38 ideas
14611 | Metaphysics should avoid talk of past, present or future [Smart] |
17070 | Coherence is consilience, simplicity, analogy, and fitting into a web of belief [Smart] |
17072 | We need comprehensiveness, as well as self-coherence [Smart] |
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] |
17073 | I simply reject evidence, if it is totally contrary to my web of belief [Smart] |
17077 | The height of a flagpole could be fixed by its angle of shadow, but that would be very unusual [Smart] |
17078 | Universe expansion explains the red shift, but not vice versa [Smart] |
17061 | Explanation of a fact is fitting it into a system of beliefs [Smart] |
17074 | Explanations are bad by fitting badly with a web of beliefs, or fitting well into a bad web [Smart] |
17076 | Deducing from laws is one possible way to achieve a coherent explanation [Smart] |
17071 | An explanation is better if it also explains phenomena from a different field [Smart] |
17062 | If scientific explanation is causal, that rules out mathematical explanation [Smart] |
17075 | Scientific explanation tends to reduce things to the unfamiliar (not the familiar) [Smart] |
22405 | Negative utilitarianism implies that the world should be destroyed, to avoid future misery [Smart] |
22404 | Any group interested in ethics must surely have a sentiment of generalised benevolence [Smart] |
22745 | Pherecydes said the first principle and element is earth [Pherecydes, by Sext.Empiricus] |
14613 | Special relativity won't determine a preferred frame, but we can pick one externally [Smart] |
17063 | Unlike Newton, Einstein's general theory explains the perihelion of Mercury [Smart] |
14615 | If time flows, then 'how fast does it flow?' is a tricky question [Smart] |
14614 | The past, present, future and tenses of A-theory are too weird, and should be analysed indexically [Smart] |
5883 | Pherecydes was the first to say that the soul is eternal [Pherecydes, by Cicero] |