52 ideas
| 3593 | The only way to specify the corresponding fact is asserting the sentence [Williams,M] |
| 3585 | Coherence needs positive links, not just absence of conflict [Williams,M] |
| 3584 | Justification needs coherence, while truth might be ideal coherence [Williams,M] |
| 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] |
| 3599 | Deduction shows entailments, not what to believe [Williams,M] |
| 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] |
| 3591 | We could never pin down how many beliefs we have [Williams,M] |
| 3582 | Propositions make error possible, so basic experiential knowledge is impossible [Williams,M] |
| 3592 | Phenomenalism is a form of idealism [Williams,M] |
| 3579 | Sense data avoid the danger of misrepresenting the world [Williams,M] |
| 3581 | Sense data can't give us knowledge if they are non-propositional [Williams,M] |
| 3564 | Is it people who are justified, or propositions? [Williams,M] |
| 3595 | What works always takes precedence over theories [Williams,M] |
| 3580 | Experience must be meaningful to act as foundations [Williams,M] |
| 3578 | Are empirical foundations judgements or experiences? [Williams,M] |
| 3576 | Foundationalists are torn between adequacy and security [Williams,M] |
| 3577 | Strong justification eliminates error, but also reduces our true beliefs [Williams,M] |
| 3589 | Why should diverse parts of our knowledge be connected? [Williams,M] |
| 3590 | Coherence theory must give a foundational status to coherence itself [Williams,M] |
| 3571 | Externalism does not require knowing that you know [Williams,M] |
| 3574 | Externalism ignores the social aspect of knowledge [Williams,M] |
| 3569 | In the causal theory of knowledge the facts must cause the belief [Williams,M] |
| 3567 | How could there be causal relations to mathematical facts? [Williams,M] |
| 3586 | Only a belief can justify a belief [Williams,M] |
| 3573 | Externalist reliability refers to a range of conventional conditions [Williams,M] |
| 3565 | Sometimes I ought to distrust sources which are actually reliable [Williams,M] |
| 3566 | We control our beliefs by virtue of how we enquire [Williams,M] |
| 3594 | Scepticism just reveals our limited ability to explain things [Williams,M] |
| 3575 | Scepticism can involve discrepancy, relativity, infinity, assumption and circularity [Williams,M] |
| 3587 | Seeing electrons in a cloud chamber requires theory [Williams,M] |
| 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] |
| 3588 | Foundationalists base meaning in words, coherentists base it in sentences [Williams,M] |
| 13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
| 20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |