32 ideas
| 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] |
| 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] |
| 1350 | Continuity is needed for existence, otherwise we would say a thing existed after it ceased to exist [Reid] |
| 21322 | We treat slowly changing things as identical for the sake of economy in language [Reid] |
| 21320 | Identity is familiar to common sense, but very hard to define [Reid] |
| 1367 | Identity can only be affirmed of things which have a continued existence [Reid] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 23644 | Without memory we could have no concept of duration [Reid] |
| 23643 | We all trust our distinct memories (but not our distinct imaginings) [Reid] |
| 15282 | Facts should be deducible from the theory and initial conditions, and prefer the simpler theory [Osiander, by Harré/Madden] |
| 1356 | A person is a unity, and doesn't come in degrees [Reid] |
| 1359 | Personal identity is the basis of all rights, obligations and responsibility [Reid] |
| 21319 | I can hardly care about rational consequence if it wasn't me conceiving the antecedent [Reid] |
| 21323 | The identity of a thief is only known by similarity, but memory gives certainty in our own case [Reid] |
| 21321 | Memory reveals my past identity - but so does testimony of other witnesses [Reid] |
| 21324 | If consciousness is transferable 20 persons can be 1; forgetting implies 1 can be 20 [Reid] |
| 21325 | Boy same as young man, young man same as old man, old man not boy, if forgotten! [Reid] |
| 21327 | If a stolen horse is identified by similitude, its identity is not therefore merely similitude [Reid] |
| 1366 | If consciousness is personal identity, it is continually changing [Reid] |
| 1352 | Thoughts change continually, but the self doesn't [Reid] |