Having said this, what are the presuppositions of the Calvinist and the Arminian?
The presupposition of the Calvinist is that God has an eternal decree whereby he has decreed all that will ever come to pass.
Calvinist, James White, explains: "The conjunction of God's absolute freedom and His Creatorship results in the doctrine of God's decrees: the soul-comforting truth that God has wisely and perfectly decreed whatsoever comes to pass in this universe." (The Potter's Freedom, p.45, emphasis mine)
This is the primary presupposition of the Calvinist who puts on these glasses, so to speak, whenever they attempt to interpret Scripture. As an example, with these glasses, the Calvinist will turn to Ephesians 1:11 and read "works all things after the counsel of His will," but because of the Calvinistic glasses of Determinism, see causes all things.
On the other hand, the Calvinist accuses the Arminian of possessing the presupposition that Free Will must be preserved at all costs, which is absurd. The true presupposition of the Arminian, that is, the rose colored glasses of the Arminian, is the wild belief that God's word is not the charade of contradictions that Calvinism makes it out to be.
In terms of contradictions, take note of what Calvinist, John McArthur, explains: "That's one of the reasons I know the Bible is written by God, because men would fix it. If I wrote a book that had those contradictions, Phil [Johnson] would edit them all out. One of the bench marks of divine inspiration is the fact that you're dealing with transcendence." (http://www.gty.org/resources.php?section=articles&aid=231301, emphasis mine)
The presupposition of the Arminian makes no allowance for any alleged contradiction in the Bible, and cannot accept a Calvinistic "Secret Will" theory which flatly contradicts Scripture, such as at Matthew 23:37. The primary complaint of the Arminian is that Calvinism makes the Bible into a charade. For more on this point, refer to the book, Debating Calvinism, p.309, in which Dave Hunt argues that Calvinism turns the Bible into a "charade." That's where the Arminian is coming from.