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Single Idea 10126

[from 'Philosophies of Mathematics' by A.George / D.J.Velleman, in 5. Theory of Logic / K. Features of Logics / 2. Consistency ]

Full Idea

If there is a sentence such that both the sentence and its negation are theorems of a theory, then the theory is 'inconsistent'. Otherwise it is 'consistent'.

Gist of Idea

A 'consistent' theory cannot contain both a sentence and its negation

Source

A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.7)

Book Reference

George,A/Velleman D.J.: 'Philosophies of Mathematics' [Blackwell 2002], p.177