61 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] |
13201 | ∈ says the whole set is in the other; ⊆ says the members of the subset are in the other [Enderton] |
13204 | The 'ordered pair' <x,y> is defined to be {{x}, {x,y}} [Enderton] |
13206 | A 'linear or total ordering' must be transitive and satisfy trichotomy [Enderton] |
13200 | Note that {Φ} =/= Φ, because Φ ∈ {Φ} but Φ ∉ Φ [Enderton] |
13199 | The empty set may look pointless, but many sets can be constructed from it [Enderton] |
14239 | The empty set is usually derived from Separation, but it also seems to need Infinity [Oliver/Smiley] |
14240 | The empty set is something, not nothing! [Oliver/Smiley] |
14241 | We don't need the empty set to express non-existence, as there are other ways to do that [Oliver/Smiley] |
14242 | Maybe we can treat the empty set symbol as just meaning an empty term [Oliver/Smiley] |
13203 | The singleton is defined using the pairing axiom (as {x,x}) [Enderton] |
14243 | The unit set may be needed to express intersections that leave a single member [Oliver/Smiley] |
13202 | Fraenkel added Replacement, to give a theory of ordinal numbers [Enderton] |
13205 | We can only define functions if Choice tells us which items are involved [Enderton] |
14234 | If you only refer to objects one at a time, you need sets in order to refer to a plurality [Oliver/Smiley] |
14237 | We can use plural language to refer to the set theory domain, to avoid calling it a 'set' [Oliver/Smiley] |
14245 | Logical truths are true no matter what exists - but predicate calculus insists that something exists [Oliver/Smiley] |
14246 | If mathematics purely concerned mathematical objects, there would be no applied mathematics [Oliver/Smiley] |
18518 | Infinite numbers are qualitatively different - they are not just very large numbers [Heil] |
14247 | Sets might either represent the numbers, or be the numbers, or replace the numbers [Oliver/Smiley] |
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] |
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] |
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] |