73 ideas
| 13736 | Quinean metaphysics just lists the beings, which is a domain with no internal structure [Schaffer,J on Quine] |
| 10987 | Three traditional names of rules are 'Simplification', 'Addition' and 'Disjunctive Syllogism' [Read] |
| 11004 | Necessity is provability in S4, and true in all worlds in S5 [Read] |
| 11018 | There are fuzzy predicates (and sets), and fuzzy quantifiers and modifiers [Read] |
| 11011 | Same say there are positive, negative and neuter free logics [Read] |
| 3302 | Set theory is full of Platonist metaphysics, so Quine aimed to keep it separate from logic [Quine, by Benardete,JA] |
| 10211 | Quine wants V = L for a cleaner theory, despite the scepticism of most theorists [Quine, by Shapiro] |
| 11020 | Realisms like the full Comprehension Principle, that all good concepts determine sets [Read] |
| 3336 | Two things can never entail three things [Quine, by Benardete,JA] |
| 10986 | Not all validity is captured in first-order logic [Read] |
| 10972 | The non-emptiness of the domain is characteristic of classical logic [Read] |
| 11024 | Semantics must precede proof in higher-order logics, since they are incomplete [Read] |
| 10985 | We should exclude second-order logic, precisely because it captures arithmetic [Read] |
| 10970 | A theory of logical consequence is a conceptual analysis, and a set of validity techniques [Read] |
| 10984 | Logical consequence isn't just a matter of form; it depends on connections like round-square [Read] |
| 10973 | A theory is logically closed, which means infinite premisses [Read] |
| 8453 | If we had to name objects to make existence claims, we couldn't discuss all the real numbers [Quine] |
| 10311 | No sense can be made of quantification into opaque contexts [Quine, by Hale] |
| 10538 | Finite quantification can be eliminated in favour of disjunction and conjunction [Quine, by Dummett] |
| 11007 | Quantifiers are second-order predicates [Read] |
| 10793 | Quine thought substitutional quantification confused use and mention, but then saw its nominalist appeal [Quine, by Marcus (Barcan)] |
| 10978 | In second-order logic the higher-order variables range over all the properties of the objects [Read] |
| 10971 | A logical truth is the conclusion of a valid inference with no premisses [Read] |
| 10988 | Any first-order theory of sets is inadequate [Read] |
| 10975 | Compactness does not deny that an inference can have infinitely many premisses [Read] |
| 10974 | Compactness is when any consequence of infinite propositions is the consequence of a finite subset [Read] |
| 10977 | Compactness blocks the proof of 'for every n, A(n)' (as the proof would be infinite) [Read] |
| 10976 | Compactness makes consequence manageable, but restricts expressive power [Read] |
| 11014 | Self-reference paradoxes seem to arise only when falsity is involved [Read] |
| 11025 | Infinite cuts and successors seems to suggest an actual infinity there waiting for us [Read] |
| 10979 | Although second-order arithmetic is incomplete, it can fully model normal arithmetic [Read] |
| 10980 | Second-order arithmetic covers all properties, ensuring categoricity [Read] |
| 10997 | Von Neumann numbers are helpful, but don't correctly describe numbers [Read] |
| 8466 | For Quine, intuitionist ontology is inadequate for classical mathematics [Quine, by Orenstein] |
| 8467 | Intuitionists only admit numbers properly constructed, but classical maths covers all reals in a 'limit' [Quine, by Orenstein] |
| 11016 | Would a language without vagueness be usable at all? [Read] |
| 11019 | Supervaluations say there is a cut-off somewhere, but at no particular place [Read] |
| 11012 | A 'supervaluation' gives a proposition consistent truth-value for classical assignments [Read] |
| 11013 | Identities and the Indiscernibility of Identicals don't work with supervaluations [Read] |
| 10667 | A logically perfect language could express all truths, so all truths must be logically expressible [Quine, by Hossack] |
| 16021 | Quine says we can expand predicates easily (ideology), but not names (ontology) [Quine, by Noonan] |
| 3325 | For Quine everything exists theoretically, as reference, predication and quantification [Quine, by Benardete,JA] |
| 8534 | Quine says the predicate of a true statement has no ontological implications [Quine, by Armstrong] |
| 10295 | Quine suggests that properties can be replaced with extensional entities like sets [Quine, by Shapiro] |
| 3322 | Quine says that if second-order logic is to quantify over properties, that can be done in first-order predicate logic [Quine, by Benardete,JA] |
| 6078 | Quine brought classes into semantics to get rid of properties [Quine, by McGinn] |
| 8479 | Don't analyse 'red is a colour' as involving properties. Say 'all red things are coloured things' [Quine, by Orenstein] |
| 3751 | Universals are acceptable if they are needed to make an accepted theory true [Quine, by Jacquette] |
| 7970 | Quine is committed to sets, but is more a Class Nominalist than a Platonist [Quine, by Macdonald,C] |
| 10558 | Abstract objects are actually constituted by the properties by which we conceive them [Zalta] |
| 15783 | Definite descriptions can't unambiguously pick out an object which doesn't exist [Lycan on Quine] |
| 10995 | A haecceity is a set of individual properties, essential to each thing [Read] |
| 11001 | Equating necessity with truth in every possible world is the S5 conception of necessity [Read] |
| 15782 | Quine wants identity and individuation-conditions for possibilia [Quine, by Lycan] |
| 10989 | The standard view of conditionals is that they are truth-functional [Read] |
| 10992 | The point of conditionals is to show that one will accept modus ponens [Read] |
| 11017 | Some people even claim that conditionals do not express propositions [Read] |
| 2796 | For Quine the only way to know a necessity is empirically [Quine, by Dancy,J] |
| 10983 | Knowledge of possible worlds is not causal, but is an ontology entailed by semantics [Read] |
| 10982 | How can modal Platonists know the truth of a modal proposition? [Read] |
| 10996 | Actualism is reductionist (to parts of actuality), or moderate realist (accepting real abstractions) [Read] |
| 10981 | A possible world is a determination of the truth-values of all propositions of a domain [Read] |
| 11000 | If worlds are concrete, objects can't be present in more than one, and can only have counterparts [Read] |
| 8450 | Quine's empiricism is based on whole theoretical systems, not on single mental events [Quine, by Orenstein] |
| 3868 | To proclaim cultural relativism is to thereby rise above it [Quine, by Newton-Smith] |
| 4713 | For Quine, theories are instruments used to make predictions about observations [Quine, by O'Grady] |
| 10998 | The mind abstracts ways things might be, which are nonetheless real [Read] |
| 10557 | Abstract objects are captured by second-order modal logic, plus 'encoding' formulas [Zalta] |
| 4712 | Quine says there is no matter of fact about reference - it is 'inscrutable' [Quine, by O'Grady] |
| 11005 | Negative existentials with compositionality make the whole sentence meaningless [Read] |
| 10966 | A proposition objectifies what a sentence says, as indicative, with secure references [Read] |
| 7330 | The principle of charity only applies to the logical constants [Quine, by Miller,A] |
| 17862 | Essence gives an illusion of understanding [Quine, by Almog] |