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Single Idea 10258

[filed under theme 10. Modality / A. Necessity / 6. Logical Necessity ]

Full Idea

For many philosophers the logical notions of possibility and necessity are exceptions to a general scepticism, perhaps because they have been reduced to model theory, via set theory. Thus Φ is logically possible if there is a model that satisfies it.

Gist of Idea

Logical modalities may be acceptable, because they are reducible to satisfaction in models

Source

Stewart Shapiro (Philosophy of Mathematics [1997], 7.1)

Book Ref

Shapiro,Stewart: 'Philosophy of Mathematics:structure and ontology' [OUP 1997], p.216

A Reaction

Initially this looks a bit feeble, like an empiricist only believing what they actually see right now, but the modern analytical philosophy project seems to be the extension of logical accounts further and further into what we intuit about modality.

The 40 ideas with the same theme [necessity because of logic or definitions]:

17852 A thing has a feature necessarily if its denial brings a contradiction [Aristotle]
12259 Reasoning is when some results follow necessarily from certain claims [Aristotle]
16490 Some facts about experience feel like logical necessities [Russell]
9001 Frege moved Kant's question about a priori synthetic to 'how is logical certainty possible?' [Quine]
12188 Contrary to some claims, Quine does not deny logical necessity [Quine, by McFetridge]
15230 Logical necessity is grounded in the logical form of a statement [Harré/Madden]
13820 The idea that anything which can be proved is necessary has a problem with empty names [Bostock]
15083 The fundamental case of logical necessity is the valid conclusion of an inference [McFetridge, by Hale]
15084 In the McFetridge view, logical necessity means a consequent must be true if the antecedent is [McFetridge, by Hale]
12180 Logical necessity requires that a valid argument be necessary [McFetridge]
12181 Traditionally, logical necessity is the strongest, and entails any other necessities [McFetridge]
12183 It is only logical necessity if there is absolutely no sense in which it could be false [McFetridge]
12184 Logical necessity overrules all other necessities [McFetridge]
12192 The mark of logical necessity is deduction from any suppositions whatever [McFetridge]
12189 Logical necessity involves a decision about usage, and is non-realist and non-cognitive [Wright,C, by McFetridge]
14681 Logical necessity is free of constraints, and may accommodate all of S5 logic [Salmon,N]
13394 Entailment does not result from mutual necessity; mutual necessity ensures entailment [Jubien]
12185 Logical necessity is epistemic necessity, which is the old notion of a priori [Edgington, by McFetridge]
10258 Logical modalities may be acceptable, because they are reducible to satisfaction in models [Shapiro]
15417 Logical necessity has two sides - validity and demonstrability - which coincide in classical logic [Burgess]
15419 General consensus is S5 for logical modality of validity, and S4 for proof [Burgess]
12206 Broadly logical necessity (i.e. not necessarily formal logical necessity) is an epistemic notion [Edgington]
12208 An argument is only valid if it is epistemically (a priori) necessary [Edgington]
8260 Logical necessity can be 'strict' (laws), or 'narrow' (laws and definitions), or 'broad' (all logical worlds) [Lowe]
16973 Explain logical necessity by logical consequence, or the other way around? [Correia]
15085 'Broadly' logical necessities are derived (in a structure) entirely from the concepts [Hale]
15088 Logical necessities are true in virtue of the nature of all logical concepts [Hale]
13709 Logical truths must be necessary if anything is [Sider]
19285 Logical necessity is something which is true, no matter what else is the case [Hale]
19287 Maybe each type of logic has its own necessity, gradually becoming broader [Hale]
18848 Something may be necessary because of logic, but is that therefore a special sort of necessity? [Rosen]
9481 Logical necessitation is not a kind of necessity; George Orwell not being Eric Blair is not a real possibility [Bird]
18478 Wittgenstein's plan to show there is only logical necessity failed, because of colours [MacBride]
11084 Logical necessity is truth in all logically possible worlds, because of laws and concepts [Hanna]
16042 The metaphysically and logically possible worlds are the same, so they are the same strength [Bennett,K]
22150 Logical possibility needs the concepts of the proposition to be adequate [Boulter]
18825 S5 is the logic of logical necessity [Rumfitt]
12193 Logical necessity is when 'necessarily A' implies 'not-A is contradictory' [Rumfitt]
12200 A logically necessary statement need not be a priori, as it could be unknowable [Rumfitt]
12202 Narrow non-modal logical necessity may be metaphysical, but real logical necessity is not [Rumfitt]