66 ideas
| 8605 | In addition to analysis of a concept, one can deny it, or accept it as primitive [Lewis] |
| 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] |
| 8607 | Supervenience is reduction without existence denials, ontological priorities, or translatability [Lewis] |
| 8606 | A supervenience thesis is a denial of independent variation [Lewis] |
| 8580 | Materialism is (roughly) that two worlds cannot differ without differing physically [Lewis] |
| 8571 | Universals are wholly present in their instances, whereas properties are spread around [Lewis] |
| 10717 | Natural properties figure in the analysis of similarity in intrinsic respects [Lewis, by Oliver] |
| 16217 | Lewisian natural properties fix reference of predicates, through a principle of charity [Lewis, by Hawley] |
| 8613 | Objects are demarcated by density and chemistry, and natural properties belong in what is well demarcated [Lewis] |
| 8585 | Reference partly concerns thought and language, partly eligibility of referent by natural properties [Lewis] |
| 8586 | Natural properties tend to belong to well-demarcated things, typically loci of causal chains [Lewis] |
| 8589 | For us, a property being natural is just an aspect of its featuring in the contents of our attitudes [Lewis] |
| 15460 | All perfectly natural properties are intrinsic [Lewis, by Lewis] |
| 15726 | Natural properties fix resemblance and powers, and are picked out by universals [Lewis] |
| 7031 | Lewis says properties are sets of actual and possible objects [Lewis, by Heil] |
| 8572 | Any class of things is a property, no matter how whimsical or irrelevant [Lewis] |
| 18433 | There are far more properties than any brain could ever encodify [Lewis] |
| 8604 | We need properties as semantic values for linguistic expressions [Lewis] |
| 14499 | Properties are classes of possible and actual concrete particulars [Lewis, by Koslicki] |
| 15120 | Lewisian properties have powers because of their relationships to other properties [Lewis, by Hawthorne] |
| 8573 | Most properties are causally irrelevant, and we can't spot the relevant ones. [Lewis] |
| 8569 | I suspend judgements about universals, but their work must be done [Lewis] |
| 21961 | Physics aims to discover which universals actually exist [Lewis, by Moore,AW] |
| 8576 | The One over Many problem (in predication terms) deserves to be neglected (by ostriches) [Lewis] |
| 8570 | To have a property is to be a member of a class, usually a class of things [Lewis] |
| 8574 | Class Nominalism and Resemblance Nominalism are pretty much the same [Lewis] |
| 17785 | Real numbers as abstracted objects are now treated as complete ordered fields [Mayberry] |
| 8579 | Psychophysical identity implies the possibility of idealism or panpsychism [Lewis] |
| 8614 | A sophisticated principle of charity sometimes imputes error as well as truth [Lewis] |
| 8615 | We need natural properties in order to motivate the principle of charity [Lewis] |
| 13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
| 8608 | Counterfactuals 'backtrack' if a different present implies a different past [Lewis] |
| 8584 | Causal counterfactuals must avoid backtracking, to avoid epiphenomena and preemption [Lewis] |
| 8581 | Physics discovers laws and causal explanations, and also the natural properties required [Lewis] |
| 15727 | Physics aims for a list of natural properties [Lewis] |
| 8611 | A law of nature is any regularity that earns inclusion in the ideal system [Lewis] |
| 20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |