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The addition of natural numbers is an obvious and verifiable procedure but evolutionary biology is not observable or verifiable."
But we do observe the processes of evolution. Mutation, selection, recombination, gene flow, migration, etc. We see new genes being formed. We see novel features in organisms. We see new species apearing.
We also have a wealth of observations about changes in the past through observations in areas such as the fossil record, genetics, homology, ontogeny, atavisms, vestiges and biogeography.
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Can you name one biological application that would fall if evolution were abandoned tomorrow?"
I'll let someone far better qualified than me make the case.
Nothing in Biology Makes Sense Except in the Light of Evolution by Theodosius Dobzhansky.
http://www.2think.org/dobzhansky.shtml
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The testing and validation of good science is its predictive results that can be verified. Evolutionary biology has no such offerings."
Not true.
Let's take a simple example. If you look at whales, you will notice that they are mammals. From their development we know that they have little rear legs that are absorbed before birth. Some whales have been documented as being born with rear legs. There are vestiges of a pelvis. It is a safe prediction that whales descended from land animals.
All the way back, Darwin mistakenly supposed some swimming bear that evolved into a whale. The bear part was far from correct, but you can see how long ago it was recognized that whales had land dwelling ancesotors. So a prediction could be made that we should be able to find such ancestors.
Well, with some digging, scientists were able to discover that whales did evolve from lad dwelling ancestors. A series of transitional fossils have been found. Some of these include Pakicetus, Ambulocetus, Dalanistes, Rodhocetus, Tackrecetus, Indocetus, Gaviocetus, Durodon, and Basilosaurus.
One thing that became apparent in the fossil studies was that whales not only evolved from land animals, but that they evolved from even toed hooved animals. So another prediction can be made that whales should test as genetically similar to modern even toed hooved animals.
As it turns out, they do.
"Molecular evidence from retroposons that whales form a clade within even-toed ungulates," Shimamura M, Yasue H, Ohshima K, Abe H, Kato H, Kishiro T, Goto M, Munechika I, Okada N, Nature. 1997 Aug 14;388(6643):666-70.
It also should seem a reasonable prediction that whales should also possess vestiges of genes from land dwelling animals. Once again, it turns out that they do.
"Olfactory receptors in aquatic and terrestrial vertebrates," J. Freitag, G. Ludwig, I. Andreini, P. Rössler, H. Breer, Journal of Comparative Physiology A: Sensory, Neural, and Behavioral Physiology, Volume 183, Number 5, November 1998, Pages: 635 - 650.
This is a limited example. But for all of the types of evidence that support evolution, one can make predictions about what types of additional findings should be and should not be found.