44 ideas
| 6961 | An analogy begins to break down as soon as the two cases differ [Hume] |
| 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] |
| 21285 | Events are baffling before experience, and obvious after experience [Hume] |
| 7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |
| 6959 | We can't assume God's perfections are like our ideas or like human attributes [Hume] |
| 6957 | The objects of theological reasoning are too big for our minds [Hume] |
| 21255 | No being's non-existence can imply a contradiction, so its existence cannot be proved a priori [Hume] |
| 21254 | A chain of events requires a cause for the whole as well as the parts, yet the chain is just a sum of parts [Hume] |
| 1435 | If something must be necessary so that something exists rather than nothing, why can't the universe be necessary? [Hume] |
| 6962 | The thing which contains order must be God, so see God where you see order [Hume] |
| 6958 | How can we pronounce on a whole after a brief look at a very small part? [Hume] |
| 6963 | Why would we infer an infinite creator from a finite creation? [Hume] |
| 21282 | Design cannot prove a unified Deity. Many men make a city, so why not many gods for a world? [Hume] |
| 21280 | From a ship you would judge its creator a genius, not a mere humble workman [Hume] |
| 21281 | This excellent world may be the result of a huge sequence of trial-and-error [Hume] |
| 21283 | Humans renew their species sexually. If there are many gods, would they not do the same? [Hume] |
| 6966 | Creation is more like vegetation than human art, so it won't come from reason [Hume] |
| 21284 | This Creator god might be an infant or incompetent or senile [Hume] |
| 21286 | Motion often begins in matter, with no sign of a controlling agent [Hume] |
| 21287 | The universe could settle into superficial order, without a designer [Hume] |
| 21288 | Ideas arise from objects, not vice versa; ideas only influence matter if they are linked [Hume] |
| 21256 | A surprise feature of all products of 9 looks like design, but is actually a necessity [Hume] |
| 6960 | Analogy suggests that God has a very great human mind [Hume] |
| 6965 | The universe may be the result of trial-and-error [Hume] |
| 6967 | Order may come from an irrational source as well as a rational one [Hume] |
| 6964 | From our limited view, we cannot tell if the universe is faulty [Hume] |
| 21279 | If the divine cause is proportional to its effects, the effects are finite, so the Deity cannot be infinite [Hume] |