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I'll have to take your word on that, as that's far outside my field.
All you have to do is read the Bible :-)
e.g. Genesis 6:20 {KJV)
20 Of fowls after their kind, and of cattle after their kind, of every creeping thing of the earth after his kind, two of every sort shall come unto thee, to keep them alive.
Kinds of cattle ? Does that make sense if "kind" is at the taxonomic level of "family" ?
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I am only going by what I have read on creationist websites and seen posted on threads like this. One example is:
What are the Genesis “kinds”? Baraminology”classification of created organisms
That seems to be pretty clear that the terminology was essentially invented by creationists.
In fact the issue is purely artificial. If a creationist accepts an evolutionary relationship it is "within kinds" if he does not it is "between kinds". The presumed limits on evolution are assumed to "explain" why the creationist is right. All the creationist is saying is that reality has to conform to his beliefs.
To show evolution between kinds you need to find a well-documented example of evolution that the creationist will refuse to accept (whale evolution is good) and get them to agree that it would be evolution between kinds. Then hope that he's open-minded enough to accept the evidence. (Good luck there).