In some forms of the Native American creation story of Turtle Island, North America started when a spirit placed soil taken from the bottom of the planetary sea by a muskrat onto the back of a turtle. Other loosely similar metaphysical notions hold that the planet, shaped like a dome with a flat bottom, is situated on the back of elephants that in turn stand on the back of an enormous turtle. Still another concept would entail that the world is more directly on the shell of a turtle or tortoise, with that turtle/tortoise resting on another, even larger one, and that one resting on yet another, and so on, perhaps infinitely. Variations of this overlap in that they feature the same kind of animal and take some stance on the nature of the world. The alternative versions also have their own sometimes differing reasons for being false or extremely improbabilistic, with some being outright impossible by logical necessity (more on that below).
The Native American legend differs from the concept of a more supreme cosmic sort of turtle that actually holds the world on itself in that Turtle Island (in its aforementioned version) comes about inside of a world that already exists, and it is just one landmass inside this world. In some notions of the world being on top of a turtle, there could be just one turtle, and in some there are up to an infinite number of them stacked on each other. This latter idea is what the phrase "turtles all the way down" is supposed to refer to whether out of asinine agreement or sarcastic mockery. Now, sensory evidence accessible on Earth's surface, as epistemologically fallible and incomplete as it is, suggests the world is indeed spherical [1] and not physically propped by any giant animal, and photographic evidence from outer space concurs. Nevertheless, the infinite regress of turtles leading up to Earth, whether it is allegedly a dome or disc, that could only be erroneous regardless of whatever scientific evidence there could have been for or against the spherical shape of the planet, for it involves logical impossibilities.
If there was an infinite number of turtles/tortoises below the one on which the world stands, then the one on which we are ultimately positioned would never have its place in this cosmic stack arrive. Infinity can never go backwards except in mathematical concepts (like negative numbers) that are neither a physical world of causes and events nor the moments in metaphysical time which are a fundamental prerequisite to events. Time can elapse forever into the future even if the universe was to cease to exist, but it, like the universe, cannot have always existed [2], for then the present moment would have never been reached because an infinite amount of time must pass first, and an infinity can never fully elapse because it is endless. This is the same basic reason why, even if the cosmos has inflated and retracted billions of times, the universe (or multiverse) could not have had an infinite age even if there was not scientific evidence for this. As for a world turtle, this creature's body itself would be made of material substance, however large and powerful it is, and thus it could not have preceded the universe of matter and its finite age.
The Native American story (or at least the version I have mentioned) is not logically impossible in the way that the universe creating itself or always existing is, but the infinite regress of some turtle-based metaphysics is. Of course, it is all because of logical necessity that infinite regress is impossible. It is not because of theistic or scientific reasons; it is reason itself that makes base theism and science logically possible or true only because they are consistent with this. There is no infinite regress in the grounding of truth or the knowledge of it. Metaphysically, logic is inherently true because its falsity would still inescapably require its veracity. There is nothing that makes logic true but logic itself: everything else depends on it, not the other way around, so it cannot be a construct of the mind, an illusion of perception, or part of the natural world. Epistemologically, reason is self-evident and what all other true knowledge would hinge on, but in both the ontology and epistemology of logic, there is no infinite regress. There is objective truth and there can be absolutely certain knowledge of certain truths, but it is reason alone that makes this so.
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