26 ideas
| 21695 | The set scheme discredited by paradoxes is actually the most natural one [Quine] |
| 21693 | Russell's antinomy challenged the idea that any condition can produce a set [Quine] |
| 8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
| 21691 | Antinomies contradict accepted ways of reasoning, and demand revisions [Quine] |
| 21690 | Whenever the pursuer reaches the spot where the pursuer has been, the pursued has moved on [Quine] |
| 21689 | A barber shaves only those who do not shave themselves. So does he shave himself? [Quine] |
| 21694 | Membership conditions which involve membership and non-membership are paradoxical [Quine] |
| 21692 | If we write it as '"this sentence is false" is false', there is no paradox [Quine] |
| 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] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 22330 | Grice said patterns of use are often semantically irrelevant, because it is a pragmatic matter [Grice, by Glock] |
| 18045 | Grice's maxim of quality says do not assert what you believe to be false [Grice, by Magidor] |
| 18044 | Grice's maxim of manner requires one to be as brief as possible [Grice, by Magidor] |
| 18046 | Grice's maxim of quantity says be sufficiently informative [Grice, by Magidor] |