Suppose an omnipotent being exists in a universe, and that universe operates under some fundamental laws that among other things define what can exist vs. what is a contradiction.
Contradictions are feature of a language (or some more formal system used to describe the universe), not of the universe. What we call physical laws are regularities which allow us to compress the observed data a bit - e.g. instead of keeping a list of planet positions at each moment, it is enough to have the initial positions, velocities and few equations of motion. Absence of contradictions is not such a law. (It is easy to imagine what violation of a particular physical law would look like, but try to imagine how a contradiction would look like. What would you observe if there was a lizard on your table and simultaneously there was no lizard on your table?)
Alternatively we could ask "Can God make 1+1 add up to something other than 2?" and the answer is "Of course; even mathematicians can do this, by redefining the axioms or working in the integers (mod 2) or something." In terms of this example, then, Level 1 Power is asking "If the universe is a formal system of sorts, can God change the axioms?"
This is exactly changing the language, and very uninteresting to theologians when, as you correctly note, mere mathematicians can do it. "1+1=2" is a string in some formal system which acquires its meaning by isomorphism with real world situations. You can redefine your alphabet to exchange the symbols "2" and "4", which would make "1+1=4" true, but its meaning would be absolutely the same as the meaning of "1+1=2" before the redefinition. It has nothing to do with fundamental laws of the universe, whatever they are.
I suppose I am assuming that the universe operates under some set of formal rules (though they might not be deterministic) independently of our ability to describe the universe using formal rules. I would also say that our inability to comprehend a given contradiction is related to the fact that we are inside the system. If God were outside the system he would not necessarily have this problem.
I disagree with your second point, though. Sure, 1 and 2 are labels for concepts that exist within a formal system we've developed, and sure, we can create an iso...
[This is a draft intended to be developed into a top-level post - it wouldn't feel wrong to make it such right now, but it wouldn't quite feel right. I am not entirely sure how to end it or if I could generalize better at the end. I kind of like the ending I have, but I'm not sure if the point overall is coherent enough. Thoughts/suggestions/criticism would all be appreciated. ETA: The problem here may be that this is actually a follow up (or a footnote) to another article I've been thinking of about Weasel Words and the art of misleading through langauge; related to my earlier post on Not Technically Lying]
When I was a teenager, I remember hearing a couple of riddles that I thought were neat:
"Could God draw a square circle?"
"Could God create a stone so large that even He could not lift it?"
Let me just disclaim that this post has pretty nothing to do with religion. I just think that these are great examples that many people may be familiar with. That said, consider: do either of these problems pose a threat to the existence of an omnipotent God?
The answer, as will be clear on a full exposition, is a resounding "No." These are terrible, awful, misleading arguments, and the second one illustrates a relatively common trick used to sneak past an audience's intellectual defenses.
These riddles both fail to provide relevant counterexamples for the exact same reason, even though the second may seem to make more sense. The first is simpler: a square circle is not a thing. In a practical sense, we can put the words next to each other, but there is simply no way to translate the sound "square circle" into some kind of expectation or thing in the real world, in the same way one could translate, "red barn" or "white unicorn" into an expected observation. It is impossible for anything to be both square and circular, so the fact that God cannot do something that cannot be done does not limit His omnipotence. By the same token, God could not create a married bachelor (using the strict definitions of the terms), as a bachelor is an unmarried man. The inability to violate the law of non-contradiction does not appear to be a legitimate refutation of omnipotence. If we taboo, "square circle," there isn't really a meaningful way of describing the thing you are insisting God be able to draw.
"A stone so large that God cannot lift it," is exactly the same thing as a square circle. It sounds like a problem, since it's showing that God can't create a big enough stone. But an omnipotent being could presumably lift an object of any arbitrary size. Therefore, no stone could ever meet these criteria. If we taboo "so large that God cannot lift it," there is no actual weight you could describe such a stone as having. Presumably, God could lift a stone that weighted 3^^^3 tons, or even 3^^^^^^3 tons. You've created a hollow adjective: a descriptor whose actual meaning makes an argument self-evidently bad, but which is appealing if you don't actually think about it. It's not Not Technically Lying, because it isn't untrue, it's meaningless, which makes it harder to detect (though less common).
This is an extreme example. Usually, hollowness allows a speaker to be vague enough that they sound like they have a point when a clear definition of their terms would disprove this. Offenses in common language are usually a bit less egregious. "The president hasn't done enough to fix the economy," comes to mind as an example. What exactly, should he have done? There has probably never been a president in history whom people would generally agree has done "enough to fix the economy;" indeed, most economists would question the power of the president to seriously influence such things. "Hasn't the president failed to end the recession?" may be technically true, but it isn't really useful to call someone a failure for not doing something they lack the power to do. This example is merely illustrative; it is often easy to create descriptors that make your conclusion apparently foregone, despite their actual lack of substance.
Using such slanted terms is among the darker of the Dark Arts. It plays on its audience not by appealing to the irrational vagaries of the human mind; such efforts are, at least, often transparent. Rather, it masquerades as a rational argument, requiring complex nuance to refute. For those who are not disposed to disagree, it can escape the defense mechanisms of even a cautious mind. Understanding this concept can make it far easier to pinpoint the error in some beguiling arguments.