Horse manure. It is the postulate (it doesn't even rise to the level of "theory") that, as the name "Intelligent Design" explicitly states, some (unspecified) form of (unspecified) intelligence added some (unspecified) amount of (unspecified) "design" into life on Earth at some (unspecified) time(s).
Any "model of probabilities and improbabilities" employed by the IDer's is done solely in support of their attempts to "prove" that certain aspects of life "could not have" evolved. The purpose of this is to try to bolster the credibility of "intelligent design" as the "obvious" alternative, but they obviously aren't clear on how science works. Weakening one theory in no way supports a different hypothesis. ID is not the "default" explanation which "wins" by eliminating the competition. Mankind outgrew that particular fallacy centuries ago.
So please stop repeating nonsense like trying to claim that Intelligent Design "is" an "appeal to a mathematical model of probabilities", as if it's nothing more than a particular analytical method. Instead, probability calculations (usually naive and bogus ones) are just one of the *tools* they attempt to employ in order to flail about for "support" for what ID actually *is* -- the notion that life was "designed", that it was CREATED. In short, creationism by another name.
Creationism is a theory of origins that posits God bringing about, in 6 days as per the judeo-christian bible, all that we see in the universe.
So you're claiming there's no such thing as an "old Earth creationist"? Are you remarkably naive, or just dishonest?
Yes, young-Earth Biblical creationists are one *kind* of creationist. But there are many other kinds. By definition, anyone who posits that an act of conscious creation was involved in the formation of life can fairly be classified as a "creationist", although obviously there are many different "flavors". One of those flavors is the pseudo-scientific postulate of "ID".
Creationism is a particular school of thought, and it is as I described it.
Those who posit an old earth are not accepted into that school, and I'm really sure of that.
If you are using "creation" in a general sense, in that all who posit a creator God are therefore, "creationists," then there's nothing wrong with that so far as the English language is concerned that I can see.
Intelligent design, though, doesn't answer who or what is the intelligence behind the design. Nor does that intelligence have to be a god.
It really is a mathematical model speaking to the improbability of such a complex thing as living systems coming about accidentally, and therefore having had to have been designed.