53 ideas
| 5988 | Anaximander produced the first philosophy book (and maybe the first book) [Anaximander, by Bodnár] |
| 17713 | After 1903, Husserl avoids metaphysical commitments [Mares] |
| 18781 | Inconsistency doesn't prevent us reasoning about some system [Mares] |
| 1496 | The earth is stationary, because it is in the centre, and has no more reason to move one way than another [Anaximander, by Aristotle] |
| 18789 | Intuitionist logic looks best as natural deduction [Mares] |
| 18790 | Intuitionism as natural deduction has no rule for negation [Mares] |
| 18787 | Three-valued logic is useful for a theory of presupposition [Mares] |
| 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] |
| 18793 | Material implication (and classical logic) considers nothing but truth values for implications [Mares] |
| 18784 | In classical logic the connectives can be related elegantly, as in De Morgan's laws [Mares] |
| 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] |
| 18786 | Excluded middle standardly implies bivalence; attacks use non-contradiction, De M 3, or double negation [Mares] |
| 18780 | Standard disjunction and negation force us to accept the principle of bivalence [Mares] |
| 18782 | The connectives are studied either through model theory or through proof theory [Mares] |
| 10896 | Propositional logic just needs ¬, and one of ∧, ∨ and → [Zalabardo] |
| 18783 | Many-valued logics lack a natural deduction system [Mares] |
| 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] |
| 18792 | Situation semantics for logics: not possible worlds, but information in situations [Mares] |
| 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] |
| 18785 | Consistency is semantic, but non-contradiction is syntactic [Mares] |
| 17715 | The truth of the axioms doesn't matter for pure mathematics, but it does for applied [Mares] |
| 10891 | If a set is defined by induction, then proof by induction can be applied to it [Zalabardo] |
| 17716 | Mathematics is relations between properties we abstract from experience [Mares] |
| 18788 | For intuitionists there are not numbers and sets, but processes of counting and collecting [Mares] |
| 14874 | Anaximander saw the contradiction in the world - that its own qualities destroy it [Anaximander, by Nietzsche] |
| 17703 | Light in straight lines is contingent a priori; stipulated as straight, because they happen to be so [Mares] |
| 17714 | Aristotelians dislike the idea of a priori judgements from pure reason [Mares] |
| 17705 | Empiricists say rationalists mistake imaginative powers for modal insights [Mares] |
| 17700 | The most popular view is that coherent beliefs explain one another [Mares] |
| 17704 | Operationalism defines concepts by our ways of measuring them [Mares] |
| 17710 | Aristotelian justification uses concepts abstracted from experience [Mares] |
| 17706 | The essence of a concept is either its definition or its conceptual relations? [Mares] |
| 18791 | In 'situation semantics' our main concepts are abstracted from situations [Mares] |
| 17701 | Possible worlds semantics has a nice compositional account of modal statements [Mares] |
| 17702 | Unstructured propositions are sets of possible worlds; structured ones have components [Mares] |
| 405 | The essential nature, whatever it is, of the non-limited is everlasting and ageless [Anaximander] |
| 13222 | The Boundless cannot exist on its own, and must have something contrary to it [Aristotle on Anaximander] |
| 404 | Things begin and end in the Unlimited, and are balanced over time according to justice [Anaximander] |
| 1495 | Anaximander introduced the idea that the first principle and element of things was the Boundless [Anaximander, by Simplicius] |
| 17708 | Maybe space has points, but processes always need regions with a size [Mares] |
| 1746 | The parts of all things are susceptible to change, but the whole is unchangeable [Anaximander, by Diog. Laertius] |