Sorry but logic isn't claiming that apes can turn into humans.
Nor is logic making assertions that no one in the past or present has observed or documented such as a global ice age. Those are the things of science fiction.
Logic is not limited to things you see yourself. Logic and science tell us that the Sun is made mostly of hydrogen, yet no one has ever been there, nor collected a sample, nor could we ever. Logic and science tell us that the Moon is held in orbit by gravity, the same force that pulls an apple straight down to the ground. Logic and science tell us that the Earth revolves around the Sun, rather than vice versa, yet damned if it doesn't look and feel slightly different.
Logic and science do not tell is that apes can turn into men, it tells us that modern man and modern apes have common ancestors. Apparently the Bible doesn't have pictures of the various other hominids that have lived on this planet, but they clearly did exist and you can see their fossils. The 'missing link' between those hominids and man, was found long ago leaving us with quite a strong understanding of the evolution of man over the past few million years.
Science tells us about one "global" ice age that I know of (aka "Snowball Earth") but it is more hypothesis at this stage. There have been many glacial periods that were less than global, though, as your eyes and logic can demonstrate if you your eyes and mind remain open. If you come to places in New York, there is clear evidence of glaciation. It was not a theory developed on a whim it was a process of slowly accumulating evidence for it, until eventually few who viewed the evidence could dispute it as the most likely explanation for what we see. It was a theory that virtually everyone resisted at first, until the evidence became overwhelming. If you see me come into your house wet and holding an umbrella, logic does not require that you see the rain and feel it on your skin to accept that it was there. Without seeing it yourself the most you'd ever have is circumstantial evidence of it, but the empiricism of science is not naive experientialism that requires direct proof in every case. Indeed, there is no direct proof that subatomic particles exist, and when Einstein proved that atoms exist he did it by means of the circumstantial evidence that we call "Brownian motion."
(Geologists might, as might biologists about evolution, be
wrong in their beliefs about glaciation, but, again, the Sun may not rise tomorrow too. Anything is possible, though some things are so very unlikely that you can ignore the possibility of their happening in a million lifetimes.)
Surely it is not logic that made people take comfort in the story of a man who healed the sick, raised the dead, and performed miracles in the name of God, wandered around from one end of the middle east to the other gathering his followers and teaching all who would listen, was executed because the movement he started angered the authorities, and later rose from the dead and was seen alive again by his disciples. It's fine if you choose to believe it, though, all logic aside. Still logic has to be left aside to believe in that, since regular experience runs counter to the fantastic elements of that story.
You may also believe in Jesus, who's life (we read) was also very similar to that described above. It's certainly not "logic" that leads you conclude that the man described in the last paragraph (Apollonius of Tyana) is some sort of fiction made up by his crazy followers, whereas Jesus is *real,* it's just preference.
