Ideas from 'The Logic of What Might Have Been' by Nathan Salmon [1989], by Theme Structure

[found in 'Metaphysics, Mathematics and Meaning' by Salmon,Nathan [OUP 2005,0-19-928471-7]].

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4. Formal Logic / D. Modal Logic ML / 2. Tools of Modal Logic / b. Terminology of ML
A world is 'accessible' to another iff the first is possible according to the second
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / d. System T
For metaphysics, T may be the only correct system of modal logic
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / f. System B
In B it seems logically possible to have both p true and p is necessarily possibly false
System B has not been justified as fallacy-free for reasoning on what might have been
System B implies that possibly-being-realized is an essential property of the world
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / g. System S4
What is necessary is not always necessarily necessary, so S4 is fallacious
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / h. System S5
The unsatisfactory counterpart-theory allows the retention of S5
S5 modal logic ignores accessibility altogether
S5 believers say that-things-might-have-been-that-way is essential to ways things might have been
4. Formal Logic / D. Modal Logic ML / 4. Alethic Modal Logic
Metaphysical (alethic) modal logic concerns simple necessity and possibility (not physical, epistemic..)
9. Objects / D. Essence of Objects / 15. Against Essentialism
Any property is attached to anything in some possible world, so I am a radical anti-essentialist
10. Modality / A. Necessity / 3. Types of Necessity
Logical possibility contains metaphysical possibility, which contains nomological possibility
10. Modality / A. Necessity / 5. Metaphysical Necessity
Metaphysical necessity is said to be unrestricted necessity, true in every world whatsoever
Bizarre identities are logically but not metaphysically possible, so metaphysical modality is restricted
Metaphysical necessity is NOT truth in all (unrestricted) worlds; necessity comes first, and is restricted
Without impossible worlds, the unrestricted modality that is metaphysical has S5 logic
In the S5 account, nested modalities may be unseen, but they are still there
10. Modality / A. Necessity / 6. Logical Necessity
Logical necessity is free of constraints, and may accommodate all of S5 logic
10. Modality / A. Necessity / 7. Natural Necessity
Nomological necessity is expressed with intransitive relations in modal semantics
10. Modality / C. Sources of Modality / 5. Modality from Actuality
Necessity and possibility are not just necessity and possibility according to the actual world
10. Modality / E. Possible worlds / 1. Possible Worlds / b. Impossible worlds
Impossible worlds are also ways for things to be
Denial of impossible worlds involves two different confusions
Without impossible worlds, how things might have been is the only way for things to be
10. Modality / E. Possible worlds / 1. Possible Worlds / e. Against possible worlds
Possible worlds rely on what might have been, so they can' be used to define or analyse modality
10. Modality / E. Possible worlds / 2. Nature of Possible Worlds / a. Nature of possible worlds
Possible worlds are maximal abstract ways that things might have been
Possible worlds just have to be 'maximal', but they don't have to be consistent
10. Modality / E. Possible worlds / 2. Nature of Possible Worlds / c. Worlds as propositions
You can't define worlds as sets of propositions, and then define propositions using worlds