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I believe that in order to answer this question one must start by defining the core aspects of the question. I will attempt to help with the sin part of the question. As many words in the English langue sin has multiple uses. In this question we a referring to the verb usage. Can God do, commit, or preform sin? Is at its core to "miss the mark." If stated another way it say, "to deviate from the best possible corse of action" or "to alter your designed path." These are simply possible methods of understanding the word and not necessarily definitions. Let's break down some logic. Can a cup sin? If I fashion a cup out of steel can it choose to be a vase? We control it's fate and decide wether it ever fulfills it's purpose. We humans have choice. But between what? Our choice boils down to this: our best possible path or a deviation. (Granted our ignorance of perfect path is the most common cause for deviation but we can never truly understand the depth of our purpose no more than God Himself. We can only act on the knowledge we currently have.) Knowingly or unknowingly we can choose to deviate. God can choose but He cannot deviate because Every choice He makes is in perfect alignment with His perfect design. God cannot choose to be anything other than Himself anymore than I can choose to be Aristotle or the cup can choose to be a vase. And because He is beyond creation there is no other possible purpose besides just Being God. For this reason God cannot sin because cannot be anything other than God. Gods omnipotence is completely intact.
Regarding omnipotence, God can do anything because his power is limitless. Can he then sin, is the question. This question can be answered depending upon understanding the definition of sin, who defines what is sinful or who is a sinner and to whom the Law is for. Undoubtedly, as God is the only and ultimate judge, he is the only one who defines what sin is, who is a sinner and what is sinful. Everyone knows that sin is a violation of God's law. Is the Law above God that he needs to follow? One who defines the Law has to be out of reach of the law. Moreover, the "law was made for man" (I Tim. 1:9), not for God. In fact, God can kill anyone, yet sinless. He can do anything "we call" sinful, yet He is sinless. And, he can also declare and call a person "perfect in his eyes" like Job, even when no one is perfect but God.(Job 1:1, 8; 2:3). So, our understanding of omnipotence should include the power to do all, whether or not "we define" that as sinful. Yet God who did any of it is "sinless". Therefore, on these grounds, omnipotence includes no possibility for God to sin (as in "lie" in Heb 6:18; Titus 1:2).
Since God is the creator of all things, he is also automatically the judge of whether his creation is fulfilling the purpose for which he created it. So a better definition of sin would be "any rebellion against the will of God". What is the will of God? It is the revelation God has given us in his Word, the bible. Everything God has said in his word that expresses his expected behaviour from human beings represents his will. We often measure sin by comparison to the "law of God" but his revelation also includes everything he expects us to do, not just those things we are to avoid. So getting back to the question of whether God can sin, let's summarize it by two logical statements. The will of God is: I will do what I want to do The sin of God would be: I won't do what I want to do If God can logically sin then: I won't do what I will do This statement is a logical impossibility therefore God cannot sin.
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