34 ideas
| 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] |
| 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] |
| 10896 | Propositional logic just needs ¬, and one of ∧, ∨ and → [Zalabardo] |
| 11115 | 'All horses' either picks out the horses, or the things which are horses [Jubien] |
| 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] |
| 11116 | Being a physical object is our most fundamental category [Jubien] |
| 11117 | Haecceities implausibly have no qualities [Jubien] |
| 11119 | De re necessity is just de dicto necessity about object-essences [Jubien] |
| 11118 | Modal propositions transcend the concrete, but not the actual [Jubien] |
| 11108 | Your properties, not some other world, decide your possibilities [Jubien] |
| 11111 | Modal truths are facts about parts of this world, not about remote maximal entities [Jubien] |
| 11105 | We have no idea how many 'possible worlds' there might be [Jubien] |
| 11107 | If there are no other possible worlds, do we then exist necessarily? [Jubien] |
| 11106 | If all possible worlds just happened to include stars, their existence would be necessary [Jubien] |
| 11112 | Possible worlds just give parallel contingencies, with no explanation at all of necessity [Jubien] |
| 11109 | If other worlds exist, then they are scattered parts of the actual world [Jubien] |
| 11113 | Worlds don't explain necessity; we use necessity to decide on possible worlds [Jubien] |
| 11110 | We mustn't confuse a similar person with the same person [Jubien] |
| 22040 | Freedom is produced by the activity of the mind, and is not intrinsically given [Hegel] |
| 22039 | Geist is distinct from nature, not as a substance, but because of its normativity [Hegel, by Pinkard] |