50 ideas
| 10354 | Correspondence could be with other beliefs, rather than external facts [Kusch] |
| 10353 | Tarskians distinguish truth from falsehood by relations between members of sets [Kusch] |
| 17926 | Rejecting double negation elimination undermines reductio proofs [Colyvan] |
| 17925 | Showing a disproof is impossible is not a proof, so don't eliminate double negation [Colyvan] |
| 17924 | Excluded middle says P or not-P; bivalence says P is either true or false [Colyvan] |
| 17929 | Löwenheim proved his result for a first-order sentence, and Skolem generalised it [Colyvan] |
| 17930 | Axioms are 'categorical' if all of their models are isomorphic [Colyvan] |
| 17928 | Ordinal numbers represent order relations [Colyvan] |
| 17923 | Intuitionists only accept a few safe infinities [Colyvan] |
| 17941 | Infinitesimals were sometimes zero, and sometimes close to zero [Colyvan] |
| 17922 | Reducing real numbers to rationals suggested arithmetic as the foundation of maths [Colyvan] |
| 17936 | Transfinite induction moves from all cases, up to the limit ordinal [Colyvan] |
| 17940 | Most mathematical proofs are using set theory, but without saying so [Colyvan] |
| 17931 | Structuralism say only 'up to isomorphism' matters because that is all there is to it [Colyvan] |
| 17932 | If 'in re' structures relies on the world, does the world contain rich enough structures? [Colyvan] |
| 10337 | We can have knowledge without belief, if others credit us with knowledge [Kusch] |
| 10357 | Methodological Solipsism assumes all ideas could be derived from one mind [Kusch] |
| 10339 | Foundations seem utterly private, even from oneself at a later time [Kusch] |
| 10331 | Testimony is reliable if it coheres with evidence for a belief, and with other beliefs [Kusch] |
| 10338 | The coherentist restricts the space of reasons to the realm of beliefs [Kusch] |
| 10340 | Individualistic coherentism lacks access to all of my beliefs, or critical judgement of my assessment [Kusch] |
| 10345 | Individual coherentism cannot generate the necessary normativity [Kusch] |
| 10350 | Cultures decide causal routes, and they can be critically assessed [Kusch] |
| 10343 | Process reliabilism has been called 'virtue epistemology', resting on perception, memory, reason [Kusch] |
| 10341 | Justification depends on the audience and one's social role [Kusch] |
| 10334 | Testimony is an area in which epistemology meets ethics [Kusch] |
| 10336 | Powerless people are assumed to be unreliable, even about their own lives [Kusch] |
| 10324 | Testimony does not just transmit knowledge between individuals - it actually generates knowledge [Kusch] |
| 10327 | Some want to reduce testimony to foundations of perceptions, memories and inferences [Kusch] |
| 10329 | Testimony won't reduce to perception, if perception depends on social concepts and categories [Kusch] |
| 10330 | A foundation is what is intelligible, hence from a rational source, and tending towards truth [Kusch] |
| 10325 | Vindicating testimony is an expression of individualism [Kusch] |
| 10335 | Myths about lonely genius are based on epistemological individualism [Kusch] |
| 10323 | Communitarian Epistemology says 'knowledge' is a social status granted to groups of people [Kusch] |
| 10348 | Private justification is justification to imagined other people [Kusch] |
| 17943 | Probability supports Bayesianism better as degrees of belief than as ratios of frequencies [Colyvan] |
| 17939 | Mathematics can reveal structural similarities in diverse systems [Colyvan] |
| 17938 | Mathematics can show why some surprising events have to occur [Colyvan] |
| 17934 | Proof by cases (by 'exhaustion') is said to be unexplanatory [Colyvan] |
| 17933 | Reductio proofs do not seem to be very explanatory [Colyvan] |
| 17935 | If inductive proofs hold because of the structure of natural numbers, they may explain theorems [Colyvan] |
| 17942 | Can a proof that no one understands (of the four-colour theorem) really be a proof? [Colyvan] |
| 17937 | Mathematical generalisation is by extending a system, or by abstracting away from it [Colyvan] |
| 10349 | To be considered 'an individual' is performed by a society [Kusch] |
| 10344 | Our experience may be conceptual, but surely not the world itself? [Kusch] |
| 10358 | Often socialising people is the only way to persuade them [Kusch] |
| 20057 | Philosophy of action studies the roles of psychological states in causing behaviour [Mele] |
| 10333 | Communitarianism in epistemology sees the community as the primary knower [Kusch] |
| 10351 | Natural kinds are social institutions [Kusch] |
| 10332 | Omniscience is incoherent, since knowledge is a social concept [Kusch] |