I think that Calvin's use of the word 'predestination' for unbelievers didn't mean what we mean by it these days. Calvin seemed to use the theological terms "ordain" and "predestine" interchangeably, but I can't say for sure what his thinking was. I only say this because in his writings he would clearly be contradicting Himself. To put it another way, Calvin did not believe that God was the Author and finisher of an unbelievers unbelief.
"The blame lies solely with ourselves, if we do not become partakers of this salvation; for he calls all men to himself, without a single exception, and gives Christ to all, that we may be illuminated by him." (Calvin. Commentary on Isaiah the Prophet).
That's what the term double predestination means, as I see it, that God causes unbelief just as He causes belief. For some, in the Calvinist system, if a person is positively caused to believe, naturally, those who were not caused to believe were indirectly left with one option, and that option is considered a predestination of sorts.
I disagree with this whole line of thinking.
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By grounding election in it's first decree and placing it before creation and the fall, supralapsarianism abstracts election from it's biblical heart, namely that the people of God are chosen in Christ. (Ephesians 1:4; 2 Timothy 1:9). "Supralapsarianism theology removes the attention of the believer from the historical person of Christ and His work, and centers it on the eternal decree of God, cold and intellectual, before all time" (Brown "heresies") taken from why I am not an Arminian.
While I do agree that in the correct context, God's decree, or His eternal purpose can be different from His desire, I would only agree that while He hates sin, He does allow it for His purposes. Naturally, this is understandable because man is not forced to believe, but is given a choice and enough common grace to accept or deny it. BUT...I don't think that line of reasoning is supported in the idea of election. I believe election to be corporate. In other words, Jesus was elect, we become elect with Him when we are placed in Him.
In the end, this double predestination debate is basically the infra - supra debate using the reading definitions into theological terms that the writers/theologians of long ago probably never intended. We start with a debate about things that seemingly has no scriptural solution...
"IBID. Ultimately both infralapsarianism and supralapsarianism are unsatisfying. As John Frame has observed, the entire discussion of an order of decrees was engaged in a speculation that the Bible simply does not underwrite. One must "try to picture the process of God's thinking before He created the world." But "scripture warns against trying to read God's mind. His thoughts are not our thoughts (Isaiah 55:8). This discussion runs great risks of engaging in speculation into matters God has kept secret" Doctrine of God pp. 335-37 Brown.
I'll save the infralapsarianism vs. supralapsarianism for another thread. Interesting though, that it was Theodore Beza (Calvin's son in law) who popularized supralapsarianism/double predestination because he was willing to go beyond where even Calvin would go. Calvin was content to leave questions as questions if he felt that the text was ambiguous. But it was Beza who wanted to take Calvin's work, systematically fit it into a philosophy. Sound familiar? Reverse engineering. And also from that you have Arminius, who was a student of Beza who did not agree with either infralapsarianism or supralapsarianism because they didn't fit his philosophy of libertarian free will. Twenty years ago, most reformed people, up until then were infralapsarians. These days it's something different.
...and then, as Spurgeon once famously said, these discussion become narrowed down to being arguments about the meanings of the terms used by those who debated these things so long ago.
I think that the term predestination is for all things that are positively caused by God. Ordain covers everything God created and is governing even today, both predestined and positively allowed.
Dave