First, thank you for the informative link which specifically addressed the question. I apparantly had trouble finding the right search parameters. The ultimate answer it gave (inbreeding), however, is something I had already considered and ruled too unlikely, because it would be required in every case, and many animals don't have big litters of offspring. Every new level of unlikelihood pushes the evolutionary timescale back immensely as you know, and if gets pushed too far back then we don't have enough time since the Earth has been around.
This article demonstrates my point about assuming "Givens" though. You said:
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Science is based on certain axioms, or prerequisite beliefs. If you do not have these beliefs, then science is useless to you, except in a purely hypothetical sense. These axioms are pretty much as simple as this: logic and observation.
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The article says :
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The only way to be sure what happened is to look at numerous species which we assume are all descended from a recent common ancestor, and then assume that the most common chromosome number was the same in the ancestral species, from which all the others are descended. (emphasis mine)
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Now I am sure you will say logic and observation led them to make these assumptions. Direct observation of evolution is impossible. That leaves logic. And now we come full circle with my assertion that science is inseparable from humanity. Science is absolutely dependent on human reason. That reasoning determines what will be the assumptions and how the data will be interpreted. To put it another way, they
assumed evolution in order to
prove it.