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Single Idea 18785

[filed under theme 5. Theory of Logic / K. Features of Logics / 2. Consistency ]

Full Idea

The difference between the principle of consistency and the principle of non-contradiction is that the former must be stated in a semantic metalanguage, whereas the latter is a thesis of logical systems.

Gist of Idea

Consistency is semantic, but non-contradiction is syntactic

Source

Edwin D. Mares (Negation [2014], 2.2)

Book Ref

'Bloomsbury Companion to Philosophical Logic', ed/tr. Horsten,L/Pettigrew,R [Bloomsbury 2014], p.184

The 27 ideas from Edwin D. Mares

17700 The most popular view is that coherent beliefs explain one another [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]
17704 Operationalism defines concepts by our ways of measuring them [Mares]
17703 Light in straight lines is contingent a priori; stipulated as straight, because they happen to be so [Mares]
17705 Empiricists say rationalists mistake imaginative powers for modal insights [Mares]
17706 The essence of a concept is either its definition or its conceptual relations? [Mares]
17708 Maybe space has points, but processes always need regions with a size [Mares]
17710 Aristotelian justification uses concepts abstracted from experience [Mares]
17713 After 1903, Husserl avoids metaphysical commitments [Mares]
17714 Aristotelians dislike the idea of a priori judgements from pure reason [Mares]
17715 The truth of the axioms doesn't matter for pure mathematics, but it does for applied [Mares]
17716 Mathematics is relations between properties we abstract from experience [Mares]
18781 Inconsistency doesn't prevent us reasoning about some system [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]
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]
18785 Consistency is semantic, but non-contradiction is syntactic [Mares]
18787 Three-valued logic is useful for a theory of presupposition [Mares]
18788 For intuitionists there are not numbers and sets, but processes of counting and collecting [Mares]
18789 Intuitionist logic looks best as natural deduction [Mares]
18790 Intuitionism as natural deduction has no rule for negation [Mares]
18791 In 'situation semantics' our main concepts are abstracted from situations [Mares]
18792 Situation semantics for logics: not possible worlds, but information in situations [Mares]
18793 Material implication (and classical logic) considers nothing but truth values for implications [Mares]