Showing posts with label Modality. Show all posts
Showing posts with label Modality. Show all posts

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:
"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.

Tuesday, March 29, 2011

Metaphysical Possibility

As I've said in a previous post, I wonder (and in great ignorance, no doubt) what could confer support on the proposition possibly, God exists.

Edward Feser has an intriguing, short article on Plantinga's ontological argument in which he says,
"...a failed attempt to discover a contradiction in some concept itself provides at least some actual evidence to think the concept describes a real possibility"
The distinctions between logical, broadly logical and metaphysical possibility are quite confusing to me.  If a concept doesn't entail any contradictions, then this would surely imply (narrowly) logical possibility.  But what kind of conceptual analysis takes us further into broadly logical possibility?  William F. Vallicella often discusses this perplexing topic (on which he is has also written at length in published journals) on his blog, but I am still a bit fuzzy on these distinctions.

Sunday, March 27, 2011

Possible Worlds

In many cases, philosophers consider something possible if it hasn't been shown to be impossible.  So much the better for asserting possibly God exists.  But suppose we wanted to confer support on that proposition anyhow.  As any good theist should be, we aren't satisfied with relying on the prevalent attitudes among philosophers.  Can we show that possibly God exists?  Sounds easy enough, doesn't it?  I mean come on, all these arguments for God's existence...at least cumulatively they should give us a remote possibility.

This is where philosophical language is tricky if we don't pay close attention.  There is a difference between asserting what's possible to be known, and asserting what's possible period.

For example:
It's possible that it will rain today.
It's impossible for Clark Kent to jump over a tall building in a single bound.

These are normally taken to be a statements about the actual world given what we know.  In the first case, given what we know about weather systems, we maintain that rain is epistemically possible.  In the second example, given what we know about the laws of physics, we might intend to say that this feat is physically impossible.  There are other forms of possibility that philosophers talk about.

We wouldn't say that it's logically impossible for Clark Kent to clear a tall building.  But we would say that it's logically impossible for 2+2=5.  Thus, in that sense, it is possible for Clark Kent to jump over a tall building in a single bound.  Perhaps the laws of nature could have been different such that this would be permitted (interestingly, some have argued that he laws of nature could not have been different).  Assuming we think the laws of nature might have been different, we could say that it's metaphysically possible for Clark Kent to make his jump.

So to which kind of possibility do we refer when we say that God's existence is possible?  Metaphysical possibility ... or is it broadly logical possibility?  It depends on who you ask.

And thus, as far as I can see, a posteriori arguments for God's existence won't help the theist show that God exists is metaphysically possible.  I'm honestly not sure (and this is a statement about my ignorance) how one would go about showing that something is metaphysically possible.  Perhaps this is why philosophers tend to assume it unless shown otherwise?  We can show that something is conceptually incoherent and thus logically (and I will assume this entails metaphysically) impossible.  But how do we show something is metaphysically possible if it isn't already subsumed under what's physically possible?  Does this require mere conceptual analysis?