If you don't understand what the words "possibly" and "possibility" have to do with science then you don't understand what science is. Maybe that's why we disagree.
Misunderstanding of quotes about punctuated equilibrium
What paleontologists do get excited about are topics like the average rate of evolution. When exceptionally complete fossil sites are studied, usually a mix of patterns are seen: some species still seem to appear suddenly, while others clearly appear gradually. Once they arise, some species stay mostly the same, while others continue to change gradually. Paleontologists usually attribute these differences to a mix of slow evolution and rapid evolution (or "punctuated equilibrium": sudden bursts of evolution followed by stasis), in combination with the immigration of new species from the as-yet-undiscovered places where they first arose.
There's been a heated debate about which of these modes of evolution is most common, and this debate has been largely misquoted by laypeople, particularly creationists. Virtually all of the quotes of paleontologists saying things like "the gaps in the fossil record are real" are taken out of context from this ongoing debate about punctuated equilibrium. Actually, no paleontologist that I know of doubts that evolution has occurred, and most agree that at least sometimes it occurs gradually. The fossil evidence that contributed to that consensus is summarized in the rest of this FAQ. What they're arguing about is how often it occurs gradually. You can make up your own mind about that. (As a starting point, check out Gingerich, 1980, who found 24 gradual speciations and 14 sudden appearances in early Eocene mammals; MacFadden, 1985, who found 5 cases of gradual anagenesis, 5 cases of probable cladogenesis, and 6 sudden appearances in fossil horses; and the numerous papers in Chaline, 1983. Most studies that I've read find between 1/4-2/3 of the speciations occurring fairly gradually.)
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