2. If something is possible then there is a world in which that something is real. — TheMadFool
“Possible” means can exist in a possible world. Not actually exists in some world. — khaled
If I say an argument is invalid it means there's a world in which all the premises are true and the conclusion is false. — TheMadFool
1. It is possible that God exists.
2. If something is possible then there is a world in which that something is real.
Ergo,
3. God exists. — TheMadFool
If I say an argument is invalid it means there's a world in which all the premises are true and the conclusion is false. — TheMadFool
There's a possible world in which a contradiction is true. — Bartricks
All possible worlds are actual worlds. — TheMadFool
Possible worlds that include contradictions are called impossible worlds. — Banno
1. World x is possible & World x is not actual (true according to all the posters above) — TheMadFool
Ergo,
World x is actual can't be consistent with world x is possible. After all, world x is actual is the negation of world x is not actual. — TheMadFool
If I say an argument is invalid it means there's a world in which all the premises are true and the conclusion is false. — TheMadFool
Suppose X is a possible world and is not actual.
Ergo, the following statement is true.
1. X is possible & X is not actual
If so, the statement
2. X is possible & X is actual
has to be false because X is not actual (X is actual is false)
But then look at 2. It says something odd: X is possible and actual is false. — TheMadFool
instead of "an actual world", I'd use "the actual world", but maybe that's just me?
1. X is a possible world ∧ X is not the actual world = X is a possible world but not our's
Say, one where Napoleon drowned by suicide. At least that seems possible.
2. X is a possible world ∧ X is the actual world = X is our world
Or, instead of "an actual world", we could use "a real world", i.e. not fictional or merely imagined, despite being unknown to us.
1. X is a possible world ∧ X is not real = a possible world but imaginary/fictional
2. X is a possible world ∧ X is real = our world or another real world (unknown to us)
(Technically, there's a presumption that our world is a self-consistent whole, but that doesn't seem controversial; either way, the possible world semantics, I think, is intended to allow reasoning that includes our world, the actual world.)
If that makes any sense... — jorndoe
a possible world need not be actual. — TheMadFool
Suppose X is a possible world and that's all we know. — TheMadFool
1. X is possible & X is not actual. — TheMadFool
1. If X is possible then X is actual (False i.e. there's a gap between possible and actual)
2. If X is actual then X is possible (True? What happened to the gap mentioned above?) — TheMadFool
These "gaps" are sometimes not two way.
For example "If X is a butler, X is human", True. "If X is human, X is a butler", False. See?
Because the set of all butlers is a subset of the set of all humans. Similarly, the set of actual worlds, is a subset of the set of possible worlds. — khaled
There is a gap" is not a logical statement. — khaled
If there's a gap between point A and point B, it doesn't matter whether I'm at point A or B, there's a gap. — TheMadFool
But we're not talking about points in space are we? — khaled
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