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Ideas for 'fragments/reports', 'Philosophies of Mathematics' and 'Dynamic Logics'

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4 ideas

5. Theory of Logic / K. Features of Logics / 2. Consistency

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)

5. Theory of Logic / K. Features of Logics / 3. Soundness

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)

5. Theory of Logic / K. Features of Logics / 4. Completeness

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....