44 ideas
| 17713 | After 1903, Husserl avoids metaphysical commitments [Mares] |
| 18806 | Frege thought traditional categories had psychological and linguistic impurities [Frege, by Rumfitt] |
| 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] |
| 8490 | First-level functions have objects as arguments; second-level functions take functions as arguments [Frege] |
| 8492 | Relations are functions with two arguments [Frege] |
| 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] |
| 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] |
| 8487 | Arithmetic is a development of logic, so arithmetical symbolism must expand into logical symbolism [Frege] |
| 18899 | Frege takes the existence of horses to be part of their concept [Frege, by Sommers] |
| 4028 | Frege allows either too few properties (as extensions) or too many (as predicates) [Mellor/Oliver on Frege] |
| 8489 | The concept 'object' is too simple for analysis; unlike a function, it is an expression with no empty place [Frege] |
| 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] |
| 9947 | Concepts are the ontological counterparts of predicative expressions [Frege, by George/Velleman] |
| 10319 | An assertion about the concept 'horse' must indirectly speak of an object [Frege, by Hale] |
| 8488 | A concept is a function whose value is always a truth-value [Frege] |
| 9948 | Unlike objects, concepts are inherently incomplete [Frege, by George/Velleman] |
| 17706 | The essence of a concept is either its definition or its conceptual relations? [Mares] |
| 4972 | I may regard a thought about Phosphorus as true, and the same thought about Hesperus as false [Frege] |
| 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] |
| 17708 | Maybe space has points, but processes always need regions with a size [Mares] |
| 8491 | The Ontological Argument fallaciously treats existence as a first-level concept [Frege] |