| 14667 | System B has not been justified as fallacy-free for reasoning on what might have been [Salmon,N] |
| Full Idea: Even the conventionally accepted system B, which is weaker than S5 and independent of S4, has not been adequately justified as a fallacy-free system of reasoning about what might have been. | |
| From: Nathan Salmon (The Logic of What Might Have Been [1989], Intro) |
| 14668 | In B it seems logically possible to have both p true and p is necessarily possibly false [Salmon,N] |
| Full Idea: The characteristic of B has the form φ⊃□◊φ. ...Even if these axioms are necessarily true, it seems logically possible for p to be true while the proposition that p is necessarily possible is at the same time false. | |
| From: Nathan Salmon (The Logic of What Might Have Been [1989], Intro) |
| 14692 | System B implies that possibly-being-realized is an essential property of the world [Salmon,N] |
| Full Idea: Friends of B modal logic commit themselves to the loaded claim that it is logically true that the property of possibly being realized (or being a way things might have been) is an essential property of the world. | |
| From: Nathan Salmon (The Logic of What Might Have Been [1989], V) | |
| A reaction: I think this 'loaded' formulation captures quite nicely the dispositional view I favour, that the possibilities of the actual world are built into the actual world, and define its nature just as much as the 'categorial' facts do. |
| 9745 | The system B has the 'reflexive' and 'symmetric' conditions on its accessibility relation [Fitting/Mendelsohn] |
| Full Idea: The system B has the 'reflexive' and 'symmetric' conditions imposed on its accessibility relation - that is, every world must be accessible to itself, and any relation between worlds must be mutual. | |
| From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 1.8) |
| 13711 | System B introduces iterated modalities [Sider] |
| Full Idea: With system B we begin to be able to say something about iterated modalities. ..S4 then takes a different stand on the iterated modalities, and neither is an extension of the other. | |
| From: Theodore Sider (Logic for Philosophy [2010], 6.4.4) |