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 2014,978-1-4725-2303-0]].

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2. Reason / A. Nature of Reason / 9. Limits of Reason
Inconsistency doesn't prevent us reasoning about some system
4. Formal Logic / E. Nonclassical Logics / 2. Intuitionist Logic
Intuitionist logic looks best as natural deduction
Intuitionism as natural deduction has no rule for negation
4. Formal Logic / E. Nonclassical Logics / 3. Many-Valued Logic
Three-valued logic is useful for a theory of presupposition
5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
Material implication (and classical logic) considers nothing but truth values for implications
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
Excluded middle standardly implies bivalence; attacks use non-contradiction, De M 3, or double negation
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
The connectives are studied either through model theory or through proof theory
5. Theory of Logic / H. Proof Systems / 4. Natural Deduction
Many-valued logics lack a natural deduction system
5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
Situation semantics for logics: not possible worlds, but information in situations
5. Theory of Logic / K. Features of Logics / 2. Consistency
Consistency is semantic, but non-contradiction is syntactic
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
For intuitionists there are not numbers and sets, but processes of counting and collecting
19. Language / C. Assigning Meanings / 2. Semantics
In 'situation semantics' our main concepts are abstracted from situations