Allow me to rephrase my objection to the omnipotence paradox by quoting C. Wade Savage:
Now allow me to clarify what is meant by God not being able to be inconsistent with any of his basic attributes. Let’s begin with a basic attribute that it is not omnipotence. According to Hebrews 6:13 God cannot swear by a being higher than himself. This is no limit to his power because God is the greatest conceivable being (This phrase is taken from Alvin Plantinga’s form of the Ontological argument using possible worlds) and there is no being higher than himself to swear by. The phrase that God cannot do anything that is inconsistent with his attributes is therefore used because much of the discussion surrounding omnipotence deals with how it relates with his other attributes. God not being able to be inconsistent with his attributes does not limit his power and debate on this would need to be an attribute by attribute basis.“we might imagine one being (y) who cannot lift a stone heavier than seventy pounds. If some other being (x) cannot create a stone heavier than y can lift, then obviously x’s power to create is limited. But suppose that y can lift a stone of any weight; in other words, imagine that y’s lifting power is unlimited. Then it follows that if x cannot create a stone heavy for y to lift, x’s power to create is not limited. What then has our theologian surrendered? Is it the unlimited power to create stones? No doubt. But what stone is it which God is now precluded from creating? The stone too heavy for Him to lift., of course. But…nothing in the argument required the theologian to admit any limit on God’s power with regard to the lifting of stones. He still holds it to be unlimited. And if God’s power to lift is infinite, then His power to create may run to infinity also without outstripping the first power. The supposed limitation turns out to be no limitation at all, since it is specified only by reference to another power which is itself infinite. Our theologian need have no regrets, for he has given up nothing. The doctrine of the power of God remains just what it was before.”
Further, your argument that Rowe’s definition of omnipotence makes everything omnipotent within its own attributes fails because human beings do not have absolute defining attributes. For example, Sam (this was the first name that came to my mind) may be a very honest person, therefore it could be said that honesty is one of Sam’s attributes. However, Sam’s honesty is not absolute, while Sam may be a very honest person, it would not break the law of non-contradiction for him to tell a lie, though it would be inconsistent with his attribute of honesty. God’s attributes are absolute and therefore if he is inconsistent in any of his attributes it breaks the law of non-contradiction. Think of it as the difference between a person being the embodiment of all truth and a person who speaks true things. It is possible that this type of attribute is not what you meant. In that case, I would ask for you to give a definitive example of what you mean.
Therefore, I am arguing that any contention that omnipotence can be reduced to the power left behind after certain attributes subtract from one’s power is to misunderstand what is meant by Rowe’s definition. To better understand why I reject the omnipotence paradox as a means to show that there is a contradiction in the attributes of God I would recommend InspiringPhilosophy’s video on the ontological argument. For the specific argument that I’m referring to skip to 6:59 if you’d rather not watch the entire video. https://www.youtube.com/watch?annotation_id=annotation_411430&feature=iv&src_vid=ixqsZP7QP_o&v=RQPRqHZRP68#t=6m59s
I have two final points. First, I believe that the doctrine of omnipotence is justifiable through Scripture alone, however, it can also be inferred through philosophy alone (see Plantinga’s Ontological argument.) However, the discussion is not on whether or not the doctrine is justifiable, but rather on whether the concept of omnipotence is incoherent because of the omnipotent paradox. My answer is “no”, but I’m willing to change my mind if I can be shown otherwise. However, I would like to suggest that there is a reason why this objection to theism is widely rejected by theists and non-theists alike in academia. J.L Mackie, an Australian philosopher and avid atheist, writes in his book Omnipotence,
Note that I am not committing the fallacy of an appeal to authority or majority here because I am not claiming that my position should be accepted as true because of these observations. I’m still willing to be shown to be wrong. Also I'd be interested in reading your arguments about physics put into layman's terms."Once we have decided that omnipotence is not to include the power to achieve logical impossibilities--and it must not include this, if it is to be discussable--there cannot be any contradiction within the concept itself. (pg. 24-25)"