Some think there can be a compromise between Calvinism and Arminianism, that there is some way to reconcile these two positions or, at least, come up with a mediating position that avoids the extremes of both. When the issue is framed properly, however, it becomes clear that this isn't the case. How, then, should the debate between Calvinists and Arminians be framed?
The heart of the matter, it seems, can be summed up in this question: Is God's grace sufficient? (Sufficient, that is, to bring about the salvation of his people.)
Throughout the history of the faith, there have only been three answers to this question: Augustinianism (now called Calvinism), Pelagianism (now called liberalism), and synergism (everything else). Logically, these three positions are exhaustive. That is, they cover every possible answer to the question. Aside from these three positions, there simply is no other position for one to hold. It is imperative, then, to understand the three positions. So, what are they?
First, there is Pelagianism. Pelagius believed that man could save himself. Grace, for a Pelagian, is not even necessary for salvation. This position was rightly condemned as heretical. There's nothing even remotely Christian about the idea that men are able to achieve their own salvation.
In answer to Pelagius, Augustine argued that salvation is all of grace. Man adds nothing to his salvation, he merely receives it (through faith and repentance, which are themselves gifts of God's grace) as a free gift of grace. Grace, for Augustine (and Calvin after him), was not merely necessary but sufficient. This is Augustinianism.
Unfortunately, the majority of the church has been unwilling to accept Augustine's response (at least not without major qualifications). The result is a mediating position: synergism. For the synergist, grace is necessary for salvation, but it is not sufficient. What, then, must be added? Some form of human effort (what exactly this entails would differ depending on which theological tradition the synergist represents). This position is held by the vast majority of professing Christians whether Orthodox, Catholic, or Protestant (including Arminians). While it is a vast improvement over the heresy of Pelagianism, it is still a far cry from the consistent Christianity of the Calvinist.
All believers agree that God's grace is necessary for salvation. Not all agree, however, that God's grace is sufficient. Only the Calvinist believes in the sufficiency of grace. There can be no mediating position, then, between Calvinism and Arminianism. Arminianism is the mediating position, being located between the God-glorifying theology of Calvin and Augustine, and the rank unbelief of Pelagius and his followers.