more on this theme
|
more from this thinker
Single Idea 18783
[filed under theme 5. Theory of Logic / H. Proof Systems / 4. Natural Deduction
]
Full Idea
Many-valued logics do not have reasonable natural deduction systems.
Gist of Idea
Many-valued logics lack a natural deduction system
Source
Edwin D. Mares (Negation [2014], 1)
Book Ref
'Bloomsbury Companion to Philosophical Logic', ed/tr. Horsten,L/Pettigrew,R [Bloomsbury 2014], p.182
The
14 ideas
from 'Negation'
|
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]
|