I will define a miracle as: God interrupting his divine habit of controlling and sustaining all in his usual manner, called natural order. Having planned and inserted from eternity past, a supernatural happening that causes a subsequent chain reaction of "normal" events that follow. 1689 LBC Chapter 3:1 In simple terms.
See, that wasn't so hard. Somewhat obtuse, though. Why is there a "subsequent chain of 'normal' events"?
I prefer to follow Francis Shaeffer, following Aquinas, I think it was, in that a miracle is when God reaches down from the realm of grace into the realm of nature, and causes an event that is contrary to nature.
Or in NT terms, a miracle is a "sign": an event showing that God is with the miracle worker: Jesus or an apostle.
Now please define providence. How is it different from "miracle"?
One of my students very wisely differentiated in this way: a miracle is an event, but providence is a process.
Normally, if the text speaks for itself, no comment is needed.
Not one single time have I thought that the verse you quoted proved your point, so explanations would have helped.
I believe all are under God's wrath and stubborness is part of it. Just as with Pharaoh and the Jews God blinded so they could not repent.
So is man's stubbornness providential or not?