78 ideas
| 18495 | The best philosophers I know are the best people I know [Heil] |
| 18494 | Using a technical vocabulary actually prevents discussion of the presuppositions [Heil] |
| 18506 | Questions of explanation should not be confused with metaphyics [Heil] |
| 18535 | Without abstraction we couldn't think systematically [Heil] |
| 17774 | Definitions make our intuitions mathematically useful [Mayberry] |
| 17773 | Proof shows that it is true, but also why it must be true [Mayberry] |
| 18534 | Truth relates truthbearers to truthmakers [Heil] |
| 18531 | Philosophers of the past took the truthmaking idea for granted [Heil] |
| 18509 | Not all truths need truthmakers - mathematics and logic seem to be just true [Heil] |
| 17796 | There is a semi-categorical axiomatisation of set-theory [Mayberry] |
| 17795 | Set theory can't be axiomatic, because it is needed to express the very notion of axiomatisation [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] |
| 18518 | Infinite numbers are qualitatively different - they are not just very large numbers [Heil] |
| 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] |
| 18500 | How could structures be mathematical truthmakers? Maths is just true, without truthmakers [Heil] |
| 18539 | Our categories lack the neat arrangement needed for reduction [Heil] |
| 18505 | Fundamental ontology aims at the preconditions for any true theory [Heil] |
| 18499 | Our quantifications only reveal the truths we accept; the ontology and truthmakers are another matter [Heil] |
| 18512 | Ontology aims to give the fundamental categories of being [Heil] |
| 18508 | Most philosophers now (absurdly) believe that relations fully exist [Heil] |
| 18532 | If causal relations are power manifestations, that makes them internal relations [Heil] |
| 18510 | We need properties to explain how the world works [Heil] |
| 18522 | Categorical properties were introduced by philosophers as actual properties, not if-then properties [Heil] |
| 18513 | Emergent properties will need emergent substances to bear them [Heil] |
| 18540 | Predicates only match properties at the level of fundamentals [Heil] |
| 18533 | In Fa, F may not be a property of a, but a determinable, satisfied by some determinate [Heil] |
| 18511 | Properties have causal roles which sets can't possibly have [Heil] |
| 18523 | Are all properties powers, or are there also qualities, or do qualities have the powers? [Heil] |
| 18524 | Properties are both qualitative and dispositional - they are powerful qualities [Heil] |
| 17785 | Real numbers as abstracted objects are now treated as complete ordered fields [Mayberry] |
| 18498 | Abstract objects wouldn't be very popular without the implicit idea of truthmakers [Heil] |
| 18507 | Substances bear properties, so must be simple, and not consist of further substances [Heil] |
| 18515 | Spatial parts are just regions, but objects depend on and are made up of substantial parts [Heil] |
| 18516 | A 'gunky' universe would literally have no parts at all [Heil] |
| 18514 | Many wholes can survive replacement of their parts [Heil] |
| 18517 | Dunes depend on sand grains, but line segments depend on the whole line [Heil] |
| 12732 | Some necessary truths are brute, and others derive from final causes [Leibniz] |
| 18502 | If basic physics has natures, then why not reality itself? That would then found the deepest necessities [Heil] |
| 18496 | If possible worlds are just fictions, they can't be truthmakers for modal judgements [Heil] |
| 19438 | Our large perceptions and appetites are made up tiny unconscious fragments [Leibniz] |
| 18525 | Mental abstraction does not make what is abstracted mind-dependent [Heil] |
| 18504 | Only particulars exist, and generality is our mode of presentation [Heil] |
| 18503 | You can think of tomatoes without grasping what they are [Heil] |
| 19415 | Passions reside in confused perceptions [Leibniz] |
| 18537 | Linguistic thought is just as imagistic as non-linguistic thought [Heil] |
| 18538 | Non-conscious thought may be unlike conscious thought [Heil] |
| 18536 | The subject-predicate form reflects reality [Heil] |
| 18497 | Many reject 'moral realism' because they can't see any truthmakers for normative judgements [Heil] |
| 18519 | If there were infinite electrons, they could vanish without affecting total mass-energy [Heil] |
| 18526 | We should focus on actual causings, rather than on laws and causal sequences [Heil] |
| 18527 | Probabilistic causation is not a weak type of cause; it is just a probability of there being a cause [Heil] |
| 18520 | Electrons are treated as particles, but they lose their individuality in relations [Heil] |
| 18501 | Maybe the universe is fine-tuned because it had to be, despite plans by God or Nature? [Heil] |
| 19439 | God produces possibilities, and thus ideas [Leibniz] |