50 ideas
17729 | Examining concepts can recover information obtained through the senses [Jenkins] |
10633 | 'Some critics admire only one another' cannot be paraphrased in singular first-order [Linnebo] |
17740 | Instead of correspondence of proposition to fact, look at correspondence of its parts [Jenkins] |
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] |
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] |
17730 | Combining the concepts of negation and finiteness gives the concept of infinity [Jenkins] |
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] |
17719 | Arithmetic concepts are indispensable because they accurately map the world [Jenkins] |
17717 | Senses produce concepts that map the world, and arithmetic is known through these concepts [Jenkins] |
23441 | Logical truth is true in all models, so mathematical objects can't be purely logical [Linnebo] |
17724 | It is not easy to show that Hume's Principle is analytic or definitive in the required sense [Jenkins] |
23442 | Game Formalism has no semantics, and Term Formalism reduces the semantics [Linnebo] |
17727 | We can learn about the world by studying the grounding of our concepts [Jenkins] |
14091 | There may be a one-way direction of dependence among sets, and among natural numbers [Linnebo] |
17720 | There's essential, modal, explanatory, conceptual, metaphysical and constitutive dependence [Jenkins, by PG] |
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] |
17728 | The concepts we have to use for categorising are ones which map the real world well [Jenkins] |
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] |
17726 | Examining accurate, justified or grounded concepts brings understanding of the world [Jenkins] |
17734 | It is not enough that intuition be reliable - we need to know why it is reliable [Jenkins] |
17723 | Knowledge is true belief which can be explained just by citing the proposition believed [Jenkins] |
17739 | The physical effect of world on brain explains the concepts we possess [Jenkins] |
17718 | Grounded concepts are trustworthy maps of the world [Jenkins] |
17731 | Verificationism is better if it says meaningfulness needs concepts grounded in the senses [Jenkins] |
17732 | Success semantics explains representation in terms of success in action [Jenkins] |
10634 | Predicates are 'distributive' or 'non-distributive'; do individuals do what the group does? [Linnebo] |
17725 | 'Analytic' can be conceptual, or by meaning, or predicate inclusion, or definition... [Jenkins] |
1513 | The Egyptians were the first to say the soul is immortal and reincarnated [Herodotus] |