display all the ideas for this combination of texts
2 ideas
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. |
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. |