Is there any reason to think that God is omnipotent?

Omnipotence, typically understood as the property of being all-powerful, is one of the unique properties of God in the classical theistic conception. Here, I shall examine two common objections raised against the view that God is omnipotent. Although the objections may sound persuasive at first glance, I shall argue that none of them are effectively knock-down arguments against the omnipotence of God. Hence I shall attempt to sustain the view that it is reasonable to think that God is omnipotent.
Since the conception of God is hardly univocal, I shall limit this discussion to the God of classical theism – the God who is omnipotent, omniscient, omnibenevolent and depends on nothing for His own existence. 
In this brief entry I shall examine two distinct objections of the following type: the first objection aims to demonstrate that omnipotence as a concept is incoherent, and the second objection that omnipotence cannot be reconciled with God’s other divine attributes.
The first objection is often formulated as a question. Similar forms such as this have often advanced by the sceptic: ‘Is God able to lift a rock so heavy that He himself is unable to lift it?’ This creates a paradox for theists: either way, God cannot be omnipotent because (1) if he can create such a rock, he is not powerful enough to lift it, and clearly the case (2) if he cannot create such a rock.
The most satisfactory response so far known to this paradox is to offer an alternative definition of ‘omnipotence’. With this definition, God is not plainly ‘all-powerful’; God is ‘all-powerful, but bounded by the laws of logic’. The second step of this response is to then, point out that ‘a rock so heavy that it cannot be lifted’ is a concept which is logically incoherent, and hence one cannot reasonably ask God to create such an object. It would be akin to asking God to create, for instance, a married bachelor or a square circle, which are all logically impossible ‘objects’.
I find this response valid. To consider the alternative – as held by Descartes - that God is all-powerful and is unlimited by logic - is itself an incomprehensible view, and hence unsustainable. It would be meaningless to employ reason and logic in arguing for the existence of God; for how could any comprehensible conclusion be reached if God is beyond the realms of reason? Moreover, the ‘heavy rock’ concept is one that does not seem to be conceivable, and it seems justify to describe it as a logically impossible concept.
The second objection which I plan to look at attacks the incoherence between omnipotence and another divine attribute: omnibenevolence, or all-good-ness. Again, the objection is most efficiently phrased in a question: can God do evil? This objection seems to place the proponents of theism in a dilemma: if God is omnipotent, then it seems definite the case that God can do evil; however, being all-good, it seems that God cannot do evil. Thus, the objection seems to place theists in a dichotomy where one of the aforementioned attributes must be rejected.
One possible response to this objection is to employ some analysis of the idea of omnibenevolence. The property of being all-good does not necessarily have to be an intrinsic property in the sense that it can limit God’s power; God can simply be all-good because all the actions which stem from God are good, in a somewhat Sartre-esque sense. While this may entail problems which come with the metaphysical view that an external, objective value of ‘good’ exists beyond God, it does demonstrate that God is indeed all-powerful in his nature. I admit that this response is not ideal as it cannot demonstrate that God is all-powerful in effect; but it seems to be more sustainable than its alternatives e.g. redefining ‘omnipotence’ as ‘all-powerful but bound by the laws of logic and morality’.
But is it reasonable to think that God is omnipotent? Although some reasonable theistic responses have been elucidated, admittedly, I don’t think my defence of theism has completely removed the force in its critics’ objections. It is, I think, no longer possible nor consistent to hold ‘omnipotence’ in its original starting definition.