57 ideas
| 2319 | Metaphysics is the clarification of the ontological relationships between different areas of thought [Kim] |
| 9641 | Definitions should be replaceable by primitives, and should not be creative [Brown,JR] |
| 9634 | Set theory says that natural numbers are an actual infinity (to accommodate their powerset) [Brown,JR] |
| 9613 | Naïve set theory assumed that there is a set for every condition [Brown,JR] |
| 9615 | Nowadays conditions are only defined on existing sets [Brown,JR] |
| 9617 | The 'iterative' view says sets start with the empty set and build up [Brown,JR] |
| 9642 | A flock of birds is not a set, because a set cannot go anywhere [Brown,JR] |
| 9605 | If a proposition is false, then its negation is true [Brown,JR] |
| 9649 | Axioms are either self-evident, or stipulations, or fallible attempts [Brown,JR] |
| 9638 | Berry's Paradox finds a contradiction in the naming of huge numbers [Brown,JR] |
| 9604 | Mathematics is the only place where we are sure we are right [Brown,JR] |
| 9622 | 'There are two apples' can be expressed logically, with no mention of numbers [Brown,JR] |
| 9648 | π is a 'transcendental' number, because it is not the solution of an equation [Brown,JR] |
| 9621 | Mathematics represents the world through structurally similar models. [Brown,JR] |
| 9646 | There is no limit to how many ways something can be proved in mathematics [Brown,JR] |
| 9647 | Computers played an essential role in proving the four-colour theorem of maps [Brown,JR] |
| 9643 | Set theory may represent all of mathematics, without actually being mathematics [Brown,JR] |
| 9644 | When graphs are defined set-theoretically, that won't cover unlabelled graphs [Brown,JR] |
| 9625 | To see a structure in something, we must already have the idea of the structure [Brown,JR] |
| 9628 | Sets seem basic to mathematics, but they don't suit structuralism [Brown,JR] |
| 9606 | The irrationality of root-2 was achieved by intellect, not experience [Brown,JR] |
| 9612 | There is an infinity of mathematical objects, so they can't be physical [Brown,JR] |
| 9610 | Numbers are not abstracted from particulars, because each number is a particular [Brown,JR] |
| 9620 | Empiricists base numbers on objects, Platonists base them on properties [Brown,JR] |
| 9639 | Does some mathematics depend entirely on notation? [Brown,JR] |
| 9629 | For nomalists there are no numbers, only numerals [Brown,JR] |
| 9630 | The most brilliant formalist was Hilbert [Brown,JR] |
| 9608 | There are no constructions for many highly desirable results in mathematics [Brown,JR] |
| 9645 | Constructivists say p has no value, if the value depends on Goldbach's Conjecture [Brown,JR] |
| 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] |
| 9619 | David's 'Napoleon' is about something concrete and something abstract [Brown,JR] |
| 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] |
| 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] |
| 9611 | 'Abstract' nowadays means outside space and time, not concrete, not physical [Brown,JR] |
| 9609 | The older sense of 'abstract' is where 'redness' or 'group' is abstracted from particulars [Brown,JR] |
| 9640 | A term can have not only a sense and a reference, but also a 'computational role' [Brown,JR] |
| 13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
| 9635 | Given atomism at one end, and a finite universe at the other, there are no physical infinities [Brown,JR] |
| 20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |