HERBERT FEIGL and MAY BRODBECK Editors UNIVERSITY OF MINNESOTA
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THE, P H I LOS O P HY OF SC I E .N CE
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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
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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. 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
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( . '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