The Logic of Explanation

HERBERT FEIGL and MAY BRODBECK Editors UNIVERSITY OF MINNESOTA

ReadingsLn

THE, P H I LOS O P HY OF SC I E .N CE

New Tork APPLETON- CENTURY- CROFTS. INC.

The Logic of Explanation. A ND C ARL G. HE MP E L PAUL OP P E NHE IMl

Sr. lntrodu.ction in the world of our experience,to answer the To prprerN THEpHENorvrBNe question "whyf" rather than only the question "what?", is one of the foremost objectives of all rational inquily; and especially, scientific research in its various branches strives to go beyond a mere description of its subject matter by providing an explanation of the phenomena it investigates. While there is rather general agreement about this chief objective of science,there existsconsiderabledifference of opinion as to the function and the essential characteristics of scientific explanation. In the present essay,an attempt will be made to shed some light on these issuesby means of an elementary survey of the basic pattern of scientific explanation and a subsequentmore rigorous analysisof the concept of law and of the logical srructure of explanatory arguments. The elementary survey is presented in Part I of this article; Part II contains an analysis of the concept of emergence; in Part III, an attempt is made to exhibit and to clarify in a more rigorous manner some of the peculiar and perplexing Iogical problems to which the familiar elementary analysisof explanationgives rise. * Reprintedby kind permission of the authorsand the editorfrom Philosopltyof Science,r5, 1948. r This paper representsthe outcome of a seriesof discussionsamong the authors; rheir indiviilual contributionscannot be separatedin detail.The technicaldevelopments conrainedin Part IV, however,are due to'the first author, who also put the aniile into its final form. IPart IV omitted in this reprinting.l Someof the ideaspresentedin Part I[ were suggestedby our common friend, Kurt Grelling, who, together with his wife, bccamea victim of Nazi terror during the rvar. Those ideaswere developedby Grelling in a discussion,by correspondencewith the presentauthors,of enrergenceand related concepts.By including at leastsome of that material,which is indicatedin the text, in the presentpaper,we feel that we are realizing the hope expresscdby Grelling that his contributions might not entirely fall into oblivlon,

trVewish to expressour thanksto Dr. Rudolf Carnap,Dr. Herbert Feigl, Dr. Nelson and constructivecriticism. Goodman, and Dr. W. V. Quine for stimulating discussions

3 I9

SCIENTIFIC EXPLANATION

320

Penr I. Er,rnanNtenv

Sunvey

or ScrnNrrrlc

THE

ExpreNerroN

Sz, Some lllustrations A mercury thermometer is rapidly immersed in hot water; there occurs a temporary drop of the mercury column, which is then followed by a swift rise. How is this phenomenon to be explained?Tl-re increasein temperature affects-at first only the glasstube of the thermometer; it expands and thus provides a larger space for the mercury inside, whose surface therefore drops. As soon as by heat conduction the rise in temperature reachesthe mercury, however, the latter expands,and as is coefficient of expansion-isconsiderably larger than that of glass,a rise of the mercury level results.-This account consists of statements of two kinds. Those of the first kind indicate cerrain conditions which are realizedprior to, or at the sametime as,the phenomenon ro be explained;we shall refer to them briefly as antecedent conditions. In our illustration, the antecedent conditions include, among orhers, the fact that the thermometer consistsof a glass tube which is partly filled with mercury, and that it is immersed

LOGIC OF' EXPLANATION

32r

larity consistsin subsuming it under another, more comPrehensiveregularity, under a more general law.-Similarly, the validity of Galileo's law for the free fall of bodies near the earth's surface can be explained by deducing it from a more comprehensive set of laws, namely Newton's laws of motion and his law of gravitation, together with son-restatetnents about particular facts, namely the massand the radius of the earth' 5s. The Basic Pattern of Scientific Explanotion From the preceding sample caseslet us now abstract some general characteristicsof scientific explanation.We divide an erplanation into two By the explanarrmajor constituents, the explanandum ancl the explanans.'9 dum, we understand the sentence describing the phenomenon to be explained (not that phenomenonitself); by the explanans,the classof those sentenceswhich are adduced to account for the phenomenon. As was noted one of these contains certain llefore, the explanansfalls into two subclasses; sentencesC' C", . . , Cu which state specific antecedent conditions; the L, which represent general lau's.
discussionis explained by subsuming it under general laws, i.e., by shorving that it occurred in accordancewith those laws, by virtue of the realization of certain specified antecedent conditions.

phenomenon happen?" is construed as meaning "according to what general laws, and by virtue of what antecedent conditions does the phenomc. non occur?" So far, we have considered exclusively the explanation of particular events occurring ar a cerrain time and place. But the question ',Why?" may be raised also in regard to general laws. Thus, in our last illustration, the question might be asked: Why does the propagation of light confor.ur to the law of refractionl Classicalphysics answers in tcnns
I. Logical conditions of adequacy (Rr ) The explanandummust be a logical consequenceof the explanans; in other words, the explanandum must be logically deducible from the information contained in the explanans,for otherwisc, the explananswould not constitute adequategrounds for the explanandum. (Rz ) The explanansmust contain general laws, and thesemust actually be required for the derivation of the explanandum'-We slrall not make it a necessarycondition for a sound explanation, ltowever, that the explanansmust contain at least one statement wlriclr is not a law; for, to mention just one reason,we would strlcly want to consider as an explanation the derivation of thc gcrtcrll regularities governing the motion of double stars from thc lnws of celestial mechanics, even though all the statementsin tlrc cxplanans are general laws. (lt3)'Ihe explanansmust have empirical content; i.e., it rtrttst bc capablc,at least in principle, of test by expcrinrctttor tlllscrvir2'l 'frcsc tw o cxP rc s s i < l rrsdc , ri v c d fronr thc Lnti n ex pl andrc ,.w c rc :ttl oP totl i tr J rrt:ft:rr.ncc to rhc pcrh:rpi nt orc c us l ()ul l try tc rnrs "c x pl i c atrrl trttr"arrc l"c x pl i c l trts " i l r ot' rl c r ttr is. cxrcst'rvc tl rc l i rrt"r i ,,r u s c i rr tl rc c ori tc x t of c x l l l i c :tti orr of rrtc :trti rrg,-or.' ;rrrrl y s ()rt A l rl rrc v i :i tc tl ri tl c s ' i n l rrl t:k c tu pl i r.uri orr i rr rhi s scrrsc ,< ' f. O:urrrrp l (i rnc c pts l , p.5rl . rcl cr to tl rc l ri l rl i ogl up l ry rrt tl rc c ttrl of tl ti s rtrti t' l c '

t22

Scil,lN',t'ilrl(j l,)xl,t,AN^'l'toN

ti.r.-'l'his c.^clitio' is irnplicitin (Rr); for sincethc exprarranchurris assumedto describesome empirical phenomenon,it follows from (Rr) that the explanans entailsatleast one consequenc: of empirical character,and this fact confers upon it testability and empirical content. But the point deservesipecial mention because, aswill be seenin $4,certainargumentswhich have beenoffered asexplanationsin the narural and in the social sciencesviolatethis requirement. ll. Empirical condition of adeEmcy (Ra) The sentences constitutingthe explanansmust be true. That in a sound explanation,the statementsconstituting the explananshaveto satisfysomecondition of factual correctnessis obvious.But it might seemmore appropriateto stipulatethat the_explanans has to be highly confirmed by all tlie relevant evidenceavailablerarherthan thar it shouldbe tfue. This stipulation however,leadsto awkward consequences. Supposethat a certainphenomenpnwas explainedat an earlierstagi-of science, by means of an explananswhich was well supportedby the evidencethen ar hand,bur which had beenhighly disconfirmed by more recent empirical findirrgs.In such a case,we would haveto saythat originally the explanatoryaccountwasa correct explanation,but that it ceasedto be onelater, when unfavorable evidencewas discovered.This doesnot appearto accord with sound commonusage,which directsus to iay that on the basis of the limited initial evidence,rhe truth of the explanans,and thus the soundness of the explanation,had beenquite probable, but that the amplerevidencenow availablemadeii highly probablethat the explanans was not true, and hencethat the account in quesdonwas not-and had never been-a correct explanation. (A similarpoint will be madeand illustrated,with respict to the reqlirement of trurh for laws,in the beginningof $0.) ^ Some of the ch4racreristicsof an explanationwhicfi have been indicatedso far may be summarizedin the following schema: Statemenm of antecedentI conditions I Explanans General Laws I Descriptionof the l empiricalphenomenon fExplanandum to be explained J

' t' i l 1,1l ,o(;l (;

()l f

Ii x l ' l .A N A l ' l ()N

323

and a suitalllc set of statenrcntsC,, C., ' , C,, L' I'r, . . . ,I', is prrlvided afterwards,we speakof an explanationof tlrc plrcnotrtcnotrirt rlrtcs tion. If the latter statements are given and E is dcrivcd Prior to thc occurrence of the phenomenon it describes,we speak of a prcdictirlrr. It mav be said, therefore, that an explanation is not fully adequate rtrrlcssits explanans,if taken account of in time, could have served as a basisfor prcdicting the phenomenon under eonsideration.2o-Consequently, wltntcvcr v'ill be said in this article concerning the logical characteristicsof explnnntion or prediction will be applicable to either, even if only onc of tlteltt should be mentioned. It is this potential predictive force which gives scientific explnnatiortits importance: only to the extent that we are able to explain empirical fnc'ts can we attain the major obiective of scientific research,namely not ntcrcly to record the phenomena of our experience, but to learn from drem, by basing upon them theoretical generalizationswhich enable us to anticipnte new occurrences and to control, at least to some extent, the chartgcs in our environment. Many explanationswhich are customarily offered, especially in llroscientific discourse,lack this predictive character, however. Thus, it rttny be explained that a car turned over on the road "because" one of its tircr blew but while the car was travelling at high speed. Clearly, on thc ltnsis of just this information, the accident could not have been predicted, for tltc explanansprovides no explicit general laws by means of which the prctliction might be effected, nor does it state adequately the anteccderrt con' ditions which would be needed for the prediction.-The same poirtt rney be illustrated by reference to W. S. Jevons's view that every explnnation consists in pointing out a resemblance between facts, and that in sottte casesthis processmay,require no reference to laws at all and "may itrvtllvc nothing more than a single identity, as when we explain the apPcnrnnce of shooting stars by showing that they are identical with portions of n comet".3 But clearly, this identity does not provide an explanation of tltc phenomenon of shooting stars unless we PresuPposethe laws g
2aThe logicalsimilarityof explanation and prediction,and the ftct tlrnt ottc it lt directedto*tidr p"rt o""uir.n.es,'theothertowardsfuturc orrcs,is wcll cxltt'csser in l()rrrrrrtrr the terms "posrdictabiliry" and "predictability"usedby Reichcnbach Mcchanicsl, p. r3. 3 [P ri nciplcsJ, p. 533.

l2+

scil,;N t uit ( ; t , ) x t , t , ANA' t ' t ( ) N

that.a lurnp of strgartlisallpcarcd"bccause"it was put into hot tea, but it is surely not satisficd in many other c in the work of an artist are explainr neurosis, this observation may cont does not afford a sufficient basisfor Iiarities. In casesof this kind, an in considered as indicating some positir conditions adduced and the type of phenomenon to be explained, and as pointing out a direction in which further research miqht bi carried on in order to complete the explanatory account The type of explanation which has been consideredhere so far is often referred to as causalexplanation.If E describesa particular event, then the antecedent circumstances described in the sentenies C' Cr, . . . Crc may ; be said jointly to "cause" that event, in the sensethat there are certain empirical regularities,.expressed gy r!: laws L' Lr, . . . , L,, which imply that whenever conditions of the kind indicated by C' Cr, . . . , C, occui, an event of the kind described in E will take place. Statements such as L' L", . . . , L,, which assertgeneral and unexteptional connections be_ tween specified characteristicsof events, are custo-arily called causal.or deterministic laws. They are to be distinguishedfrom the so-calledstatistical laws which asserrthat in the long an explicitly staredpercentageof all fun, cases.satisfyilga given set of conditions are accompaniedby an ev-entof a certain specified kind. certain casesof scientific explanation involve ,,subsumption" of the explanandum under a set of laws-of which at leasr some are statistical in character. Analysis of the peculiar logical structure of that ty.pe.of subsumption involves difficult spe-ial problems. The present essay will be restricred to an examination of the causalrype of explanation, whicir hasretained its significancein large segmenrsof contempoiary science,and even in some areas where a more adequate account calls for reference to statistical laws.a

sectionr,) Similarly,Jevons, whosegeneral ly discussed above,stresses that ,,th-emost

t'l i l t

l .( x;t( i o tr l ,l .\l ,l ,AN Ai l ( ) N

t15

54. Expla'nation in the Non-Physical Sciences. Motiaational mLl 'l'alt'ological Approaches Our characterization of scientific explanation is so far basedon a study of casestaken from the physical sciences.But the general principles thus obtained apply also outside this area.5Thus, various types of behavior in laboratory animals and in human subjects are explained in psychology by subsumption under laws or even general theories of learning or conditioning; and while frequently, the regularities invoked cannot be stated with the samegenerality and precision asin pliysics or chemistry, it is clear, at least, that the general character of those explanations conforms to our earlier characterization. Let us now consider an illustration involving sociological and economic factors. In the fall of r946, there occurred at the cotton exchanges of the United Statesa price drop which was so severe that the exchanges in New York, New Orleans, and Chicago had to suspend their activities temporarily. In an attempt to explain this occurrence, newspapers traced it back to a large-scale speculator in New Orleans who had feared his holdings were too large and had therefore begun to liquidate his stocks; smaller speculatorshad then followed his example in a panic and had thus touched off the critical decline. Without attempting to assessthe merits of the argument, let us note that the explanation here suggestedagain involves statementsabout antecedent conditions and the assumption of general regularities. The former include the facts that the first speculator had large stocks of cotton, that there were smaller speculators with considerable holdings, that there existed the institution of the cotton exchanges with their specific mode of operation, etc. The general regularities referred ro are-as often in semi-popular explanations-not explicitly mentioned; buc there is obviously implied some form of the law of supply and demand to account for the drop in cotton prices in terms of the greatly increased supply under conditions of practically unchanged demand; besides' reliance is necessaryon certain regularities in the behavior of individuals who are trying to preserve or improve their economic position. Such laws cannot be formulated at present with satisfactory precision and generality, and therefore, the suggestedexplanation is surely incomplete, but its intention is unmistakably to account for the phenomenon by integrating it into a general pattern'of economic and socib-psychological regularities. We turn to an explanato{y argument taken from the field of linguistics.uIn Northern France, there exist a large variety of words synonytnotls explanation is given in HosperslExplanation],and a concisesurveyof many of thc in the firsr two partsof thc which are considered esientials of scientificexplanation

ories,cf., for example, Hull's concisedis_

en)entary examination of certain aspects of

pp. 284ff. m.aybe found f-ound.in Feigl Feigl. IOperationjsm], present ent study study may I 6 On th6 subiect of explanatioriin tlie socialscieni6s,cspeciallyin history, cf . 'rlso thc'bricf tlistlissupplement'andryplLfy amplify tlre_bricf rvhich may rvhich mav serve serveto supplement-an9 the follou'ing follou'inp publications, rtuLlicationsi cussionto tre presentedhere: Hempel [Larvsl; Popper [SocieryJ;Wlritc [li.xplarr:rFloolt ool t I ll'crrninologvl. ' c rrni nol ogy l . tirrrrl: and and tfre rfre'articles Causean
126

r i( :ll,:N,t,llr t( i

l,:](1 ,t,,^ NA t,l( ) N

' l ' i l t,]

1,0(;l o

otr

l ,l \l ' l ,A N A

l l ()N

t lt c r t r gt t t t t c: tis t t it t t 'r lr r t 'lt r inst ir nccs. 'l'ht t s, ti cs, but n11tof thc il ir r t livicluill sive.It gives occasion,howcvcr, to crlphnsiz.can itttpot'tantlloittr-cottcct'tring oui earlier analysis:When we spol<eof thc cxplarrarionof a singlc ev-ent,the tefm "event" teferred tO the oqculrellcC Of sotttc ttt
established.

j

8C f., for exampl e, F. H . K ni ght' s pres entati on of thi s argunrc nt i n l l ,i rrri ttti orrs l , l )l ).25r-52.

l:tl

s oil, r N' t ' ilr t ( : t , l\ t ' t , ANA' t , t ( ) N

co l l (l i ti ollsof n llr ot ir ' ; r ri o rrlcl tp l :rn rrti o rr, :rrrtltl rc l c i s no f1;r.rrrnl l i l l cl crrcc on this accor.rntllct*'ccn llr()tivationarand causrl explarrnti'r. Neither doesthc fact that tnotivesare not acccsiilrleto clircct ollscrvntion by an outside observer constitute an essentialdifference bctrvccn tlrc two of explanation; for also the deternrining factors acrduccd in .kinds physicalexplanationsare very frequently inaccessiblJto direct observati.n. This is the case,for instance, when opposite electric charges are adcl'cccl in-explanation of the mutual attraction bf t*o metal spherJs. The prcsencc of those charges, rvhile eluding all direct observatiori, can be ascertainecl by various kinds of indirect tesi, and that is sufficient to guarantee the em_ pirical character of the explanatory staremenr.Similarlf, rhe presence of certain motivations may be ascertainableonly by indirett metliods, which may includc referenc-eto linguistic urteranc;s or tn" subject in question, slips of.the.pen or of.the tongue, etc.; but as long as th'ese methods are "operationally-determined" wiih reasonableclaritliand precision, there is no essentialdifference in this respect between motivational explanation and causal explanation in physics. A potential danger of expranation by motives Iies in the fact that the method lends itself to the facile constrlction of ex-post-facto accounts rvithout predictive force. It is a widespread tendency to',,explain,, an acrior.t by ascribing it to motives conjectuied onry after the aJtio' has tal<en place.while.this procedure is not in itself objectionabre,its soundness requires that ( r ) the motivational assumpdoni in question be capable of tesr, and (z) that suitable.generar raws be availabieto,lend .*pirnr,o.y power to the assumedmotives. Disregard of these requirements fiequentry deprives alleged motivationar expranationsof their cognitive significance. The explanation of an action in terms of the of tfie agent is sometimesconsidered as a special kind of teleological -ot]u., explanation. As ,ras pointed our above, motivational explanation, ii adequitely formulated, conforms to the conditions for causaiexplanation, ,o thrt thl term ,,teleoIogical" is a nrisnomer if it is meant to implv either a non-causal character of the explanation or a peculiar determinaiion of the present by the future. If this is borne in mind, however, the term "tereologicar" be vierved, ^ i in this conrexr, as referring to causal explanationsIn which'some of the antecedent conditions are motives of thi agent whose actions are to be explained.,

ti l t,)

l ,(x ;l ()

()tf

l ,l \l ' 1,,,\N A ' ,l l ()N

319

cxaurirtcdlteforc, thc ends are not assumedhere to be consciottsly
to l<ecpingthe organism alive or to preserving the.spccict.l" Att rlttcrlll)t ,u.rrr" piecisely ivhat is meant ny this latter assertiorl-ot'by tlrc sirrril:tt' ,rnc tl',at without those characteristics,and other things bcirtg crlttrtl,tltt' tlifrlrganismor the specieswould not survive-encollnters c
t l t t ' t r' l i t l c s t t t ; t t ' l t t ' l o t t l t rl r ,,.,\n r ut,r l v s i s o I rc l c o l o q t c rrl s t rl rc n rc n t s i t r l ri o l o g r' , t l , rt t g l\ l l . l (' s \ (' l l t i : l l l v l l t t r: l t t t t i l l t (l l )l (" rl l ' rrt r r r r \\'r r 0tl qr .r . l l r r .i r r, . i l t l t . s l . e i l t c ri , rl l r' . 1 )l t . 4 1 . : t l l rrp t t ' l ' i t ' i rl | \ l c t l r" , l o l ' rg v l . l ) \'l \;tr l l ll l ; l l l l l :r l r or ':ttt,i

3 lt r

s(:il, : N' , l' lt f t ( : t , t x t , l, ANA, t , t ( ) N

tc rlrri rto l o gy . lt ntrl v lt ic lt in c tc u s co rrr s t' i c l rti fi cl i n o u ,l crl gc < l f t6c crrrrs:rl conr'tcctionsllctr.vccnbiol
irr<|ce d.misread ing.For whiIe,"-: ::'.'ffff ':#,:T,il"ftT'j'i n H: effecr, itis by- no

meansuniversal: Tie free fail of a physical Psychrlogical Irody nray. well be said to be a more familiar phenornenon than the raw rf gravitation, by meansof which it can be expl'airred; ,"d ,;;it the basic itlcasof the theory of rerativity will appear tomany ro be far ressfamiliar ttttll tlte phenomenafor which the theory accounts. ; not only noc necessaryfor a sound 5[e1y-, but it is not sufficient either. r which a proposed explicans sounds ser inspection proves io be a mere tability, or a set of statementswhich rre lacks explanatory power. A casein p.int is the neovitalistic artempt to explain bioiogical phino-.n, by refcrcncc ro an enrelechy or vital force. The crucial -point'here is not_as it is s.rrretinresmade out to be-that entelechiescannot be seen or otherwise dircctly observed; for that is true arso.of gravitationar fietat, refcrcrce to such fields is essentialin the 6xplanation "nJyer, of various physical Phc'rourena.The decisive difierence befween the two casesis that the phvsical explanation provides ( r ) methods of testing, albeit indirectry, asserrio.'sabout gravitational fields, and (z)-generar liws corrcerning t(e strcngth of gravitational fierds, and the behivior of obiects moviig in tlrc.r. Iixplanations.,by entelechiessatisfy the analogue 'neither of of these t'uvoconditions. Failure.to satisfv the fiist gonditioi represents a violation rf (lli); it renders alr statementsabout entelechies inaccessiblero empi.ical tcsr and thus devoid of empiricar meaning. Failure to comply wirh the scc'nd condition involves a viblation of (Ri). It deprives th.'.u.,..p, lrt; for explanatory power never re_ general laws in which it functions. r of farniliarity of the metaphor it I t lg't no tp ro vi det lr eor et ic alu n d e rs ta n d t-1'." prcccding observationsabout fanriliarity and unclcrstanclillg cn' , l r c r lt llli ctl , i n n s ir r r il: rllt r nnr l c r,to th c v i c u ,h c l rl l l y s o rrrcscl rol l rr.s thnt rl rc

i l i l i L ( ) ( ;l ( i ( ) tf t'txl ,l ,AN n 't t( ) N

33|

cxpl:rnltion, or thc nrrtlcrstancling, of hurnan actionsrcquircs rn empathic rundcrstanclingof thc pcrsonalities of the agents.lr This understanding of :rrrotherperson in terms of one's own psychological functioning may prove :r rrscful hcuristic device in the search for general psychological principles rvhich might provide a theoretical explanation; but the existence of empathy on rhe part of the scientist is neither a necessary nor a sufficient condition for the explanation,or the scientific understanding, of any human rrction. It is not necessary,for the behavior of psychotics or of people Irclonging to a culture very different from that of the scientist may sometirnes be explainable and predictable in terms of general principles even though the scientist who establishesor applies those principles may not be rrbleto understand his subiects empathically. And empathy is not sufficient to guaranteea sound explanation, for a strong feeling of empathy may exist cvcn in caseswhere we completelv misjudge a given personaliry. Moreover, as the late Dr. Zilsel has pointed out, empathy leads with ease to incompatible results; thus, when the population of a rown has long been subjected to heavy bombing attacks, we can understand, in the empathic scnse,that its morale should have broken down completely, bur we can trnderstandwith the same easealso that ir should have developed a defiant spirit of resistance.Arguments of this kind often appear quite convincing; lrrrt they are of an elcpost facto character and lack cognitive significance tunlessthey are supplementedby testableexplanatory principles in the form
Iore or EuBncrrvcp

$5. Leaels of Explanation. Analysis of Emergence As has been shown above, a phenomenon may often be explained by scts of laws of different degreesof generality. The changing positions of a planet, for example,may be explained by subsumption under Kepler's laws, or by derivation from the far more comprehensive general law of gravitation in combination with the laws of motion. or finallv by deduction from rhc general theory of relativity, which explains-ana riigfttty modifiestlrc prccccling set of larvs. Sinrilarly, the expansion of a gas with rising rr lior 'r rrrorcdctailcddiscussion of thisvicw on thc b:rsis of the gcncralprinciplcs ottrl i rrcrl nl rovt:, cf. Zi l sclI l, ) r nPir icisrsccr nl, ior7r sand8,: r ndI lcnr PclI l, nvsl, 'sccr ioir 6.

,32

SCIENTIFIC

EXPLANATION

constructswhich function in the context of somecomprehensive theory. As the precedingillustrationsshow, the conceprof higher-levelexplanation coversproceduresof rather different character;oie of the most im-

ng the spatialparts or other constituentsof the systemsin which the phelomenaoccur, and which in this context are oftLn referredto as whbles.

ri r l i () r rl lt rt ' it l l r r i c f c x p o s i l i o t r of tlr is.itlu r , scc F c.ig l lOlr cr .u r io n i srrrl ,pp. tl t4-rti l l . trr(i rrt r'c rt lit t g t l t c t ' r , t t i ' c p t o f r r .vclty ir r ir s kr g icr r l iir r .l p iyclr ,lr g i.*l 'i ,i .,|r,,,,g*, *"" ro Strtr' t :lNov c lry l .

THE

LOGIC OF EXPLANATION

ttt

,t)

( r ) First, the question whether a given characteristic of a "whole",'t!, is emergent or llot cannot be significantly raised until it has been stated what is-to be understood by the Par$ or constituents of ru. The volume of a brick wall, for example, may be inferable by addition from the volumes of its parts if the latter-are undersrood to be the component bricks, but it is nur ro irrf.r"ble from the volumes of the molecular components of the wall. Before we can significantly ask whether a characteristic W of an obiectTl to state the intended meaning of the y defining a specific relation Pr and obiects which stand in Pt to tu count ht be defined as meaning "cottstituent , or "molecule contained in" (for any phVsical obiect), or "chemical element contained in" (with resPect to ihemi.al compourrds,or with respect to any material obf eg!), or "cell of" (with respecf to organisms), etc., The term "whole" will be used here without any of its various connotations, merely as referring to any object zr.rto which others stand in the specified reladon Pr. In order to emphasize the dependenceof the concept of part uPon the definition of the relation Pt in each case,we shall somitimes speak of Pt-parts, to refer to Parts as determined by the Particular relation Pt under consideration' second point of criticism. If a characteristicof a (z) We turn io ^ whole is to be qualified as emergent ferred from a knorvledge of all the pr has pointed out' no whole can have a illusirate bv reference to our earlier include that of forming, if suitablv which is liquid, transParent, etc. Hence the liquidity-, transParence' etc' of water can be infeired from certain PfoPerties of its chemical constituents. If the concept of emergence is not to be vacuous, therefore, it will be necessaryto specify in every case a class G of attributes and to call a characteristic Ii/ of-^n object ttl emergent relatively to G and Pr characif the occurrence of w in u cannot be inferred from a complete in G' contained the atffibutes terization of all the Pr-parts with respect to which to in G, attribute every i.e. from a sratement which indicatei, for of the parts of ?, it applies.-Evidently, the occurrence of a characteristic may be emergent wiih respect ro one classof attributes and not emergent "to anorher. The classesof attributes which the emergentists *iih r.rpect have in *ind, and which are usually not explicitly indicated, will have to be consrrued as non-trivial, i.e. as not logically entailing the property of each with consrituenr of forming, together witli the other constituents, a whole of emercases simple fairly the characteristicsunier irivestigations.-Some gcncc in the senseso far tp".Ifi"d arise when the class G is restricted i,, .".t.i', sir'plc propcrtics ,if th" portr, to the exclnsion of spatial or other several rclati
tuA

.t )+

SCIENTIFIC

EXPLANATION

constituents alone without a description, in terms of relational concepts, of the way in which the batteries are connected with each other.la (3) Finally, the predictability of a given characterisric of an object on the basis of specified information concerning its parts will obviously rlcpcnd on what general laws or theories are available.'uThus, the flow of rrn electric current in a wire connecting a piece of copper and a piece of zirrc which are partly immersed in sulfuric acid is unexplainable, on the lxrsisof information concerning any nontrivial set of attributes of copper, zinc and sulfuric acid, and the particular structure of the system under c
THE LOGIC OF EXPLANATION

55)

as the flow of the current, or the optical activity, in our Iast examples,are absolutely emergent at least in the sensethat they could not possibly have been predicted before they had been observed for the first time; in other words, that the laws requisite for their prediction could not have been arrived at on the basis of information available before their firsr observed occurrence.lu This view is untenable, hou'ever. On the strength of data availableat a given time, scienceoften establishesgeneralizationsby means of which it can forecast the occurrence of events the like of which have never before been encountered. Thus, generalizations based upon periodicities exhibited by the characteristics of chemical elements then known, enabledMendeleeff in r 87r to predict the existenceof a certain new element and to state correctly various properties of that element as well as of several of its compounds; the element in question, germanium, was not discovered until 1886.-,4. more recent illustration of the same point is provided by the develooment of the atomic bomb and the prediction, based on theoretical principles establishedprior to the event, of its explosion under specified conditions, and of its devastating releaseof energy. As Grelling has stressed,the observation that the predictability of the occurrence of any characteristic depends upon the theoretical knowledge available, applies even to those casesin which, in the language of some emergentists, the characteristic of the whole is a mere resultant of the corresponding characteristics of the parts and can be obtained from the latter by addition. Thus, even the weight of a water molecule cannot be derived from the weights of its atomic constituents without the aid of a Iaw which expressesthe former as some specific mathematical function of the latter. That this function should be the sum is by no meansself-evident; it is an empirical generalization, and at that not a strictly correct one, as relativistic physics has shown. Failure to re lize that the question of the predictability of a phenomenon cannot be significantly raised unless the theories available for the prediction have been specified has encouraged the misconception that certain phenomena have a mysterious quality of absolute unexplainability, and that their emergent status has to be accepted with "natural piety", as F. L. Atlorgan put it. The observations presented in the preceding discussion strip the idea of emergence of these unfounded connotations: emergence

n6

SCIENTIFIC

EXPLANATION

of a characteristic is not an ontological trait inherent in some phenomena; fnther it is indicative of the scope of our knowledge at a given time; thus it has no absolute,but a relative character; and what is emergent with re;pect to the theories available today may lose its emergent itrtu, tornorrow. The preceding considerations suggest the following redefinition of cmergence: The occurrence of a characteristic W in an obiect o is emergent relatively to a theory T, a part relation Pt, and a classG of attributes if that occurrence cannot be deduced by means of T from a characterization of the Pr-parts of tl with respect to all the attributes in G. This formulation explicatesthe meaning of emergencewith respecr to eaentsof a ceftain kind, namely the occurrence of some characteristic IZ in an object tu. Frequently, emergenceis attribute d to cbaracteristicsrathet than to events; this use of the concept of emergencemay be interpreted as follows: A characteristic W is emergent relatively to T,Pt, and G if its occurrence in any object is emergent i-nthe sensejust indicated. As far as its cognitive content is concerned, the emergentist assertion that the phenomena of life are emergent may now be construed, roughly, as an elliptic formulation of the following statement: Certain specifiable biological phenomena cannot be explained, by means of contemporary physico-chemical theories, on the basis of data concerning the physical nnd chen.ricalcharacteristics of the atomic and molecular constituents of organisms.Similarly, the so-called emergent status of mind reduces to the flssertionthat present-day physical, chemical and biological theories do not snfEce to explain all psychological phenomena on the basis of data conccrning the physical, chemical, and biological characteristics of the cells rrr of tl-remolecules or atoms constituting the organismsin question. But in rhis interpretation, the emergent character of biological and psychological phcnomenabecomes trivial; for the description of various biological phenorrena requires terms which are not contained in the vocabulary of present clay physics and chemistry; hence we cannot expect that all specifically :riologicalphenomenaare explainable,i.e. deductively inferable,by means rf present day physico-chemical theories gn the basisof initial conditions thernselvesare describedin exclusively physico-chemicalterms. In 'vhich rrclcr to obtain a less trivial interpretation of the assertion that the phelonlcnn of life are emergent, rve have therefore to include in the explanatory .lrcory all thoselaws known at presentwhich connect tl-rephysico-chenrical *,ith the biological "level", i.e., which contain, on the one hand, certain rlrysicaland chernicalterms, including those required for the clcscriptirln rf lrr
THE LOGIC OF EXPLANATION

)tt

ent for large classesof phenomena studied in biology and psychology.lT Assertions of this type, then, appear to represent the rational core of the doctrine of emergence.In its revised form, the idea of emergence no longer carries with it the connotation of absolute unpredictability-a notion which is objectionable not only becauseit involves and perpetuates certain logical misunderstandings,but also because,not unlike the ideas of neo-vitalism, it encouragesan attitude of resignation which is stifling for scientific research.No doubt it is this characteristic,together with its theoretical sterility, which accounts for the rejection, by the majority of contemporary scientists,of the classicalabsolutistic doctrine of emergence.ls Penr III. Locrcnr ANervsts oF LAw eNo ExpteNettoN 56. Problems of the Concept of General Lau From our general survey of the characteristics of scientific explanation, we now turn to a closer examination of its logical structure. The explanation of a phenomenon, we noted, consists in its subsumption under laws or under a theorv. Bur what is a law. what is a theorvl While the meaning of these .on.!pa, seemsintuitively clear, ,.t ,,,..np, to construct adequate explicit definitions for them encounte$ considerable difficulties. In the present section, some basic problems of the concept of law will be described and analyzed;in the next section, we intend to propose, on the basisof the suggestionsthus obtained, definitions of law and of explanation for a formalized model language of a simple logical structure. The concept of law will be construed here so as to apply to true statements only. The apparently plausible alternative procedure of requiring high confirmation rather than truth of a law seemsto be inadequate: It would lead to a relativized concept of law, which would be expressedby the phrase "sentenceS is a law relatively to the evidence E" . This does not seenl to accord with the meaning customarily assignedto the concept of law in scienceand in methodological inquiry. Thus, for example,we would not say that Bode's general formula for the distanceof the planets from the sun was a law relatively to the astronomical evidence availablein the r77os, when Bode propounded it, and that it ceasedto be a law after the discovery

| \/:rl i al rl esl , p. :75. r* l l ri s l i ri ttrtl c of tl rc s c i c rrti s t i s v oi c c d, for c x :urrP l t:,l r1, I l rrl l i rr l l )r' i nc i P l c s l , pP . ri rH .

338

SCIENTIFIC

EXPLANATION

of Neptune and the determination of its distance from the sun; rather, we would say that the limited original evidence had given a high probability to the assumptionthat the formula was a law, whereas more recent additional information reduced that probabiliqy so much as to make it practically certain that Bode's forrnula is not generally true, and hence not a law.l8n

characteristicsof a general law, with the possibleexception of truth. Hence, every law is a lawlike sentence,but not conversely. Our problem of analyzing the concept of law thus reduces to that of explicating the meaning of "lawlike sentence".We shall construe the class of lawlike sentencesas including analytic general statements,such as "A rose is a rose", as well as the lawlike sentencesof empirical science.which have empirical content.2' It will not be necessaryto reqoire that each lawIil<e sentence permissible in explanatory contexts be of the second kind; lather, our definition of explanation will be so constructed as to guarantee the factual character of the totality of the laws-though not of every single one of them-which function in an explanation of an empirical fact. What are the characteristicsof lawlike sentenceslFirst of all, lawlike scntencesare statements of universal form, such as "All robins' eggs are grecnish-blue", "All metals are conductors of electricity", "At constant pressure,any gas expandswith increasing temperature". As these examples illtrstrate, a lawlike sentence usually is not only of universal, but also of conditional form; it makes an assertionto the effect that universally, if a ccrtain set of conditions, C, is realized, then another specified set of conditions, E, is realized as well. The standardform for the symbolic exprcssion of a lawlike sentenceis therefore the universal conditional. However, sincc any conditional statement can be transformed into a non-conditional one, conditional form will not be considered as essentialfor a lawlike sentcncc, while universal character will be held indispensable. Ilut the requirement of universal form is not sufficient to charactclizc larvlike senten.Ls.Suppose,for example, that a certain basl<et,D, conrrrilrs

rrr | ( ilt rt t c rf : r c t u r l sl . r r . r z < , :'r)'l hi\ ( ir xr tlr r r llr ' s :r p llr o :r ch in [( irrrrrterf:rcttr:rl sl . l)roc c ( l t t r c u : r s s t r g g c stcr llr y I t c ic l rcrtlnc li, irr n < l c t n i l c t l c x n i i r i n,r tio r i o f th c co r r ccg r t' o f l:r w, sir r r i l rrrl y('onstnrcs l ri s ( ' t ) r r('('l )ot f t rot t ro l o g i t ' : t sl t r r l ( ' n ) c n t :r sir r clr r tlin glr o tlr a r r :r lytic:tr r r ls1 ' n tl rt.ti t'\(.l l cl ('cs; c{. I l , og i r' l , t 'lrrrpt c l V l l l .

THE

LOGIC OF EXPLANATION

339

at a celtain time t a number of red apples and nothing else.21Then the statement (S,) Every apple in basket b attime r is red is both true and of universal form. Yet the sentencedoes not qualify as a law; rve would refuse, for example,to explain by subsumption under it the fact that a particular apple chosen at random from the basket is red. What distinguishesS, from a lawlike sentence?Two points suggest themselves, which will be considered in turn, namely, finite scope, and reference to a specified object. First, the sentenceS, makes,in effect, an assertionabout a finite number of objects only, and this seemsirreconcilable with the claim to universality which is commonly associatedwith the notion of. law.z" But are not Kepler's laws considered as lawlike although they refer to a finite set of planets only? And might we not even be willing to consider as Iawlike a sentencesuch as the following? (Sr) All the sixteen ice cubes in the freezing tray of this refrigerator have a temperature of less than ro degreescentigrade. This point might well be granted; but there is an essentialdifference between S, on the one hand and Kepler's laws as well as S, on the other: The latter, while finite in scope, are known to be consequencesof more comprehensivelaws whose scope is not limited, while for S, this is not the case. Adopting a procedure recently suggestedby Reichenbach,2swe will therefore distinguish between fundamental and derivative laws. A statement will be called a derivative law if: it is of universal character and follows from some fundamental laws. The concept of fundamental law requires further clarification; so far, we may say that fundamental laws, and similarly fundamental lawlike sentences,should satisfy a certain condition of non-limitation of scope. It would be excessive,however, to deny the status of fundamental lawlil<esentenceto all statementswhich, in effect, make an assertionabout a finite classof objects only, for that would rule out also a sentencesuch as "All robins' eggs are greenish-blue", since presumably the class of all :r The difficultyillustrated wasstatedconcisely by Langford( [Reby thisexample vicrvl), who referred to it as the problem of distinguishing between universals of fact :rrrtl clusal universals. For further discussion and illustration of this point, see also Chisl rol nr l C ondi ti onal l , espec i al l y pp.3orf.-A s y s temati c anal y s i s of the probl em w as not c onc erned gi vcn by C oodnran i n ICounterfac tual s ], es pec i al l y part III.-W hi l e u'irh tlrc spccific point under discussion, the detailed examination of counterfactual corrrlitiorrals and their rclation to laws of nature, in Cllapter VIII of Lewis's work inrportant observations on several of thb issuesraised in the present ll,lll,{'s,r,,contrins r3 l 'l rc vi crv tl nt l urvs s horrl tl bc c ons truc d as not bc i ng l i mi ted to a fi ni te domai n o thc rs , by l )oppc r ( [Fors c l rung l ,--s ec ti onr 3) and by R ei c henhrr l rccrrt:xprcsscrlrrrrorrg , l rl ch (l l ,ogi cl , p. q69). rrt l l ,ogi r' 1. p. i 6 r.--( )r rr tt:r' ttti rtok rgy:ts w c l l :ts tl tt: rl c l i tti ri ortsto l l c propos c d l atc r for tl rr: l rvo t1,P t'sol l urv tk r ttol t' oi rtt' i rl t' w i tl r Itc i c l rc ri l l :tt' l t' s ,l tttw c v rrr.

J40

SCIENTIFIC

EXPLANATION

robins' eggs-past, present, and future-is finite. But again, there is an essential difference between this sentenceand, say, Sr. It requires empirical knowledge to establishthe finitenessof the classof robins' eggs, whereas, when the sentenceS. is construed in a manner which renders it intuitively unlarvlike, the terms "basket b" and "apple" are understood so as to imply finiteness of the class of apples in the basket at time t. Thus, so to speak, the meaning of its constitutive terms alone-without additional factual information-entails that S, has a finite scope.-Fundamental laws, then, will have to be construed so as to satisfy what we have called a condition of nonlimited scope; our formulation of that condition however, which refers to what is entailed by "the meaning" of certain expressions,is too vague and will have to be revised later. Let us note in passing that the stipulation here envisagedwould bar from the class of fundamental larvIike sentencesalso such undesirable candidates as "All uranic objects are spherical", where "uranic" meansthe properqF of being the planet Uranus; indeed, while this sentence has universal form, it fails to satisfy the condition of non-limited scope. In our search for a general characterization of lawlike sentences,we now turn to a second clue which is provided by the senrenceSr. In addition to violating the condition of non-limited scope,this sentencehas the peculiarity of making reference to a parricular object, the basket b; and this, too, seemsto violate the universal character of alaw.2a The restriction which seemsindicated here, should however again be applied to fundamental lawlike sentencesonly; for a true general statement about the free fall of physical bodies on the moon, while referring to a particular object, would still constitute a law, albeit a derivative one. It seemsreasonableto stipulate, therefore, that a fundamental lawlike sentence must be of universal form and must contain no essential-i.e., uneliminable-occurrences of designationsfor particular objects. But this is not sufficient; indeed, just at this point, a particularly serious difficulty presentsitself. Consider the sentence

THE

(S") Everything that is ferple is red. The statement thus obtained is of universal form and contains no t'lesigrrntions of particular objects,and it also satisfiesthe conditiorrof non-lirrritctl 2 a Ir t phy s ic s , t h c i d e a t h a t a l a w sh o u ld n o t r cfcr to r r r y p ir r ticr r lirl ol rj ct't l rrs forrrrrl it s cxl tl cs ii, t ir ilr t h c t t t a x i n t t l u t t l r c g cr r cr tl l:r ws o f llh ysicish o r r l.l t' ,,rrt'ri rrn' r(,1'r,r'ul (.c t o s p ct'i lit 's p: t t ' <' - l i t t t cp o i t t r s , t n t l t h:it sp :r tio - tt' r n lxr r :ri'l o o ltlir r r r tt,sslr oul rl occul i rr tl rcrrr ot t lv i rr tlt t ' lirlrt r o l ' t l i l k . r t ' r r c c s o r r lilIi.r ' cr r r ir r ls.

34.I

scope;yet clearly, Socan qualify as a fundamental lawlike sentenceno nlolc than can S". As long as "ferple" is a defined term of our l4nguage, the difficulry can readily be met by stipulating that after elimination of defined rernrs, a fundamental lawlike sentencemust not contain essentialoccurrenccs
(Sr) Everything that is either an apple in basket b attime f or a sample of r, ferric oxide is red. If we use a special expression,say "x is ferple", as synonymous with "r is either an apple in b at t or a sample of ferric oxide", then the content of S, can be expressedin the form

LOGIC OF EXPLANATION

<;nCarnap's proposals.

1+2

scll,) N' t ' ilft ( i t , ) xt , LANA' l' loN

thc conccpt of purcly qualitativepredicatc.The questionwhcdrcr indication of thc lleaning of a given predicate in English does or does not require reference to some one specific object does not always permit an unequivocal answer since English as a natural language does not provide explicit definitions or other clear explications of meaning for its terms. It seems therefore reasonableto attempt definition of the concept of law nor with respect to English or any other natural language, but rather with respect to a formalized language-let us call it a model language, L,-which is governed by a well-determined sysrem of logical rules, and in which every term either is characterized as primitive or is introduced by an explicit definition in terms of the primitives. This reference to a well-determined system is customary in logical research and is indeed quite natural in the context of any attempt to develop precise criteria for certain logical distinctions. But it does not by itself suffice to overcome the specific difficulry under discussion. For while it is now readily possible to characterize as nor purely qualitative all those among the defined predicates in L whose definiens contains an essential occurrence of some individual name, our problem remains open for the primitives of the language, whose meanings are nor determined by definitions within the language, but rather by semantical rules of interpretation. For we want to permit the interpretation of the primitives of L by nreansof such attributes as blue, hard, solid, warmer, but not by the properties of being a descendant of Napoleon, or an arctic animal, or a Greek statue; and the difficulty is precisely that of srating rigorous criteria for the distinction between the permissible and the non-permissibleinterpretations.Thus the problem of setting up an adequatedefinition for purely qualitative attributes now arises again; namely for the conceprs of the metalanguagein which the semantical interpretation of the primitives is formulated. We may postpone an encounter with the difficulty by presupposing fornralization of the semantical meta-language,the mera-meraIanguage, and so forth; but somewhere, we will have to srop at a nonformalized meta-language, and for it a chancterization of purely qualitative predicates will be needed and will present much the same problems as non-formalized English, with whigJr we began. The characterization of a purely qualitative predicate as one whose meaning can be made explicit without reference to any one particular otrject points to the intended meaning but doesnot explicate it precisely, and the problem of an adequate definition of purely qualitative predicatesremains open. There can be Iittle doubt, however, that there exists a Iarge number of property and relation terms which would be rather generally iecognizcd rs purely qualitative in the sensehere pointed out, and as permissible in thc fornrr.rlationof fundamental lawlike sentences;some exanrpleshave becn and thc list could be lcadily enhrgcd. Whcd wc spcal
'l'nlt Loclc otf t,lxt)LANA'r'loN

t+ l

In the following scction,a nrodel languagcL of a r:athcrsirrrplclogicnl structrlrewill be described,whosc prinritiveswill be assunrcdt
3++

SCIENTIFIC EXPLANATION

versalform and not equivalenr ro a singular senrence.s is cailed essentiaily generalizedif it is not equivalent to a iingular sentence.

concerninq the semanticarinterpretation of L, we ray down the following two stiiulations: primitive predicares of L arc all purely qualitative. \Z.za.).!\e (7.2b) The universeof discourseof L,i.e.,th^e do;ain;i;i;;,, covered consists of all physical obj.",r, or or n rfir-i*._porrt lJ.j**:*.ifiers,

tn accordancewith the considerationsdeveloped in section 6, we now o,-.e n ne:

1 'i l t,) L ( X;tC ( ) l r l ,l xt,t,AN A'i l 0 N

1+5

of being a father, and 'Q' that of bcing male.-'l'hc tlcrivrrtivclrrrvs,orr thc other hand,include neither of thesecategories;indccd, no frrntlrrrrrcntnl Inr,v is also a derivative one. As the primitives of L are purely qualitative, all the statementsof universal form in L also satisfy the requirement of non-limited scope, ancl thus it is readily seen that the concept of law as defined above satisfiesall the conditions suggestedin section 6.27 The explanation of a phenomenon may involve generalized sentences which are not of universal form. We shall use the term "theory" to refer to such sentences,and we define this term by the following chain of definitions: Q.+a) S is a fundamental theory if S is purely generalized and true. Q.+b) S is a derivative theory in L if ( r ) S is essentially,but not purely, generalizedand (z ) there existsa set of fundamental theories in L which has S as a consequence. Q.+c) S is a theory in L if it is a fundamental or a derivative theory in L. By virtue of the above definitions, every law is also a theory, and every theory is true. With the help of the concepts thus defined, we will now reformulatc more precisely our earlier characterization of scientific explanation witlr specific reference to our model language L. It will be convenient to statc our criteria for a sound explanation in the form of a definition for thc expression "the ordered couple of sentences,(7, C), constitutes an explanansfor the sentence8." Our analysiswill be restricted to the explanation of particular events, i.e., to the case where the explanandum, E, is a singular sentence.28 In analogy to the concept of lawlike sentence,which need not satisfy a requirement of truth, we will first introduce an auxiliary concept of potential explanans,which is not subject to a requirement of truth; the notiorr e?As defined above, fundamental laws include universal conditional statcments witlt vacuous antecedents, such as "All mermaids are brunettes". This point does not apllcru' ro lead to undesirable consequences in the definition of the explanation to be proposctl later.-For an illuminating analysis of universal conditionals with vacuous antccc(lcnts,

rs a consequence. 3.:c) S is a Iaw in L if it is a fundamental or a derivative law in L.

3+6

SCIENTIF'IC

EXPLANATION

of explanans will then be definedwith the help of this auxiliaryconcepr.Th..econsiderations presentedin part I suggesithe foilowing iiliti"t stipura_ trons: (z'-i) An orderedcouple of sentences, (7, c), consrituresa pocentialexplanansfor a singularsentenceE only if (r) T is essentiallygeneralizedand C is sinsular (z) E is derivablein L from ? and c jointl"y,but not from c alone. rces,(7, C), constitutesan explanans rif mansfor E definition of.explanationin terms of the concepr l_l_i"pl]:i, ^. _1I],]: ot potentlalexpranation.le on the other hand,(z.s) is nor suggested as^a definition,bur asa sraremenr of necessary conditionsof pot.nft?l explanation. Theseconditionswilr presentlybe shown nor ro'be sufficient, and additionalrequirementswill be discussed by- r.vhich(7.5) has to be sup_ plementedin order to provide a definition of potentii'e'xpr"nation. Beforewe turn to this point, some,.-".k, are calredfor concerning the formulation of (7.5). The analysispresentedin part I suggests that an explanans for a singularsentenceconiirtr of a classof gener?izedsentencesand a classof singularones.In (7.5), the elements6f each of these classes sep.arately-are assumed to te conloinedto one sentence.This provision will simplify our formulations,and in the caseof generarized sentences'it servesan additionalpurpose:A crassof essentiilrygenerarized be equivalenrto a singular sentence;ttus," the class :::r:1.._r,1ay with the sentence lP(a)v(x)Q(x)','P(a)v - (x)e(x)') Ts equivalent 'P(a)'. since scientificexplanationmakesessential use of generalizedsen_ tences'setsof lawsof this kind haveto be ruled out; this is'achieved above by combiningall the generalizedsentences in the explanans into one conjunction,?, andstipulatingthat T hasto be essentially generarized.-Again, sincescientificexplanationmakesessential useof gJnlrafizedsentences, E e: The law of gravitation,combined rlondeand blue_eyed"doesnot con_ onde".The last stipulationin (Z.S) and thus prohibits complete self_ :hederivationof E from somesingu_

dispenses-with theneed foraspecial fi:T.';;ri::ru:;:::m;{::

to have factual contenr it e;c)

is to be a potential expranans for an

2sltisn eces s ar y t os t ipulat e, in ( 2. 6) ( z ) , t hat? _ b e a r h e o r y r a t h e r t h a n m e r e l y t h a t T be true, for as was sho#n.in iection 6, it'" g"".r"rir"d:;;A;;d,;il;:" planans.have to constitutea theory, and not "" "*.rr.nti"try g"r"r"i;r.d ,.;tebncewrrich "u8ry b actualty a theory, i.e., a consequ.n.. 6r-"-i"ioi,pi;;j;;;;^ilr..i',.u" ,"n_ ::_T:: tences.

THE

LOGIC OF EXPLANATION

3+7

al, then, since E is a consequenceof T must be factual, too' preclude, however, what might bc :iplanandum. Consider the sentences ) , - : 'R( a, b) 'U( h) ', Er : 'Q ( a) ' (Z'S)' but it seems R(a, b)'.They satisfy all the requirementslaid down itt E', becausethe occounter-intuiiive to say that (T';C') potentially explains E. amounts to a currence of the compbnent 'R(4, b)' of C' in the sentence it partial explanation of the explanandum by itself. Is not Possibleto rulc E sharespart. ior, Uy al additional stipulaiion, all those casesin which 'f w5ic6 consequence a common E have and C #here i.e. C, with it, .orit".rt to tltc i, .rot for*"lly true in Lt This stipulation would be tantamount sctlsc in the requirement that C and E have to be exhaustive alternatives two any which thir their alternation is formally true, for the content The,proposcd sentenceshave in common is expressedby their alternation. not sharc cvcn restriction, however, would be very sevefe.For if E does fof thc tlcrivtoart of its content with c, then c is altogether unnecessary itt E from T and C,i.e., E can be inierred from T alone. Tltcrcf.t'c, ii"" cxof thc "f I the singular conlponcl.lt randum is partly eiplnincd try irsclf' 'l',. rplanation of E,- 'Q(n)' bY . r ) ', which sat isf ies( 7. 5) , r r r lt l r vlr ich Its three collrPonentstllny llc cr;trivitlt ences: T, ' : ' ( x) ( - I '( r ) vQ ( r ) ) '; ' ( - l'( a) v t ) ) 'iE, ' - '( P( a) vQ ( a) ) csplitrtrtrrtlrc It Part of the content of cxplirltittts of thc : singularconPoncnt and is, in this sense,explained by itself' l'ttlttlvc Our analysishas ieached a point here where tlle cttst.ttlnfy gtritlrrrtccf.r idea of explalation becomestoo vague to providc ftr't5cr strggcststlt:tt rational re.onstruction. Indeed, the last illusiratio' stx)llgly i.tuitivcly thc be no sharp boundary line rvhich-scprr'irtcs ;i.r; ft't' sclf-cx'lrrrrirti.tt;'cr'of p'r'tial typ.t -"y colnterintuiiiu" the from rrrissible i. its rrcccpt:rlrlc tn. potential explanation j'st cbnsidcrcd,wlriclr is ^nright be.'iudgedunacccptablcrtrl itttttitive:gt',tlttrls "rr"., original firnulation, qivctr llrrrvc. trrnrforrned into the equivalent vcrsitln l,uI.,"e., cxPlit'irly irr The point illtrstratedby tl'relast exarttplcis statctl rtrorc witltoilt l)l'o()1. thc foll
3+8

SCIENTIFIC

EXPLANATION

In more intuitive terms, this means that if we represent the deductive structure of the given potential explanation by the'schema {7, C} -_>E, then this schemacan be restated in ihe form {i C, .Er} _, al . E, where E, follows from T alone, so that C1 is entireiy unn.".rr"ry as a premire; hence, the deductive schema under considJration ."r, 6"-r"auced to {7, Er}+E,.. E, which can be decomposed into the t-o d.do.tiu. schemata{T} * E" and {Er} -->Er.

completely unnecessary involvesa partialself_explanation of fliT-T,1-i"t the explanandum.sl Tg prohibit partial self-expranarionartogether would therefore mean ,. . rlmrtatron of explanation to purely theoredcal explanation. This measure seemstoo severely restrictive. on the other hand, rtt.-pt to delimit, by "n some specialrule, the permissibledegree of self-explan"tion'does nor appear to be warranted because,as we saw, customary usage provides no guidance for such a delimitation, and because,ro ,yrt..n"tiJ seemsto be "iurnt"ge gained by drawing some arbirrary dividing line. For th"!e ,e"ror,r, _. retrarn from laying down stipulations prohibiting partiar self-explanation. The conditions raid down in ral tlo'precrude 1i.5y y.t ,noth., rgumenr, which is closely related to r will have to be ruled out by an ad_ efly, that if we were to acce t (7.5) a statement of necessaryconditions, :onsequenceof (7.6), any given par_ means of any true lawlike sentence a true singular sentence_sa/, .,Mt. law-say, "All metals are good conC 'T' are nanles or name variables for sen_ n will be designated by ,S.?l, and ,SvT', re_ tecedent and I as coniequent will be desie_ . (Incidentally, this convention has alreajy

'i l i l |

L ( x;l o

( ) l r l ,l xl ,l ,AN A'l 'l ( ) N

r+9

( . 'st r t 'lt ducto r s of lr eat ", - t hen t her c cxist salr vnvsa t r r r c sir r qr r l: lls( 'r lr ( 'n( 'c (l that E is derivable from T ancl C, bttt not frtlrrr rtlottc;itt otltcr r,t'ot'tls, clr osct tp: t r such t hat ( Z. S) is sat isf ied.I ndeed, let T* bc sor nc'. t t 'lr it t ': r t 'ily ticular instanceof T, such as "If the Eiffel Tou'er is rrtctrl, it is n gootl cortductor of heat". Now since E is true, so is the conditional 7-* I F),nntl if the latter is chosenas the sentenceC, then T, C, E satisfy thc cotrtliti
atomic sentencein L. Verification of a molecular sentenccS rlr:ty tltctt llc:

rs parcial self_explanation has to be distin_ circularity of lcientific explanation. The rely differenr ideas. (a) One of rhese is the

E as a consequence. As brief reflection shows, this stipulation may lrc cx1'rrcsst:tlin tllc following form, which avoids referenceto truth: T nrust ltc cortllxrtilrlcirt 'J s2 It i s i rnportant to di s ti ngui s h c l c arl y bc tw c c rr thc _fol k rw i nl l rw o (' :l s c s : (:r) l f (,' t' rtttttol l tt' i s rrrrc tl rc rr O' c errnot bc tnrc i ri tl ,,,,' t F) l i c i ng trttc ; l trtl (tr) If ? i s trrrt' , ycri fi c < l rv i rl tgur /i [c :i ng v c l i { i erl . (]ol rrl i ti orr-(:r) ttttts r l tc s rrti s fi c tll .rv .:tttypot.ettti rtlc x ' (l r) rrrrrs rttot Irc s rtti s l i t' tli f ( /' ,(j ) i s to 1l l ;r1: rti s rr;rl rc rrrrrr' l 1rr,i i " r"s tri c ti v c c ttnrl i ri ott bc l l l orc rtti :tl c x pl rtttrtnsfor /' J .

35 0

SCIENTIFIC

EXPLANATION

L with at leastone classof basic sentenceswhich has c but not E as a consequence; or, equivalently: There must exist at least one class of basic sentenceswhich has C, but neither T nor E as a conseouencein L. If this requirement is met, then surely E cannot be a consequenceof ^ C, for otherwise there could be no class of basic sentenceswhiih has C but not E as a consequence;hence, supplementationof (l.S) by the new condition renders rhe second stipulation in (Z.S) (z) superfluous.-We now define potential explanation as follows:

THE

LOGIC OF EXPLANATTON

35r

langtage'An article in P' L' Harriman' ed" Bonfante,G. [Semantics]Semantics, fttit6rophical Lib-rary,Nerv York, r946. pr'.tofogy. o'f The encyclop"ai" New YorK' r925' Broad,C. D.'tMildl The-mind andits placein nature' Harvard University semantics' to ittu"aot''iot' c"i""ir, irra.jr.lSi*"*i.tt Press,1942. PhilosoPhyof science'vol' Iz flnductive Logic] On inductive logic'

(7.8) An ordered couple of senrences(7, C), constitutes a potential explanansfor a singular sentenceE if and only if the following conditions are satisfied: ( r ) T is essentiallygeneralizedand C is singular (z) E is derivable in L from T and C jointly b) T is compatible with ar least one class of basic senrenceswhich has C but not E as a consequence. The definition of the concepr of explanansby means of that of potential explanansas formulated in (7.6) remains unchanged. ln terms of our concept of explanans,we can give the following interpretation to the frequently used phrase "this facr is explainable by means of that theory": Q.il L singular senrenceE is explainable by a theory T if there exists a singular sentenceC such that (T, C) constitutes an explanansfor E. The concept of causal explanation, which has been examined here, is capable of various one of these consists in permitting T -generalizations. to include statistical laws. This re_quire1, however, a previous strengtheriing of the meansof expressionavailablein L, or the use oi a complex th-eoreticJ apparatusin the metalanguage.-on the other hand, and independently of the admissionof statistical laws among the explanatory principles, we may replace.the.strictly deductive requirement that E has to be a consequenceof ? and c joindy by the more liberal inductive one that E has to haie a high degree of confirmation relatively to the conjunction of r and c. Both-of these extensionsof the concept of e4planation open important prospec$ and raise__a variety of new problems. In the present .rr"y, ho-eu"t, ihrr" issueswill not be further pursued.

BIBLIOGRAPHY Througbout the article, tbe abbreaiatedtitles in bracketsare used for reference. Beard,charles A., and Ho_ok,Sidney. fTerminologyJ problemsof terrninolosv in hisroricalwriting. chapter IV of rheory xig prrcricc in lrist.rical sru
ctl. r tt74.) tltc s.ci:tl scicttccs. Ncw fMctlr.<6l.gy'l Mct5.d.l.gy,f t<.r,i,rr.n,',,-liclix. Y ork, r944. 'l'lr c lir r r it : r r i'r r s scict r t ilic: nrctltorl it't ccoti ,,i gi .' rli ,:rri rl l I l . I l , ir r r ir r r r i. r|r s 'f

352

SCIENTIFIC

EXPLANATION

White, Morron G. fExplanation] Historical explanation.Mind, vol. 5z (tg16,), pP. 212-229. Biologicalprinciples.New york, r929. I1ogdE"I,J. {. IPrinciples] zi,r.f [Empiriciiml probre-msof empiricism. ln trtrr'n)iiiial encycro!-.o,gil. peat* 0l untfiectscrcnce,vol. l[, no. g. The university of chicago Fress, r9+ r . -and.rhe problem.of historico_sociological laws. pbj_:,.[111-lJ.Physics rcs opnyoI s c r c n c ev,o l .8 (r9 4 r),p p . S 6 l _ S l g .