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Full Idea
Armstrong says what is actual (namely a certain roster of universals) might have been impossible. Hence his modal logic is S4, without the 'Brouwersche Axiom'.
Gist of Idea
If what is actual might have been impossible, we need S4 modal logic
Source
report of David M. Armstrong (A Theory of Universals [1978]) by David Lewis - Armstrong on combinatorial possibility 'The demand'
Book Ref
Lewis,David: 'Papers in Metaphysics and Epistemology' [CUP 1999], p.202
A Reaction
So p would imply possibly-not-possibly-p.
| 15544 | If what is actual might have been impossible, we need S4 modal logic [Armstrong, by Lewis] |
| 14972 | S4 has 14 modalities, and always reduces to a maximum of three modal operators [Cresswell] |
| 16958 | In S4 the actual world has a special place [Dummett] |
| 14671 | What is necessary is not always necessarily necessary, so S4 is fallacious [Salmon,N] |
| 9747 | The system S4 has the 'reflexive' and 'transitive' conditions on its accessibility relation [Fitting/Mendelsohn] |
| 7794 | There are seven modalities in S4, each with its negation [Girle] |
| 15102 | S4 says there must be some necessary truths (the actual ones, of which there is at least one) [Cameron] |