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I been reading the net for this topic and just stumbled on this question asked and answered by a hindu to a hindu. Have t o say, they are not Christian but of all the answers I found, this explanation makes the most sense for me and is most spiritually and intellectually edifying to me. So I post it here and then you can tell me what is wrong with this explanation from a Catholic point of view. If nothing, then this is my solution until God says otherwise!
not sure about the stone god cannot lift part, as I am about the square circle bit, but hey, that God can make it, AND lift it, seems to be at least as satisfying as “there are things God cannot do”.
Don’t get it, but that’s irrelevant if we are talking god. I also saw a similar understanding in an orthodox discusson but cant find it again. They did not say that God can make the stone but they did deny that logical contradictions are per se impossible for god to do which is what my mind disagrees with as well. I read that Descartes also denied in his philosophy that god cannot perform logical impossiblilities-contradictions.
So leaving aside the God and stone, how is this quote solution for square-circle sit with the church? if its ok then this is what I accept and not “God cannot make a logical contradiction” which God has not said.

Can God make a square circle?
Posted by Chaitanya Charan das • June 30, 2010 • Printer-friendly
Question: If God can do anything, can he make a square circle?
Answer: Questions like these arise from not understanding the definition of God as the Supreme Being. Let’s consider the two kinds of impossibilities: practical and logical.
1.Practical impossibility: When the sacred scriptures describe that, say, Lord Krishna lifted the huge Govardhana hill in Vrindavana during his descent to this world five thousand years ago, skeptics may dismiss this as impossible, because they deem possession of such strength practically impossible. However, notice their self-centric mentality implicitly operating here; they presume that what is impossible for them is impossible for anyone. By such a mentality, an ant crawling on a table may consider the glass that blocks its way impossible to lift, but we humans do it all the time – nonchalantly. Just as we, humans, being much stronger than ants, can do what they think practically impossible, similarly, God, being Supreme, being infinitely stronger than us, can do what we think practically impossible.
thespiritualscientist.com/2010/06/a-square-circle-2/2. Logical impossibility: Activities like making a square circle seem not just practically impossible, but even logically impossible. Our mind tends to think that a geometrical object can either be a circle or a square, but never both. However, this is a limitation of our mind, not a limitation of God. Our mind functions by discerning in the world around us features like logicality, causality and repeatability. Our mind needs the intellectual framework formed by such attributes to make sense of the world. But that very framework limits our mind from “thinking outside the box”, and so we mistakenly infer that those activities that are impossible for us to think logically must also be impossible for God to do practically. However, our framework of thought does not limit God. For his cognition, God does not need any such framework, and so he is completely free to think and act independent of it.
Let’s now apply this background analysis to our specific question. God can surely make a square circle, but our minds can never understand how. Is this an evasive answer? Not at all. The sixteenth-century devotee-scholar Jiva Goswami insightfully reminds us that if God’s actions were limited to the conceiving abilities of our mind, then our mind would be supreme, not God, thus violating the very definition of God. Therefore, by his very definition, God has inconceivability (achintyatva in Sanskrit) as his integral attribute.
not sure about the stone god cannot lift part, as I am about the square circle bit, but hey, that God can make it, AND lift it, seems to be at least as satisfying as “there are things God cannot do”.

So leaving aside the God and stone, how is this quote solution for square-circle sit with the church? if its ok then this is what I accept and not “God cannot make a logical contradiction” which God has not said.