Can God Create a Stone So Heavy That Even He Cant Lift it?

I've heard this question many times, and I'm sure many of us have.  It is an old school-yard question that pops up sometimes in adulthood.  Today a friend wrote me to tell me about being asked this question in his philosophy class.

This thought experiment is sometimes called an "omnipotence paradox" because it is proposed that if God cannot make such a stone then he cannot do "everything/anything" and if he can make such a stone and cant lift it then again there is something that he "cant do"

First it is important to point out that what is being proposed here in the thought experiment is logically impossible, along the same lines as making a square circle.  The task at question is not a task at all but simply a combination of self contradictory words.

Second I would point out that the definition of omnipotence has never included that God can do the logically impossible

Third I would say that if the person continues and insists that God should be able to do even the logically impossible if He is to be omnipotent then Wonderful!

If God can do the logically impossible then answer yes, God can make a stone so heavy that he couldn't lift it...then he would go ahead and lift it.  The objection to that answer is that does not make sense and is logically impossible.  But granting this premise God can do the logically impossible.