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The Logic Ninja |
Sunday, October 02, 2011
Get acquainted with predicate logic in one sitting
Saturday, October 01, 2011
Losing my marbles over Mawson
Mawson introduces philosophy of religion with nuance and style, and with plenty of his own authentic recipes. However, I can't make heads or tails of this passage:
I am assuming he means, "could still have created everything other than himself." Let's take "could" and "might have" as synonyms for "true in at least one (logically) possible world."
God might have chosen not to create a world. But even a for creationless reality it holds that God could have chosen to create everything other than himself.
The fog hasn't lifted yet though, since "everything other than himself" picks out different items in different worlds (perhaps God only creates sea monkeys in some world). Mawson is probably referring to the contents of the actual world when he says "everything other than himself." But this led me to some interesting conclusions, which I'm have likely been mapped out and explored in more detail in advanced logical systems.
My general conclusion: it is necessarily true that p is true in some W so long as p is possibly true or necessarily true.
More specifically:
(1) Possibly, God has the property of being creator.
(2) Necessarily, it's possible that God has the property of being creator.
Any statement expressing a possible-world indexed proposition, like (1), will itself give rise to a statement that expresses a necessary truth. On the other hand, if (1) is false then it would be false in all possible worlds. Why is this? Here is my unprofessional attempt at finding out:
(3) It will snow in June next year
(4) It will snow in some month next year
If (3) is true, then obviously (4) is true. More generally, as long as at least one month has snow, then (4) is true. On the other hand, it must (*actually*) snow in June for (3) to be true. This example isn't perfect, but it helps me see why we should affirm this:
(5) If p is true in some possible world, then that p is true in some possible world is necessarily true.
Let's see if we can stretch it even further here.
(6) p is true in this world (the actual world)
(7) therefore, p is true in some possible world
(8) that p is true in some possible world is true in all possible worlds
So perhaps Mawson is trying to say something very precise here (I'm switching from possible words back to good ol' fashioned possible here just to make the sentences less awkward)
(6') in this world, God created something
Therefore
(7') it is possible that God created something
(8) necessarily, it is possible that God created something
Moral of the story: even in worlds where (6') is false, (7') is true
"God might have chosen not to create a world but rather have remained the sole existent thing, in which case he would not have had the property of being creator, although strictly speaking, he would still have created everything other than himself."Mawson, T.J. Belief in God: An Introduction to the Philosophy of Religion. Clarendon Press, 2005. 81.
I am assuming he means, "could still have created everything other than himself." Let's take "could" and "might have" as synonyms for "true in at least one (logically) possible world."
God might have chosen not to create a world. But even a for creationless reality it holds that God could have chosen to create everything other than himself.
The fog hasn't lifted yet though, since "everything other than himself" picks out different items in different worlds (perhaps God only creates sea monkeys in some world). Mawson is probably referring to the contents of the actual world when he says "everything other than himself." But this led me to some interesting conclusions, which I'm have likely been mapped out and explored in more detail in advanced logical systems.
My general conclusion: it is necessarily true that p is true in some W so long as p is possibly true or necessarily true.
More specifically:
(1) Possibly, God has the property of being creator.
(2) Necessarily, it's possible that God has the property of being creator.
Any statement expressing a possible-world indexed proposition, like (1), will itself give rise to a statement that expresses a necessary truth. On the other hand, if (1) is false then it would be false in all possible worlds. Why is this? Here is my unprofessional attempt at finding out:
(3) It will snow in June next year
(4) It will snow in some month next year
If (3) is true, then obviously (4) is true. More generally, as long as at least one month has snow, then (4) is true. On the other hand, it must (*actually*) snow in June for (3) to be true. This example isn't perfect, but it helps me see why we should affirm this:
(5) If p is true in some possible world, then that p is true in some possible world is necessarily true.
Let's see if we can stretch it even further here.
(6) p is true in this world (the actual world)
(7) therefore, p is true in some possible world
(8) that p is true in some possible world is true in all possible worlds
So perhaps Mawson is trying to say something very precise here (I'm switching from possible words back to good ol' fashioned possible here just to make the sentences less awkward)
(6') in this world, God created something
Therefore
(7') it is possible that God created something
(8) necessarily, it is possible that God created something
Moral of the story: even in worlds where (6') is false, (7') is true
"God might have chosen not to create a world ... [but] ... he could still have created everything other than himself."Am I stretching this too far? Probably so. But at least I didn't completely waste my morning on a typo.
