30 ideas
| 21544 | It seems that when a proposition is false, something must fail to subsist [Russell] |
| 19053 | Logic would be more natural if negation only referred to predicates [Dummett] |
| 21539 | Excluded middle can be stated psychologically, as denial of p implies assertion of not-p [Russell] |
| 8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
| 19052 | Natural language 'not' doesn't apply to sentences [Dummett] |
| 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] |
| 21538 | If two people perceive the same object, the object of perception can't be in the mind [Russell] |
| 21534 | The only thing we can say about relations is that they relate [Russell] |
| 21540 | Relational propositions seem to be 'about' their terms, rather than about the relation [Russell] |
| 21536 | When I perceive a melody, I do not perceive the notes as existing [Russell] |
| 21535 | Objects only exist if they 'occupy' space and time [Russell] |
| 21533 | Contingency arises from tensed verbs changing the propositions to which they refer [Russell] |
| 21537 | I assume we perceive the actual objects, and not their 'presentations' [Russell] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 21532 | Full empiricism is not tenable, but empirical investigation is always essential [Russell] |
| 21542 | Do incorrect judgements have non-existent, or mental, or external objects? [Russell] |
| 21541 | The complexity of the content correlates with the complexity of the object [Russell] |
| 21543 | If p is false, then believing not-p is knowing a truth, so negative propositions must exist [Russell] |