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4 ideas
10119 | Consistency is a purely syntactic property, unlike the semantic property of soundness [George/Velleman] |
Full Idea: Consistency is a purely syntactic property, unlike the semantic property of soundness. | |
From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.6) |
10126 | A 'consistent' theory cannot contain both a sentence and its negation [George/Velleman] |
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'. | |
From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.7) |
10120 | Soundness is a semantic property, unlike the purely syntactic property of consistency [George/Velleman] |
Full Idea: Soundness is a semantic property, unlike the purely syntactic property of consistency. | |
From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.6) |
10127 | A 'complete' theory contains either any sentence or its negation [George/Velleman] |
Full Idea: If there is a sentence such that neither the sentence nor its negation are theorems of a theory, then the theory is 'incomplete'. Otherwise it is 'complete'. | |
From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.7) | |
A reaction: Interesting questions are raised about undecidable sentences, irrelevant sentences, unknown sentences.... |