Ideas from 'Negation' by Edwin D. Mares [2014], by Theme Structure
[found in 'Bloomsbury Companion to Philosophical Logic' (ed/tr Horsten,L/Pettigrew,R) [Bloomsbury 2014,9781472523030]].
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2. Reason / A. Nature of Reason / 9. Limits of Reason
18781

Inconsistency doesn't prevent us reasoning about some system

4. Formal Logic / E. Nonclassical Logics / 2. Intuitionist Logic
18789

Intuitionist logic looks best as natural deduction

18790

Intuitionism as natural deduction has no rule for negation

4. Formal Logic / E. Nonclassical Logics / 3. ManyValued Logic
18787

Threevalued logic is useful for a theory of presupposition

5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
18793

Material implication (and classical logic) considers nothing but truth values for implications

18784

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

5. Theory of Logic / D. Assumptions for Logic / 1. Bivalence
18786

Excluded middle standardly implies bivalence; attacks use noncontradiction, De M 3, or double negation

18780

Standard disjunction and negation force us to accept the principle of bivalence

5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
18782

The connectives are studied either through model theory or through proof theory

5. Theory of Logic / H. Proof Systems / 4. Natural Deduction
18783

Manyvalued logics lack a natural deduction system

5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
18792

Situation semantics for logics: not possible worlds, but information in situations

5. Theory of Logic / K. Features of Logics / 2. Consistency
18785

Consistency is semantic, but noncontradiction is syntactic

6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
18788

For intuitionists there are not numbers and sets, but processes of counting and collecting

19. Language / C. Semantics / 1. Semantics
18791

In 'situation semantics' our main concepts are abstracted from situations
