2011 | A Priori |
01.5 | p.6 | 17700 | The most popular view is that coherent beliefs explain one another |
02.2 | p.16 | 17701 | Possible worlds semantics has a nice compositional account of modal statements |
02.3 | p.17 | 17702 | Unstructured propositions are sets of possible worlds; structured ones have components |
02.9 | p.31 | 17703 | Light in straight lines is contingent a priori; stipulated as straight, because they happen to be so |
02.9 | p.31 | 17704 | Operationalism defines concepts by our ways of measuring them |
03.01 | p.34 | 17705 | Empiricists say rationalists mistake imaginative powers for modal insights |
03.10 | p.49 | 17706 | The essence of a concept is either its definition or its conceptual relations? |
06.7 | p.97 | 17708 | Maybe space has points, but processes always need regions with a size |
08.1 | p.123 | 17710 | Aristotelian justification uses concepts abstracted from experience |
08.2 | p.125 | 17713 | After 1903, Husserl avoids metaphysical commitments |
08.9 | p.135 | 17714 | Aristotelians dislike the idea of a priori judgements from pure reason |
11.4 | p.178 | 17715 | The truth of the axioms doesn't matter for pure mathematics, but it does for applied |
11.7 | p.182 | 17716 | Mathematics is relations between properties we abstract from experience |
2014 | Negation |
1 | p.181 | 18781 | Inconsistency doesn't prevent us reasoning about some system |
1 | p.181 | 18780 | Standard disjunction and negation force us to accept the principle of bivalence |
1 | p.182 | 18782 | The connectives are studied either through model theory or through proof theory |
1 | p.182 | 18783 | Many-valued logics lack a natural deduction system |
2.2 | p.183 | 18784 | In classical logic the connectives can be related elegantly, as in De Morgan's laws |
2.2 | p.184 | 18785 | Consistency is semantic, but non-contradiction is syntactic |
2.2 | p.185 | 18786 | Excluded middle standardly implies bivalence; attacks use non-contradiction, De M 3, or double negation |
3.1 | p.185 | 18787 | Three-valued logic is useful for a theory of presupposition |
5.1 | p.196 | 18788 | For intuitionists there are not numbers and sets, but processes of counting and collecting |
5.5 | p.200 | 18789 | Intuitionist logic looks best as natural deduction |
5.5 | p.202 | 18790 | Intuitionism as natural deduction has no rule for negation |
6.1 | p.204 | 18791 | In 'situation semantics' our main concepts are abstracted from situations |
6.2 | p.206 | 18792 | Situation semantics for logics: not possible worlds, but information in situations |
7.1 | p.208 | 18793 | Material implication (and classical logic) considers nothing but truth values for implications |