A theological question I heard yesterday..

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Can God make a rock so heavy he can't lift it up himself?

That's not so much of a theological question as it is a pointless paradox.
As far as I can tell, the only answer is to allow a superposition of seemingly contradictory states, the answer is simultaneously yes and no.

Theoretically yes... but the gravitational pull would be so great on the rock itself... it would become a black hole instantly...

Stephen Hawking is the man...

It seems to me that no would be the correct answer. First of all, God is omnipresent. Secondly, according to the bible, the is nothing He cannot do. Lastly, doesnt this sound like the question, 'if a tree falls down and there is no one around to hear it, does it make a sound?'
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-- but you just said that creating a rock that he cannot lift is something he cannot do!

'this sentence is false' <-- is this statement true or false?

similar kinda thing.

or from set theory-

given that:

-a set is simply a collection of things, (eg the set of all whole numbers between 0 and 3 = [1,2])

-sets can be infinite (eg the set of all whole numbers bigger than 0 = [1,2,3,4...]

-sets can contain other sets (eg the set of all sets containing only one element, which is bigger than 0 = [ [1] , [2], [3], [4] ... ]

consider the set: 'the set of all sets which do not contain themselves'

now this set will contain most sets, as most sets do not contain themselves. The question is: does this set contain itself or not? If it doesn't then it fulfills the condition of being 'a set that doesn't contain itself' and thus because it fulfills the condition it must be inside itself. But now it has ceased to fulfill that same condition, so must be taken out. But now it doesn't contain itself.....ad infinitum.

Personally, i think the question is really going nowhere. According to Christianity, the one thing God cannot do is evil deeds. Acording to Socrates, the one thing not even God can do is change the past. I think that it would be more interesting to argue with Socrates. What do you think about his statement?
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If you believe in God, the answer is no. If you don't, you must not have an opinion on this issue.

Iam speaking as to what Christianity believes as I came from a Christian family.
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Oh.... ...so now we exclude all opinions except of those that are christians

thats how it looks to me
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What does the word God mean?

This is one of those interesting conundrums: similar in theme to the one about irresistible force meeting unmoving object. Think too long on it and your brain is liable to implode.

people who say there isn't anything that god can't do have no imagination... i can think of a lot of things god can't do, according to the mythology...

god can't get lost
god can't miss church
god can't find fault with himself
god can't misplace his car keys

just to name a few...

The Great Cat God can and then She can lift it simply by licking it.

It's a nonsense question, and a straw man. And it's been asked here before. Probably several times.

First of all, God, being incorporeal, wouldn't physically "lift" anything. That requires hands, arms, a place to stand on, etc. Sure, God could appear in human form (called a theophany in philosophical/theological terminology) to do it - but what would be the point?

Second, as jrknothead correctly pointed out, there are lots of things God can't do. Omnipotent doesn't mean you can do absolutely everything, even ridiculous, nonsensical or illogical things. God can't make a square circle, for instance. And there are lots of things in the Bible that it says God can't do, such as it is impossible for God to lie, and He cannot deny Himself.

But at the outset, the question is nonsense. It’s like asking, “Can God win an arm wrestling match against Himself?” or, “If God beat Himself up, who would win?” Basically you're asking, “Can God’s power defeat His own power?” Which is a stupid question.

This is indeed an paradox,however only in the case if you consider a God that is separate entity from creation,and if you consider a God as a person.
So if there is a God that is separate from creation,than he can indeed 'make the stone',but then God would be separate thing from stone...so there would be a border between God and stone.
And if God is separate thing from creation,that would mean that God is limited by the border between himself and creation.
If God is limited,then he is not God,since God is non plus ultra by definition.

God also cannot be personal,since person can only be person toward something different from himself,and therefore limited by that 'other'.But God cannot be limited.