26 ideas
| 22438 | Philosophy is largely concerned with finding the minimum that science could get by with [Quine] |
| 22436 | Logicians don't paraphrase logic into language, because they think in the symbolic language [Quine] |
| 22431 | Good algorithms and theories need many occurrences of just a few elements [Quine] |
| 22435 | The logician's '→' does not mean the English if-then [Quine] |
| 22433 | It is important that the quantification over temporal entities is timeless [Quine] |
| 22437 | Logical languages are rooted in ordinary language, and that connection must be kept [Quine] |
| 8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
| 22434 | Reduction to logical forms first simplifies idioms and grammar, then finds a single reading of it [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] |
| 22432 | Normally conditionals have no truth value; it is the consequent which has a conditional truth value [Quine] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 22430 | If we understand a statement, we know the circumstances of its truth [Quine] |
| 20751 | As a young girl assumes her status as feminine, she acts in a more fragile immobile way [Young,IM] |
| 13713 | Quine holds time to be 'space-like': past objects are as real as spatially remote ones [Quine, by Sider] |