50 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] |
| 10170 | While true-in-a-model seems relative, true-in-all-models seems not to be [Reck/Price] |
| 10166 | ZFC set theory has only 'pure' sets, without 'urelements' [Reck/Price] |
| 3599 | Deduction shows entailments, not what to believe [Williams,M] |
| 10175 | Three types of variable in second-order logic, for objects, functions, and predicates/sets [Reck/Price] |
| 10165 | 'Analysis' is the theory of the real numbers [Reck/Price] |
| 10174 | Mereological arithmetic needs infinite objects, and function definitions [Reck/Price] |
| 10164 | Peano Arithmetic can have three second-order axioms, plus '1' and 'successor' [Reck/Price] |
| 10172 | Set-theory gives a unified and an explicit basis for mathematics [Reck/Price] |
| 10167 | Structuralism emerged from abstract algebra, axioms, and set theory and its structures [Reck/Price] |
| 10169 | Relativist Structuralism just stipulates one successful model as its arithmetic [Reck/Price] |
| 10179 | There are 'particular' structures, and 'universal' structures (what the former have in common) [Reck/Price] |
| 10181 | Pattern Structuralism studies what isomorphic arithmetic models have in common [Reck/Price] |
| 10182 | There are Formalist, Relativist, Universalist and Pattern structuralism [Reck/Price] |
| 10168 | Formalist Structuralism says the ontology is vacuous, or formal, or inference relations [Reck/Price] |
| 10178 | Maybe we should talk of an infinity of 'possible' objects, to avoid arithmetic being vacuous [Reck/Price] |
| 10176 | Universalist Structuralism is based on generalised if-then claims, not one particular model [Reck/Price] |
| 10177 | Universalist Structuralism eliminates the base element, as a variable, which is then quantified out [Reck/Price] |
| 10171 | The existence of an infinite set is assumed by Relativist Structuralism [Reck/Price] |
| 10173 | A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price] |
| 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] |
| 3586 | Only a belief can justify a belief [Williams,M] |
| 3567 | How could there be causal relations to mathematical facts? [Williams,M] |
| 3569 | In the causal theory of knowledge the facts must cause the 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] |
| 3588 | Foundationalists base meaning in words, coherentists base it in sentences [Williams,M] |
| 5049 | Intelligent pleasure is the perception of beauty, order and perfection [Leibniz] |
| 5048 | Perfection is simply quantity of reality [Leibniz] |
| 5050 | Evil serves a greater good, and pain is necessary for higher pleasure [Leibniz] |