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Ideas for 'works', 'A Slim Book about Narrow Content' and 'Philosophy of Mathematics'

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2 ideas

10. Modality / A. Necessity / 5. Metaphysical Necessity
Is 'Hesperus = Phosphorus' metaphysically necessary, but not logically or epistemologically necessary? [Segal]
     Full Idea: It is metaphysically necessary that Hesperus is Phosphorus, but not logically necessary, since logical deduction could not reveal its truth, and it is not epistemologically necessary, as the ancient Greeks didn't know the identity. (Natural necessity?)
     From: Gabriel M.A. Segal (A Slim Book about Narrow Content [2000], 1.6)
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.