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Full Idea
While Fine suggests defining a narrow notion of logical necessity in terms of metaphysical necessity by 'restriction' (to logical truths that can be defined in non-modal terms), this seems unpromising for broad logical necessity, which is modal.
Gist of Idea
Narrow non-modal logical necessity may be metaphysical, but real logical necessity is not
Source
Ian Rumfitt (Logical Necessity [2010], §2)
Book Ref
'Modality', ed/tr. Hale,B/Hoffman,A [OUP 2010], p.46
A Reaction
[compressed] He cites Kit Fine 2002. Rumfitt glosses the non-modal definitions as purely formal. The metaphysics lurks somewhere in the proof.
| 14532 | A distinctive type of necessity is found in logical consequence [Rumfitt, by Hale/Hoffmann,A] |
| 12193 | Logical necessity is when 'necessarily A' implies 'not-A is contradictory' [Rumfitt] |
| 12194 | Contradictions include 'This is red and not coloured', as well as the formal 'B and not-B' [Rumfitt] |
| 12195 | Soundness in argument varies with context, and may be achieved very informally indeed [Rumfitt] |
| 12198 | Geometrical axioms in logic are nowadays replaced by inference rules (which imply the logical truths) [Rumfitt] |
| 12199 | There is a modal element in consequence, in assessing reasoning from suppositions [Rumfitt] |
| 12201 | We reject deductions by bad consequence, so logical consequence can't be deduction [Rumfitt] |
| 12200 | A logically necessary statement need not be a priori, as it could be unknowable [Rumfitt] |
| 12202 | Narrow non-modal logical necessity may be metaphysical, but real logical necessity is not [Rumfitt] |
| 12203 | If a world is a fully determinate way things could have been, can anyone consider such a thing? [Rumfitt] |
| 12204 | The logic of metaphysical necessity is S5 [Rumfitt] |