79 ideas
| 19275 | You cannot understand what exists without understanding possibility and necessity [Hale] |
| 10308 | Questions about objects are questions about certain non-vacuous singular terms [Hale] |
| 19291 | A canonical defintion specifies the type of thing, and what distinguish this specimen [Hale] |
| 10314 | An expression is a genuine singular term if it resists elimination by paraphrase [Hale] |
| 19297 | The two Barcan principles are easily proved in fairly basic modal logic [Hale] |
| 19301 | With a negative free logic, we can dispense with the Barcan formulae [Hale] |
| 10888 | Sets can be defined by 'enumeration', or by 'abstraction' (based on a property) [Zalabardo] |
| 10889 | The 'Cartesian Product' of two sets relates them by pairing every element with every element [Zalabardo] |
| 10890 | A 'partial ordering' is reflexive, antisymmetric and transitive [Zalabardo] |
| 10886 | Determinacy: an object is either in a set, or it isn't [Zalabardo] |
| 10887 | Specification: Determinate totals of objects always make a set [Zalabardo] |
| 10897 | A first-order 'sentence' is a formula with no free variables [Zalabardo] |
| 19296 | If second-order variables range over sets, those are just objects; properties and relations aren't sets [Hale] |
| 10893 | Γ |= φ for sentences if φ is true when all of Γ is true [Zalabardo] |
| 10899 | Γ |= φ if φ is true when all of Γ is true, for all structures and interpretations [Zalabardo] |
| 19289 | Maybe conventionalism applies to meaning, but not to the truth of propositions expressed [Hale] |
| 10896 | Propositional logic just needs ¬, and one of ∧, ∨ and → [Zalabardo] |
| 10316 | We should decide whether singular terms are genuine by their usage [Hale] |
| 10312 | Often the same singular term does not ensure reliable inference [Hale] |
| 10313 | Plenty of clear examples have singular terms with no ontological commitment [Hale] |
| 10322 | If singular terms can't be language-neutral, then we face a relativity about their objects [Hale] |
| 19298 | Unlike axiom proofs, natural deduction proofs needn't focus on logical truths and theorems [Hale] |
| 10898 | The semantics shows how truth values depend on instantiations of properties and relations [Zalabardo] |
| 10902 | We can do semantics by looking at given propositions, or by building new ones [Zalabardo] |
| 10892 | We make a truth assignment to T and F, which may be true and false, but merely differ from one another [Zalabardo] |
| 10895 | 'Logically true' (|= φ) is true for every truth-assignment [Zalabardo] |
| 10900 | Logically true sentences are true in all structures [Zalabardo] |
| 10894 | A sentence-set is 'satisfiable' if at least one truth-assignment makes them all true [Zalabardo] |
| 10901 | Some formulas are 'satisfiable' if there is a structure and interpretation that makes them true [Zalabardo] |
| 10903 | A structure models a sentence if it is true in the model, and a set of sentences if they are all true in the model [Zalabardo] |
| 10632 | The real numbers may be introduced by abstraction as ratios of quantities [Hale, by Hale/Wright] |
| 10891 | If a set is defined by induction, then proof by induction can be applied to it [Zalabardo] |
| 19295 | Add Hume's principle to logic, to get numbers; arithmetic truths rest on the nature of the numbers [Hale] |
| 19281 | Interesting supervenience must characterise the base quite differently from what supervenes on it [Hale] |
| 10512 | The abstract/concrete distinction is based on what is perceivable, causal and located [Hale] |
| 10517 | Colours and points seem to be both concrete and abstract [Hale] |
| 10519 | The abstract/concrete distinction is in the relations in the identity-criteria of object-names [Hale] |
| 10520 | Token-letters and token-words are concrete objects, type-letters and type-words abstract [Hale] |
| 10524 | There is a hierarchy of abstraction, based on steps taken by equivalence relations [Hale] |
| 19278 | There is no gap between a fact that p, and it is true that p; so we only have the truth-condtions for p [Hale] |
| 10521 | If F can't have location, there is no problem of things having F in different locations [Hale] |
| 10511 | It is doubtful if one entity, a universal, can be picked out by both predicates and abstract nouns [Hale] |
| 10318 | Realists take universals to be the referrents of both adjectives and of nouns [Hale] |
| 10310 | Objections to Frege: abstracta are unknowable, non-independent, unstatable, unindividuated [Hale] |
| 10518 | Shapes and directions are of something, but games and musical compositions are not [Hale] |
| 10513 | Many abstract objects, such as chess, seem non-spatial, but are not atemporal [Hale] |
| 10514 | If the mental is non-spatial but temporal, then it must be classified as abstract [Hale] |
| 10523 | Being abstract is based on a relation between things which are spatially separated [Hale] |
| 10307 | The modern Fregean use of the term 'object' is much broader than the ordinary usage [Hale] |
| 10315 | We can't believe in a 'whereabouts' because we ask 'what kind of object is it?' [Hale] |
| 19302 | If a chair could be made of slightly different material, that could lead to big changes [Hale] |
| 10522 | The relations featured in criteria of identity are always equivalence relations [Hale] |
| 10321 | We sometimes apply identity without having a real criterion [Hale] |
| 15086 | Absolute necessity might be achievable either logically or metaphysically [Hale] |
| 19290 | Absolute necessities are necessarily necessary [Hale] |
| 8261 | Maybe not-p is logically possible, but p is metaphysically necessary, so the latter is not absolute [Hale] |
| 15081 | A strong necessity entails a weaker one, but not conversely; possibilities go the other way [Hale] |
| 15080 | 'Relative' necessity is just a logical consequence of some statements ('strong' if they are all true) [Hale] |
| 19286 | 'Absolute necessity' is when there is no restriction on the things which necessitate p [Hale] |
| 19288 | Logical and metaphysical necessities differ in their vocabulary, and their underlying entities [Hale] |
| 15082 | Metaphysical necessity says there is no possibility of falsehood [Hale] |
| 15085 | 'Broadly' logical necessities are derived (in a structure) entirely from the concepts [Hale] |
| 15088 | Logical necessities are true in virtue of the nature of all logical concepts [Hale] |
| 19285 | Logical necessity is something which is true, no matter what else is the case [Hale] |
| 19287 | Maybe each type of logic has its own necessity, gradually becoming broader [Hale] |
| 12432 | Explanation of necessity must rest on something necessary or something contingent [Hale] |
| 12434 | Why is this necessary, and what is necessity in general; why is this necessary truth true, and why necessary? [Hale] |
| 12435 | The explanation of a necessity can be by a truth (which may only happen to be a necessary truth) [Hale] |
| 19282 | It seems that we cannot show that modal facts depend on non-modal facts [Hale] |
| 12433 | If necessity rests on linguistic conventions, those are contingent, so there is no necessity [Hale] |
| 15087 | Conceptual necessities are made true by all concepts [Hale] |
| 12436 | Concept-identities explain how we know necessities, not why they are necessary [Hale] |
| 19276 | The big challenge for essentialist views of modality is things having necessary existence [Hale] |
| 19293 | Essentialism doesn't explain necessity reductively; it explains all necessities in terms of a few basic natures [Hale] |
| 19294 | If necessity derives from essences, how do we explain the necessary existence of essences? [Hale] |
| 19279 | What are these worlds, that being true in all of them makes something necessary? [Hale] |
| 19299 | Possible worlds make every proposition true or false, which endorses classical logic [Hale] |
| 20653 | Six reduction levels: groups, lives, cells, molecules, atoms, particles [Putnam/Oppenheim, by Watson] |
| 19300 | The molecules may explain the water, but they are not what 'water' means [Hale] |