33 ideas
| 22864 | Philosophy is the study and criticsm of cultural beliefs, to achieve new possibilities [Dewey] |
| 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] |
| 22873 | Liberalism should improve the system, and not just ameliorate it [Dewey] |
| 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] |
| 13472 | Hilbert aimed to eliminate number from geometry [Hilbert, by Hart,WD] |
| 9546 | Euclid axioms concerns possibilities of construction, but Hilbert's assert the existence of objects [Hilbert, by Chihara] |
| 18742 | Hilbert's formalisation revealed implicit congruence axioms in Euclid [Hilbert, by Horsten/Pettigrew] |
| 18217 | Hilbert's geometry is interesting because it captures Euclid without using real numbers [Hilbert, by Field,H] |
| 10891 | If a set is defined by induction, then proof by induction can be applied to it [Zalabardo] |
| 22869 | Knowledge is either the product of competent enquiry, or it is meaningless [Dewey] |
| 22867 | The quest for certainty aims for peace, and avoidance of the stress of action [Dewey] |
| 22870 | No belief can be so settled that it is not subject to further inquiry [Dewey] |
| 22866 | Mind is never isolated, but only exists in its interactions [Dewey] |
| 22872 | Liberals aim to allow individuals to realise their capacities [Dewey] |
| 22880 | The things in civilisation we prize are the products of other members of our community [Dewey] |
| 22879 | 'God' is an imaginative unity of ideal values [Dewey] |
| 22877 | We should try attaching the intensity of religious devotion to intelligent social action [Dewey] |
| 22878 | Religions are so shockingly diverse that they have no common element [Dewey] |