54 ideas
2319 | Metaphysics is the clarification of the ontological relationships between different areas of thought [Kim] |
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] |
2317 | Reductionism is good on light, genes, temperature and transparency [Kim, by PG] |
2310 | Supervenience is linked to dependence [Kim] |
2315 | Mereological supervenience says wholes are fixed by parts [Kim] |
2329 | Causal power is a good way of distinguishing the real from the unreal [Kim] |
2320 | Properties can have causal powers lacked by their constituents [Kim] |
17785 | Real numbers as abstracted objects are now treated as complete ordered fields [Mayberry] |
530 | There are two contradictory arguments about everything [Kim] |
13314 | Protagoras says arguments on both sides are always equal [Kim, by Seneca] |
2065 | Not every person is the measure of all things, but only wise people [Plato on Kim] |
1550 | Why didn't Protagoras begin by saying "a tadpole is the measure of all things"? [Plato on Kim] |
2318 | Agency, knowledge, reason, memory, psychology all need mental causes [Kim, by PG] |
2325 | It seems impossible that an exact physical copy of this world could lack intentionality [Kim] |
2324 | Intentionality as function seems possible [Kim] |
2314 | Maybe intentionality is reducible, but qualia aren't [Kim] |
2313 | Emergentism says there is no explanation for a supervenient property [Kim] |
2328 | The only mental property that might be emergent is that of qualia [Kim] |
2309 | Non-Reductive Physicalism relies on supervenience [Kim] |
2311 | Maybe strong supervenience implies reduction [Kim] |
2308 | Identity theory was overthrown by multiple realisations and causal anomalies [Kim] |
2322 | Multiple realisation applies to other species, and even one individual over time [Kim] |
2327 | Knowledge and inversion make functionalism about qualia doubtful [Kim] |
2323 | Emotions have both intentionality and qualia [Kim] |
7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |