Of Turtles and Tortoises
How can we satisfy ourselves without going on in infinitum? And, after all, what satisfaction is there in that infinite progression?
David Hume, Dialogues Concerning Natural Religion (1779)
We all know the famous ‘testudinal regress’ story.
A scientist is giving a public lecture on astronomy and is interrupted by an old lady who points out that the world is not as described, unsuspended and hurtling through space, but really rests on the back of a turtle. Asked by the scientist what this turtle itself stands on, the old lady replies: “it’s turtles all the way down!” It doesn’t matter who said this. The point is, a strong (scientific) intuition is that there has to be a terminus. It can’t be turtles all the way down if we want things to make sense; this would be worse than a castle built on sand. There has to be a bottommost turtle, and this bottommost turtle is usually required to ‘provide the ground’ for those above. The idea is, of course, that the compositional structure of physical reality is something like stacking blocks of Lego to produce a bigger, more complicated object possessing different properties to those found at the level of individual Legos. But we aren’t supposed to ask what the blocks are made of, since we would have to then ask the question again, possibly ad infinitum. The fundamentalist intuition is that there must be some end to the questioning.Many philosophers assume this makes an exhaustive pair of alternatives: regress versus bottom (or top) layer—e.g. “So why believe that there is a fundamental level? Why not an infinite descending hierarchy of levels?” ([10], p. 499)—, and the regress option is usually rejected. For example, Paul Oppenheim and Hilary Putnam simply assume that the number of structural levels “must be finite,” and “[t]here must be a unique lowest level” which in their view must be supplied by the elementary particles ([9], p.
409). Jonathan Schaffer provides at least some intuitive reason for the same, stating that in the ‘turtles all the way down’ scenario, “Being would be infinitely deferred, never achieved”([11], p. 62)—the same intuition that lies behind the Kalam cosmological argument for the existence of an uncreated creator of the universe. This clearly lands us into Zenonian paradox territory, from turtles to tortoises (and Achilles)—being in this case would require that the universe performs something akin to a ‘supertask’! I don’t think it’s exactly straightforward that infinite regress means that being could never be achieved: so long as for any layer there is another on which it depends, that would seem to secure everything that needs to be secured—there is also the issue of whether there can be actual infinities or not. This aside, Zeno was on the side of Parmenides, who believed that the fundamental thing was the whole: fundamental reality was indivisible, unchanging, eternal Oneness. The atomists countered the Parmenidean problems of plurality (and change), not by allowing infinite divisibility of matter, but calling a conceptual endpoint to the possibility of division, by splitting reality into atoms and void, and then pointing to the absence of void in their atoms. Their atoms were uncuttable precisely because that would require void to appear between the divided parts. There was change (in the recombinations) without change (in the basic ontology). Atomism has two types of plurality: in the basic fundamental ontological kinds (atoms and void), and in the atoms themselves, which are many. Parmenideanism is monistic: there’s no true plurality at all.The atomic principle (nothing but atoms and their motion in the void) can then be used to explain complexity from simplicity (though these atoms can be any shape and size) via combinations. One builds up here from the ground floor: the ontological basement. The Parmenidean principle is to start from the full complexity of the world (the One: a finite unity of the things that are) and work down to other entities (including space, time, matter, and motion: all non-fundamental according to this theory), which are derivative.
One starts from the very uppermost floor here: the ontological attic. In both cases, the world we experience (the floors in between) is mere ‘appearance’: not the true fundamental reality. Two fundamentalist positions. Both explaining the world as we see it. One matches the received view on what we require from a fundamental physical theory, the other not so (though similar examples can be found from recent history of physics).There is an anti-fundamentalist alternative to this fundamentalist pair, in Anaxagoras’ cosmology, which allows infinite divisibility of matter, but not into simples of any kind. Here is there no least magnitude (no atoms) and neither is there a largest magnitude, and so there exists no fundamental layer (upper or lower) whatsoever—he expresses it as ‘there is a portion of everything in everything’ (philosophers call this a ‘gunky ontology’). In many ways, the atomist concept was a compromise between the divisibility of Anaxagoras and the indivisibility of Parmenides: division/plurality is possible, but stops at what are many and varied micro-Onenesses, namely the atoms. This has tended to provide the primary explanatory strategy in both physics and metaphysics ever since.
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