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To humbly investigate God's nature, to try to discover His thoughts, is not a pointless or unwise endeavor. To humbly offer up our understanding of his thoughts is not necessarily arrogance, if we are reasonable during the discussion that follows.
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To declare His thoughts unknowable, at the start of the game, would be to plug our ears to anything He had to say. Would a confident pronouncement of "We know there to be no answer possible!" be, itself, arrogant?
Fortunately your 4th paragraph, LR, conceded His thoughts to be legible in at least one real-life situation. The naming of sports teams: "Name them anything you want." ;- )