Notation

For lack of diagrams, I represent the graphs of elemental transformation textually. A directed graph has nodes. A node is bi- or uni-directional. Any element capitalized is to be considered a True Element in that graph; I don’t insist on monism, so some graphs will have multiple True Elements. That is, Thales’s system gives us a graph that looks like this:

Water ↔ Water
air ↔ Water
earth ↔ Water
fire ↔ Water

A True element is one of the elements identified as primary or special in some sense. Thales identified water as his True element, but air is the True element for Anaximenes, and others hold all 4 (or 5) to be True elements, while someone like Anaximander introduce a new element as the True element.

It’s not always clear what makes the True element the true element. It could simply be that it was the historically first and only element, which then turned into the other elements which then recombined to generate all material things. This is a little unsatisfactory because it’s hard to see how, this distant from the beginning of the universe, we could possibly choose between any element as the True element. Another interpretation might be the Trueness relates to how the elements change (as is implied by identifying only one element as the True element). This interpretation rescues the falsifiability of the theories.

Elemental Trapdoors

To see what I mean, consider this: either all the other elements can turn into the True Element, or not.

Suppose the latter possibility – there are one-way transformations. Then the graph might look like

Water → earth
Water ↔ air
Water ↔ fire

(I use earth here as the terminal node, but the argument works for any element.)

If we assume this, it is saying that “once an atom of earth comes into existence, it will never turn back into water, air, or fire”. The dice are loaded in favor of a particular element. Given this, we should expect to observe a cosmos composed of earth, or at least a cosmos suffering irreversible diminution in air, fire, and water as they cycle through their transformations and occasionally turn permanently to earth. We do not observe such a cosmos. Thus we can reject the possibility of irreversible transformation on empirical grounds. (Not to mention simplicity and symmetry.)

A determined apologist for this scheme could argue from the incompleteness of our observations; if we expect an excess of water, perhaps there is simply a vast universal ocean of excess water we haven’t noticed yet, or perhaps the process is slow enough that the imbalance has not built up much and we are still far from ‘the inevitable earth-death of the universe’. Even if we think we have made careful observations of just the Earth and have not observed any ‘leak’ to such an ocean or any local excess water building up, we could still be mistaken. This seems a little ad hoc and desperate, especially in many ancient cosmologies where the Earth is sealed off. In its defense, though, modern physics believes (with much better empirical grounds) that this is true of the property entropy—the Earth is pushed to a local high level of order, but only by the constant destruction of the Sun’s initial low entropy, thereby avoiding the Second Law of Thermodynamics.

This turns out to be close to an existing criticism of Thales’s cosmogony, by Anaximander—if all things came from water, why have they not returned to water? This argument from history is reminiscent of Boltzmann brains, and may be answerable in s similar way: we observe a universe of mixed elements because we are creatures of mixed elements and could not exist in an all-water universe (like we are creatures of low-entropy regions of the universe and could not exist in the usual high-entropy regions), but the rebuttal comes quickly—how did this low-water state come to exist? Should we appeal to the Atomists’ great Swerve, for elements?

(Anaximander’s second objection—asking how opposites could turn into each other, like fire into water—is less germane, but still worth considering. If water just ‘jumps’ into a fiery state to accomplish the transformation, then this seems quite as arbitrary as assuming the universe began with equal amounts of fire and water rather than a philosophically pleasing single element; but if water shades continuously into fire, then the standard skeptical arguments against infinitely fine continuity can be applied.)

Free Trade

Let us assume the other hypothesis: all elements can be converted to the original element, and from the original into any other.

But given that premise, why do we prefer any graph to any other? They look identical! That is,

air ↔ Water
earth ↔ Water
fire ↔ Water

is empirically identical to

Air ↔ water
earth ↔ water
fire ↔ water

or

Fire ↔ earth
air ↔ earth
water ↔ earth

(And so on.) All three graphs predict we’d observe a mix of air/water/fire/earth, and no obvious trends. Even if we could rule out for certain a graph like

Air ↔ earth
Air ↔ fire
Air ↔ water

we still would have no reason to claim that the first node with multiple links is the True Element! Why not have a cosmogony in which fire gives birth to air, which is convertible to all the other elements and from thence all things? It is no stranger or more convoluted than the divine chain of being we see in Hesiod’s Theogony, for example.

Wrong or Meaningless

Denoting any node as the True Element and the other nodes as just elements doesn’t add anything to our graph. If you claim a system of elemental substances, then you cannot claim to have a True Element and also allow elements to turn into each other—because then your system either is obviously wrong as it conflicts with observed reality, or, your suggestion is meaningless. At the least, reconciling elemental elements with elemental change is harder than it looks.