What is a Law of Nature?

184 Pages·1983·1.57 MB·English

by  D. M. Armstrong

Cotnetns
Acknolewdgeenmts X
PART 1A critoifq uRteeh ugel artihteyo ry 1
1 Introductory 3
1 Tihmep aonrctoefo utro pic 3
2 pAo ssibdlifiefc ulitniy n vteiasgtgio nutro pic 5
3 Assputmions 7
4 TRheeg luartihteyo ry 9
2 Critioqfu eRt ehega urlitthye o()r1Ty:h ep orbleomf
acicdenutnoaimrlfi ties 11
1T heN aivRee gluartihteyoo rflya w 11
2 Clasastiiofiofccn r iitsimocsft hRee gluarity th1e2o ry
3 Signl-ecausneoi rfmiiets 13
4 Howt op asforsm s ignl-ecausneoi mrfittioems u lti-
causneoi rfimties 15
5 Howt op asfrsmo lolcu anoirfimtiteoHs u mean
unoimrfities 17
6 Unerailzepdh yslpi ocsbasiilities 17
7 Humeuannoi rfimtsiw eitnho- neixtsesnutjb cets 19
3 Critoifq uRteeh gelu artihteyo( r2y) 24
1 Spiaatt-emplollryia miltaewds 24
2 Locauln oimrfitaisle as ws 26
3 Infiniqtuaelliylfi aewds 27
4 Proabbiislltaiwcs 29
5 Proabbiislltai:wc s trheet rteoPa ots imt ivis 35
6 Functlliwaos n a 37
4 Critioqfu eRt ehgel uairttyh eo(r3y) 39
1 Lacokfi nnceorn nection 39
2 Lawosf tnuaraesP rciinpolfEe xsp lanation 40
3 TheP arxaedosofC onfirmation 41
Vll
4 Tphreo bolfec mo uenratfcutals 46
5 TheP robolfeIm n duction 52
5 Cant hRee gultahreiobtreysy o ipshticated? 60
1 Perlmiinary 60
2 Epistreetmisricct uipoonun n iformities 61
3 TheR esilsiloeuntciyo n 64
4 Syesmtatriecs triucptouinno oinrfsmi iets 66
PARn TL awosfn tauraesrl eatiboewnteseu nn irvasels 75
6 Lawosfn ateau srrl eatibotenwseu enni vaelrss 77
1T hen eefdoru nivaelrss 77
2 Thet heoorfuy n iversals 81
3 fiAr fsortm ulation 85
4 Lawassu nivaelrss 88
5 Cauisoaantsa r elabteitoewnnpe atriculars 93
6 Neceastsnii,uot nivearnsldaa lwss 96
7 Advantaangsdeo sm desi avdangteoasfc onceoifv ing
lawosfn atausrrl eea tibotenwseu enni svlaesr 99
8 Braith'waasni Pdto eprp'easr gument 170
7 Functliaownsa l 111
8 Unisntantliaawtse d 171
1T ooely'csa ses 117
2 Tooely'cso lnucsions 118
3 Tooely'csa sselosv ebdyt hien trioodonufp c otwres?1 21
4 sAec ptitcramelean totfT ool'ecsya ses 132
5 Uninstalnatwwisia ttnheo dm ilcliaym psoisbaln-et e
cedents 162
9 Proabbiisltic laws 182
1 Tfhorem o fp roabbiislltaiwcs 182
2 Proabbiislltaiwcas sp roabbiloifnt eicseeiss tatio1n3 1
3 Othetry poefps r oabblitiislca ws 153
10F urthceorn esriadtcioocnnesr ntihnfeorg m o flaws 173
1 Sicentiidfiecn tification 173
2 Lawwsi tuhn ivesorcspael 104
3 Arteh earneEy x lcusliao?wn s 134
4 Irolna wasn Oda kelna ws 174
Vlll
5 Dijsnutcilvaew s 105
6 Dloa wasl walyitsnh kpe r opieeorsft tmheeo jbsceat?1 35
7 Forlmp aorpretioefNs e cseisitoant 155
11A rteh lea wosfn atnuercese asroyrc oinntgte?n 185
1 Arguemnftorst hnee cseisotflya ws 195
2 SrtonNge ceys sit 136
3 WeaNke cessity 166
4 Uninsitaeatdln atws 196
Conlcusions 127
Wokrsc ited 147
Index 177
IX
Acknowldegemetns
I acmo nisocuosfg redaetbt toms a npyoe plient hceo mspiotoifo n
thiwso r.k wIo ulldi kteot haJnokh n BMaiccohnBa,re allde ,y
GregoCruryr iPee,t Feorr rsetL,a ureGnocletd es,i Hnerbert
HochbeFrrga,Jnc akk osnB,r ucLeag ntrDya,v iLde iw,sC hris
Morntse,eL neOn' NeiDlalv,iS dna ofrJda,kc S marDtav,iS dot ve,
RichSawridn burCnherS,iw so yMearr,t Tiwne edPaelteVe,ar n
Inwgaeann d JWoakhtnin.s hIo pteh Iah ta vneol tet af nybody out.
Speciaficck nloewdgemoenn ttpsia cruploairn tmsa daiernt e h e
te.xB tuIth ave rescome uicvvhea dal bulceo mmetnhtaI k tn ow
thtahte irsse o moefi wth iIch ha vfeia lteoda ssiilmaatnpedr ofit
formI.h ave laelasrgonr ted aeatfa orlm m ys tudientn htceso urse
ofg iivnsge minoantr hsLe a wosf N autraet t hUen iverosfi ty
Syndey tahnUedn iveorfTseixtaayAts u is.nt shI oultdo ltihkaen k
AnhteBaan kfo,fP aTtr oinffoa fnJda kciWea ltfeorrm uhct yping
anrde tyopfid nrtga.s f
Il eatvoe ltahmseet n toifom ny q uistpeie acdle bttoM ichael
Tool.Ae syI h opteh attht ee xmta kecsla erh,eh aesv erhyewre
influemnyct ehdi nkointn hgti hsro ny daifinfcudl tto poiftc h e
natuofrt ehl ea wosfn at.u re
SydnUeneyisr vyi t D.M .A.
1982
X
PARTI
A criuiqetof
thReeg ualirytt heory

1
Introyd uctor
THIEMP ORTANOCFOE U RT OPIC
1
Theq ueiso'tnWh aitas l aowfn ateu?ir'asc entral forqt uhees tion
phliosyo opfhs icen.Bc ueit tism portgaonebcsee y otnhdri esl a­
tiverletiysr ctceodn tteoxe tm brea gceneerpsaitl emolaongdy
metaph.Iy nts hisiccesst iIwo inl ld ifisrcsttuhi sems pr otaonftc hee
quesftorit ohpneh isloopohfsyi c encet haeinntid'sm protaein ntc he
widcenort e.x t
Nautrasilce ntcrea diltlciyoo nncaeirtlnsfwse i thl eaattsh tr ee
tas.Tk hsefi rsits dtios ecrot hvgee ograanphdhsi yt oorfty h e
uneirvstea,k 'iengogg ra'tp oh ycaolsvlpe eara c nd t'oh'rti yocs over
altli miecn,l udfiutnugtrm iee A.st rnoomiybs e ignnitnogg i vuesa
pictoufhr oewt huen ivaesrw shaeo illsea oiudit ns peaa cntdi me.
Soemo htenra tusricaelng cievuses a no vervioefmw o rree scttreid
spiaott-emrpaoalra es.
A secotnadist sko d icsover swohroatftts h ianngwd h astot rosf
porpertthyea rreie nt huen iverhsoew t ahneadyr c eo nstituted,
witphra ticeumlpahrau spiotsnh seo trso ft hianngtd h seo trso f
propeirntt eyr msw hoihfc o htetrh inagresex pnlea.d(i These
explamianyoe rrm sa yn obteu ltiemxaptlea .i)n ers
Thet hitradis skt o s tatthleea wwsh itchhte h gisin ns paacned
timoeb e.Oy rp,ut tiinitgn ttehreum ssei dnd ecsribtihsneeg c ond
tastkht,eh itradis tsko s tatthleea wwsh ichs olorifttn h ki wnigt h
sortt hgoi,afn n pdr oeprwtiyt phr orpt.ey
Itm ayn obte o bvitohuastt h eirsae s ceontda stkob ed is­
tingufiorsmht ehder dtB.hu icto nstihdseeic re ntdiifiseccr oyv that
heaitsm olecmuoltai.orI n its voiobtuhsta htii nsso ath sitioacrl/
gegoraphtircu.at slhIhl aalr gauatel atert hpiaoittins no attl aowf
natuerveea,n' birdge (lCa.h1 w,0'S ec1.)I .ti _s s moetihndgi­ f
free:ni tgti vtehcse o nisttutoifpo rano tpyeo,rrr anogfpe r orpte,i es
int eromfms orueli tmaptrepo eer.ts( iIcto ubleds atiodg ivteh e
'egograp'oh fayp rorpt.ey)
3
Whaitts ruitse h tahtte h reeneq uiarriiene escx atbrblioyu nupd
witehah co hte.Tr helyo cgailplrye suepaphoco hsteear n cda onn ly
bep ursiunce odjn nuctiwointeh ah co hte.rN evretlhseest,h eayr e
distinbgl.ue isha
If dtichsoev eorfy l tahweos fn autrieos n oef tthhrege reet arta ­
dititoansaoklfns au trsailce ntcheet,nh n ea tuorfale a owf tnuare
must acb een torntaogllci oaclo nrcnfe ort hpehl iosoopfhi yse cn.c e
Asf or tihmep toaren csocfi eintlcs,fee t Ia kiet' sav nugarrdo lien'
thgeia nionfkg n owleadngodre/r easbolbneea laibeoftu htwe o lrd
tob eo bvieonuogsuh .
Howevoeurqr,u es'tWihoaintas l aowfn autr?ei'os f i lswlti der
phisloophlii mcpatoarn.Tc oes eweh ,yw em aya ppeaHlu m.te o
Humseia d( rTetaiBske1 ,P, tI ISIe,Ic I.t) h tahtoe n rlleya twihoinc h
enabulste osi nefrfo rmo bservmeatdt eorffs ca t utnoo bserved
maetrtosff ca tit sh ree laotfci aounas need ffe c.It nfo s uhcr leation
extieswde,w ouhladv ew anyo r teoa bseoyno ndo borsuveirao t.n s
Humsep oel kitotfllae.wN sevtehresli,ect sa bnes iadt hath ehled
al atwh eoorfcy a uasneedf fe cStte.t iansgi dmee ntthcaeol mo pnent
whihcehf ounidno ucro ncoefcp atu hsece o,en icvoeftd h ree lation
betweceanu asneed ffe cta l aa-swl irkeeil oan(tT.h lea iwnt urhne
coenicvoefda sa m erree gul.aW)re ic taytnh eorreiefn voke his
authotrosi atyy i tnehfraetn tcope rast icmuatltaeorrfu s n oebrsved
fcatw oulndo bte r eliianbfleer iefnt cheesr e nwole arweos f
nature.
Buti hsiar td rleyq utihrwaeetda ppteoHa ulm .eT hper oiptoison
is obevnioouuigsnih tl s.fTe hsei ceinstttr ytiont gae bsltihgseeh o ­
grapahnyhds i toorfty h uen obrvseepdot riont huoenf i vmeursste .
depeunpdow nh ahtet akteobs et hlea wosft huen ivee.Or thser­
wishee hiesl spl(.eI istts r ausleo o,fc ouer,ts hwahta htet aktehse
lawtsob ew ililn part dewpheahntetd a kutephshoe in s taonrdy
geogratpobh e)y.I no ridnalreiy,f cboyn ttr,wa hsemna king
inefrentcope asir ctumlaatrt eorfus n oebrsvfecadtw ,em aklei ttle
appeaaln wdto ou,lb deu nabtlose t atthese,u ppolsaewwdsh ich
grouonudir n fer.eB nuictt es sitiltslh c ea se otnth hsaeut ,ps piotion
thtahte arrene ol a,wt shiene frenwcoeusln do tr abtei .o nal
AsH umeu ndetrosoadn de mpha,si inzeferdenfcorem the
obrsveetdot huen oebrsvecde nittsro oa ulwr h olleiea fsh uman
bei.nW gesh aves tsj euehno,w evtehra,tt heiwrfee r neo laws
(whatael vaeiwr,s b ei rte guloarsr oimteyt ehli,snt egh) esnuh c
inefrenwcoeusln do bte r eilab.Hl eenctehn eo tioofln a iws o,r
4
shoublead,c entcroanlcf eorpe tp istgey.m oslIofow, e w ilallo s
wanttoe nquiinritetoo s n tgoy.lW oew iwlaln ttok nowwh aalt a w
ofn atui.rs e
Theirseo nter uelcyc envtirebiwrc,o g uhtto m ya ttenbtyi on
PetFeorrs rtwe,h iwcoh uld tehvaiarsdmg eeu n.Tt hiists h vei ew
thaatl,tu hghot hearrereg e ulariintt hwieoe lrsd t,h earrene ol aws
ofn atuSruhec .va i eawrg eweist chr iotfti hces Regtuhlreayoor fi ty
latwh maetr rege ularairitenui sfifecsi feornl ta wB.u ti,n Eltiim­ina
visstpi itir,tg oeosnt od eny tthhweao tr lcdo ntaanitynihsn g
exctehpetrs eeg uel.saT rhiiDtsii seaaprpavniceoewfa lwc anne ver­
thleesmsai ntatihanit ne frentcoet shu en oebrsvaerdre ei lable,
becaaulsteh,o tuhwgeoh lr di nso lta w-govieitr,s bn yel du,co kr
fors omoeht erre oansr,e gaurl.
Suhc vai e,hw owevweirhl,al v teof c aet hqeu eswthiaogtno od
reawseon c haanvt eot hitnhkta htwe o rilrsde lgau.Ir wti hlalv teo
fcaet hPer obloefIm n diuocnIt.tw ilblea rgueCdh aipn4t ,e r
Sceti5o,tnh naotR eghrutiyt hetow,rh iestohrne orh te pirse pared
toc lahli rse guiiltea'srl a'wc,sa ens cianpdeiu vcsetec ptmi.c is
2 AP OSBSLDIEFI IFCLUTIYN I NVTEISGATOIUNRTG O PIC
Som ucbhy w ayo f apofloroo ugtrio acp B.iu itmt a ys eetmob e
smoewhraetc alctiopt hlrioapsnhoti icnavlte isga.Ht eirowenem ay
relcSlao rctae'as nGd. E.e 'M'soaP orradoofx A lny'asI.iwfs e a sk
whasto rtt ihonafgn X is( ar igahctat l ,a owf n at.ur).te .h en
eitwheek rn ow wahnXa it,so rw ed on oItwf.e k nowt,h etnh ere
is no ansetkeh dqe u tteoiosn I.wf e d on ot ktnhoetwnh, e irse no
way bteog tihnie n vtgeitasoinT.h ee nquiiser iyt phoeirln estos r
impsois.b le
Theo rtdhooxa,n Idt hicnokr rselocutt,oi fo ntp huizszi tsl hea t
wed on osttr atw itbhal nikg rnnaocoefw haatnX i.sI nstweea d,
stawritta hnu nrefleucntlsicfevoecn,is oourms e replrya clgt riacsap
of tthhniegT .h ep hliosioclpoa hjbceitts o p afsorsm t htioas n a tri­
culaetxep,la incrdie ta soneodfw hgaratanX s ip.sW ed on ot go
formb lkan cigthodt a ylibgufhtort m,t wiglhtitod aiyglht.
Ins uhci nvteiasgtionasg rieta ti sa dtvosay atn htleae tgai,eswf ,e
casneu creildye yni tntisnafceosfX. G ivseuncp haa rdgimswe,c atno
some etxiteee nnttqh uedi ornwy.A na ccooufwn hta itit s bteao n
X issu gesgtbeydp hai slohope.r wIecf a ns ubree a i tsh Xa,att nh en
wec auns oeht etrh giswn hiwcehk noowrb leieavbeoa ut toc heck
5
thper opoascecdo oufnX t.B utw ithporauatid gmtsh weh ole
busionfte essst tihpnerg po olsb aecmeovse ry mmourcdehifi fcul.t
Ourp robilnseo mwb efour.sTe h earree s enucorp era adigms of
lawosfn atuCroesn.i dceorn tempnoartausrircyea nl.Ic iteps e ercft­
lyp ossibelpei,s ctaelpmloiyis bsltehw,ae td o knnootaw s inel galw
ofn autr.eT h,ii smt ayb e jocebteidsa,c ondseirahbalned itcoa p
answetrhipenh gis loophlqi uceas'tWihoaintas l aowfn taure?'
Tot hoijbsce itotnw,ao n swmearybs e m ade.
Fitre,sv etnoh ugwhec nap ointton os ecpuraraed iogflmw ass,
thseic enttihfirecio wehsi cwhen oww orwki th obavrei oau sly
resaobnlaaep pxriomattioao ltane s t osfo mrteeh laeal wo sfn autr.e
Foirof u trh eodriindeo snt ea rglrya tshpte r uattmh a npyoi n,t sit
woulbdei nexpltihctaahtbe slyhe o upledr msiomt u cshu ccuels sf
perdiocntT.ih eocrlaec tailculwahtiiccoahrnn es t muernnfor mt he
moowni tshlp ietc-osancdc ucraahnca yr dblemy e rfena teassW.ie
maym akaen' n iefretnocte h e ebxepsltan n'faor tmti hoper eidviec t
succoefcs osn tempsoicreanrttyih fiecot roty h ceo nclutshiaot n
suhct heory amtli erasrsootmro seft he olfan wast uorvees ro em
parotft heriarnw giet h toalcecaruca.ryb le
Actaul,li yste etmhsea vte tnhr eo guh-anadd-gyrne eeralizations
ofp r-ecsienptritafiicccw aidlso mr epreasr eenatsb oldneea rgeoef
approaxtiitmoogn e nulian.weC s onsiHduem'rees x amp:fi lrees
bunr,sb renaodui rsh,we atsesruf ofact.eI stfh ewreern eo lta ws to
whicthh egseen eirzaaltrieopnrses soeemrn otu agphp roximation,
thewnes houallbdled ea. d
Imta yb er emariknpe sads itnhgta htfii rsrs etp tloty h oejb cetion
formt haeb nsceoefp raadiignmdsi tchaietm epso rtiantn hficege h,t
agiasnte psticmis,co fd elvoepias ntagia scfttohreyoo rfdy e groefe s
clsoneestsot hter uatt hh,e oorfpy ra ttiralu. t h
Thes ecoannds wteor otjbhceet iiotsnh aetv,ei nf kwneo nwo
la,ww sed ok notwh feor mwsh iscatht emeonfltatswa .kC eondseir
thfeol olwinforgm ulwahei ucshde u mme:is
(1I)it as l atwh Fast are Gs
(2) lIatw iatsnFh h aaat asc earitpnr oabbi(l>i0 t,<y 1o)f being
a G
(3I)it as l atwh tahte a nqtuiPta ineQds c o-viansr uyca wh a y
thQa ti asc ertfuanicnt oiofPn ( jQ( )P).
=
Ittu ronusat sa,m attoeffcar t t,h tahtse o orfftun dmaentianlv es­
tiagtiwohni cwhea ruen dertcaaknig nelglpa yrrc oeed mweirteh
6