Combining Philosophers

Ideas for Hermarchus, Mark Colyvan and Engelbretsen,G/Sayward,C

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2 ideas

5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle

17924	Excluded middle says P or not-P; bivalence says P is either true or false [Colyvan]
	Full Idea: The law of excluded middle (for every proposition P, either P or not-P) must be carefully distinguished from its semantic counterpart bivalence, that every proposition is either true or false.
	From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 1.1.3)
	A reaction: So excluded middle makes no reference to the actual truth or falsity of P. It merely says P excludes not-P, and vice versa.

5. Theory of Logic / D. Assumptions for Logic / 4. Identity in Logic

13851	Unlike most other signs, = cannot be eliminated [Engelbretsen/Sayward]
	Full Idea: Unlike ∨, →, ↔, and ∀, the sign = is not eliminable from a logic.
	From: Engelbretsen,G/Sayward,C (Philosophical Logic: Intro to Advanced Topics [2011], Ch.3)