Hi Richard.
That sentence was intended to demonstrate that observation is always theory laden! Formally, perhaps, contingency is just contingency: there is no way to say with certainty that this post was not created randomly by a lucky electrical storm.
To the groups I mentioned, the distinction is easy, because (to oversimplify) the Epicurean attributes everything ultimately to chance, so even something like an undeniable Resurrection is luck; the Deist being committed to Clockwork Order will assume that even the miracles have lawlike causes (remember all those sandbars explaining walking on water, or generous people sharing loaves and fishes in homeopathic amounts).
I would argue that the theist, believing in a God who is immanent in his good creation, might find it hard to see where “chance” comes into it at all, and will be open both to hidden laws and free acts of God.
In reality, those three groups are not watertight - people can be persuaded by, for example, seeing a miracle and deciding that their Epicurean explanation won’t wash.
In the case of ID, part of the issue is that, whether theists or not, they apply the possibility of final and formal causation - the essence of design - to the “natural” world as well as to human affairs. So they “see” what the Epicurean, who denies the existence of formal and final causes, and the Deist, who is only interested in efficient causes, have excluded ideologically. In that sense, design can’t be proven. Maybe that edges towards answering your #1.
Your #2 (first sentence) confuses me. “Methodological Naturalism” is to explain nature as if there were no God, supposedly to have a better chance of discovering the laws which (ECs will say) God made. It’s hard for me to see how God could explain creation apart from himself.
But in theory, God might be a Deist, I suppose, and put all his design eggs (as per your second sentence) in the origin of the Universe so it ran “on a perpetual motion” (Leibniz). The problem there is theological - the Deist God is not the Yahweh of the Bible. Additionally there are many emoirical indicators that the Universe is not that much a precision clock, unless there are a bunch of hidden laws of which we have no scientific inkling.
If such were the case though, to try and speak for ID as I understand it from the outside, it wouldn’t alter the design inference: formal and final causation are present whether a designed object is made by hand or manufactured by a completely automated algorithmic process.
But specifically:
I’ve never heard an ID person denying the existence of laws: only that laws are not sufficient to account for contingency. They don’t even have to deny the universal applicability of laws. After all, human actions, though not predictable by natural laws, nevertheless never act against them. In fact, it seems to me that those who rule out design do so usually by renaming it as “chance”, which (as in Monod) becomes a force NOT covered by law.
Your last sentence, I think, is a non-sequitur. The possibility, even self-evidence, of design was held by nearly everybody before a couple of centuries ago. Aristotle was not interested in proving Genesis. Granted, my Epicureans would deny on metaphysical principle the creation accounts - but in essence ECs are in agreement with IDists on the fact of creation. Even the Deists might be happy with the core teaching of Genesis 1 - it’s the rest of the Bible, in which God is involved with his world, that they would reject. But the secular man in the street is as comfortable with a God who does stuff as any IDist.