50 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] |
| 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] |
| 10901 | Some formulas are 'satisfiable' if there is a structure and interpretation that makes them true [Zalabardo] |
| 10894 | A sentence-set is 'satisfiable' if at least one truth-assignment makes them all 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] |
| 16588 | I prefer a lack of form to mean non-existence, than to think of some quasi-existence [Augustine] |
| 3523 | Shadows are supervenient on their objects, but not reducible [Maslin] |
| 3517 | 'Ontology' means 'study of things which exist' [Maslin] |
| 22979 | Three main questions seem to be whether a thing is, what it is, and what sort it is [Augustine] |
| 22977 | I can distinguish different smells even when I am not experiencing them [Augustine] |
| 22980 | Memory contains innumerable principles of maths, as well as past sense experiences [Augustine] |
| 22981 | Mind and memory are the same, as shown in 'bear it in mind' or 'it slipped from mind' [Augustine] |
| 22982 | Why does joy in my mind make me happy, but joy in my memory doesn't? [Augustine] |
| 22983 | We would avoid remembering sorrow or fear if that triggered the emotions afresh [Augustine] |
| 3538 | Analogy to other minds is uncheckable, over-confident and chauvinistic [Maslin] |
| 22978 | Memory is so vast that I cannot recognise it as part of my mind [Augustine] |
| 3540 | If we are brains then we never meet each other [Maslin] |
| 3518 | I'm not the final authority on my understanding of maths [Maslin] |
| 22984 | Without memory I could not even speak of myself [Augustine] |
| 5982 | If the future does not exist, how can prophets see it? [Augustine] |
| 3530 | Denial of purely mental causation will lead to epiphenomenalism [Maslin] |
| 3520 | Token-identity removes the explanatory role of the physical [Maslin] |
| 22976 | Memories are preserved separately, according to category [Augustine] |
| 22985 | Everyone wants happiness [Augustine] |
| 3528 | Causality may require that a law is being followed [Maslin] |
| 3525 | Strict laws make causation logically necessary [Maslin] |
| 3527 | Strict laws allow no exceptions and are part of a closed system [Maslin] |
| 22888 | To be aware of time it can only exist in the mind, as memory or anticipation [Augustine, by Bardon] |
| 5984 | Maybe time is an extension of the mind [Augustine] |
| 5980 | How can ten days ahead be a short time, if it doesn't exist? [Augustine] |
| 5979 | If the past is no longer, and the future is not yet, how can they exist? [Augustine] |
| 5981 | The whole of the current year is not present, so how can it exist? [Augustine] |
| 5978 | I know what time is, until someone asks me to explain it [Augustine] |
| 5983 | I disagree with the idea that time is nothing but cosmic movement [Augustine] |
| 5977 | Heaven and earth must be created, because they are subject to change [Augustine] |
| 5976 | If God is outside time in eternity, can He hear prayers? [Augustine] |
| 22887 | If God existed before creation, why would a perfect being desire to change things? [Augustine, by Bardon] |