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Single Idea 18790

[filed under theme 4. Formal Logic / E. Nonclassical Logics / 2. Intuitionist Logic ]

Full Idea

In intuitionist logic each connective has one introduction and one elimination rule attached to it, but in the classical system we have to add an extra rule for negation.

Gist of Idea

Intuitionism as natural deduction has no rule for negation

Source

Edwin D. Mares (Negation [2014], 5.5)

Book Ref

'Bloomsbury Companion to Philosophical Logic', ed/tr. Horsten,L/Pettigrew,R [Bloomsbury 2014], p.202


A Reaction

How very intriguing. Mares says there are other ways to achieve classical logic, but they all seem rather cumbersome.

Related Idea

Idea 18789 Intuitionist logic looks best as natural deduction [Mares]


The 14 ideas from 'Negation'

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