Against the Miletians and the One True Element

Exploring consequences of material monism and conflict with observations
2008-10-172011-11-25 finished certainty: certain importance: 3

One of my prob­lems with the Mile­tians (and / in par­tic­u­lar) is that the dis­cus­sions of onto­log­i­cally basic ele­ments (a major topic of the sur­viv­ing frag­ments) seem either vac­u­ous or ill-de­fined. In par­tic­u­lar­ly, they don’t seem to have any empir­i­cally dis­tin­guish­able con­se­quences in a plau­si­ble equi­lib­rium or to have any mean­ing­ful dis­tinc­tion between a ‘true’ fun­da­men­tal ele­ment or mere ‘deriv­a­tives’ which are trans­formed ver­sions of it.

Against the Miletians and the One True Element


For lack of dia­grams, I rep­re­sent the graphs of ele­men­tal trans­for­ma­tion tex­tu­al­ly. A 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 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 —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 , 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 ’ great , 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


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 , 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.