Combining Texts

Ideas for 'Philosophy of Mathematics', 'The Logic of Infinity' and 'There are no ordinary things'

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2 ideas

10. Modality / A. Necessity / 6. Logical Necessity
Logical modalities may be acceptable, because they are reducible to satisfaction in models [Shapiro]
     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.
     From: Stewart Shapiro (Philosophy of Mathematics [1997], 7.1)
     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.
10. Modality / E. Possible worlds / 1. Possible Worlds / a. Possible worlds
Why does the 'myth' of possible worlds produce correct modal logic? [Shapiro]
     Full Idea: The fact that the 'myth' of possible worlds happens to produce the correct modal logic is itself a phenomenon in need of explanation.
     From: Stewart Shapiro (Philosophy of Mathematics [1997], 7.4)
     A reaction: The claim that it produces 'the' correct modal logic seems to beg a lot of questions, given the profusion of modal systems. This is a problem with any sort of metaphysics which invokes fictionalism - what were those particular fictions responding to?