 13250 | Free logic terms aren't existential; classical is non-empty, with referring names [Beall/Restall] |
| 19663 | We can allow contradictions in thought, but not inconsistency [Meillassoux] |
| 19664 | Paraconsistent logics are to prevent computers crashing when data conflicts [Meillassoux] |
| 19665 | Paraconsistent logic is about statements, not about contradictions in reality [Meillassoux] |
| 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] |
| 13235 | Logic studies consequence; logical truths are consequences of everything, or nothing [Beall/Restall] |
| 13238 | Syllogisms are only logic when they use variables, and not concrete terms [Beall/Restall] |
| 17786 | The mainstream of modern logic sees it as a branch of mathematics [Mayberry] |
| 13234 | The view of logic as knowing a body of truths looks out-of-date [Beall/Restall] |
| 13232 | Logic studies arguments, not formal languages; this involves interpretations [Beall/Restall] |
| 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] |
| 13241 | The model theory of classical predicate logic is mathematics [Beall/Restall] |
| 13253 | There are several different consequence relations [Beall/Restall] |
| 13240 | A sentence follows from others if they always model it [Beall/Restall] |
| 17787 | Big logic has one fixed domain, but standard logic has a domain for each interpretation [Mayberry] |
| 13236 | Logical truth is much more important if mathematics rests on it, as logicism claims [Beall/Restall] |
| 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] |
| 13237 | Preface Paradox affirms and denies the conjunction of propositions in the book [Beall/Restall] |
| 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] |
| 19677 | What is mathematically conceivable is absolutely possible [Meillassoux] |
| 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] |
| 19659 | The absolute is the impossibility of there being a necessary existent [Meillassoux] |
| 19662 | It is necessarily contingent that there is one thing rather than another - so something must exist [Meillassoux] |
| 19654 | We must give up the modern criterion of existence, which is a correlation between thought and being [Meillassoux] |
| 17785 | Real numbers as abstracted objects are now treated as complete ordered fields [Mayberry] |
| 13244 | Relevant necessity is always true for some situation (not all situations) [Beall/Restall] |
| 19660 | Possible non-being which must be realised is 'precariousness'; absolute contingency might never not-be [Meillassoux] |
| 19671 | The idea of chance relies on unalterable physical laws [Meillassoux] |
| 19651 | Unlike speculative idealism, transcendental idealism assumes the mind is embodied [Meillassoux] |
| 19647 | The aspects of objects that can be mathematical allow it to have objective properties [Meillassoux] |
| 19652 | How can we mathematically describe a world that lacks humans? [Meillassoux] |
| 19668 | Hume's question is whether experimental science will still be valid tomorrow [Meillassoux] |
| 19650 | The transcendental subject is not an entity, but a set of conditions making science possible [Meillassoux] |
| 13239 | Judgement is always predicating a property of a subject [Beall/Restall] |
| 13248 | We can rest truth-conditions on situations, rather than on possible worlds [Beall/Restall] |
| 13233 | Propositions commit to content, and not to any way of spelling it out [Beall/Restall] |
| 19667 | If the laws of nature are contingent, shouldn't we already have noticed it? [Meillassoux] |
| 19670 | Why are contingent laws of nature stable? [Meillassoux] |
| 19653 | The ontological proof of a necessary God ensures a reality external to the mind [Meillassoux] |
| 19658 | Now that the absolute is unthinkable, even atheism is just another religious belief (though nihilist) [Meillassoux] |