more on this theme
|
more from this thinker
Single Idea 18780
[filed under theme 5. Theory of Logic / D. Assumptions for Logic / 1. Bivalence
]
Full Idea
If we treat disjunction in the standard way and take the negation of a statement A to mean that A is false, accepting excluded middle forces us also to accept the principle of bivalence, which is the dictum that every statement is either true or false.
Gist of Idea
Standard disjunction and negation force us to accept the principle of bivalence
Source
Edwin D. Mares (Negation [2014], 1)
Book Ref
'Bloomsbury Companion to Philosophical Logic', ed/tr. Horsten,L/Pettigrew,R [Bloomsbury 2014], p.181
A Reaction
Mates's point is to show that passively taking the normal account of negation for granted has important implications.
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]
|