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Single Idea 5740

[filed under theme 5. Theory of Logic / G. Quantification / 5. Second-Order Quantification ]

Full Idea

Permitting quantification into predicate position and adding second-order variables leads to second-order logic.

Gist of Idea

Second-order logic needs second-order variables and quantification into predicate position

Source

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

Book Ref

Melia,Joseph: 'Modality' [Acumen 2003], p.40

A Reaction

Often expressed by saying that we now quantify over predicates and relations, rather than just objects. Depends on your metaphysical commitments.

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]