82 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] |
22317 | Truth does not admit of more and less [Frege] |
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] |
13455 | Frege did not think of himself as working with sets [Frege, by Hart,WD] |
16895 | The null set is indefensible, because it collects nothing [Frege, by Burge] |
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] |
3328 | Frege proposed a realist concept of a set, as the extension of a predicate or concept or function [Frege, by Benardete,JA] |
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] |
9179 | Frege frequently expressed a contempt for language [Frege, by Dummett] |
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] |
13473 | Frege thinks there is an independent logical order of the truths, which we must try to discover [Frege, by Hart,WD] |
6076 | For Frege, predicates are names of functions that map objects onto the True and False [Frege, by McGinn] |
3319 | Frege gives a functional account of predication so that we can dispense with predicates [Frege, by Benardete,JA] |
9871 | Frege always, and fatally, neglected the domain of quantification [Dummett on Frege] |
17787 | Big logic has one fixed domain, but standard logic has a domain for each interpretation [Mayberry] |
16884 | Basic truths of logic are not proved, but seen as true when they are understood [Frege, by Burge] |
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] |
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] |
3331 | If '5' is the set of all sets with five members, that may be circular, and you can know a priori if the set has content [Benardete,JA on Frege] |
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] |
16880 | Frege aimed to discover the logical foundations which justify arithmetical judgements [Frege, by Burge] |
8689 | Eventually Frege tried to found arithmetic in geometry instead of in logic [Frege, by Friend] |
19659 | The absolute is the impossibility of there being a necessary existent [Meillassoux] |
5657 | Frege's logic showed that there is no concept of being [Frege, by Scruton] |
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] |
3318 | Frege made identity a logical notion, enshrined above all in the formula 'for all x, x=x' [Frege, by Benardete,JA] |
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] |
16885 | To understand a thought, understand its inferential connections to other thoughts [Frege, by Burge] |
19651 | Unlike speculative idealism, transcendental idealism assumes the mind is embodied [Meillassoux] |
16887 | Frege's concept of 'self-evident' makes no reference to minds [Frege, by Burge] |
16894 | An apriori truth is grounded in generality, which is universal quantification [Frege, by Burge] |
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] |
16882 | The building blocks contain the whole contents of a discipline [Frege] |
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] |
5816 | Frege said concepts were abstract entities, not mental entities [Frege, by Putnam] |
7307 | A thought is not psychological, but a condition of the world that makes a sentence true [Frege, by Miller,A] |
7309 | Frege's 'sense' is the strict and literal meaning, stripped of tone [Frege, by Miller,A] |
7312 | 'Sense' solves the problems of bearerless names, substitution in beliefs, and informativeness [Frege, by Miller,A] |
7725 | 'P or not-p' seems to be analytic, but does not fit Kant's account, lacking clear subject or predicate [Frege, by Weiner] |
7316 | Analytic truths are those that can be demonstrated using only logic and definitions [Frege, by Miller,A] |
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] |
3307 | Frege put forward an ontological argument for the existence of numbers [Frege, by Benardete,JA] |
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] |