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Single Idea 14668
[filed under theme 4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / f. System B
]
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.
Gist of Idea
In B it seems logically possible to have both p true and p is necessarily possibly false
Source
Nathan Salmon (The Logic of What Might Have Been [1989], Intro)
Book Ref
Salmon,Nathan: 'Metaphysics, Mathematics and Meaning' [OUP 2005], p.130
Related Idea
Idea 14667
System B has not been justified as fallacy-free for reasoning on what might have been [Salmon,N]
The
27 ideas
from 'The Logic of What Might Have Been'
14669
|
For metaphysics, T may be the only correct system of modal logic
[Salmon,N]
|
14667
|
System B has not been justified as fallacy-free for reasoning on what might have been
[Salmon,N]
|
14668
|
In B it seems logically possible to have both p true and p is necessarily possibly false
[Salmon,N]
|
14670
|
Metaphysical (alethic) modal logic concerns simple necessity and possibility (not physical, epistemic..)
[Salmon,N]
|
14671
|
What is necessary is not always necessarily necessary, so S4 is fallacious
[Salmon,N]
|
14674
|
Impossible worlds are also ways for things to be
[Salmon,N]
|
14672
|
Possible worlds are maximal abstract ways that things might have been
[Salmon,N]
|
14675
|
Possible worlds just have to be 'maximal', but they don't have to be consistent
[Salmon,N]
|
14673
|
You can't define worlds as sets of propositions, and then define propositions using worlds
[Salmon,N]
|
14676
|
Nomological necessity is expressed with intransitive relations in modal semantics
[Salmon,N]
|
14678
|
Any property is attached to anything in some possible world, so I am a radical anti-essentialist
[Salmon,N]
|
14677
|
Metaphysical necessity is said to be unrestricted necessity, true in every world whatsoever
[Salmon,N]
|
14679
|
Bizarre identities are logically but not metaphysically possible, so metaphysical modality is restricted
[Salmon,N]
|
14681
|
Logical necessity is free of constraints, and may accommodate all of S5 logic
[Salmon,N]
|
14680
|
Logical possibility contains metaphysical possibility, which contains nomological possibility
[Salmon,N]
|
14682
|
Denial of impossible worlds involves two different confusions
[Salmon,N]
|
14687
|
Without impossible worlds, how things might have been is the only way for things to be
[Salmon,N]
|
14683
|
Possible worlds rely on what might have been, so they can' be used to define or analyse modality
[Salmon,N]
|
14689
|
Necessity and possibility are not just necessity and possibility according to the actual world
[Salmon,N]
|
14690
|
In the S5 account, nested modalities may be unseen, but they are still there
[Salmon,N]
|
14685
|
Metaphysical necessity is NOT truth in all (unrestricted) worlds; necessity comes first, and is restricted
[Salmon,N]
|
14684
|
A world is 'accessible' to another iff the first is possible according to the second
[Salmon,N]
|
14688
|
Without impossible worlds, the unrestricted modality that is metaphysical has S5 logic
[Salmon,N]
|
14686
|
S5 modal logic ignores accessibility altogether
[Salmon,N]
|
14691
|
S5 believers say that-things-might-have-been-that-way is essential to ways things might have been
[Salmon,N]
|
14692
|
System B implies that possibly-being-realized is an essential property of the world
[Salmon,N]
|
14693
|
The unsatisfactory counterpart-theory allows the retention of S5
[Salmon,N]
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