57 ideas
4697 | There has been a distinct 'Social Turn' in recent philosophy, like the earlier 'Linguistic Turn' [O'Grady] |
4731 | Good reasoning will avoid contradiction, enhance coherence, not ignore evidence, and maximise evidence [O'Grady] |
10633 | 'Some critics admire only one another' cannot be paraphrased in singular first-order [Linnebo] |
4735 | Just as maps must simplify their subject matter, so thought has to be reductionist about reality [O'Grady] |
4703 | The epistemic theory of truth presents it as 'that which is licensed by our best theory of reality' [O'Grady] |
4701 | To say a relative truth is inexpressible in other frameworks is 'weak', while saying it is false is 'strong' [O'Grady] |
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] |
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] |
4705 | Logical relativism appears if we allow more than one legitimate logical system [O'Grady] |
4700 | A third value for truth might be "indeterminate", or a point on a scale between 'true' and 'false' [O'Grady] |
4704 | Wittgenstein reduced Russell's five primitive logical symbols to a mere one [O'Grady] |
10783 | Plural quantification depends too heavily on combinatorial and set-theoretic considerations [Linnebo] |
10635 | Second-order quantification and plural quantification are different [Linnebo] |
10641 | Traditionally we eliminate plurals by quantifying over sets [Linnebo] |
10640 | Instead of complex objects like tables, plurally quantify over mereological atoms tablewise [Linnebo] |
10778 | Can second-order logic be ontologically first-order, with all the benefits of second-order? [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] |
13007 | Archimedes defined a straight line as the shortest distance between two points [Archimedes, by Leibniz] |
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] |
4711 | Anti-realists say our theories (such as wave-particle duality) give reality incompatible properties [O'Grady] |
4698 | What counts as a fact partly depends on the availability of human concepts to describe them [O'Grady] |
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] |
4715 | We may say that objects have intrinsic identity conditions, but still allow multiple accounts of them [O'Grady] |
4719 | Maybe developments in logic and geometry have shown that the a priori may be relative [O'Grady] |
4720 | Sense-data are only safe from scepticism if they are primitive and unconceptualised [O'Grady] |
4722 | Modern epistemology centres on debates about foundations, and about external justification [O'Grady] |
4724 | Internalists say the reasons for belief must be available to the subject, and externalists deny this [O'Grady] |
4723 | Coherence involves support from explanation and evidence, and also probability and confirmation [O'Grady] |
4709 | Ontological relativists are anti-realists, who deny that our theories carve nature at the joints [O'Grady] |
4725 | Contextualism says that knowledge is relative to its context; 'empty' depends on your interests [O'Grady] |
4732 | One may understand a realm of ideas, but be unable to judge their rationality or truth [O'Grady] |
4710 | Verificationism was attacked by the deniers of the analytic-synthetic distinction, needed for 'facts' [O'Grady] |
10634 | Predicates are 'distributive' or 'non-distributive'; do individuals do what the group does? [Linnebo] |
4717 | If we abandon the analytic-synthetic distinction, scepticism about meaning may be inevitable [O'Grady] |
4706 | Early Quine says all beliefs could be otherwise, but later he said we would assume mistranslation [O'Grady] |
4734 | Cryptographers can recognise that something is a language, without translating it [O'Grady] |
4727 | The chief problem for fideists is other fideists who hold contrary ideas [O'Grady] |