25 ideas
| 18274 | Analysis complicates a statement, but only as far as the complexity of its meaning [Wittgenstein] |
| 16908 | We can dispense with self-evidence, if language itself prevents logical mistakes [Jeshion on Wittgenstein] |
| 8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
| 18276 | A statement's logical form derives entirely from its constituents [Wittgenstein] |
| 6563 | 'And' and 'not' are non-referring terms, which do not represent anything [Wittgenstein, by Fogelin] |
| 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] |
| 23472 | The sense of propositions relies on the world's basic logical structure [Wittgenstein] |
| 23500 | My main problem is the order of the world, and whether it is knowable a priori [Wittgenstein] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 22323 | The philosophical I is the metaphysical subject, the limit - not a part of the world [Wittgenstein] |
| 23481 | Propositions assemble a world experimentally, like the model of a road accident [Wittgenstein] |
| 20746 | One is not born, but rather becomes a woman [Beauvoir] |
| 4678 | Absolute prohibitions are the essence of ethics, and suicide is the most obvious example [Wittgenstein] |