30 ideas
| 9376 | A sentence may simultaneously define a term, and also assert a fact [Boghossian] |
| 19053 | Logic would be more natural if negation only referred to predicates [Dummett] |
| 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] |
| 9375 | Conventionalism agrees with realists that logic has truth values, but not over the source [Boghossian] |
| 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] |
| 9369 | 'Snow is white or it isn't' is just true, not made true by stipulation [Boghossian] |
| 9367 | The a priori is explained as analytic to avoid a dubious faculty of intuition [Boghossian] |
| 9373 | That logic is a priori because it is analytic resulted from explaining the meaning of logical constants [Boghossian] |
| 9380 | We can't hold a sentence true without evidence if we can't agree which sentence is definitive of it [Boghossian] |
| 9384 | We may have strong a priori beliefs which we pragmatically drop from our best theory [Boghossian] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 9374 | If we learn geometry by intuition, how could this faculty have misled us for so long? [Boghossian] |
| 9378 | If meaning depends on conceptual role, what properties are needed to do the job? [Boghossian] |
| 9377 | 'Conceptual role semantics' says terms have meaning from sentences and/or inferences [Boghossian] |
| 9372 | Could expressions have meaning, without two expressions possibly meaning the same? [Boghossian] |
| 17721 | There are no truths in virtue of meaning, but there is knowability in virtue of understanding [Boghossian, by Jenkins] |
| 9368 | Epistemological analyticity: grasp of meaning is justification; metaphysical: truth depends on meaning [Boghossian] |