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4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / d. System T

[version imposing one condition on accessibility]

4 ideas
If possibilitiy is relative, that might make accessibility non-transitive, and T the correct system [Dummett]
     Full Idea: If some world is 'a way the world might be considered to be if things were different in a certain respect', that might show that the accessibility relation should not be taken to be transitive, and we should have to adopt modal logic T.
     From: Michael Dummett (Could There Be Unicorns? [1983], 8)
     A reaction: He has already rejected symmetry from the relation, for reasons concerning relative identity. He is torn between T and S4, but rejects S5, and opts not to discuss it.
For metaphysics, T may be the only correct system of modal logic [Salmon,N]
     Full Idea: Insofar as modal logic is concerned exclusively with the logic of metaphysical modality, ..T may well be the one and only (strongest) correct system of (first-order) propositional logic.
     From: Nathan Salmon (The Logic of What Might Have Been [1989], Intro)
     A reaction: This contrasts sharply with the orthodox view, that S5 (or at the very least S4) is the correct system for metaphysics.
The system T has the 'reflexive' conditon imposed on its accessibility relation [Fitting/Mendelsohn]
     Full Idea: The system T has the 'reflexive' condition imposed on its accessibility relation - that is, every world must be accessible to itself.
     From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 1.8)
T adds □p→p for reflexivity, and is ideal for modeling lawhood [Schaffer,J]
     Full Idea: System T is a normal modal system augmented with the reflexivity-generating axiom □p→p, and is, I think, the best modal logic for modeling lawhood.
     From: Jonathan Schaffer (Causation and Laws of Nature [2008], n46)
     A reaction: Schaffer shows in the article why transitivity would not be appropriate for lawhood.