27 ideas
| 6211 | Laughter is a sudden glory in realising the infirmity of others, or our own formerly [Hobbes] |
| 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] |
| 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] |
| 21354 | It may be that internal relations like proportion exist, because we directly perceive it [MacBride] |
| 21353 | Internal relations are fixed by existences, or characters, or supervenience on characters [MacBride] |
| 21352 | 'Multigrade' relations are those lacking a fixed number of relata [MacBride] |
| 6213 | A man cannot will to will, or will to will to will, so the idea of a voluntary will is absurd [Hobbes] |
| 6208 | Conceptions and apparitions are just motion in some internal substance of the head [Hobbes] |
| 6209 | There is no absolute good, for even the goodness of God is goodness to us [Hobbes] |
| 6210 | Life has no end (not even happiness), because we have desires, which presuppose a further end [Hobbes] |
| 6212 | Lust involves pleasure, and also the sense of power in pleasing others [Hobbes] |