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 Atom­ists’ 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.