49 ideas
6161 | Structuralism is neo-Kantian idealism, with language playing the role of categories of understanding [Rowlands] |
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] |
6163 | If bivalence is rejected, then excluded middle must also be rejected [Rowlands] |
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] |
6155 | Supervenience is a one-way relation of dependence or determination between properties [Rowlands] |
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] |
6154 | It is argued that wholes possess modal and counterfactual properties that parts lack [Rowlands] |
6157 | Tokens are dated, concrete particulars; types are their general properties or kinds [Rowlands] |
6159 | Strong idealism is the sort of mess produced by a Cartesian separation of mind and world [Rowlands] |
6152 | Minds are rational, conscious, subjective, self-knowing, free, meaningful and self-aware [Rowlands] |
6173 | Content externalism implies that we do not have privileged access to our own minds [Rowlands] |
6174 | If someone is secretly transported to Twin Earth, others know their thoughts better than they do [Rowlands] |
6158 | Supervenience of mental and physical properties often comes with token-identity of mental and physical particulars [Rowlands] |
6168 | The content of a thought is just the meaning of a sentence [Rowlands] |
10634 | Predicates are 'distributive' or 'non-distributive'; do individuals do what the group does? [Linnebo] |
6167 | Action is bodily movement caused by intentional states [Rowlands] |
6177 | Moral intuition seems unevenly distributed between people [Rowlands] |
6156 | The 17th century reintroduced atoms as mathematical modes of Euclidean space [Rowlands] |
6170 | Natural kinds are defined by their real essence, as in gold having atomic number 79 [Rowlands] |
6178 | It is common to see the value of nature in one feature, such as life, diversity, or integrity [Rowlands] |