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Ideas for 'fragments/reports', 'The Concept of Law' and 'Which Logic is the Right Logic?'

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3 ideas

5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic

10766	Logic is either for demonstration, or for characterizing structures [Tharp]
	Full Idea: One can distinguish at least two quite different senses of logic: as an instrument of demonstration, and perhaps as an instrument for the characterization of structures.
	From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2)
	A reaction: This is trying to capture the proof-theory and semantic aspects, but merely 'characterizing' something sounds like a rather feeble aspiration for the semantic side of things. Isn't it to do with truth, rather than just rule-following?

5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic

10767	Elementary logic is complete, but cannot capture mathematics [Tharp]
	Full Idea: Elementary logic cannot characterize the usual mathematical structures, but seems to be distinguished by its completeness.
	From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2)

5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic

10769	Second-order logic isn't provable, but will express set-theory and classic problems [Tharp]
	Full Idea: The expressive power of second-order logic is too great to admit a proof procedure, but is adequate to express set-theoretical statements, and open questions such as the continuum hypothesis or the existence of big cardinals are easily stated.
	From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2)