63 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] |
17749 | Post proved the consistency of propositional logic in 1921 [Walicki] |
17765 | Propositional language can only relate statements as the same or as different [Walicki] |
17764 | Boolean connectives are interpreted as functions on the set {1,0} [Walicki] |
17752 | The empty set is useful for defining sets by properties, when the members are not yet known [Walicki] |
17753 | The empty set avoids having to take special precautions in case members vanish [Walicki] |
17759 | Ordinals play the central role in set theory, providing the model of well-ordering [Walicki] |
17741 | To determine the patterns in logic, one must identify its 'building blocks' [Walicki] |
17747 | A 'model' of a theory specifies interpreting a language in a domain to make all theorems true [Walicki] |
17748 | The L-S Theorem says no theory (even of reals) says more than a natural number theory [Walicki] |
17761 | A compact axiomatisation makes it possible to understand a field as a whole [Walicki] |
17763 | Axiomatic systems are purely syntactic, and do not presuppose any interpretation [Walicki] |
17758 | Ordinals are transitive sets of transitive sets; or transitive sets totally ordered by inclusion [Walicki] |
17755 | Ordinals are the empty set, union with the singleton, and any arbitrary union of ordinals [Walicki] |
17756 | The union of finite ordinals is the first 'limit ordinal'; 2ω is the second... [Walicki] |
17760 | Two infinite ordinals can represent a single infinite cardinal [Walicki] |
17757 | Members of ordinals are ordinals, and also subsets of ordinals [Walicki] |
18518 | Infinite numbers are qualitatively different - they are not just very large numbers [Heil] |
17762 | In non-Euclidean geometry, all Euclidean theorems are valid that avoid the fifth postulate [Walicki] |
17754 | Inductive proof depends on the choice of the ordering [Walicki] |
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] |
17742 | Scotus based modality on semantic consistency, instead of on what the future could allow [Walicki] |
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] |
468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
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] |