56 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] |
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] |
10301 | The axiom of choice is controversial, but it could be replaced [Shapiro] |
10588 | First-order logic is Complete, and Compact, with the Löwenheim-Skolem Theorems [Shapiro] |
10298 | Some say that second-order logic is mathematics, not logic [Shapiro] |
10299 | If the aim of logic is to codify inferences, second-order logic is useless [Shapiro] |
10300 | Logical consequence can be defined in terms of the logical terminology [Shapiro] |
10290 | Second-order variables also range over properties, sets, relations or functions [Shapiro] |
10590 | Up Löwenheim-Skolem: if natural numbers satisfy wffs, then an infinite domain satisfies them [Shapiro] |
10296 | The Löwenheim-Skolem Theorems fail for second-order languages with standard semantics [Shapiro] |
10297 | The Löwenheim-Skolem theorem seems to be a defect of first-order logic [Shapiro] |
10292 | Downward Löwenheim-Skolem: if there's an infinite model, there is a countable model [Shapiro] |
18518 | Infinite numbers are qualitatively different - they are not just very large numbers [Heil] |
10294 | Second-order logic has the expressive power for mathematics, but an unworkable model theory [Shapiro] |
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] |
10591 | Logicians use 'property' and 'set' interchangeably, with little hanging on it [Shapiro] |
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] |
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] |
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] |
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] |
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] |
22489 | 'Good' is an attributive adjective like 'large', not predicative like 'red' [Geach, by Foot] |
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] |