53 ideas
| 17713 | After 1903, Husserl avoids metaphysical commitments [Mares] |
| 18781 | Inconsistency doesn't prevent us reasoning about some system [Mares] |
| 12223 | It is a fallacy to explain the obscure with the even more obscure [Hale/Wright] |
| 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] |
| 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] |
| 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] |
| 12230 | Singular terms refer if they make certain atomic statements true [Hale/Wright] |
| 18783 | Many-valued logics lack a natural deduction system [Mares] |
| 18792 | Situation semantics for logics: not possible worlds, but information in situations [Mares] |
| 18785 | Consistency is semantic, but non-contradiction is syntactic [Mares] |
| 10631 | If 'x is heterological' iff it does not apply to itself, then 'heterological' is heterological if it isn't heterological [Hale/Wright] |
| 17715 | The truth of the axioms doesn't matter for pure mathematics, but it does for applied [Mares] |
| 10624 | The incompletability of formal arithmetic reveals that logic also cannot be completely characterized [Hale/Wright] |
| 8784 | Neo-logicism founds arithmetic on Hume's Principle along with second-order logic [Hale/Wright] |
| 8787 | The Julius Caesar problem asks for a criterion for the concept of a 'number' [Hale/Wright] |
| 10629 | If structures are relative, this undermines truth-value and objectivity [Hale/Wright] |
| 10628 | The structural view of numbers doesn't fit their usage outside arithmetical contexts [Hale/Wright] |
| 17716 | Mathematics is relations between properties we abstract from experience [Mares] |
| 8788 | Logicism is only noteworthy if logic has a privileged position in our ontology and epistemology [Hale/Wright] |
| 10622 | The neo-Fregean is more optimistic than Frege about contextual definitions of numbers [Hale/Wright] |
| 8783 | Logicism might also be revived with a quantificational approach, or an abstraction-free approach [Hale/Wright] |
| 12225 | Neo-Fregeanism might be better with truth-makers, rather than quantifier commitment [Hale/Wright] |
| 12224 | Are neo-Fregeans 'maximalists' - that everything which can exist does exist? [Hale/Wright] |
| 18788 | For intuitionists there are not numbers and sets, but processes of counting and collecting [Mares] |
| 18933 | Not-Being obviously doesn't exist, and the five modes of Being are all impossible [Gorgias, by Diog. Laertius] |
| 12226 | The identity of Pegasus with Pegasus may be true, despite the non-existence [Hale/Wright] |
| 12229 | Maybe we have abundant properties for semantics, and sparse properties for ontology [Hale/Wright] |
| 18443 | A successful predicate guarantees the existence of a property - the way of being it expresses [Hale/Wright] |
| 10626 | Objects just are what singular terms refer to [Hale/Wright] |
| 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] |
| 10630 | Abstracted objects are not mental creations, but depend on equivalence between given entities [Hale/Wright] |
| 8786 | One first-order abstraction principle is Frege's definition of 'direction' in terms of parallel lines [Hale/Wright] |
| 12227 | Abstractionism needs existential commitment and uniform truth-conditions [Hale/Wright] |
| 12228 | Equivalence abstraction refers to objects otherwise beyond our grasp [Hale/Wright] |
| 12231 | Reference needs truth as well as sense [Hale/Wright] |
| 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] |
| 10627 | Many conceptual truths ('yellow is extended') are not analytic, as derived from logic and definitions [Hale/Wright] |
| 9866 | Gorgias says rhetoric is the best of arts, because it enslaves without using force [Gorgias, by Plato] |
| 5864 | Destroy seriousness with laughter, and laughter with seriousness [Gorgias] |
| 17708 | Maybe space has points, but processes always need regions with a size [Mares] |