63 ideas
| 6405 | Moore's 'The Nature of Judgement' (1898) marked the rejection (with Russell) of idealism [Moore,GE, by Grayling] |
| 17992 | The main aim of philosophy is to describe the whole Universe. [Moore,GE] |
| 7527 | Analysis for Moore and Russell is carving up the world, not investigating language [Moore,GE, by Monk] |
| 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] |
| 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] |
| 21342 | A relation is internal if two things possessing the relation could not fail to be related [Moore,GE, by Heil] |
| 17785 | Real numbers as abstracted objects are now treated as complete ordered fields [Mayberry] |
| 6672 | Moore's Paradox: you can't assert 'I believe that p but p is false', but can assert 'You believe p but p is false' [Moore,GE, by Lowe] |
| 20147 | Arguments that my finger does not exist are less certain than your seeing my finger [Moore,GE] |
| 6349 | I can prove a hand exists, by holding one up, pointing to it, and saying 'here is one hand' [Moore,GE] |
| 22190 | If a theory is more informative it is less probable [Gorham] |
| 22189 | Why abandon a theory if you don't have a better one? [Gorham] |
| 22192 | Is Newton simpler with universal simultaneity, or Einstein simpler without absolute time? [Gorham] |
| 22194 | Structural Realism says mathematical structures persist after theory rejection [Gorham] |
| 22195 | Structural Realists must show the mathematics is both crucial and separate [Gorham] |
| 22197 | Theories aren't just for organising present experience if they concern the past or future [Gorham] |
| 22196 | For most scientists their concepts are not just useful, but are meant to be true and accurate [Gorham] |
| 22193 | Consilience makes the component sciences more likely [Gorham] |
| 22302 | Moor bypassed problems of correspondence by saying true propositions ARE facts [Moore,GE, by Potter] |
| 7526 | Hegelians say propositions defy analysis, but Moore says they can be broken down [Moore,GE, by Monk] |
| 21233 | The beautiful is whatever it is intrinsically good to admire [Moore,GE] |
| 8039 | Moore tries to show that 'good' is indefinable, but doesn't understand what a definition is [MacIntyre on Moore,GE] |
| 22151 | The Open Question argument leads to anti-realism and the fact-value distinction [Boulter on Moore,GE] |
| 11056 | The naturalistic fallacy claims that natural qualties can define 'good' [Moore,GE] |
| 8033 | Moore cannot show why something being good gives us a reason for action [MacIntyre on Moore,GE] |
| 8032 | Can learning to recognise a good friend help us to recognise a good watch? [MacIntyre on Moore,GE] |
| 11050 | Moore's combination of antinaturalism with strong supervenience on the natural is incoherent [Hanna on Moore,GE] |
| 23726 | Despite Moore's caution, non-naturalists incline towards intuitionism [Moore,GE, by Smith,M] |
| 18676 | We should ask what we would judge to be good if it existed in absolute isolation [Moore,GE] |
| 11057 | It is always an open question whether anything that is natural is good [Moore,GE] |
| 5925 | The three main values are good, right and beauty [Moore,GE, by Ross] |
| 5902 | For Moore, 'right' is what produces good [Moore,GE, by Ross] |
| 5903 | 'Right' means 'cause of good result' (hence 'useful'), so the end does justify the means [Moore,GE] |
| 5907 | Relationships imply duties to people, not merely the obligation to benefit them [Ross on Moore,GE] |
| 22198 | Aristotelian physics has circular celestial motion and linear earthly motion [Gorham] |