on the ultimate origination of things

volume21,no.5

january2021

On the Ultimate

Origination of Things

David GunnIndependent

© 2021 DavidGunnThis work is licensed under a Creative Commons

Attribution-NonCommercial-NoDerivatives 3.0 License. <www.philosophersimprint.org/021005/>

1. Introduction

Theproblemofdeterminingtheultimateoriginofthingsisoneoftheoldestproblems inphilosophy.Here,weproposeanewsolution tothisoldproblembasedonadvancesingeneraldynamics,theuniversaltheoryofphysicalforceoraction.AlthoughourarticlewaspromptedinpartbyLeibniz’sfamousessayontheoriginofthings,fromwhichitalsotakesitstitle,itdoesnotfurnishascholarlycritiqueofthatessay.Instead,itemploysaprovocativeargumentcontainedthereintoframeandorientacontemporarydiscussionofthesubject,onethatinduecourse arrives at conclusions thatdiffer fromLeibniz’s ownbut aresupportedbytheprinciplesofmodernphysics.1

Leibnizbeginshisessaybyrejectingtheideathatthereasonfortheuniverse’sexistencecanbefoundbylookingtotheuniverseitself:

I certainlygrant thatyoucan imagine that theworld iseternal.However,sinceyouassumeonlyasuccessionofstates, and sinceno reason for theworld canbe foundin any one of them whatsoever (indeed, assuming asmany of them as you like won’t in any way help youtofinda reason), it isobvious that the reasonmustbefoundelsewhere…insomethingextramundane,differentfromthechainofstates,orfromtheseriesofthings,thecollectionofwhichconstitutestheworld.2

1. Itissomewhatironicthatoneoftheseprinciples,theso-calledprincipleofleastorstationaryaction,actuallyhasconceptualrootsinLeibnizianphysicsandmetaphysics.Terekhovich(2018)hasaccordinglyofferedamodalinter-pretationofthisprinciplethatdrawsuponLeibniz’sconceptofessencesorpossibles striving forexistence.Ourownapplicationof theprincipledoesnotrelyonamodalinterpretationoronLeibniz’sconcept,butitdoesrequire,in agreementwith thedynamical character of Leibnizianphysics, that theprinciplebeacknowledgedasagenuinedynamicalprinciple,onethatspeci-fies thegeneralnatureof realphysical forceoraction, andas suchmakespossiblegenuineexplanationsofphysicalphenomena.Thisrealistviewpointcontrastswiththeinstrumentalistviewoftheprincipleasameremathemati-caltoolthataidstheconstructionandanalysisofphysicaltheories,butdoesnotaffordexplanations.

2. Leibniz(1989:149-150).

davidgunn On the Ultimate Origination of Things

philosophers’imprint –2– vol.21,no.5(january2021)

There is,however, another issueconcerning scope thatneeds tobe addressedhere. Forwhereas the above-mentioned cosmologicalschemes apply only to the universe as somethingphysical or in itsphysicalaspect,temporalrealityhasnotbeenunanimouslyidentifiedwithphysicalreality.Somephilosophers,forinstance,haveheldtheuniverse toconsistpartlyofmentalor immaterialentities thatexistindependentlyofphysicalentities.Others,includingLeibnizhimself,havemaintained that theuniverse consistsultimatelyof immaterialentitiesalone (minds, souls,monads),and thatphysicalentitiesareonly“ideas”orsensationsorwell-foundedphenomena.4Therefore,inarguingthatdynamicaltheoryenablesustoexplaintheexistenceandgeneralcharacteroftheuniverse,wewould,itseems,needtoclarifybeforehandnotonly the temporal scopeof theword ‘universe’, butalsoitsontologicalscope.

That such a prior clarification of ontological scope is not in factnecessary,however,followsfromthenatureofourargument,whichinvolvesdemonstratingthatmattercontainsitsownmerelyphysicalground. For such a demonstration, if sound,would undermine anyontologyaccordingtowhichmatterisdependentonorderivedfromsomething immaterial, including idealism in its various forms. Itwouldalsounderminepropertydualismordualaspecttheory,whichholdsthatmatter(ormateriality)isonlyanattribute;foranythingthatcontains its own ground, and thereby exists independently, shouldrather be deemed substance than attribute. Finally, even substancedualismwouldbeundermined,if,inthecourseofourargument,weweretoshow(asweintend)thatthisphysicalgroundofmaterialbeingalso constitutes the sole ground of material motion. For substancedualismrequiressomematerialmotionstohaveanimmaterialorigin,whereas our dynamical argument, by explaining the existence ofmotioninamerelyphysicalway,wouldruleoutthispossibility.

4. Garber(1985)hasarguedthatLeibnizadoptedhismonadologicalmetaphys-icsonlyafterthe1690s,andthusonlyafterhewrotehisclassic1697paperontheoriginationofthings.Sofarasthepresentenquiryisconcerned,however,nothinghangsonthetruthorfalsehoodofGarber’sclaim.

Asforthecaseofanon-eternalworld,ofauniversethathasnotalwaysexisted,Leibnizdoesnotexplicitlyconsideritinhisessay,presumablybecausehethoughtitobviousthatsuchauniversestandsinneedofanextramundaneorigin.Forheevidentlyexcludesthepossibilityofithavingarisenfromnothing,since“existingthingscannotderivefromanythingbutexistingthings”.3

Leibnizconcentrates,therefore,onthecaseofauniversethathasnobeginningintime,andindoingsoposesachallengetothosewhoseektoevadethepossibilityofanextramundaneoriginbypositinganendlesstemporal(andcausal)sequenceofimmanentthingsorstatesthatstretchesintotheinfinitepast.Therationalehereis,ofcourse,thatifsuchthingsorstatesonlyeveroriginateinearlierthingsorstatesofthe samesort, thennootherkindoforigin is required.ButLeibnizcountersthatthisapproachbegsthequestioninregardtotheentiresequenceofstates:explainingindividualstatesintermsofearlieronesdoesnotexplainwhythesequence itselfexists,why therearesuchstatesinthefirstplace,andthuswhythereissomethingratherthannothingatall.Therefore,eveninthecaseofaneternaluniverse,onemust,itseems,haverecoursetoanextramundaneorigin.

Furthermore, none of the developments in cosmology sinceLeibniz’stimeappeartohaveunderminedhischallenge.Inparticular,none of the cosmological models or theories that go beyond theknownuniverseorpositatimebeforetheBigBang—suchascyclicalcosmology,with itsendlesssequenceofalternatingexpansionsandcontractions,orthemultiverseasgeneratedperhapsbyaprocessofeternalinflation—haveunderminedit.ForLeibniz’sargumentextendswith impunity to thetemporally largerdomainsconsidered intheseschemes.Accordingly,we shall in the remainderof this article takethewords‘universe’and‘world’toapplysynonymouslytotemporalrealityingeneralratherthantoapropertemporalpartthereof.Inthisway,we shall avoid any ambiguityoverusageof thesewords as totheirtemporalscope.

3. Ibid.,152.



assumes,orseemstoassume,thatmatterissuchthatitstandsinneedofanexplanation—anassumptionthatmaywellbefalse.

Despitethisdifficulty,anddespitethelongtraditionofphilosophers,materialistandotherwise,whohaveconsideredmatterafundamentalconstituentofreality,Leibnizsurelyhasapointwhenheobservesthatthereseemstobenothinginmatterortheuniverse(asheconceivesit)thatassuresusofitsprimitiveorunconditionedcharacter.Forwefind there, he says, only “physical or hypothetical necessity, whichdeterminesthelaterthingsintheworldfromtheearlier”,whereasinordertobeconvincedthatwehavereachedrockbottomontologicallyspeaking,werequirenothypotheticalbut“absoluteormetaphysicalnecessity”,wheretheexistenceofathingdependsnotonotherthingsbutfollowsfromitsessence,fromitsownnature.5Intheabsenceofknowledgeaboutmetaphysicalnecessityofthissort—whetherthereis any, and whether it belongs to matter or something else—thequestionofmatter’sontologicalstatuswouldseemtobeundecidable.

Perhapsthemostthatcouldbedoneinthatcasewouldbetoarguethatthereisnoconvincingempiricalorscientificevidencethatmatterisnotprimitive.Butwhilethisstrategymightappeartobesatisfactoryfromanepistemologicalpointofview,alingeringdoubtwouldremain.Forwantofevidenceheredoesnotassureusthatmatterisprimitive.Itassuresusonlythatbeliefinthecontrarystateofaffairslackswarrant.Ontheotherhand,apositivedemonstrationthatmatterderivesfromsomethingelsewoulddispelallcontroversy.

Inwhatfollows,weshallattemptsuchademonstration.Weshallargue, in the first place, that there is after all evidence, and goodscientific evidence no less, that matter is a derived rather than aprimitiveentity.Butweshallalsoargue,contrarytoLeibniz,thatthatfromwhichmatterisderivedconsistsnotofsomekindofimmaterialor spiritual power, with which physics does not deal, but only ofmatter’sowninnerandpurelyphysical force, thenatureofwhichisrepresented symbolically by the principles of dynamics. From this

5. Leibniz(1989:150).

Infollowingthislineofreasoning,then,itisevidentwhywedonotafterallneedtospecifyinadvancetheontologicalscopeoftheword‘universe’.Forifwearesuccessfulinourendeavour,thefundamentallymaterialconstitutionoftheuniverse,oftemporalrealityingeneral,willemergeasaby-productofourargument,theotherseriousontologicalcontendershavingbeeneliminated along theway. In this case, ourexplanationoftheexistenceofmatterwillautomaticallyconstituteanexplanationoftheexistenceoftheuniverseassuch.

As to thegeneralcharacterof theuniverse—why it is theway itis—itisobviousthattheexplanationhereistobefoundinthatverysameentitywhichconstitutestheultimateoriginofthethings.Thus,whereas Leibniz takes the character of the universe to derive fromthe metaphysical and moral perfection of an extramundane being,we shall take it to derive froma certain “geometrical” perfection ofmatter’sownpurelyphysicalground,thedetailsofwhichwillbecomeclearerasweproceed.

2. Primitive and Derived Matter

Before getting underway, it is necessary to consider briefly whatappears to be a third possibility concerning material existence, inadditiontothosescenarioswherematterhaseitheranimmaterialoramerelyphysicalground.Foritmightbethatmatterhasnogroundatall,thatitisaprimitiveratherthanderivedentity,andassuchdoesnotrequireanyexplanation.

Indeed,agreatmanyphilosophers,pastandpresent,havedeemedmatter to be primitive, andnot all of themhavebeenhard-headedmaterialists. Dualists like Anaxagoras and Plato, for instance, arein this camp. For the intellectualprinciples theypositedare relatedtomatternot as creators to created things,but as artisansor artiststoworks of art. Thus,Anaxagoras’sMind and Plato’sDemiurge actupon a formless or chaotic but already existingmatter, bringing toitdefinitionandorderbutwithoutaddingtoorsubtractingfromitsoriginalquantity.Suchcaseshighlightadifficultywith thequestion‘Whydoesmatterexist?’thatarisesintheveryaskingofit:thequestion



wholesaleconfusion,asLucretiushassocolorfullydepicted,8contrarytobothuntutoredexperienceandmethodicalscientificenquiry.

Accordingly, scientific explanations always involve accountingforsomethingintermsofsomething:thepresentstateofaphysicalsystem in termsof an earlier state, the evolutionof life in termsofgenetic mutations and environmental pressures. This obtains eveninquantumtheory,whichhasastatisticalaspectthatseemstoallowforspontaneousoccurrences,andsomightappear togivecredenceto the notion thatmatter itself is a spontaneous occurrence.While,however,thisstatisticalaspectdoesindeedimplyacertainloosenessor indeterminism in the observed behavior of quantum systems,such looseness never involves a coming-into-being from nothingwhatsoever.Forthereisalwayssomethingphysicalalreadyinexistenceonwhich thebehavior is predicated, namely, thequantum systemsthemselves. Thus, in radioactive decay, unstable atoms constitutethe already existing systems; in the pair production of elementaryparticles, there are underlying quantum fields. Extrapolating, then,from such examples to matter in general, it is clear why quantumstatisticsfurnishesnowarrantfortheideathatmatterhascomeintobeingfromnothing.

Other, more positive reasons for rejecting this idea includethe conservation laws of physics and the materiality of time. Theconservation laws, which imply that the total amount of matter inexistencedoesnotchangeovertime,appeartocontradictthethesisthatmattercame intobeingat somepoint.For ifmatterdid indeedbegintoexist,therewould,priortothemomentofitsbeginning,existanemptytime,thatis,atimewithoutmatter,implyingthatachangeinthetotalquantityofexistingmatterhadoccurredatthatmoment,contrarytotheconservationlaws.Thisargumentassumes,ofcourse,that time is not itself material, whereas general relativity seems toindicate the contrary, insofar as it identifies the geometry of spaceandtime,takentogether,withamaterialentity,thegravitationalfield.

8. Lucretius(1997:7-11).

result, we shall infer that matter is itself a locus of metaphysicalnecessity,6 that it contains the reason for its existence within itself,therebyprecludinganextramundaneoriginbothofitandultimatelyofallthingsthatdependonit.7

3. How to Explain the Existence of Matter

Webeginourtreatmentbyclarifyingfurtherjustwhatisinvolvedinexplainingtheexistenceofmatter,aswellaswhatisnotinvolved,foritiseasytogoastrayhere.

There are twopossibilities to consider: eithermatter has alwaysexistedor itbegan toexistat somepoint.But if itbegan toexistatsomepoint,andif,asLeibnizsupposed,existingthingscannotderivefromanythingbutexistingthings,thenmattercanonlyhavederivedfromsomethingimmaterial.Why,however,shouldweacceptLeibniz’ssuppositionhere?Whycouldnotsomeexistingthing,suchasmatter,havecomefromnothing?

Of course, it seems prima facie preposterous that itmight have,forthiswouldjustmeanthattheexistingthinginquestionhascomeintobeingwithoutanycause,thatithassimplypoppedintoexistenceungenerated.Andifmaterialthingscouldcomeandgointhatfashion,irrespectiveofthepresenceorabsenceofanythingelse,therewouldbenorhymenorreasontoNaturebutonlyarhapsodyofphenomena,a

6. Nolan(2011)hasnotedthevarietyinusageof‘metaphysicalnecessity’incon-temporaryfundamentalenquiry.AlthoughweadhereinthisarticletoLeib-niz’susage,ourapplicationofthetermtomatterendsupbeingratherKrip-kean,insofarastheestablishmentofmetaphysicalnecessityinthiscaseisnotapurelyaprioriaffair,akintotheontologicalargumentforGod’sexistence,butdependsonprinciplesthathaveprovedtheirworthaselementsofem-piricallysuccessfultheoriesofmatter—eveniftheseprinciplesare,inthem-selves,amongthemostrational(i.e.,leastempirical)ofallphysicalprinciples.

7. Strictly speaking,our resultdoesnotpreclude things that existbeyondor“outside” thematerialworld, that is tosay, independentlyofmatter. Itonlyprecludesthemfromconstitutingtheoriginofmaterialthingsandtheirmo-tions—thoughonemightwellaskinthatcasewhatthepointwouldbeofpositingsuchinconsequentialtranscendentbeings,andwhatwarranttherecouldbeforbelievinginthem.



of thingsor statesorphenomena in termsofearlier thingsor statesorphenomena.Themotionsoftheplanets,forinstance,orelectricalconductivityoreyecolorarenoneofthemexplainedinthisefficient-causalmanner,butintermsofconcurrent,underlyingcauses.Inthisway,too,areallmaterialcompoundsexplainedintermsofthechemicalelements,allchemicalelementsintermsoftheiratomicconstituents,andallatomsintermsofthesubatomicentitiesthatcomposethem.

Therefore, when Leibniz, in addressing his reader or imaginaryopponent, writes, “you assume only a succession of states”,11 wefind ourselves unable to concur. For in addition to the temporalorder of succession, we assume an atemporal or ontological orderof composition, andwithout in anyway leavingmaterial nature. Inotherwords,weconsidermaterialnature tohaveontologicaldepth,whichopensupthepossibilityofmattercontaining itsownground.Furthermore, it isobvious thatonly in termsofphysicalcauses thatareontologicallyratherthantemporallypriorcouldtheexistenceofeternalmatterbeexplainedinascientificway.

Yet here, too, a difficulty arises. For however far we descend intheontologicalorderofcomposition,wealwaysseemtoendupwithmaterialobjectsofsomesort—objectswhichare,forthetimebeinganyway,unexplained.Thus, if thematerialobjectscurrentlyheld tocompose the atomwere someday adequately explained in termsofstillmore fundamental objects, suchas supersymmetric strings, theexplanation provided would not explain the more fundamentalobjects themselves, leaving us bereft of the very thingwe seek: anexplanationofmatteringeneral.Nor,obviously,couldthisdifficultybeovercomebypositingabottomlesshierarchyofmaterialobjects,forthenwewouldbefacedwithanontologicalanalogofLeibniz’sinfinitetemporalsequenceofstates,noneofwhichexplainsthewhole.12

11. Leibniz(1989:149).

12. Leibnizhimselfactuallypositedabottomlesshierarchy inmatter,asSchaf-fer(2003:499)hasnoted.ButwhereasSchafferchampionsbruteontologicalinfinitisminmaterialistmetaphysicsasaseriousrivaltofoundationalism(initsvariousforms),Leibnizappears,inhismaturephilosophyatleast,tohavetakentheinfiniteontologicalregressioninmattertobeexplicableintermsof

Werewetoassert,then,thatmatterbegantoexistatsomepoint,wewouldalsohavetoassertthattimebegantoexistthen,whichimpliesthattherewasatimewhentimewasnot,amanifestabsurdity.9

Thus,therearegoodscientificaswellasgoodphilosophicalreasonsfordiscountingthepossibilitythatmatterhascomeintobeingfromnothing. Indeed, the reasons adduced above urge us very stronglytoward theviewthatmatterhasnotcome intobeingatall,buthasalwaysexisted.This,atanyrate,isthescenariothatLeibnizconsidersinhisessay,andwhichweshallpursuehere.10

Evidently, since explaining the existence of matter in this casecannotinvolveshowinghowmattercameintoexistence,itcanonlyinvolveshowinghowitcontinuallyexists,orpersistsinitsbeing.Yettheideaofexplainingtheabsolutepersistenceofmattermightseemabitodd.Fordonotscientificexplanationsalwaysinvolveaccountingforthingsintermsofantecedentcauses,thatis,bywayofotherthingsthatarepriortothemintime?Andclearly,ifmatterhasalwaysexisted,therecouldnothavebeenanythingwhichexistedbeforeitdid.

It turns out, however, that not all explanations in naturalscience—perhaps not even the majority—involve the explanation

9. Demonstrations, such as that in Hawking and Ellis (1973: 356-359), of aninitial cosmic singularity, might seem to be at odds with this conclusion.However,thisandothernon-coordinatespace-timesingularitiesinmodelsofgeneralrelativitytheoryphysicistsdonotusuallyinterpretrealisticallyasdenotingactualfeaturesoftheuniverse,butonlypathologicallyasindicatingwherethetheorybecomesinapplicableor“breaksdown”andrequiresrevi-sion.See,forexample,Wald(1984:212,241).

10. Theother sideofKant’sfirst antinomy, that theuniverse, and thusmatter,musthavea temporalbeginning,otherwisesomethingapparently impossi-ble—thetraversalofanactualinfinityofstatesortemporalmoments—wouldhaveoccurred,hasbeenthesubjectofsomediscussionlately(Puryear(2014),TerErnLoke(2016),Dumsday(2016)).Aristotle (1934:vol. II, 181),havingdeniedthattimeconsistsofmoments,wasabletoaffirmtheeternityoftheuniversewithoutencounteringthisproblem.Asforthefinitistview,itsuffersfromaseriousdifficultyofitsown.Foritseemstoimply,asKant(1996:458-461)pointedout,theexistenceofanemptytimepriortotheworldofthings;andifEinstein(1982:375)isright,notimecanbeempty,justbecausetimeandspaceareinseparableandnospace-timecanbeempty,thatis,existinde-pendentlyoffield.



matterdependsonsuchforces,itfollowsthatdynamicsisconcernedwithmaterialexistenceaswellaswithmaterialmotion.

Itisonething,ofcourse,tousedynamicaltheorytoexplainhigherformsofmatterintermsoflowerforms,andquiteanothertoexplainmatteringeneralwiththetheory.Forthosematerialformsthatareatanygiventimedeemedtobelowestorelementalwillnotthemselvesbe explicable by means of a dynamical coupling of constituents,sincetheyareinvariablytreatedassimpleentities,asbeingswithoutconstituents—evenifinsomecases,asinstringtheory,theydonotalwaysseemtobehave likesimples, 14or,as in theancientatomism,theyconsistofinseparableparts.15Nevertheless,itwillappearoverthenexttwosectionsthatacertainanalogyobtainsbetweenexplanationsofmaterialmotionandexplanationsofmaterialexistencethatpointsto theway inwhichdynamics can after all be employed to explainmatterassuch.Inbrief,justasdynamicscanbeusedtoaccountfortheexistenceofmotioningeneralaswellastheexistenceorcharacterofindividualmotions,so,too,candynamicsbeusedtoaccountfortheexistenceofmatteringeneralaswellastheexistenceofspecificformsofmatter.

Itisalreadyclear,however,thatthekindofdynamicaltheorythatisable toexplain theexistenceofmatterwillnotbemechanistic incharacter.Thatis,theforceswhichthetheorypositswillnotbesolelyor principally of themechanical type. For by ‘mechanical force’,wemeanrelationalorother-determiningforce,forcethroughwhichonething(thebodyacting)determinesanotherthing(thebodyactedon),

material constituents’ actions—due to theposited inertial andmechanicalforcesbeingmerelyadditive—thisdoesnotobtain in thepost-Newtoniannon-mechanisticdynamicswithwhichthisarticleisconcerned.Here,onthecontrary,physicalforceisnotadditive(Gunn(2013:194-195)),fromwhichitfollowsthatat leastsomeinanimatematerialcomposites(hydrogenatoms,forinstance,butnotheapsofsand)aredynamicallyirreducibletotheircon-stituents—whichinturnopensthedoortonaturalkinds.

14. Baker(2016).

15. Lucretius(1997:20).

Butifexplainingmaterialobjectsintermsofothermaterialobjectsisunsatisfactoryforourpurpose,asitclearlyis,perhapswecouldtryexplainingthemintermsofphysicalentitiesofadifferentkind.Afterall,physicsconcernsitselfnotonlywithmaterialobjectsbutalsowithphysicalforces,ofwhichdynamicsisthegeneraltheory.Ournexttask,then,istoconsiderwhethertheexistenceofmaterialthingsingeneral,ormatterassuch,canbeexplainedbyusingdynamicalprinciples.

4. The Role of Dynamics

Butwhywouldweeventhinkthatdynamicalprincipleshaveanythingto do with the existence of matter? For dynamics, as traditionallydefined,isthetheoryofphysicalforceinsofarasitproducesorchangesmaterial motion. There is no mention in this definition of materialexistence. Yet it is obvious to anyonewho hasmore than a passingacquaintance with physics that dynamics is relevant to existentialquestions.For inthehierarchyofmaterialcompositiondiscussedinthe previous section—consisting of material compounds, chemicalelements,atoms,andsoforth—entitiesexistingathigherlevelsarenotforthemostpartsimpleaggregatesoftheir lower-levelconstituentsbut result fromabinding togetherorcouplingof the latter throughtheagencyofphysical forces, including those forcesresponsible formotion.13 To the extent, then, that the existence of higher forms of

somethingtranscendent(themonads),justashetooktheinfinitetemporalregressionincosmologytobeexplicableintermsofsomethingtranscendent(God).Forclarificationofthisimportantpoint,seePuryear(2020:360-365).(I am indebted to an anonymous referee for this observation and the sup-porting reference.)As for recentdiscussionsof foundationalism, includingSchaffer’s,itistypicalthatonlymaterialparticlesorphysicalpropertiesareconsideredascandidatesfortheultimatelyreal,whileagentsorforcesareleftoutofcontention.Ourview,however,isthatforcesarefundamental.AndifJorati(2019)isright,thiswasalsoLeibniz’sview,thedifferencebeingthatourprimitiveforcesarephysical,whereasLeibniz’swereimmaterialorspiritual.

13. van Inwagen (1990) has disputed this standard scientific view ofmaterialcomposition, arguing that all inanimate things except for elementary ma-terial particles are just aggregatesor “arrangements” after all and thusnotobjectsproper,unlikelivingbeings.While,however,Newton’smechanisticdynamicsappearstosupportvanInwagenhere, insofaras itconceivestheactionsofmaterial composites asmere sumsorproductsof theirultimate



Pneumatical force, being non-relational or only reflexivelyrelational, arises fromwithinmaterial things not between them, incontrast tomechanical force.As such, pneumatical force, unlike itsmechanical counterpart, isnotnecessarilyontologicallyposterior tomatter:itmaybeontologicallycoexistentwithmatter,oritmayevenbeontologicallypriortosuch,whichisobviouslywhatisrequiredifdynamicsistoaccountformatter’sexistence.

Classical physics identifies at least two pneumatical powers:Newtonianinertialforce,which(unlikemechanicalforce)actsnottochangebuttopreserveabody’sstateofmotion;andLeibnizianlivingforce, an original power of self-motion in bodies. Neither of thesepneumatical powers are, however, up to the task of explaining theexistenceofmatter,onaccountoftheirpurelykineticcharacter.Thatis,evenifthepowersaredeemedtobeinnatetoandthusconstitutiveofmatter,thesepowersdonot,throughtheiraction,actuallyproducematter,sincetheyaremerelypowersofself-motion.Assuch,theyareonlyontologicallycoexistentwithmatter,notontologicallypriortoit.

Thekindofpneumaticalforceweareseeking,ontheotherhand,is required tobenot only apowerof self-motionbut also apowerofself-generation,andassuchmustconstituteaninternalsourceofmaterialbeingaswellasofmaterialmotion.Ofcourse,theveryideaofself-generation,orofthatwhichcausesitself,mightseemtobeanimpossibleone.Forhowcouldsomething(e.g.,matter)thatdoesnotalreadyexistbeacauseororiginofanything?Andifitdoesalreadyexist,howcoulditthenbringitselfintoexistence?Thesimpleansweris:“Itcouldn’t”.Unless,thatis,ithappenstobeeternal,inwhichcaseitmightcontinuallybringitselfintoexistenceinthesenseofpersistingthroughitsownpower.Ourcentralclaiminthisarticleisthatdynamicaltheoryhasnowprogressedtoapointwhereitcomprehendssuchapowerofself-generationinmatter.

5. The Dynamical Explanation of Motion

Although this article has primarily to do with explaining theexistenceofmatter rather than theexistenceofmotion, there is, as

such as percussive force or Newtonian centripetal force;16 and it isobviousthatforceofthismerelyrelationalkindpresupposesmatter,and as such is ontologically posterior to matter. Therefore, evenif mechanical-type forces can be invoked to explain how materialcompositescometoexistfrommaterialsimples,theyobviouslycannotbeinvokedtoexplaintheexistenceofthematerialsimplesthemselves.Consequently,theycannotbecalledupontoexplainmatteringeneralorassuch.

Adifferentkindofforce,then,isrequiredforthispurpose.Butonlyoneotherkindofforcebesidesmechanicalforceisconceivable.Forif the latter is other-determining force, that leaves self-determiningforce as the sole remaining possibility. Since, however, there is noready-madegenericterminphysicsforthiskindofforce,letuscallitpneumatical forceinviewofthefactthattheGreekwordpneumaanditsderivativeshaveinphilosophicalandtheologicalcontextsalwaysreferredtopowersofself-determination,17irrespectiveofwhetherthesepowersweredeemedtobephysicalorspiritualinnature—althoughinthispaper,ofcourse,weareconcernedonlywithself-determiningpowersthatarephysical.

16. The term ‘mechanical force’ is sometimes restricted to contact forces. Buthere,weapplythetermtoallother-determiningforces.EinsteinandInfeld(1966: 10-11) likewise held themechanical viewpoint to admit other-deter-miningforcesofthenon-contacttype.

17. Thewordpneumaliterallymeansablowingorbreath.Its“firstextantuse”,ac-cordingtoKirk,Raven,andSchofield(1983:158-160)wasmadeinthesixthcenturyBCbytheGreekphilosopherAnaximenes,forwhomitsignifiedAir,thesupposedmaterialprincipleofallthings.AnaximenesconceivedAirinitscosmiccapacityasakindofworldbreathorworldsoul,bywhichtheuni-verseholdsitselftogetherandmaintainsitself.ThetermwaslateremployedbytheStoicsinasimilarway,withtheimportantadditionthatthepoweritdenotedwasdeemedthe immediateoriginofall rationality.Muchlater, intheseventeenthandearlyeighteenthcenturies,‘pneumatology’signifiedthatbranch ofmetaphysics concernedwith spiritual entities, and later still de-notedrationalpsychology,anaprioriscienceofthemind.(See,forexample,Hegel (1971:2-3)or the “pneumatology”entry inFlew(1984)).What thesevaried applications have in common, however, is that in every case, pow-ersofself-determination(ortheoriesaboutsuch)aredenoted,whichiswhywehaveinthisarticlechosentheword‘pneumatical’tobetheoppositeof‘mechanical’.



anextramundanebeing.18Thereis,however,noneedforustobotherwith such non-dynamical theories, in view of their gross empiricalinadequacy. Nor will contact forces more generally give us anytrouble,providedthattheyareunderstoodinthewaythatphysiciststodaygenerallyunderstandthem:asforcesthatarenotprimitive,butderivedfromnon-contactforces.

TheNewtoniandynamicalexplanationoftheexistenceofmotion,then,runsas follows.First,westipulate,aswedidwithmatter, thattoexplaintheexistenceofmotionistoexplainnothowitcameintoexistence,buthowitpersistsorcontinuestoexist.InNewtonianphysics,thepersistenceofmotionisexpressedbythelawsfortheconservationof the totalquantityofmomentum,where linearmomentum is justtheproductofmassandvelocity,whileangularmomentumis(inthesimplestcase)theproductoflinearmomentumandthedistancefromapointoraxis.Whatweareseeking,therefore,istoexplaintheselawsintermsofNewtonianimpressedormechanicalforce.Thisturnsouttobeveryeasyfor linearmomentum,sinceitsconservationfollowsdirectlyfromNewton’sSecondandThirdLawsofMotion.Forangularmomentum,theexplanationlikewisefollowsfromtheselawsbut ismoreinvolved,19soweshallonlyconsiderthelinearcasehere.

Newton’sSecondLawofMotionstatesthatthechangeinthelinearmomentumofabodyisproportionaltotheforceimpresseduponit,while his Third Law states that for every impressed force, there isanotherforceofthiskindwhichisequalinmagnitudebutoppositein direction to the first. It follows that the change in momentuminducedbythefirstforceisequalinmagnitudebutoppositeinsignto the change inmomentum induced by its reciprocal complement(and so on for every pair of reciprocal impressed forces). In otherwords,thesetwochangesexactlycounterbalanceoneanother,sothatthereisnooverallchangeinlinearmomentum.Thetotalquantityofrectilinearmotionisthereforeconserved,whichiswhatwesetoutto

18. Descartes(1985:vol.I,240).

19. Goldstein(1980:6-7).

wementionedintheprevioussection,animportantanalogybetweenthe two that points us toward the correct explanation of materialexistence. Furthermore, a dynamical and thus purely physicalexplanationof theexistenceofmotionwouldunderminesubstancedualism, as per our remarks in Section 1, and thereby permit us totakeourdynamicalexplanationoftheexistenceofmattertobealsoadynamicalexplanationoftheexistenceoftheuniverseassuch.Finally,sincethedynamicalexplanationofmotionis theeasierexplanationtograsp,appearingasitdoeseveninNewtoniandynamics,itallowsustointroduceinarelativelystraightforwardwaythekeyideasthatareneededtoappreciatethedynamicalexplanationofmatter,whichdependsonresourcesfrompost-Newtonianphysics.Letusthereforebeginwiththeeasiercaseandproceedtothemoredifficult.

ThefirstthingtoobserveisthatNewtoniandynamicsisaninstanceofmechanisticdynamics.Andwhile,aswepointedout,adynamicsofthistypeisunabletoexplaintheexistenceofmatter,itiscapableofexplainingtheexistenceofmotion,becausemotion,unlikematter,is not prior tomechanical force.At least, that is trueofNewtoniancentripetalforce,whichactsevenwhenbodiesarenotincontactwithoneanotherandnotmovingrelativelytooneanother.Ontheotherhand,inthecaseofprimitivecontactforces(assuming,forthemoment,that such forces exist), it ismanifestlyuntrue. Forhere,mechanicalforcearisesonlywiththepressingofonebodyuponanother,resultingeitherfromacollision,whichrequiresapriorrelativemotionofthetwobodies,or,inthecontextofamechanicalmedium,fromamotionpre-existing in thewhole.Eitherway,motion isprior tomechanicalforceinthiscase,andsocannotbeexplainedbythelatter.

Consequently, non-dynamical theories of matter, such as thoseof the ancient atomists and Descartes, who conceived matter asinert and so allowed that bodies can affect one another only bycontact,areunable toaffordaphysicalexplanationof theexistenceofmotion.Descartes,accordingly,explaineditsexistenceintermsof



atmost, on their differences in position, that is, on their distancesfromoneanother.For if the force’smagnitudedependedmerelyontheir positions, reciprocity would not in general obtain, given thatinteractingbodiesalwaysoccupydifferentpositionsfromoneanother.Accordingly,Newtoniangravitationalforceisindependentofposition:its strength depends only on the inverse square of the distancesbetweenbodies.

Now, thisposition-independenceofmechanical forceconstitutesan invariance or symmetry of the force, but a different kind ofsymmetryfromthereciprocityofmechanicalforce.Inthefirstplace,itisnotareflectionsymmetrybutatranslationsymmetry:itsignifiesthattransportingasystemofinteractingbodiestoanyotherlocationinspacewouldnotaffectthestrengthoftheforcesacting.Theseforcesarethereforesaidtobesymmetricorinvariantunderspacetranslations.Butthissymmetryis,inthesecondplace,internal21inthesensethatitobtainsforeachindividualinstanceoftheforce,whereasreciprocityonly ever applies to pairs of forces: to a mechanical force and itsreciprocalcomplement.Thus,internalsymmetryiswhatcarriesovertopneumaticalforce,andsoitisthiskindofsymmetrywhich,inpost-Newtonianphysics,enablesustofurnishadynamicalexplanationnotonlyoftheexistenceofmotionbutalsooftheexistenceofthatwhichmoves,namely,ofmatteritself.

6. The Dynamical Explanation of Matter

The first step in the dynamical explanation ofmaterial existence istoidentifytheconservationlawstobeexplainedandthedynamicalprinciplestobeusedinexplainingthem.

The conservation laws are just those for electrical charge, theweakisospinandcolorchargesofnuclearphysics,andgravitationalcharge or energy. For these conserved quantities are not merelykinetic, like linearandangularmomentum,but“substantial”,andassuch, constitute thematerial sourcesof the four fundamental kinds

21. Thisusageof‘internal’isdistinctfromtheusagethatdenotesfieldorgaugesymmetriesasopposedtospace-timesymmetries.

show.Ananalogousdynamicalargumentholdsforcurvilinearmotion.That dynamics enables us to explain the conservation of the totalquantityofmotioninamerelyphysicalwayimpliesthattherecouldbenoimmaterialcontributiontothisquantity,contrarytosubstancedualism.20

Evidently, the decisive factor in this dynamical explanation ofmotion is the reciprocalnatureofmechanical force as expressed inNewton’sThirdLawofMotion.Thatis,theexistence(i.e.,persistence)of motion has been explained in terms of the reciprocal action ofsuch force.We shall see later that something similar obtains in thedynamicalexplanationofmatter,althoughitisclearthattheanalogywill not be exact. For the notion of reciprocal action only makessense in the case of mechanical force, which is other-determiningor relational, whereas pneumatical force, which is required for theexplanationofmatter,isself-determiningforce.Assuch,itcannothavea reciprocalcomplement.Whatweneed tonotice, therefore, is thatreciprocalactionisakindofsymmetricaction:amechanicalforceanditsreciprocalcomplement,beingequalandoppositetoeachother,are,sotospeak,mirrorimagesofeachother.They,orrathertheirvectormeasures,exhibitreflectionsymmetry,andindynamics,thiskindofsymmetryimpliesanother,whichpertainsnotonlytomechanicalbutalsotopneumaticalforce.

Specifically,thereciprocityofNewtonianmechanicalforceimpliesthat such force cannotdependon thepositionsof bodies, but only,

20.In his recent defence of substance dualism, Swinburne (2013: 112-115) at-tempts to circumvent conservation arguments from classical physics byclaimingthatinquantumphysics,Heisenberg’sUncertaintyPrincipleimpliesthat the conservation lawsholdnot strictlybutonly statistically.However,asweshallindicate,analogoustheoreticaldemonstrationsshowingthattheconservationlawsholdstrictlyalsoinmodernfieldtheories,includingthoseofquantumphysics,revealthatSwinburneismistakenonthispoint.Heisen-berg’sUncertaintyPrinciplepertains to theappearanceormeasurementofphysical things, as Swinburne acknowledges, but if theuncertainties it de-notesaretomakeroomfortheinteractionbetweenmaterialandimmaterialsubstancethatheenvisages,theyreallyneedtopertaintophysicalthingsastheyexist in themselves, something that theconservation laws, strictlyob-taining,andthedeterministicevolutionofthewavefunctionpreclude.



willalso(orrather)beexpressibleintermsofdynamicalvariablesoftheformψ(t,x),whichrepresenttheconfigurationsofphysicalfields.

There is, however, one further condition that our dynamicalprinciplemust satisfy. LikeNewton’s Second Law ofMotion, it hastopertainnotonlytothemotionofmaterialthingsbutalsototheircoupling,giventhatphysicalcharge,thepersistenceofwhichwearehereseekingtoexplain,constitutesthesourceofthelatter.Therefore,thepneumaticalactionmeasureappearinginourdynamicalprinciplewillnotbepurelykinetic(likethemeasureofLeibnizianlivingforce),butbesuchthatitcanadmitcouplingtermsaswellaskineticterms.

The general dynamical principle that satisfies these threeconditions and applies to all of the fields in modern fundamentalphysics, fermionic and bosonic, including the gravitational field ofgeneralrelativitytheory,isHamilton’sPrincipleofStationaryAction.23 Thisprinciple,whichisthemoderncounterpartofNewton’sSecondLawofMotion, states that physical systemsevolve in a such awaythat the first-order variation of a certain dynamical quantity, theiraction,vanishes.Theactionmeasure S,ascalarquantity,isanintegral

23.Hamilton’sPrinciple, aspreviouslynoted,we consider tobeagenuinedy-namicalprinciple—onethatdenotestheactionofrealphysicalpower—andthisenablesustouseittoexplaintheexistenceofmatterandmotion.Katzav(2004:212)asks:“Whyarethedeductionsthatthe[principle]affordsexplan-atory?”Theyaresobecauseapower isbydefinition thatwhichgeneratesthingsoreffectschange,andsucharepreciselywhatoneseeks toexplaininnatural science.Katzav, tobe sure, argues that the actionprinciple con-flictswiththeviewthatthereareelementarypowersintheworld.Butthekindofpowershehasinmindarethoseofdispositionalismordispositionalessentialism,powers that are “notwhollymanifest in thepresent” andbe-comemanifest“inresponsetoappropriateprompting”(2004:206),whereasthepowerdenotedbyHamiltonian“action”cannotbeofthissortduetotheatemporalanduniversalcharacterofitsprinciple.Ourinterpretationoftheactionprincipleasagenuinedynamicalprincipleismotivatedbyitsconcep-tualprovenanceinNewtonianandLeibniziandynamics,andbythefactthatitstandstomodernphysicaltheoriesjustasNewton’sdynamicalprinciplesdotothetheoriesofclassicalphysics,asageneralprincipleofphysicalac-tionthatconstitutes theformal frameworkofmoredeterminatedynamicallaws—one that likewise makes possible an explanation of certain funda-mentalconservationlaws.Somecommentatorshave,admittedly,arguedthatNewtonhimselfwasnotarealistaboutphysicalforce,butseeJaniak(2007)foracontraryview.

ofphysical couplinguponwhichall thehigherpropertiesofmatterdepend.Ifitcanbeshownthattheconservationofthesequantitiesisexplicableintermsofthepropertiesofphysicalforce,adynamicalandthus entirelynaturalistic explanationof the existenceofmatterwillhavebeenafforded.

The dynamical principles from which the conservation lawsof physical charge are to be derived consist, as in the Newtonianmechanicalexplanationoftheconservationofmotion,of(1)agenerallawofphysicalforceoraction,analogoustoNewton’sSecondLawofMotion,and(2)specificdynamicallawsthatconstraintheforcesactingto be symmetric, analogous to Newton’s Third Law ofMotion—or,more correctly, to the space-translation and rotational invariancesimplied by that law. The general dynamical law in this case differs,however, fromitsNewtoniancounterpart intwoways.For it is,andmust be, a pneumatical rather than a mechanical law, as we havealreadydetermined,anditmustalsobeapplicabletophysicalfields,sinceallofthemodernfundamentaltheoriesofmatterare,atbottom,fieldtheories,notparticletheories.22

Thesetworequirementsimplythatthemathematicalformofourgeneraldynamicalprinciplewill satisfy certain conditions.First, themathematicalmeasureofphysicalforceoractionappearingintheprin-ciplewill,likethemeasuresofinertialforceandlivingforce,beascalarratherthanavectorquantity.Foravectorforcemeasure,inpointingfromthethingactingtothethingactedupon,is“directional”andthusappropriatetoother-determiningormechanicalforce,whereaspneu-maticalforceisbydefinitionapowerofself-determination.Therefore,onlyascalarmeasure,whichhasamagnitudebutnodirection,willdo.Second,theprinciplewillnotberestrictedtodynamicalvariablesoftheformx(t),whichdenotethetrajectoriesofmaterialparticles,but

22. Thequestionofwhetherquantumfieldtheoriesshouldbeaccordedaparticleorafieldinterpretationremainscontentious(Deckert,Esfeld,andOldofredi(2019),Bigaj(2018)).Whatislessdebatable,ifindeeditisquestionableatall,isthefactthatthedynamicalvariablesofthetheoryarefieldvariablesratherthanparticlevariables,whichisthesolefactofrelevancetoourargument.



space-translation invariance, however, which involves continuousglobal27transformationsofthespatialco-ordinatesxi (t),threeoftheseinvariances or symmetries are gauge or field symmetries. That is,theyinvolvecontinuousglobaltransformationsofthefieldvariablesψi (t,x), where the transformation operators belong to the unitarygroups U(1), SU(2), and SU(3). The symmetries or invariances ofHamiltonianactionunderthesethreekindsoftransformationyieldtheconservationlawsfortheelectrical,weaknuclear,andstrongnuclearchargesrespectively,providedthattheactionisalsostationary.28Asforgravitational charge or energy, its conservation follows analogouslyfromthetime-translationinvarianceofHamiltonianaction.29

Buthow,exactly,dothesecontinuoussymmetriesofHamiltonianaction lead to the conservation of the four fundamental physicalcharges?Ineachcase,thesymmetrytransformationthatistoleavetheactionmeasureunchangedisappliedtotheboundaryorendpointsofthephysicalsystem’spath(inconfigurationspace)forwhichtheactionmeasurehasastationaryvalue.Normally,thatis,whenderivingtheconditionsunderwhichHamilton’sPrincipleobtains,theseendpointsare not varied but are held fixedwhile the path is varied, and theresulting conditions are a set of equations ofmotion for the fieldsinvolved.Butinthepresentcase,wheretheendpointsarevariedandthepathisthenspecifiedtobethestationaryone,differentconditionsappearintheformofquantitiesthataretime-constantsofthemotion,thatis,conservedquantities,oneforeachofthecontinuoussymmetrytransformations applied. This shows that if a physical system’saction is not only stationary but also continuously symmetric, thenthere is a conserved quantity corresponding to that symmetry, as

27. Thatis,transformationswhicharenotfunctionallydependentonspace-timecoordinates.

28.MandlandShaw(2010:221,225-227,391-395).

29.Goldstein(1980:588),Ryder(1996:85-88).Ingeneralrelativitytheory,ener-gyconservationanditsrelationshiptodynamicalsymmetryarerathermoreinvolved than thiscompactstatementcanconvey.See, forexample,Duerr(2019)andreferencestherein.

over kinetic terms and coupling terms that take on different formscorrespondingtothedifferentparticlesorfieldstowhichtheprincipleis applied,24 just as the Newtonian mechanical force measure F inNewton’sSecondLawofMotiontakesondifferentformsfordifferentmechanical systems. But Hamilton’s Principle itself—the stationarycharacterof the action, the vanishingof itsfirst-order variation—isthesameforallapplications.Fromthisvanishingcondition,aphysicalsystem’sequationsofmotionareeasilyderived.25

Inorder,however,toderiveandtherebyexplaintheconservationof physical charge, we require not only stationary action but alsosymmetricaction.26 Justas theconservationof linearmomentum inNewtonian physics is derived from the space-translation invarianceofNewtonianmechanical force, so theconservationof thedifferentfundamental charges in modern field theory are derived frominvariances of the action measure in Hamilton’s Principle. Unlike

24.Hamilton(1940:vol.2,160,167).Inquantumtheory,forinstance,thesetermsinvolvenottheordinary-numbervariablesofclassicalphysicsthatHamiltonhimselfused,butoperatorvariables.See,forexample,YourgrauandMandel-stam(1968:139)orSchwinger(1951:SectionII).

25. Goldstein(1980:43-45,548-552).

26.Ourclaimthatsymmetriesofacertainsortarefundamentalinnature,andthusexplaintheexistenceofmaterialthings,runscountertosomerecentlyexpressedviewson thematter.McKenzie (2014), for instance,doubts thatsymmetriesareontologicallypriortomaterialobjectsonthegroundthatitisunclearhowtocomprehendthemasgenuinelyphysicalindependentlyofsuchobjects.Wecontend,however,thatthisispossibleifonetakesthemtobepropertiesofphysicalforceofthepneumaticaltype.Comprehendingsym-metries in this dynamicalway alsomeets theobjectionposedbyRomero-Maltrana(2015)andBrownandHolland(2004),thatsinceonecanderivethesymmetriesoftheactionfromtheconservationlawsaswellastheconverse,noarrowofexplanationcanbeinferred.Yettheactionconceptitselfmustbegivenpriortoanyderivationofthesymmetriesofaction,andthisconcept,wemaintain, isnomeremathematicalconstruct,butdenotes realphysicalforce,andofsuchatypethatcanexplainbutnot, inturn,beexplainedbytheconservationofphysicalcharge.Romero-Maltrana(2015:366)assertstheconverse,that“conservedchargesexplainforces”,andheisinawaycorrectifby“forces”hemeansmechanicalorother-determiningforces.However,suchforces,wemaintain,arenotultimatebut,likephysicalchargeitself,ultimate-lyderivefrompneumaticalforce,andinsofararenotrealpowersbutatmostonlywell-foundedphenomena.



That the pneumatical power ofwhichHamiltonian action is themeasureisnotdeterminablefromwithoutfollowsfromthemeasure’sstationarycharacter.Fortheprincipleofstationaryactionis,ineffect,a generalization of Newton’s First Law of Motion, as Whitehead(1929:77)hasobserved—anextension, that is,of thenotionof freeorunconditionedmaterial action from the isolatedphysical entitiestowhichNewton’sFirstLawappliestosystemsofphysicallycoupledentitiestowhichhisSecondLawapplies.32Thestationaryorextremalpathofasystemofphysicallycoupledentitiesinconfigurationspaceis theHamiltonian analogue of the geodesic path in space-time ofan inertiallymoving Newtonian particle. In the degenerate case ofasystemthatconsistsofonlyonesuchparticle,thelatter’sgeodesicpathisatthesametimeapathofstationaryaction.Accordingly,non-stationarypathsinconfigurationspacearetheHamiltoniananalogsofnon-geodesicpathsinspace-time,andsowould,weretheyphysicallypossible,signifydeterminationfromwithout.

Thus, ‘stationary action’ denotes physical force that is constantor unconditioned in the sense that there exists nothing external tothephysicalsystemitgovernsthatconditionsit,asitconditionsthethingswithin thesystem itself. 33 In this respect, stationaryaction is

(Euler-Lagrange equations) arederivable from rather than identical to theprincipleofaction.

32.NeitherofNewton’slawsapplytophysicalfields,ofcourse,yetHamilton’sactionprincipledoesso,anditappliesequallytofreefieldsandtosystemsofcoupledfields.

33. Thedifferencebetweenourownrealistinterpretationoftheprincipleofsta-tionaryactionandthemodalonedevelopedbyTerekhovich(2018)comesintosharpestfocusatthispoint.WeregardHamilton’sactionmeasureasthemeasureofapowerthatisnotonlyrealbutalsonon-dispositional,withthestationarypathalonehavingphysicalsignificanceindenoting,aswesay,apowerthatisfreeorunconditionedfromwithout.Terekhovich,ontheotherhand, in accord with dispositional essentialism, takes the actionmeasuretobeameasureofphysicalessencethatisrealized,ormadeactual,onlyincertaincases,butwherea“collision”or“competition”ofpossiblepaths,sta-tionaryandnon-stationary,explainstheactualityofthestationarypath.Wenote also that Terekhovich takes inspiration from Feynman’s path-integralformulationofquantumtheoryon thebasis thatboth theactionprincipleand the path integral contain the same actionmeasure. Yet hemakes no

EmmyNoether30was thefirst todemonstratequitegenerally.Allofthis is rather technical, of course, evenwithout our employing thecorrespondingmathematicalsymbolism,andsoprovideslittlebywayofanintuitivegraspoftheimportantresultsthatNoether’sTheoremaffords.Therefore,letusnowattemptamoreintuitivejustificationofthem.

Noether’sTheoremshowsthatthefundamentalconservationlawsof physics can be explained dynamically in terms of the stationary,symmetric character of Hamiltonian action. The conservation lawsspecifywhatinmatterandmotionpersistsabsolutely,whatsuffersnooverallaugmentationordiminution.However,thelawsofstationaryandsymmetricactionthemselvesexpressconstancyofasort,notasitobtainsinmatterassuch,butasitobtainsinphysicalforce,andtheydosointwoways,pertainingrespectivelytotheexteriorandinteriorof a physical system. Intuitively, there could be no guarantee ofconstancyinaphysicalsystemif(1)thepneumaticalpowergoverningit were determinable from without, as, for example, NewtonianinertialforceandLeibnizianlivingforceare(insofarasthebodiestowhichtheybelongaresodeterminable),or(2)thegoverningpowerwere changeable in itself,making the system’s laws ofmotion alsochangeable, and thusnot laws strictly speaking.We thereforeneedto exclude these possibilities.Our principles of physical action anddynamicalsymmetry31excludethemasfollows.

30.Noether(1971).

31. BrownandHolland(2004:1133)denoteby‘variationalsymmetry’whatwecall ‘dynamical symmetry’, and reserve the latter term for “transformationswhichmapsolutionsof theequationsofmotion…intosolutions”,whileap-plyingtheformertosymmetriesoftheHamiltonianaction,asif“action”werenotadynamicalconceptafterallbutonlyamathematicalone.Theirusagemaybeinlinewithrecentconvention,buttoourminditwouldbemoreinaccordwiththeetymologyof‘dynamics’,andwithLeibniz’sintroductionofthattermtophysics,toapplyittoprinciplesandmeasuresofphysicalforceoractionratherthantoequationsofmotion,thesymmetriesofwhichmightbe better called “kinetic symmetries”. InNewtonian physics, of course, dy-namical symmetries and kinetic symmetries are identical, since Newton’sdynamicalprinciplesareidenticaltohisgenerallawsofmotion.ButinthehigherdynamicsofHamilton,thisisnotthecase:thegenerallawsofmotion



havelongbeenknown.Buttheyhavenot,sofaraswecantell,beeninterpretedaswehaveinterpretedthemhere,asresultsofexistentialsignificance. Noether’s Theorem in particular, which embraces allof theseresults, isnotgenerallyunderstood inanontologicalsenseas an existence theorem, but only methodologically as furnishing anefficient procedure or algorithm for deducing from the symmetriesof a physical system’s actionmeasure the corresponding conservedquantities,whichcanthenbeusedtofacilitatethesolvingofproblemswhenapplyingtheorytothephenomena.

OnepossiblereasonforthisneglectisthatdiscussionsofNoether’sTheoremanditsapplicationsarenotnormallyprecededbyacarefulanalysis of what it means to explain the existence of matter andmotion, suchaswehaveattemptedhere,andwhichhasconcludedthat explaining their existence involves accounting not for theircoming-to-bebutfortheircontinuing-to-be.Anotherpossiblereasonistheprevailingyetanachronisticunderstandingofphysicalforceasmechanical force, as something that arises betweenmaterial thingsratherthanfromwithinthem,makingitimpossibletograsphowsuchforce could constitute the origin or ground of matter in particular.Yetathirdreasonmightbethatfundamentalphysics,anddynamicsspecifically,aregenerally(andrightly)regardedasincomplete,fromwhichonemightnaturallyconcludethatanyattemptatthisstagetousedynamicstoexplaintheexistenceofmatterispremature.

Now,weagree thatdynamics is incomplete insofar asphysicistsstillacknowledgefourfundamentalcouplingsratherthanone,aswellas a number of different kinds of fundamental physical object (i.e.,differentkindsoffield)ratherthanasinglekind.Inshort,physicistshave not yet obtained a fully unified theory that both explains ourcurrentfundamentaltheoriesandisadequatetoalltherelevantknownphenomena.Butthisfact,inourview,concernsonlythespecific content ofdynamics,thenon-unifiedcharacterofitsactionmeasure,whereaswe have based our explanation for the existence of matter not onthiscontentbutonmatter’sgeneraldynamicalformasexpressedbyHamilton’sPrincipleofStationaryActionandacertainabstractand

akintoAristotle’sunmovedmover,34whichitresembleseveninname,althoughitsurpassesAristotle’sabsoluteinconstitutingnotonlyanunmovedoriginofmaterialmotionbutalsoanungeneratedoriginofmaterialbeing.

Yetstationaryactionis,aswehaveseen,notsufficienttoguaranteeconstancyorpersistence inaphysical system.Forwhile it excludesexternalsourcesofchange, itdoesnotdothesameforthesystem’sinterior.Inparticular,itimpliesnothingatallinthisregardaboutthespecificdynamicallaworlawsthatgovernthesystem.Andasystemwhose dynamical laws varied in characterwith time, place,motion,andsoforthcouldhardlybeoneinwhichthereisanycontinuityorpersistenceofthekindweareseeking,thatis,withrespecttoitsquantityofmatterandmotion.Therefore,werequirenotonlystationaryactionbutalsocontinuouslysymmetricaction.Forsuchactionis,bydefinition,invariantwithrespecttotime,place,etc.Itis,tospeaknon-technically,action that is in maximal agreement with itself. Thus, if stationaryaction is akin toAristotle’s unmovedmover, then symmetric actionisakintotheCartesiandeity,notinbeingtranscendentorimmaterial,butinsofarasitconservesthetotalquantityofmatterandmotionintheuniverseby“operatinginamannerthatisalwaysutterlyconstantandimmutable”.35

Tothisextent,then,canwegraspintuitivelywhytheconservationlaws of physics, and thus the existence of matter and motion, aredynamically explicable in terms of the stationary and symmetriccharacterofpneumaticalorself-determiningforce.

These results from fundamental physics, which concern therelationshipbetweendynamicalsymmetryandtheconservationlaws,

mentionofSchwinger’svariationalformulation,whichcontainsnotjusttheactionmeasure(inoperatorform)buttheactionprincipleitself,andwhichisarguablymorealignedwiththeclassicalunderstandingoftheprincipleasdenotingevolutionalongasinglepaththanwiththemany-pathsalternativeheproposes(Schwinger(1951:SectionII),YourgrauandMandelstam(1968:138-139)).

34.Aristotle(1934:vol.II,333-337).

35. Descartes(1985:vol.I,240).



matter,althougheternal,hasontologicaldepth,andofsuchakindthatitcontainsitsownground,inwhichcaseitwouldexistindependently.

As for (2), which has been accepted bymany philosophers, weconsidered this a genuine possibility but one that relies for itsplausibilityonthefollowingratherweakand,inourview,ultimatelyindefensible premise: that there is no good empirical or scientificwarrant for thinking that matter is anything but a primitive orunderivedentity.

Concerning (3), we again sided with Leibniz in rejecting theideathattheuniverse,andthusmatter,begantoexistatsomepointwithout therebeinganythingprior.Wedismissed this ideaonbothphilosophical and scientific grounds, including the conservationlawsofphysicsandthematerialityoftime.Thelatterreasons,indeed,urgedustowardtheviewthatmatterhasalwaysexisted,andthatascientific explanation of it could therefore only involve accountingforitspersistenceorcontinuedexistenceratherthanitscomingintobeing.

Option(4),whichwehavedefendedinthisarticle,callsforsuchanexplanation.Recognizing,firstofall, that ifmatter is tohaveanimmanentorphysical origin, the latter couldnot,withoutquestion-begging,beheldtoconsistofmaterialobjects.Fromthis,weinferredthatsuchanorigincouldconsistonlyofmaterialagencyorphysicalforce,thegeneraltheoryofwhichisdynamics.Itwasalsoclear,however,thatmechanisticdynamicalprinciples,suchasthoseofNewton,wouldbe incapable of explaining the existence ofmatter, simply becausemechanicalforceisrelationalorother-determiningforce,andassuch,presupposesmatter.Therefore,werequiredprinciplesofpneumaticalor self-determining force, and found suitable ones in Hamilton’sPrincipleofStationaryActionandthesymmetryprinciplesofmodernfieldtheory.Forphysicistshavelongknownthatiftheactionmeasureappearing inHamilton’s Principle is both stationary and symmetricin certain ways, it is possible to deduce the conservation not onlyofkineticquantities, like linearandangularmomentum,butalsoofelectrical, nuclear, and gravitational charge, and insofar explain the

general result within Hamilton’s dynamical scheme that concernsdynamicalsymmetry,namely,Noether’sTheorem.

Tobesure,wedidnotremainatthelevelofcompletegenerality,butdescendedtoparticularswhenwementionedthattheexistence—thatis, thepersistenceorcontinuedexistence—of the four fundamentalkindsofphysicalchargecurrentlyacknowledgedisexplicableintermsof specific dynamical symmetries, namely, those pertaining to theactionsofcertainkindsofphysicalfield.Butthiswasonlybywayofillustration,toindicatethatsuchresultsareobtainableinthecontextofphysicaltheoriesoftremendousexplanatorypower.Inthemselves,Hamilton’s Principle and Noether’s Theorem are very general andabstract, and as such, quite independent of specific dynamicaltheories.Thereisnoreasontoexpect,therefore,anyfutureandmoreunifiedphysicstoabandonthedynamicalandthuspurelynaturalisticexplanationofmatterandmotionthattheyafford.Indeed,anysuchastepwouldsurelyberetrogressive.

7. Conclusion

Prompted by Leibniz’s essay on the subject, and by certaindevelopments in general dynamical theory, we have in this articleenquired into theultimateoriginationof thingsandconsidered thefollowing possibilities: (1) that matter, eternal or otherwise, andconsequentlyeverythingthatdependsonmatter,havetheirultimateorigin in something extramundane or immaterial (this is Leibniz’sview);(2)thatmatteriseternalbutprimitive,andassuch,constitutesanoriginofotherthingsbuthasnooriginorgroundofitsown;(3)thatmattercameintobeingfromnothing;(4)thatmatteriseternalbuthasanimmanentormerelyphysicalorigin.

Inregardto(1),weagreedwithLeibnizthateveniftheuniversehasalwaysexisted,thiswouldnotprecludeanenquiryintoitsorigins.Butwedisagreedthattheviabilityofsuchanenquiryleadsinevitablyto the conclusion that the universe, and thus matter in particular,ultimatelyoriginatedinsomethingextramundane.Foritmightbethat



remarkable self-agreement that accords with the overall “harmonyof theuniverse” thatLeibnizspeaksof.37Forourpart,however, thisharmonyowesnot to theperfectionof anextramundanebeingbuttothoseimmanentdynamicalsymmetries—fromwhichtheexistenceof matter and motion are derived—being perfect in the sense ofcontinuousormaximal:inotherwords,beingsymmetriesofthesortthatledtheancientGreekstoreverethecircleandthesphereasthemostperfectofallgeometricalobjects.

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37. Ibid.,154.

persistenceofthesefundamentaland“substantial”physicalquantitiesindynamicalterms.

Fromthisresult,whichwasanticipatedandexpressedinabstractformbytheremarkabletheoremofEmmyNoether,wenowconcludethatmatteras objectisnotafterallprimitiveorontologicallyultimate,yet contains itsownground, consistingof itsown innerandpurelyphysical force. In other words, matter as agent is a metaphysicallynecessary being, a being whose existence follows from its owndynamical essence—this being such (pneumatical, unconditioned,maximallyself-agreeable)thatmattercannotnotexist.

Butiftheoriginofmatterisinternaltoitandmerelyphysicalbesides,then transcendent or immaterial origins are ruled out, contrary toidealism.Andifthisoriginisalsothesourceofallmaterialmotion,aswehaveindicated,itcannotobtainthatsomematerialmotionshavean immaterial origin, contrary to substancedualism.And if, further,mattercontainsitsownground,andisthusanindependentlyexistingentity,itoughttobedeemedsubstanceratherthanattribute,contrarytopropertydualism.Fromtheseresults,weinferthattheuniverse,ortemporalrealityingeneral,isfundamentallymaterialinitsconstitution,andthattheoriginofitsexistenceliesentirelywithinitself,contrarytoLeibniz.

Thisbringsus,finally, tothequestionofthegeneralcharacterofthe universe that is conferred by its origin. Leibniz,we recall, heldtheuniverse tobe incomplete, insofarashedeemed the reason foritsexistencetolieinsomethingextramundane.Yethealsoheldittobe“themostadmirablemachine”and“thebestrepublic”,36owingtothe metaphysical and moral perfection of its transcendent ground.In regard to thefirstpoint,weobviouslycannotagreewithLeibniz,sinceweholdtheuniversetocontainitsowngroundandthustobecompleteandsufficientuntoitself,makingittothatextentsuperiortotheuniverseasheconceivedit.Astothesecondpoint,weconcedethat, at the fundamental level at least, temporal reality exhibits a

36. Leibniz(1989:153).



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on the ultimate origination of things

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