Ideas from 'Logical Necessity' by Ian Rumfitt [2010], by Theme Structure
[found in 'Modality' (ed/tr Hale,B/Hoffman,A) [OUP 2010,]].
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4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / h. System S5
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The logic of metaphysical necessity is S5

5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
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Soundness in argument varies with context, and may be achieved very informally indeed

12199

There is a modal element in consequence, in assessing reasoning from suppositions

12201

We reject deductions by bad consequence, so logical consequence can't be deduction

5. Theory of Logic / D. Assumptions for Logic / 3. Contradiction
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Contradictions include 'This is red and not coloured', as well as the formal 'B and notB'

5. Theory of Logic / H. Proof Systems / 2. Axiomatic Proof
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Geometrical axioms in logic are nowadays replaced by inference rules (which imply the logical truths)

10. Modality / A. Necessity / 3. Types of Necessity
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A distinctive type of necessity is found in logical consequence [Hale/Hoffmann,A]

10. Modality / A. Necessity / 6. Logical Necessity
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Logical necessity is when 'necessarily A' implies 'notA is contradictory'

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A logically necessary statement need not be a priori, as it could be unknowable

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Narrow nonmodal logical necessity may be metaphysical, but real logical necessity is not

10. Modality / E. Possible worlds / 1. Possible Worlds / e. Against possible worlds
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If a world is a fully determinate way things could have been, can anyone consider such a thing?
