44 ideas
| 8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
| 10373 | Logical form can't dictate metaphysics, as it may propose an undesirable property [Schaffer,J] |
| 8763 | The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro] |
| 18249 | Cauchy gave a formal definition of a converging sequence. [Shapiro] |
| 8764 | Categories are the best foundation for mathematics [Shapiro] |
| 8762 | Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro] |
| 8760 | Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro] |
| 8761 | A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro] |
| 8744 | Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro] |
| 8749 | Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro] |
| 8750 | Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro] |
| 8752 | Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro] |
| 8753 | Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro] |
| 8731 | Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro] |
| 8730 | 'Impredicative' definitions refer to the thing being described [Shapiro] |
| 10367 | There is only one fact - the True [Schaffer,J] |
| 594 | Speusippus suggested underlying principles for every substance, and ended with a huge list [Speussipus, by Aristotle] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 10359 | In causation there are three problems of relata, and three metaphysical problems [Schaffer,J] |
| 10372 | Causation may not be transitive; the last event may follow from the first, but not be caused by it [Schaffer,J] |
| 10374 | There are at least ten theories about causal connections [Schaffer,J] |
| 10366 | Causation transcends nature, because absences can cause things [Schaffer,J] |
| 10377 | Causation may not be a process, if a crucial part of the process is 'disconnected' [Schaffer,J] |
| 10378 | A causal process needs to be connected to the effect in the right way [Schaffer,J] |
| 10382 | Causation can't be a process, because a process needs causation as a primitive [Schaffer,J] |
| 10375 | At least four rivals have challenged the view that causal direction is time direction [Schaffer,J] |
| 10389 | Causal order must be temporal, or else causes could be blocked, and time couldn't be explained [Schaffer,J] |
| 10390 | Causal order is not temporal, because of time travel, and simultanous, joint or backward causes [Schaffer,J] |
| 10380 | Causation is primitive; it is too intractable and central to be reduced; all explanations require it [Schaffer,J] |
| 10385 | If causation is just observables, or part of common sense, or vacuous, it can't be primitive [Schaffer,J] |
| 10387 | The notion of causation allows understanding of science, without appearing in equations [Schaffer,J] |
| 10388 | Causation is utterly essential for numerous philosophical explanations [Schaffer,J] |
| 10384 | If two different causes are possible in one set of circumstances, causation is primitive [Schaffer,J] |
| 10386 | If causation is primitive, it can be experienced in ourselves, or inferred as best explanation [Schaffer,J] |
| 10361 | Events are fairly course-grained (just saying 'hello'), unlike facts (like saying 'hello' loudly) [Schaffer,J] |
| 10360 | Causal relata are events - or facts, features, tropes, states, situations or aspects [Schaffer,J] |
| 10362 | One may defend three or four causal relata, as in 'c causes e rather than e*' [Schaffer,J] |
| 10368 | If causal relata must be in nature and fine-grained, neither facts nor events will do [Schaffer,J] |
| 10383 | The relata of causation (such as events) need properties as explanation, which need causation! [Schaffer,J] |
| 10393 | Our selection of 'the' cause is very predictable, so must have a basis [Schaffer,J] |
| 10394 | Selecting 'the' cause must have a basis; there is no causation without such a selection [Schaffer,J] |
| 10376 | The actual cause may make an event less likely than a possible more effective cause [Schaffer,J] |
| 10381 | All four probability versions of causation may need causation to be primitive [Schaffer,J] |
| 2632 | Speusippus said things were governed by some animal force rather than the gods [Speussipus, by Cicero] |