We can't know and it would be very presumptuous for us to believe we can know what God can do.
And yet we do say that God cannot do the logically impossible.
Do you think that is unnecessarily limiting God's power because of our logic, or is out logic sound?
Agreed. The Bible is correct, but we still don't know what those 'things' are.
The Bible says that God can do all things and does not say "God can do all things that are logically possible"
Logically impossible does seem like a good place to draw the line as to the extent of God's power however. That would mean that we would be presuming that is what Jesus meant when he said all things are possible for God.
Matt 17:20 He replied, "Because you have so little faith. I tell you the truth, if you have faith as small as a mustard seed, you can say to this mountain, 'Move from here to there' and it will move. Nothing will be impossible for you."
Genesis 11:6 The LORD said, "If as one people speaking the same language they have begun to do this, then nothing they plan to do will be impossible for them.
We assume at least that with these verses.