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Single Idea 18784

[filed under theme 5. Theory of Logic / A. Overview of Logic / 6. Classical Logic ]

Full Idea

Among the virtues of classical logic is the fact that the connectives are related to one another in elegant ways that often involved negation. For example, De Morgan's Laws, which involve negation, disjunction and conjunction.

Gist of Idea

In classical logic the connectives can be related elegantly, as in De Morgan's laws

Source

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

Book Ref

'Bloomsbury Companion to Philosophical Logic', ed/tr. Horsten,L/Pettigrew,R [Bloomsbury 2014], p.183


A Reaction

Mares says these enable us to take disjunction or conjunction as primitive, and then define one in terms of the other, using negation as the tool.


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]