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
12204

The logic of metaphysical necessity is S5

5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
12199

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

12195

Soundness in argument varies with context, and may be achieved very informally indeed

12201

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

5. Theory of Logic / D. Assumptions for Logic / 3. Contradiction
12194

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
12198

Geometrical axioms in logic are nowadays replaced by inference rules (which imply the logical truths)

10. Modality / A. Necessity / 3. Types of Necessity
14532

A distinctive type of necessity is found in logical consequence

10. Modality / A. Necessity / 6. Logical Necessity
12193

Logical necessity is when 'necessarily A' implies 'notA is contradictory'

12200

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

12202

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
12203

If a world is a fully determinate way things could have been, can anyone consider such a thing?
