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Single Idea 5741

[filed under theme 5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models ]

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.

Clarification

'Iff' means if and only if

Gist of Idea

If every model that makes premises true also makes conclusion true, the argument is valid

Source

Joseph Melia (Modality [2003], Ch.2)

Book Ref

Melia,Joseph: 'Modality' [Acumen 2003], p.48

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.

The 17 ideas from Joseph Melia

5732 'De re' modality is about things themselves, 'de dicto' modality is about propositions [Melia]
5734 Possible worlds make it possible to define necessity and counterfactuals without new primitives [Melia]
5742 In possible worlds semantics the modal operators are treated as quantifiers [Melia]
5743 If possible worlds semantics is not realist about possible worlds, logic becomes merely formal [Melia]
5738 We may be sure that P is necessary, but is it necessarily necessary? [Melia]
5737 Predicate logic has connectives, quantifiers, variables, predicates, equality, names and brackets [Melia]
5740 Second-order logic needs second-order variables and quantification into predicate position [Melia]
5741 If every model that makes premises true also makes conclusion true, the argument is valid [Melia]
5735 Maybe names and predicates can capture any fact [Melia]
5739 Sometimes we want to specify in what ways a thing is possible [Melia]
5736 No sort of plain language or levels of logic can express modal facts properly [Melia]
5744 First-order predicate calculus is extensional logic, but quantified modal logic is intensional (hence dubious) [Melia]
5746 The Identity of Indiscernibles is contentious for qualities, and trivial for non-qualities [Melia]
5748 We accept unverifiable propositions because of simplicity, utility, explanation and plausibility [Melia]
5750 Consistency is modal, saying propositions are consistent if they could be true together [Melia]
5749 Possible worlds could be real as mathematics, propositions, properties, or like books [Melia]
5751 The truth of propositions at possible worlds are implied by the world, just as in books [Melia]