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In other words, just because we see evidence of speciation does NOT mean that we see evidence of how said speciation was formed. Sure, it could have been natural (ala Evolution), but it could also have been un-natural (ala Intelligent Intervention).

Both could be true, particularly as people start tinkering with DNA. But we are faced with a situation where you have two open hypotheses, evolution and intelligent design/creation, both of which could be correct. We know life is a complex chemical system and not much else. Therefore, for all practical purposes, we are faced with selecting a single working hypothesis from the potentially infinite set of conceivable ones until such time as there is only one hypothesis left standing.

Fortunately, mathematics provides a formal solution for "best hypothesis" selection that will allow you to select the hypothesis most likely to be right. It doesn't make guarantees that the selection will be correct, but it does guarantee that it is the most probably correct. This bit of mathematics is more commonly known as "Occam's Razor", which was conjectured LONG before it was actually proven in mathematics. Occam's razor for the sake of this discussion basically states that the hypothesis with the fewest degrees of freedom is most likely to be correct. The reason I have to back the evolution hypothesis, knowing nothing else, is that it has one degree of freedom less then intelligent design. Therefore if my intent is to select the most rational hypothesis of the two, I am compelled to select evolution as the best working hypothesis because mathematics demands it. I might not even agree with it, but I would be a fool to deny that it is the most rational position lacking any bulletproof evidence for either side.

"The reason I have to back the evolution hypothesis, knowing nothing else, is that it has one degree of freedom less then intelligent design."

Please show me the specific degrees of freedom for both Evolution and Intelligent Design so that I can compare them side by side and see whether you drew your conclusion based upon real data.

"Therefore if my intent is to select the most rational hypothesis of the two, I am compelled to select evolution as the best working hypothesis because mathematics demands it.

That is utterly ridiculous. The chance of DNA producing a single gene randomly is more than winning the lottery seven or eight times in a row. To produce the over 20,000 genes in a human being is almost impossible, lets call it infinity -1. To say that the probabilities of evolution having created the life we see all around us rather than admit that an intelligent designer did it, is just an admission of close minded atheism.

Occam's Razor is a seductive principle, but it really has a very limited field of application. The problem is defining degrees of freedom, and how we count hypotheses. Someone who believes in Intelligent Design could posit one extra assumption, God, and claim that evolution requires two or three or four. Are these commensurable? Hardly. Because Occam's Razor does not tell us how to count in situations like this, it is pretty useless. On the math front--if you can PROVE mathematically that evolution has occurred, I would be glad to hear of it. So far as I am aware, the biologists have a lot of plausibility arguments and hand-waving, but no PROOFS.