26 ideas
| 2510 | Traditionally philosophy is an a priori enquiry into general truths about reality [Katz] |
| 2516 | Most of philosophy begins where science leaves off [Katz] |
| 8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
| 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] |
| 2521 | 'Real' maths objects have no causal role, no determinate reference, and no abstract/concrete distinction [Katz] |
| 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] |
| 13074 | Only natural kinds and their members have real essences [Suárez, by Cover/O'Leary-Hawthorne] |
| 2513 | We don't have a clear enough sense of meaning to pronounce some sentences meaningless or just analytic [Katz] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 2522 | Experience cannot teach us why maths and logic are necessary [Katz] |
| 2517 | Structuralists see meaning behaviouristically, and Chomsky says nothing about it [Katz] |
| 2519 | It is generally accepted that sense is defined as the determiner of reference [Katz] |
| 2520 | Sense determines meaning and synonymy, not referential properties like denotation and truth [Katz] |
| 2518 | Sentences are abstract types (like musical scores), not individual tokens [Katz] |
| 7563 | The old 'influx' view of causation says it is a flow of accidental properties from A to B [Suárez, by Jolley] |