42 ideas
| 19275 | You cannot understand what exists without understanding possibility and necessity [Hale] |
| 19291 | A canonical defintion specifies the type of thing, and what distinguish this specimen [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] |
| 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] |
| 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] |
| 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] |
| 19302 | If a chair could be made of slightly different material, that could lead to big changes [Hale] |
| 19290 | Absolute necessities are necessarily necessary [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] |
| 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] |
| 19282 | It seems that we cannot show that modal facts depend on non-modal facts [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] |
| 19300 | The molecules may explain the water, but they are not what 'water' means [Hale] |
| 5994 | Is the cosmos open or closed, mechanical or teleological, alive or inanimate, and created or eternal? [Robinson,TM, by PG] |