In order to understand what is being proposed, all you have to do is stop trying to understand what is being proposed, and just read it.
He is proposing stochastic. Nothing more. Nothing less. The specific phrase (let's see if I get it right. I'm not going to look it up, but I've read it often enough) is "of or being described by a probability distribution function."
He is proposing absolutely nothing more, nor less, than that. Can evolution be described with probability distribution functions? Yes. Can natural selection be described with probability distribution functions? Yes. There it is. Done.
No implications. No philosophy. No religion, creationism, design. No nothing. That's it.
Do biologists describe it that way? Some do. Many don't. And, most importantly, why does it matter? We know what he means, and if he is a bit eccentric in his characterizations, so be it.
That's where I become interested. It's not good enough to assume that his characterizations are odd, or out of the mainstream, or not very illuminating. That's not good enough. Since he continues to use language that isn't in the approved word list, there's this curiousity about what he "really" means by that. Maybe, some people speculate, he is lying.
That's ridiculous. Usually, when people tell you they believe something, they are telling the truth. He believes that evolution is random. Not that it matters, but by the definition he is using, he happens to be correct, but that really isn't important. The important thing is that he is not a creationist. How do I know that? Because he says so.
Generalizing this to the the general topic of this thread, it is dangerous to read anything into someone's position beyond what they say. You cannot infer that someone is a lousy scientist if they happen to be a creationist. If someone says they are not a creationist, that probably means they are not a creationist. There might be a little bit of ambiguity in definitions, as in whether someone can believe in the theory of common descent and/or evolution and still be a creationist, but there's no reason to believe that anyone is lying about his beliefs.
Articulett says that mijo and Behe have a lot in common. I disagree. I do, however, think they have something in common. Both are accused of lying, even though there's no reason to believe they are anything but honest.
May I offer another persepctive (because, while I think you started out fine, I also think there is some misrepresentation in what you wrote above)?
What I specifically object to in your above post is the idea of there being an approved word list. I do not agree. I think there are ways of facilitating communication and ways of throwing up road blocks.
We use words and words carry many connotations. The word "random" has many meanings to many people and when it comes to teaching evolution to children it is not a particularly good word to use because of these connotations.
IIRC the technical use of the word "random" was introduced into these discussions not by Mijo but by Walter Wayne (I seem to recall someone else pushing the idea too but can't remember who). Walter was very specific about its use as a technical term. I don't think anyone really disgrees with his points. The only potential problem is that when it comes to using this word out there, in the real world, most folks don't know this technical definition. They, therefore, would get an entirely wrong impression from any discussion about evolution being random unless you were to be very precise and explicit in your use of the word "random".
Mijo started his thread not with the question, "what is random?" but with the question, "How is evolution non-random?" or more precisely, "What is the evidence that evolution is non-random?".
The discussion, properly speaking, then was not about "random" but "non-random". I did not follow every bit of that discussion, but it seemed fairly clear to me (and please correct me if I am wrong here) that Mijo's particular use of the word "non-random" was as a synonym for "determined". But that is not how we use the word "non-random" in common speech. I, for one, view "determined" to be a special subset of "non-random". Non-random seems to mean, at least from the usage I have seen, any process that further limits the probability distribution we see in a random process (and to forestall the other discussion I am very well aware that random processes are limited to begin with -- non-random refers to further limitations on random outcomes).
In that sense, natural selection is non-random because it limits outcome probabilities. The outcomes are not absolutely determined in almost every instance, so evolution is still random in the technical sense. But to tell people that evolution is random and leave out the non-random aspects of natural selection in that discussion would be a gross misrepresentation of the evolutionary process. As far as I can tell, that is the real objection to the use of the word "random" in this discussion.
When we use words in non-traditional ways (using "random" in its technical sense is non-traditional) and other people do not know the technical definitions used, this creates a block to communication. This is not an issue of "words on an approved or non-approved list" but of proper communication. I think most people would agree that evolution meets the definition of "random" when narrowly defined and used in this technical sense. I think most educators who work in the real world, however, would object vociferously to describing evolution as random simply because the word out there means many, many more things and carries connotations that the technical definition does not imply.
The rest seems to be a major personality conflict.
ETA
The further point is that some folks seemed to imply that "random" in the previous discussions tells us something about the nature of reality. It does not. Ultimately the universe is deterministic or indeterministic. If it is deterministic, then evolution is deterministic and "random" is just a garbage term to describe our ignorance. If it is all indeterministic, then everything is "random", so its use is meaningless and it does no good to discuss evolution as random.
