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Single Idea 18782

[filed under theme 5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives ]

Full Idea

In studying the logical connectives, philosophers of logic typically adopt the perspective of either model theory (givng truth conditions of various parts of the language), or of proof theory (where use in a proof system gives the connective's meaning).

Gist of Idea

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

Source

Edwin D. Mares (Negation [2014], 1)

Book Ref

'Bloomsbury Companion to Philosophical Logic', ed/tr. Horsten,L/Pettigrew,R [Bloomsbury 2014], p.182


A Reaction

[compressed] The commonest proof theory is natural deduction, giving rules for introduction and elimination. Mates suggests moving between the two views is illuminating.


The 27 ideas from Edwin D. Mares

The most popular view is that coherent beliefs explain one another [Mares]
Possible worlds semantics has a nice compositional account of modal statements [Mares]
Unstructured propositions are sets of possible worlds; structured ones have components [Mares]
Operationalism defines concepts by our ways of measuring them [Mares]
Light in straight lines is contingent a priori; stipulated as straight, because they happen to be so [Mares]
Empiricists say rationalists mistake imaginative powers for modal insights [Mares]
The essence of a concept is either its definition or its conceptual relations? [Mares]
Maybe space has points, but processes always need regions with a size [Mares]
Aristotelian justification uses concepts abstracted from experience [Mares]
After 1903, Husserl avoids metaphysical commitments [Mares]
Aristotelians dislike the idea of a priori judgements from pure reason [Mares]
The truth of the axioms doesn't matter for pure mathematics, but it does for applied [Mares]
Mathematics is relations between properties we abstract from experience [Mares]
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]