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
The logic of metaphysical necessity is S5
5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
There is a modal element in consequence, in assessing reasoning from suppositions
Soundness in argument varies with context, and may be achieved very informally indeed
We reject deductions by bad consequence, so logical consequence can't be deduction
5. Theory of Logic / D. Assumptions for Logic / 3. Contradiction
Contradictions include 'This is red and not coloured', as well as the formal 'B and not-B'
5. Theory of Logic / H. Proof Systems / 2. Axiomatic Proof
Geometrical axioms in logic are nowadays replaced by inference rules (which imply the logical truths)
10. Modality / A. Necessity / 3. Types of Necessity
A distinctive type of necessity is found in logical consequence
10. Modality / A. Necessity / 6. Logical Necessity
Logical necessity is when 'necessarily A' implies 'not-A is contradictory'
A logically necessary statement need not be a priori, as it could be unknowable
Narrow non-modal logical necessity may be metaphysical, but real logical necessity is not
10. Modality / E. Possible worlds / 1. Possible Worlds / e. Against possible worlds
If a world is a fully determinate way things could have been, can anyone consider such a thing?