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.
I don't doubt that you are "really sure of that".
When I was a kid, I was "really sure" that Santa Claus delievered the presents I found under the tree.
Be that as it may, there are a large number of self-admitted creationists who would strongly disagree with you. So I don't know why you're bothering to split hairs and play definitional games or play the No True Scotsman dodge.
Intelligent design, though, doesn't answer who or what is the intelligence behind the design. Nor does that intelligence have to be a god.
I didn't say that it did. Nonetheless, you'd have to be remarkably naive to deny that the vast majority of "ID supporters" believe that the "unnamed designer" is actually the Christian God as described in the Bible.
It really is a mathematical model speaking to the improbability of such a complex thing as living systems coming about accidentally,
Again, no, it is not. That is one of the tools the ID'ers try to use to argue their case, but (as I've already said), it's quite simply false to claim that ID "is" just a "mathematical model". It most certainly isn't.
and therefore having had to have been designed.
One. More. Time....
I know this is a difficult concept to creationists/IDers/whatever (it's not a difficult *concept*, just difficult for "certain people"), but even if you could disprove evolution entirely (by "probability" or any other means), it would *NOT* be the case that, as you say, "therefore having had to have been designed".
It just doesn't work that way. Evidence *against* one possible explanation does *NOT* count as evidence *for* any other possible explanation. Creationism is *not* the "default" explanation. It doesn't "win" by eliminating one possible explanation, just as evolution would not "win" if by some means it could be proven that God(s) don't exist. Even if you could somehow bring evolution crashing down as an explanation (and good luck with *that* one), the conclusion would not be "so God must have done it, QED", since it could still be the case that any number of other possible "natural" explanations that we haven't yet thought (as well as any number of other possible "unnatural" explanations that do not involve a "maker") might be responsible for life on Earth and we just haven't discovered it yet.
Evidence *against* one explanation is not evidence *for* another one that happens to be on the table, since *it* might be wrong as well. Only *positive* evidence *for* an explanation counts *for* that particular explanation. Period. End of story.
Probability arguments "against" evolution (and the ones I've actually seen have been bogus) is in no way -- repeat, *no* *way* -- repeat, *NO* *WAY* -- evidence *for* "ID" or "creationism" or whatever you want to call it. The same goes for evidence against any particular flavor of creationism -- that itself does not count as evidence *for* evolution. Nor should it.
Are we clear now, or are you still going to be confused about this straightforward concept?