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Some argue that if predestination is true and humans have no free will, then people cannot be held responsible for their actions. Here, we will summarize philosopher and theologian Gordon Clark's response to this objection by quoting from his book/essay, God and Evil, which can be purchased from The Trinity Foundation. All bolded text has been added.
Here is how Clark defines responsibility. Notice that Clark does not make responsibility dependent upon free will.
Now, the word responsibility looks as if it has to do with making a response. Or, accountability is to give an account. A man is responsible if he must answer for what he does. Let us then define the term by saying that a person is responsible if he can be justly rewarded or punished for his deeds. This implies, of course, that he must be answerable to someone. Responsibility presupposes a superior authority that rewards and punishes. The highest authority is God. Therefore responsibility is ultimately dependent on the power and authority of God.
Next, Clark explains what it means that God is Himself the standard of right and wrong, of just and unjust.
Is it just then for God to punish a man for deeds that God himself "determined before to be done"? Was God just in punishing Judas, Herod, Pontius Pilate, and the others? The Scriptures answer in the affirmative and explain why. Not only is God the creator of the physical universe, not only is he the governor and judge of men, he is also the moral legislator. It is his will that establishes the distinction between right and wrong, between justice and injustice; it is his will that sets the norms of righteous conduct. Most people find it easy to conceive of God as having created or established physical law by divine fiat. He might have created a world with a different number of planets, had he so desired. Nor does it bother some theologians to suppose that God could have made different ceremonial requirements. Instead of commanding the priests to carry the ark on their shoulders, God might have forbidden this and ordered them to put it on a cart drawn by oxen. But for some peculiar reason, people hesitate in applying the same principle of sovereignty in the sphere of ordinary ethics. Instead of recognizing God has sovereign in morals, they want to subject him to some independent, superior, ethical law—a law that satisfies their sinful opinions of what is right and wrong.
Clark supports his position with Calvin's teaching on the subject. He says, "Calvin avoided any such inconsistent and unbiblical position. In the Institutes (III, xxiii, 2) he says,
How exceedingly presumptuous it is only to inquire into the causes of the divine will, which is in fact, and is justly entitled to be, the cause of everything that exists. For if it has any cause, then there must be something antecedent on which it depends; which it is impious to suppose. For the will of God is the highest rule of justice, so that what he wills must be considered just, for this very reason, because he wills it. When it is inquired therefore why the Lord did so, the answer must be, Because he would. But if you go further and ask why he so determined, you are in search of something greater and higher than the will of God, which can never be found.
Here is Clark's summary of his response to the objection.
God is sovereign. Whatever he does it just, for this very reason: Because he does it. If he punishes a man, the man is justly punished; and hence the man is responsible. This answers the form of argument which runs: Whatever God does is just; eternal punishment is not just; therefore God does not so punish. If the one who argues thus means that he has received a special revelation that there is no eternal punishment, we cannot deal with him here. If, however, he is not laying claim to a special revelation of future history but to some philosophic principle which is intended to show that eternal punishment is unjust, the distinction between our positions becomes immediately obvious. Calvin has rejected the view of the universe which makes a law, whether of justice or of evolution, instead of the Lawgiver, supreme. Such a view is similar to Platonic dualism which posited a world of Ideas superior to the divine Artificer. God in such a system is finite or limited, bound to follow or obey the independent pattern. But those who hold to the sovereignty of God determine what justice is by observing what God actually does. Whatever God does is just. What he commands men to do or not to do is similarly just or unjust.