70 ideas
| 1798 | He studied philosophy by suspending his judgement on everything [Pyrrho, by Diog. Laertius] |
| 1800 | Sceptics say reason is only an instrument, because reason can only be attacked with reason [Pyrrho, by Diog. Laertius] |
| 10633 | 'Some critics admire only one another' cannot be paraphrased in singular first-order [Linnebo] |
| 12585 | Most people can't even define a chair [Peacocke] |
| 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] |
| 12581 | Perceptual concepts causally influence the content of our experiences [Peacocke] |
| 12579 | Perception has proto-propositions, between immediate experience and concepts [Peacocke] |
| 6595 | If we need a criterion of truth, we need to know whether it is the correct criterion [Pyrrho, by Fogelin] |
| 6593 | The Pyrrhonians attacked the dogmas of professors, not ordinary people [Pyrrho, by Fogelin] |
| 6592 | Academics said that Pyrrhonians were guilty of 'negative dogmatism' [Pyrrho, by Fogelin] |
| 1808 | Perception of things depends on their size or quantity (Mode 8) [Pyrrho, by Diog. Laertius] |
| 1802 | Individuals vary in responses and feelings (Mode 2) [Pyrrho, by Diog. Laertius] |
| 1807 | Perception varies with viewing distance and angle (Mode 7) [Pyrrho, by Diog. Laertius] |
| 1801 | Animals vary in their feelings and judgements (Mode 1) [Pyrrho, by Diog. Laertius] |
| 1804 | Perception varies with madness or disease (Mode 4) [Pyrrho, by Diog. Laertius] |
| 1810 | Perception and judgement depend on comparison (Mode 10) [Pyrrho, by Diog. Laertius] |
| 1805 | Judgements vary according to local culture and law (Mode 5) [Pyrrho, by Diog. Laertius] |
| 1809 | Perception is affected by expectations (Mode 9) [Pyrrho, by Diog. Laertius] |
| 1803 | Objects vary according to which sense perceives them (Mode 3) [Pyrrho, by Diog. Laertius] |
| 1806 | Perception of objects depends on surrounding conditions (Mode 6) [Pyrrho, by Diog. Laertius] |
| 12586 | Consciousness of a belief isn't a belief that one has it [Peacocke] |
| 12608 | Concepts are distinguished by roles in judgement, and are thus tied to rationality [Peacocke] |
| 18568 | Philosophy should merely give necessary and sufficient conditions for concept possession [Peacocke, by Machery] |
| 18571 | Peacocke's account of possession of a concept depends on one view of counterfactuals [Peacocke, by Machery] |
| 18572 | Peacocke's account separates psychology from philosophy, and is very sketchy [Machery on Peacocke] |
| 17722 | The concept 'red' is tied to what actually individuates red things [Peacocke] |
| 11127 | If concepts just are mental representations, what of concepts we may never acquire? [Peacocke] |
| 12577 | Possessing a concept is being able to make judgements which use it [Peacocke] |
| 12578 | A concept is just what it is to possess that concept [Peacocke] |
| 12587 | Employing a concept isn't decided by introspection, but by making judgements using it [Peacocke] |
| 12605 | A sense is individuated by the conditions for reference [Peacocke] |
| 12607 | Fregean concepts have their essence fixed by reference-conditions [Peacocke] |
| 12609 | Concepts have distinctive reasons and norms [Peacocke] |
| 12584 | An analysis of concepts must link them to something unconceptualized [Peacocke] |
| 12604 | Any explanation of a concept must involve reference and truth [Peacocke] |
| 9335 | Concepts are constituted by their role in a group of propositions to which we are committed [Peacocke, by Greco] |
| 9336 | A concept's reference is what makes true the beliefs of its possession conditions [Peacocke, by Horwich] |
| 10634 | Predicates are 'distributive' or 'non-distributive'; do individuals do what the group does? [Linnebo] |
| 12610 | Encountering novel sentences shows conclusively that meaning must be compositional [Peacocke] |
| 3062 | There are no causes, because they are relative, and alike things can't cause one another [Pyrrho, by Diog. Laertius] |
| 3063 | Motion can't move where it is, and can't move where it isn't, so it can't exist [Pyrrho, by Diog. Laertius] |