Combining Philosophers

Ideas for Mark Rowlands, Joseph Melia and Numenius

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3 ideas

5. Theory of Logic / D. Assumptions for Logic / 1. Bivalence

6163	If bivalence is rejected, then excluded middle must also be rejected [Rowlands]
	Full Idea: If you reject the principle of bivalence (that a proposition is either determinately true or false), then statements are also not subject to the Law of Excluded Middle (P or not-P).
	From: Mark Rowlands (Externalism [2003], Ch.3)
	A reaction: I think Rowlands is wrong about this. Excluded Middle could be purely syntacti, or its semantics could be 'True or Not-True'. Only bivalent excluded middle introduces 'True or False'. Compare Idea 4752.

5. Theory of Logic / G. Quantification / 5. Second-Order Quantification

5740	Second-order logic needs second-order variables and quantification into predicate position [Melia]
	Full Idea: Permitting quantification into predicate position and adding second-order variables leads to second-order logic.
	From: Joseph Melia (Modality [2003], Ch.2)
	A reaction: Often expressed by saying that we now quantify over predicates and relations, rather than just objects. Depends on your metaphysical commitments.

5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models

5741	If every model that makes premises true also makes conclusion true, the argument is valid [Melia]
	Full Idea: In first-order predicate calculus validity is defined thus: an argument is valid iff every model that makes the premises of the argument true also makes the conclusion of the argument true.
	From: Joseph Melia (Modality [2003], Ch.2)
	A reaction: See Melia Ch. 2 for an explanation of a 'model'. Traditional views of validity tend to say that if the premises are true the conclusion has to be true (necessarily), but this introduces the modal term 'necessarily', which is controversial.