39 ideas
2319 | Metaphysics is the clarification of the ontological relationships between different areas of thought [Kim] |
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] |
2317 | Reductionism is good on light, genes, temperature and transparency [Kim, by PG] |
2310 | Supervenience is linked to dependence [Kim] |
2315 | Mereological supervenience says wholes are fixed by parts [Kim] |
2329 | Causal power is a good way of distinguishing the real from the unreal [Kim] |
2320 | Properties can have causal powers lacked by their constituents [Kim] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
530 | There are two contradictory arguments about everything [Kim] |
13314 | Protagoras says arguments on both sides are always equal [Kim, by Seneca] |
2065 | Not every person is the measure of all things, but only wise people [Plato on Kim] |
1550 | Why didn't Protagoras begin by saying "a tadpole is the measure of all things"? [Plato on Kim] |
2318 | Agency, knowledge, reason, memory, psychology all need mental causes [Kim, by PG] |
2325 | It seems impossible that an exact physical copy of this world could lack intentionality [Kim] |
2324 | Intentionality as function seems possible [Kim] |
2314 | Maybe intentionality is reducible, but qualia aren't [Kim] |
2313 | Emergentism says there is no explanation for a supervenient property [Kim] |
2328 | The only mental property that might be emergent is that of qualia [Kim] |
2309 | Non-Reductive Physicalism relies on supervenience [Kim] |
2311 | Maybe strong supervenience implies reduction [Kim] |
2308 | Identity theory was overthrown by multiple realisations and causal anomalies [Kim] |
2322 | Multiple realisation applies to other species, and even one individual over time [Kim] |
2327 | Knowledge and inversion make functionalism about qualia doubtful [Kim] |
2323 | Emotions have both intentionality and qualia [Kim] |
18883 | Any equivalence relation among similar things allows the creation of an abstractum [Simons] |
18884 | Abstraction is usually seen as producing universals and numbers, but it can do more [Simons] |