There are people so clever they think they can disprove God. I have met a few. One asked, “Can God do anything?” I replied, “Yes.” Now he had me! “Then could God make something so heavy that he could not lift it?” The underlying message being, if I can dismiss God with a paradox, then I am free to live any way I choose.
Jesus met some people like this. They presented him with a paradox about marriage and heaven; their hidden aim being, to dismiss anything in the spiritual realm.
Jesus replied, “You are in error because you do not know the Scriptures or the power of God.”
Matthew 22:29
Jesus’ response was that they might be intelligent enough to come up with a paradox, but they lacked knowledge of two critical factors that could have spoken to their understanding. This is ironic, because these religious people would have prided themselves in their knowledge of both the Scriptures and God.
Paul’s response to people who considered themselves experts is illuminating –
We know that “We all possess knowledge.” But knowledge puffs up while love builds up. Those who think they know something do not yet know as they ought to know. But whoever loves God is known by God.
1 Corinthians 8:1-3
The key to real understanding is when it is framed by the love of God. So, when I find my mind caught up with theories, can I make them practical, living them out to others with the love of Jesus? The key to the real knowledge of God is through applying that knowledge in love.
adaringfaith 
The answer to your “clever” sceptics question was answered by Thomas Aquinas 750 years ago: “Nothing which implies contradiction falls under the omnipotence of God.”
So we have examples in scripture … God cannot lie or change his mind (1 Sam 15:29), cannot deny himself (2 Tim 2:13), cannot be tempted by evil (James 1:13).
In contrast to your sceptic Derek, you are right when you state that the key to real knowledge of God is through applying that knowledge in love, with the discernment given us by the Holy Spirit.
Blessings