28 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] |
| 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] |
| 21110 | An understanding of the most basic physics should explain all of the subject's mysteries [Krauss] |
| 21105 | In 1676 it was discovered that water is teeming with life [Krauss] |
| 6017 | Nomos is king [Pindar] |
| 21109 | Space itself can expand (and separate its contents) at faster than light speeds [Krauss] |
| 21104 | General Relativity: the density of energy and matter determines curvature and gravity [Krauss] |
| 21107 | Uncertainty says that energy can be very high over very short time periods [Krauss] |
| 21106 | Most of the mass of a proton is the energy in virtual particles (rather than the quarks) [Krauss] |
| 21112 | Empty space contains a continual flux of brief virtual particles [Krauss] |
| 21108 | The universe is precisely 13.72 billion years old [Krauss] |
| 21111 | It seems likely that cosmic inflation is eternal, and this would make a multiverse inevitable [Krauss] |