63 ideas
| 9641 | Definitions should be replaceable by primitives, and should not be creative [Brown,JR] |
| 9376 | A sentence may simultaneously define a term, and also assert a fact [Boghossian] |
| 6345 | Minimalism is incoherent, as it implies that truth both is and is not a property [Boghossian, by Horwich] |
| 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] |
| 9375 | Conventionalism agrees with realists that logic has truth values, but not over the source [Boghossian] |
| 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] |
| 9619 | David's 'Napoleon' is about something concrete and something abstract [Brown,JR] |
| 9369 | 'Snow is white or it isn't' is just true, not made true by stipulation [Boghossian] |
| 9367 | The a priori is explained as analytic to avoid a dubious faculty of intuition [Boghossian] |
| 9373 | That logic is a priori because it is analytic resulted from explaining the meaning of logical constants [Boghossian] |
| 9380 | We can't hold a sentence true without evidence if we can't agree which sentence is definitive of it [Boghossian] |
| 9384 | We may have strong a priori beliefs which we pragmatically drop from our best theory [Boghossian] |
| 9374 | If we learn geometry by intuition, how could this faculty have misled us for so long? [Boghossian] |
| 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] |
| 9378 | If meaning depends on conceptual role, what properties are needed to do the job? [Boghossian] |
| 9377 | 'Conceptual role semantics' says terms have meaning from sentences and/or inferences [Boghossian] |
| 9372 | Could expressions have meaning, without two expressions possibly meaning the same? [Boghossian] |
| 17721 | There are no truths in virtue of meaning, but there is knowability in virtue of understanding [Boghossian, by Jenkins] |
| 9368 | Epistemological analyticity: grasp of meaning is justification; metaphysical: truth depends on meaning [Boghossian] |
| 20289 | Ethics is universalisable - it must involve an impartial and universal view of things [Singer] |
| 20286 | Following an inner voice for morality is irresponsible in a rational agent [Singer] |
| 20282 | The sanctity of a human life depends either on being of our species, or on being a person [Singer] |
| 20278 | 'Marginal utility' says something is more useful if it is in short supply [Singer] |
| 20281 | Why should I do anything for posterity? What has posterity ever done for me? [Singer] |
| 20276 | Conflict of rules might be avoided by greater complexity, or by a hierarchy of rules [Singer] |
| 20290 | Psychopaths may just be bored, because they cannot participate in normal emotional life [Singer] |
| 20288 | You can't condemn violent revolution without assessing the evils it prevents [Singer] |
| 21997 | In Marxism the state will be superseded [Singer] |
| 20287 | If 49% of the population can be wrong, so can 51% [Singer] |
| 21993 | Materialist history says we are subject to incomprehensible forces [Singer] |
| 20277 | Equality of interests is a minimal principle, not implying equal treatment [Singer] |
| 20279 | Equality of opportunity unfairly rewards those lucky enough to have great ability [Singer] |
| 20285 | If a right entails having the relevant desire, many creatures might have no right to life [Singer] |
| 20284 | Why should a potential person have the rights of an actual person? [Singer] |
| 20283 | Killing a chimp is worse than killing a human too defective to be a person [Singer] |
| 9635 | Given atomism at one end, and a finite universe at the other, there are no physical infinities [Brown,JR] |