In the first place, the absence of any plausible mechanism by which evolution
could take place would cast at least
some doubt on the proposition that it actually
has.
In the second place, if we don't have a mechanism, where is the predictive power of the theory? Given common descent plus the theory of evolution, we can predict the sorts of things that we should see in (for example) the fossil record, or in molecular phylogeny, and then we can say: "Look, see how reality matches the predictions".
Remove the
theory (mutation, recombination, lateral gene transfer, natural selection, genetic drift, etc) and where is the predictive power? With no known mechanism --- no
constraints --- the history of life could have begun with an aardvark giving birth to an aardwolf ... and so on in alphabetical order until a zebra gave birth to a zebu; or any other scheme you care to dream up --- and where, then, is the predictive power? The evidence can only confirm something sufficiently definite to be tested.
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However, this is all rather by-the-by in that (as I have explained on another thread) Plaisted's article is nonsense.