All of this, which Fisher has been discussing in various forums since 2009, is of secondary concern to his main claim, which is that the appearance of a (fictitious) southern continent on Renaissance maps convinced him that a globe-bestriding Atlantis once mapped the world. To that end, he has tried to reconcile Plato’s description of Atlantis to facts and proposes that to do so we must (a) assume that the story originates, as Plato claims, with his ancestor Solon, and (b) Solon misrepresented genuine Egyptian accounts of North and South America by trying to squeeze them into Anaximander’s intellectual framework of a cylindrical world:
As it turns out a contemporary of Solon, Anaximander, theorized that the world was cylindrical in nature and Europe, Libya and Asia sat atop one of its flat surfaces surrounded by Oceanus which in turn was contained by the outer lip of the cylinder, a “boundless” unbroken ring of land. (Fig. 5) Since there are no boundless continents surrounding an ocean in the real world and the only historical descriptions of such a landform lie in a theory formulated in Solon’s time and in an account of Atlantis also from Solon’s time, simple logic dictates that these two boundless continents surrounding a large 'true ocean' were one and the same.
I am not familiar enough with Anaximander’s philosophy, but I don’t recall there being an outer continent in it. I believe that this edge of the cylinder is traditionally seen as the support for the vault of heaven, similar to Babylonian and Hebrew versions. Nevertheless, the presence of one is implied in the Greek mythical scheme from the earliest in that the inhabited world was thought to be surrounded by the River Ocean, and rivers should have two banks. But the opposite shore of Ocean wasn’t an inhabited land of Atlanteans; it was the great opposite world, the sunset realm of the dead. But it couldn’t be much of a continent since all of the Greeks believed that the earth was enclosed within a solid dome, which rested on this shadow land on the end of Ocean. Variations on this worldview were shared by the Hebrews and Mesopotamians.
Fisher concludes that Solon invented the claim that Atlantis sank in order to reconcile Egyptian knowledge of the Americas with Anaximander’s dogma of a cylindrical world and an empty Ocean. Needless to say, this argument contains so many assumptions that it renders the search for Atlantis pointless. Once you give yourself license to change Plato at will, you can bend the story to fit any outcome you please. Why is it more reasonable to conclude that Solon invented the sinking of two continents than it is to presume he got their size or location wrong, or that they never existed at all?
Sadly, Fisher does not seem to share on his website details of how any of this helped him to overturn plate tectonics since he is saving that for a future book version. He will only say that there are land features that indicate a different view of earth science.