52 ideas
10633 | 'Some critics admire only one another' cannot be paraphrased in singular first-order [Linnebo] |
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] |
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] |
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] |
20653 | Six reduction levels: groups, lives, cells, molecules, atoms, particles [Putnam/Oppenheim, by Watson] |
10634 | Predicates are 'distributive' or 'non-distributive'; do individuals do what the group does? [Linnebo] |
23125 | Most good social changes are incremental, rather than revolutionary [Gopnik] |
23126 | Conservatives often want peace, prosperity and tolerance, but not social fairness [Gopnik] |
23132 | Conservatives believe obedience and rank are essential to social order [Gopnik] |
23128 | The opposite of liberalism is dogmatism [Gopnik] |
23142 | People are fallible, so liberalism tries to distribute power [Gopnik] |
23143 | Liberals have tried very hard to build a conscience into their institutions [Gopnik] |
23141 | Left-wingers are inconsistent in their essentialist descriptions of social groups [Gopnik] |
23124 | Liberal community is not blood ties or tradition, but shared choices, and sympathy for the losers [Gopnik] |
23127 | Liberal community includes flight from the family, into energetic reforming groups [Gopnik] |
23138 | Modern left-wingers criticise liberalism's control of culture [Gopnik] |
23129 | Right-wingers attack liberal faith in reason, left-wingers attack its faith in reform [Gopnik] |
23133 | Cosmopolitan liberals lack national loyalty, and welcome excessive immigration [Gopnik] |
23139 | Liberalism's attempt to be neutral and colour-blind erases cultural identities [Gopnik] |
23135 | Classic Marxists see liberalism as the ideology of the bourgeoisie [Gopnik] |
23140 | Environmental disasters result not from capitalism, but from a general drive for growth [Gopnik] |
23130 | Popular imperialism gives the poor the belief that their acts have world historical meaning [Gopnik] |
23131 | Patriots love their place, but nationalists have a paranoid ethnic hostility [Gopnik] |
23136 | Liberal free speech is actually paid speech [Gopnik] |
23134 | A 'free' society implies a free market, which always produces predatory capitalism and inequalities [Gopnik] |