Lexicon of Arguments

Philosophical and Scientific Issues in Dispute
 
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Theses II

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II 176
Independence/Logic/Cresswell: misunderstanding: independence of an axiom does not mean that you can discard it at will.
>Axioms, >Axiom systems.
E.g. an independence proof within the axiomatic propositional calculus, for example, the independence of
(p v q)> (q v p).
Such proof indicates that one can give a semantic definition of an operator that meets all other axioms of disjunction, but is not commutative.
But it does not show that disjunction itself is not commutative, and it also does not show that
(p v q)> (q v p)
is not a logical truth about classic disjunction.
>Disjunction, >Logical truth, >Operators.

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