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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
14 ideas
from 'Negation'
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18781
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Inconsistency doesn't prevent us reasoning about some system
[Mares]
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18780
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Standard disjunction and negation force us to accept the principle of bivalence
[Mares]
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18782
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The connectives are studied either through model theory or through proof theory
[Mares]
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18783
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Many-valued logics lack a natural deduction system
[Mares]
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18784
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In classical logic the connectives can be related elegantly, as in De Morgan's laws
[Mares]
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18786
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Excluded middle standardly implies bivalence; attacks use non-contradiction, De M 3, or double negation
[Mares]
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18785
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Consistency is semantic, but non-contradiction is syntactic
[Mares]
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18787
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Three-valued logic is useful for a theory of presupposition
[Mares]
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18788
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For intuitionists there are not numbers and sets, but processes of counting and collecting
[Mares]
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18789
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Intuitionist logic looks best as natural deduction
[Mares]
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18790
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Intuitionism as natural deduction has no rule for negation
[Mares]
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18791
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In 'situation semantics' our main concepts are abstracted from situations
[Mares]
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18792
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Situation semantics for logics: not possible worlds, but information in situations
[Mares]
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18793
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Material implication (and classical logic) considers nothing but truth values for implications
[Mares]
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