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
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14684
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A world is 'accessible' to another iff the first is possible according to the second
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4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / d. System T
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14669
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For metaphysics, T may be the only correct system of modal logic
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4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / f. System B
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14667
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System B has not been justified as fallacy-free for reasoning on what might have been
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14668
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In B it seems logically possible to have both p true and p is necessarily possibly false
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14692
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System B implies that possibly-being-realized is an essential property of the world
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4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / g. System S4
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14671
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What is necessary is not always necessarily necessary, so S4 is fallacious
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4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / h. System S5
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14686
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S5 modal logic ignores accessibility altogether
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14691
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S5 believers say that-things-might-have-been-that-way is essential to ways things might have been
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14693
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The unsatisfactory counterpart-theory allows the retention of S5
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4. Formal Logic / D. Modal Logic ML / 4. Alethic Modal Logic
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14670
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Metaphysical (alethic) modal logic concerns simple necessity and possibility (not physical, epistemic..)
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9. Objects / D. Essence of Objects / 15. Against Essentialism
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14678
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Any property is attached to anything in some possible world, so I am a radical anti-essentialist
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10. Modality / A. Necessity / 3. Types of Necessity
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14680
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Logical possibility contains metaphysical possibility, which contains nomological possibility
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10. Modality / A. Necessity / 5. Metaphysical Necessity
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14690
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In the S5 account, nested modalities may be unseen, but they are still there
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14677
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Metaphysical necessity is said to be unrestricted necessity, true in every world whatsoever
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14679
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Bizarre identities are logically but not metaphysically possible, so metaphysical modality is restricted
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14688
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Without impossible worlds, the unrestricted modality that is metaphysical has S5 logic
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14685
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Metaphysical necessity is NOT truth in all (unrestricted) worlds; necessity comes first, and is restricted
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10. Modality / A. Necessity / 6. Logical Necessity
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14681
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Logical necessity is free of constraints, and may accommodate all of S5 logic
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10. Modality / A. Necessity / 7. Natural Necessity
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14676
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Nomological necessity is expressed with intransitive relations in modal semantics
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10. Modality / C. Sources of Modality / 5. Modality from Actuality
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14689
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Necessity and possibility are not just necessity and possibility according to the actual world
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10. Modality / E. Possible worlds / 1. Possible Worlds / b. Impossible worlds
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14674
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Impossible worlds are also ways for things to be
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14682
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Denial of impossible worlds involves two different confusions
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14687
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Without impossible worlds, how things might have been is the only way for things to be
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10. Modality / E. Possible worlds / 1. Possible Worlds / e. Against possible worlds
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14683
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Possible worlds rely on what might have been, so they can' be used to define or analyse modality
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10. Modality / E. Possible worlds / 2. Nature of Possible Worlds / a. Nature of possible worlds
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14672
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Possible worlds are maximal abstract ways that things might have been
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14675
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Possible worlds just have to be 'maximal', but they don't have to be consistent
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10. Modality / E. Possible worlds / 2. Nature of Possible Worlds / c. Worlds as propositions
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14673
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You can't define worlds as sets of propositions, and then define propositions using worlds
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