...the father saved the son and the son played no part in it, you might argue that the son grabbed hold of the rope and thus played a role in him being saved..
Yes, you have identified the crux of the problem.
Again, let's get some working definitions going...
Causation : The relationship between a first event(cause) and a second event(effect) where the first event is a contributing factor to bringing about the second.
Formal Cause: where the very form or essence of the object/event, results in the effect.
Eg: the sinfulness of the flesh is a Formal Cause of Judas' betraying Jesus.
Material Cause: where what it is made from, results in the effect.
Eg: God's creation of man from the dust of the ground(in the natural flesh) and His breath of life is Not the Material Cause of Judas' betraying Jesus.
Efficient Cause: where an Agent (a person's willful action), results in the effect.
Eg: Judas is the Efficient Cause of his betraying Jesus.
Instrumental Cause: where an instrument that's used, results in the effect.
Eg: The kiss was an Instrumental Cause in Judas' betraying Jesus.
Anything you disagree with, just put it out there and we'll discuss..
..I also take a monergistic view on Salvation..
I guess this stems from our valid need to uphold "All Glory to God
alone" - and Glory is credited to the Efficient Causes alone as opposed to Instrumental causes etc. The doctrine of regeneration preceding faith serves to make God alone the Efficient Cause, for every other scenario has man also sharing credit as the Efficient Cause. As I've understood, you argue to show that man is not an Efficient Cause, hence upholding your monergistic view - have I got it right thus far?
...but the son would not have been able to grab the rope if the father had not given the choice to him(
Ephesians 2:10), in this case handing him the rope, so this too is a fallacy and the son has still played no part in saving his life.
The rope is an Instrumental factor - with the father being the Efficient Cause behind the rope too. I agree.
Listing out all possible scenarios, with combinations of contributing causative factors and subsequent effects -
Case 1: The father does not throw down the rope at all, the boy has nothing to choose to hold on to, he drowns.
Case 2: The father throws down the rope, the boy chooses to hold on, he is saved.
Case 3: The father throws down the rope, the boy chooses to not hold on, he drowns.
I understand this method - where you compare the change in final effect according to the presence/absence of each cause across all scenarios, so as to determine the nature of each cause. So you compare Case1 and Case2 to conclude that the sole distinguishing factor is the father throwing down the rope and not the boy choosing to hold on, therein making the father alone the Efficient Cause. That's still not completely convincing, but I'll not contest it now.
But why haven't you compared Case2 and Case3 - where the sole distinguishing factor is the boy choosing to hold on, therein making him too part of the Efficient Cause? That's synergism right there, isn't it?
But of course, if you split Cases 2,3 in more detail -
Case 2: The father throws down the rope, the boy chooses not to hold on, the father does not choose to have mercy in regenerating the boy, the boy continues to not hold on, he drowns.
Case 3: The father throws down the rope, the boy chooses not to hold on, the father chooses to have mercy in regenerating the boy, the regenerated boy now chooses to hold on, he is saved.
Here, the father becomes the sole Efficient Cause - hence, monergism without denying the participation of the boy's willful choosing.
According to my belief-system, the doctrine of total depravity is what denies a further case where the boy chooses to hold on to the rope when first thrown - and it is this inhibiting sinfulness of the flesh that the Father overcomes in regenerating man in the spirit, wherein he inevitably chooses to hold on. But I realize you believe differently over these things - I think you hold the father's throwing down the rope and calling to his son itself as sufficient to overcome his sinfulness of the flesh, is it?