56 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] |
10405 | In the iterative conception of sets, they form a natural hierarchy [Swoyer] |
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] |
10407 | Logical Form explains differing logical behaviour of similar sentences [Swoyer] |
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] |
10778 | Can second-order logic be ontologically first-order, with all the benefits of second-order? [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] |
14592 | Some abstract things have a beginning and end, so may exist in time (though not space) [Swoyer] |
14091 | There may be a one-way direction of dependence among sets, and among natural numbers [Linnebo] |
10421 | Supervenience is nowadays seen as between properties, rather than linguistic [Swoyer] |
14594 | Ontologists seek existence and identity conditions, and modal and epistemic status for a thing [Swoyer] |
10410 | Anti-realists can't explain different methods to measure distance [Swoyer] |
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] |
10416 | Can properties have parts? [Swoyer] |
14595 | Can properties exemplify other properties? [Swoyer] |
10399 | If a property such as self-identity can only be in one thing, it can't be a universal [Swoyer] |
14088 | An 'intrinsic' property is either found in every duplicate, or exists independent of all externals [Linnebo] |
10417 | There are only first-order properties ('red'), and none of higher-order ('coloured') [Swoyer] |
10413 | The best-known candidate for an identity condition for properties is necessary coextensiveness [Swoyer] |
10402 | Various attempts are made to evade universals being wholly present in different places [Swoyer] |
10400 | Conceptualism says words like 'honesty' refer to concepts, not to properties [Swoyer] |
10782 | The modern concept of an object is rooted in quantificational logic [Linnebo] |
10403 | If properties are abstract objects, then their being abstract exemplifies being abstract [Swoyer] |
14593 | Quantum field theory suggests that there are, fundamentally, no individual things [Swoyer] |
12887 | A whole must have one characteristic, an internal relation, and a structure [Rescher/Oppenheim] |
10406 | One might hope to reduce possible worlds to properties [Swoyer] |
10404 | Extreme empiricists can hardly explain anything [Swoyer] |
10408 | Intensions are functions which map possible worlds to sets of things denoted by an expression [Swoyer] |
10409 | Research suggests that concepts rely on typical examples [Swoyer] |
10401 | The F and G of logic cover a huge range of natural language combinations [Swoyer] |
10634 | Predicates are 'distributive' or 'non-distributive'; do individuals do what the group does? [Linnebo] |
10420 | Maybe a proposition is just a property with all its places filled [Swoyer] |
10412 | If laws are mere regularities, they give no grounds for future prediction [Swoyer] |
10411 | Two properties can have one power, and one property can have two powers [Swoyer] |