Old earth creationists accept an earth significantly older than 6,000 years (they don't deny the evidence of an old earth), but deny that today's species were created by evolution (they do deny Universal Common Ancestry - UCA).
Perhaps a short description would be:
Old Earth Creationist (Earth may be millions or billions of years old, and God created animals in their present form, not using evolution).
This position has an interesting history.
Christian geologists found more and more evidence of an old earth in the late 1700s. By the early 1800's, this mounting evidence led to a raging debate among geologists about the age of the earth - specifically, whether the geologic features found were formed during a literal, global flood, or by geologic processes over at least millions of years.
The biggest proponant of "flood geology" was the Rev. Adam Sedgewick, who was an ordained minister, and the top geologist of is day. As more and more evidence clearly showed an old earth, Rev. Sedgewick found he had a harder and harder case to make to deny that evidence. He realized that he was simply wrong, and formally recanted flood geology in 1831 as his last statement as President of the Geological Society of London (the main geological society at that time).
A much more detailed history can be found at this Christian source, here:
History of the Collapse of Flood Geology and a Young Earth
OK, notice that the reality of an old earth was accepted among those familiar with the evidence (all of whom were Christians) by 1840 -
about a century before radioactive dating was discovered. When the later discovery of radioactivity gave us powerful and reliable methods to test this early Christian conclusion again, it was confirmed over and over.
With an the reality of an old earth already accepted, when Darwin's Origin of Species was published in 1859, the controversy centered on the creation account in Genesis. Because it was already settled that the earth was much older than a literal reading, many Christians held to an Old Earth Creationist view - denying evolution (which had only some evidence at the time) and accepting an old earth.
This was the case until the late 1800's, when more and more evidence for evolution (specifically for universal common ancestry - UCA) was piling up. By 1900 or so, UCA was accepted by biologists, paleontologists, etc. However, there was still a lot of fundamentalist based opposition - almost all of which was still from old earth creationists (who made up the majority of Christians). However, at this point, those Christians (who had previously held a justifiable position based on the evidence) needed to start denying evidence - because now there was clear evidence for UCA.
Around 1940 to 1950, radioactive dating provided another area of confirmation of an old earth. At the same time, fundamentalists were finding that they were rejecting massive evidence for UCA, while still accepting an old earth. If one is going to reject evidence, then why not also reject the evidence of an old earth, going back to a literalist position for both age of the earth and UCA? So more an more evidence deniers became Young Earth Creationists (YEC), and the numbers of OEC correspondingly decreased from 1940 until today.
So today, there are very few OECs, and almost all of those who deny evidence are YECs.
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