Combining Philosophers

Ideas for Hermarchus, D.J. O'Connor and Peter Smith

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2 ideas

5. Theory of Logic / A. Overview of Logic / 4. Pure Logic

3746	Logic seems to work for unasserted sentences [O'Connor]
	Full Idea: If sentences can have truth-values only when they occur as asserted, it would be impossible to have a truth-functional basis to logic.
	From: D.J. O'Connor (The Correspondence Theory of Truth [1975], Ch.6)

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

10616	Second-order arithmetic can prove new sentences of first-order [Smith,P]
	Full Idea: Going second-order in arithmetic enables us to prove new first-order arithmetical sentences that we couldn't prove before.
	From: Peter Smith (Intro to Gödel's Theorems [2007], 23.4)
	A reaction: The wages of Satan, perhaps. We can prove things about objects by proving things about their properties and sets and functions. Smith says this fact goes all the way up the hierarchy.