The end of every free agent is either that which he effecteth, or that for whose sake he doth effect it.
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The end which God effected by the death of Christ was the satisfaction of his own justice: the end for whose sake he did it was either supreme, or his own glory; or subordinate, ours with him (John Owen, The Death of Death in the Death of Christ,Vol. 10 of the Works of John Owen, 1852 (reprinted, Edinburgh: Banner of Truth Trust, 2007), 50).
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Now, the end of the death of Christ is either supreme and ultimate, or intermediate and subservient to the last end.
1. The first is the glory of God, or the manifestation of his glorious attributes, especially of his justice, and mercy tempered with justice, unto us (89).
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2. There is an end of the death of Christ which is intermediate and subservient to that other, which is the last and most supreme, even the effects which it hath in respect of us, and that is it of which we now treat; which, as we before affirmed, is the bringing of us unto God (90).