69 ideas
| 10633 | 'Some critics admire only one another' cannot be paraphrased in singular first-order [Linnebo] |
| 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] |
| 10779 | A comprehension axiom is 'predicative' if the formula has no bound second-order variables [Linnebo] |
| 23445 | Naïve set theory says any formula defines a set, and coextensive sets are identical [Linnebo] |
| 3599 | Deduction shows entailments, not what to believe [Williams,M] |
| 10781 | A 'pure logic' must be ontologically innocent, universal, and without presuppositions [Linnebo] |
| 10638 | A pure logic is wholly general, purely formal, and directly known [Linnebo] |
| 10778 | Can second-order logic be ontologically first-order, with all the benefits of second-order? [Linnebo] |
| 10783 | Plural quantification depends too heavily on combinatorial and set-theoretic considerations [Linnebo] |
| 10635 | Second-order quantification and plural quantification are different [Linnebo] |
| 10640 | Instead of complex objects like tables, plurally quantify over mereological atoms tablewise [Linnebo] |
| 10641 | Traditionally we eliminate plurals by quantifying over sets [Linnebo] |
| 10636 | Plural plurals are unnatural and need a first-level ontology [Linnebo] |
| 10639 | Plural quantification may allow a monadic second-order theory with first-order ontology [Linnebo] |
| 23447 | In classical semantics singular terms refer, and quantifiers range over domains [Linnebo] |
| 23443 | The axioms of group theory are not assertions, but a definition of a structure [Linnebo] |
| 23444 | To investigate axiomatic theories, mathematics needs its own foundational axioms [Linnebo] |
| 6007 | If you know your father, but don't recognise your father veiled, you know and don't know the same person [Eubulides, by Dancy,R] |
| 6006 | If you say truly that you are lying, you are lying [Eubulides, by Dancy,R] |
| 6008 | Removing one grain doesn't destroy a heap, so a heap can't be destroyed [Eubulides, by Dancy,R] |
| 23446 | You can't prove consistency using a weaker theory, but you can use a consistent theory [Linnebo] |
| 23448 | Mathematics is the study of all possible patterns, and is thus bound to describe the world [Linnebo] |
| 14085 | 'Deductivist' structuralism is just theories, with no commitment to objects, or modality [Linnebo] |
| 14084 | Non-eliminative structuralism treats mathematical objects as positions in real abstract structures [Linnebo] |
| 14086 | 'Modal' structuralism studies all possible concrete models for various mathematical theories [Linnebo] |
| 14087 | 'Set-theoretic' structuralism treats mathematics as various structures realised among the sets [Linnebo] |
| 14089 | Structuralism differs from traditional Platonism, because the objects depend ontologically on their structure [Linnebo] |
| 14083 | Structuralism is right about algebra, but wrong about sets [Linnebo] |
| 14090 | In mathematical structuralism the small depends on the large, which is the opposite of physical structures [Linnebo] |
| 23441 | Logical truth is true in all models, so mathematical objects can't be purely logical [Linnebo] |
| 23442 | Game Formalism has no semantics, and Term Formalism reduces the semantics [Linnebo] |
| 14091 | There may be a one-way direction of dependence among sets, and among natural numbers [Linnebo] |
| 10643 | We speak of a theory's 'ideological commitments' as well as its 'ontological commitments' [Linnebo] |
| 10637 | Ordinary speakers posit objects without concern for ontology [Linnebo] |
| 14088 | An 'intrinsic' property is either found in every duplicate, or exists independent of all externals [Linnebo] |
| 10782 | The modern concept of an object is rooted in quantificational logic [Linnebo] |
| 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] |
| 8851 | Coherentists say that regress problems are assuming 'linear' justification [Williams,M] |
| 3595 | What works always takes precedence over theories [Williams,M] |
| 8849 | Traditional foundationalism is radically internalist [Williams,M] |
| 8853 | Basic judgements are immune from error because they have no content [Williams,M] |
| 3580 | Experience must be meaningful to act as foundations [Williams,M] |
| 3578 | Are empirical foundations judgements or experiences? [Williams,M] |
| 8855 | Sensory experience may be fixed, but it can still be misdescribed [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] |
| 8852 | In the context of scepticism, externalism does not seem to be an option [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] |
| 10634 | Predicates are 'distributive' or 'non-distributive'; do individuals do what the group does? [Linnebo] |