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Full Idea
A relation is 'Euclidean' if aRb and aRc imply bRc.
Gist of Idea
A relation is 'Euclidean' if aRb and aRc imply bRc
Source
Max J. Cresswell (Modal Logic [2001], 7.1.2)
Book Ref
'Blackwell Guide to Philosophical Logic', ed/tr. Goble,Lou [Blackwell 2001], p.141
A Reaction
If a thing has a relation to two separate things, then those two things will also have that relation between them. If I am in the same family as Jim and as Jill, then Jim and Jill are in the same family.
| 14970 | Normal system K has five axioms and rules [Cresswell] |
| 14971 | D is valid on every serial frame, but not where there are dead ends [Cresswell] |
| 14972 | S4 has 14 modalities, and always reduces to a maximum of three modal operators [Cresswell] |
| 14973 | In S5 all the long complex modalities reduce to just three, and their negations [Cresswell] |
| 14974 | A relation is 'Euclidean' if aRb and aRc imply bRc [Cresswell] |
| 14975 | A de dicto necessity is true in all worlds, but not necessarily of the same thing in each world [Cresswell] |
| 14976 | Reject the Barcan if quantifiers are confined to worlds, and different things exist in other worlds [Cresswell] |