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Full Idea
Lewis's different systems of modal logic differed about such formulae as □P implies □□P; ◊□P implies □P; and ◊S implies □◊S
Clarification
'Nec' (usually a square) and 'poss' (a diamond) are necessarily and possibly
Gist of Idea
The main modal logics disagree over three key formulae
Source
Stephen Yablo (Apriority and Existence [2000], §06)
Book Ref
'New Essays on the A Priori', ed/tr. Boghossian,P /Peacocke,C [OUP 2000], p.203
A Reaction
Yablo's point is that the various version don't seem to make much difference to our practices in logic, mathematics and science. The problem, says Yablo, is deciding exactly what you mean by 'necessarily' and 'possibly'.
| 8858 | Philosophers keep finding unexpected objects, like models, worlds, functions, numbers, events, sets, properties [Yablo] |
| 8859 | The main modal logics disagree over three key formulae [Yablo] |
| 8862 | Platonic objects are really created as existential metaphors [Yablo] |
| 8861 | Hardly a word in the language is devoid of metaphorical potential [Yablo] |
| 8863 | We must treat numbers as existing in order to express ourselves about the arrangement of planets [Yablo] |
| 8864 | We quantify over events, worlds, etc. in order to make logical possibilities clearer [Yablo] |
| 8865 | If 'the number of Democrats is on the rise', does that mean that 50 million is on the rise? [Yablo] |