25 ideas
14600 | Analysis aims at secure necessary and sufficient conditions [Schaffer,J] |
18781 | Inconsistency doesn't prevent us reasoning about some system [Mares] |
14603 | 'Reification' occurs if we mistake a concept for a thing [Schaffer,J] |
14607 | T adds □p→p for reflexivity, and is ideal for modeling lawhood [Schaffer,J] |
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] |
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] |
8698 | Modal structuralism says mathematics studies possible structures, which may or may not be actualised [Hellman, by Friend] |
9557 | Statements of pure mathematics are elliptical for a sort of modal conditional [Hellman, by Chihara] |
10263 | Modal structuralism can only judge possibility by 'possible' models [Shapiro on Hellman] |
14604 | If a notion is ontologically basic, it should be needed in our best attempt at science [Schaffer,J] |
18788 | For intuitionists there are not numbers and sets, but processes of counting and collecting [Mares] |
14599 | Three types of reduction: Theoretical (of terms), Definitional (of concepts), Ontological (of reality) [Schaffer,J] |
14605 | Tropes are the same as events [Schaffer,J] |
14601 | Individuation aims to count entities, by saying when there is one [Schaffer,J] |
14606 | Only ideal conceivability could indicate what is possible [Schaffer,J] |
18791 | In 'situation semantics' our main concepts are abstracted from situations [Mares] |