If an actual infinite set does not actually exist (which can be logically shown), how can it be that God has actually determined an infinite amount of actions stretching into an eternity of time into the future where the actions of sinners in Hell and the redeemed in the New Heaven and Earth are concerned?
I am confused. If you don't think God can determine an "infinite set" of actions, how can you defend God's knowledge of an "infinite set" of actions? Have you thought about what implications this argument has for your view of God's omniscience?
The proper definition of omniscience is "to know only and all truths". What is obvious from this standard and universally accepted definition is that there are a limited amount of truths in the universe, and if God knows all that can be known, obviously he knows a FINITE set of things, not infinite strictly taken. And yet he is omniscient still.
And yet to predetermine an actual set of things is to say that there exists a group of actions which goes on for eternity which are all meticulously laid out NOW--and yet God is laying out an actual infinite set of actions, which is impossible.
And given YOUR view, Ryan, that God's knowledge of the future is PREDICATED by his predetermination of all things (i.e. he knows all things BECAUSE he has predetermined all things), then it is you--not me--who must first answer the question as to how it is not logically incoherent to believe that God has predetermined an actual infinite set of things when an actual infinite is logically impossible.
If there are only a "finite set of [truths]," there can only be a finite set of states of affairs to which those truths correspond. If you can hold this to be true, I don't see why you won't allow us the same courtesy.
To give a more direct response, however, it seems to me your argument presupposes that we hold to a perpetually dynamic rather than an eventually static view of the way in which we will worship God &c. upon the consummation of new creation. Why do you think that this is the case? Furthermore, if you this that this is the case, how can you hold to a finite set of states of affairs?
I will add that some Calvinists would agree with you - perhaps myself included, as I have not committed myself either way - on the finite of God's knowledge:
//...if the theorems [of mathematics] are infinite in number, neither God nor man could know them all, for with respect to infinity there is no "all" to be known.//
- Gordon Clark, The Incarnation pg. 62
Against both Clark and yourself one might cite, say, the Cantor set as an uncountable set which, since it is bounded, provides an example according to which we could argue for the possibility of an infinitely knowledgeable God.
In any case, I think these arguments are pretty complex, and whichever position is true does not hurt the Calvinist any more than it hurts you.
To summarize the above points, the Calvinist can mirror whatever the Arminian's view is regarding of the scope of God's knowledge and further apply that to God's determination of events.