I have a stronger background in the philosophy of science than I have in biblical exegesis, so maybe I can explain my views in terms familiar to philosophers of science in order to make them clear.
One way of putting the point I was trying to get across is that biblical studies is perforce inductive in nature. Theologies are something like theories, Scripture is like the a database, and further historcial information is helpful in making an inference to the best explanation.
We come into this discussion with prior probabilities which differ. This is what I accept with respect to scientific theories, this is what I accept with respect to theological theories.
For me, the Calvinist has the burden of proof. Why? I'm not a Calvinist. You've got to show me. And I consider the Calvinist position to introduce a moral incoherence into the character of God. That's the nature of reason. We begin where we are, not some ideal, neutral starting point.
With respect to Calvinism, I am expected to throw away all predispositions and be "objective" about the text. Why? Even in the hardest of hard sciences, it doesn't work that way. It seems to me as if positivism is dead everywhere else, but alive and well in biblical theology.
Calvinists seem to be deductivists with respect to their arguments from Scripture. They present their passages, they summon up their exegetes, and say that this deductively entails Calvinism. But there is a lot of Scripture out there.
I have responded to the Calvinist counter-argument on John 3:16, which I find less than satisfactory simply because even if "world" doesn't mean everybody, it seems to mean everyone who's alienated from God. I don't think the most natural reading of this is that given the depravity of man, we should just be amazed that God had enough love to save anyone. The object of that love is supposed to be the Kosmos, which is either the whole world or the world alienated from God. If that love just picks the elect out of that world, then the love doesn't extend to the whole world, but only to the elect within it.
However, I have not gone into detail about the most interesting Calvinist response here. I think it won't do to deny that God loves every person, I think it far more reasonable from a Calvinist standpoint to say God does love everyone, but doesn't elect everyone. That is what Piper tries to do. If this claim can be made consistent, then this would improve the Calvinist case. I do this does violence to the meanings of terms, but there is an argument to that effect out there that has to be considered. My main concern in talking about Calvinism lately was to get to that issue. I hope soon to start going through Walls and Dongell's treatment of this, in a section entitled "Is God's Compassion for the Lost Sincere?"