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Hubert Schleichert, Elemente der physikalischen Semantik, mit einem Vorwort yon Viktor Kraft. R. Oldenbourg Verlag, Miinchen und Wien 1966, brosch., 156 Seiten. Ein auffallendes Merkmal der modernen physikalischen Beschreibungsformen ist das Auseinandertreten der begritttich-formalen Mittel und der Deutungsprinzipien, nach denen die formal-mathematischen Ausdriicke entsprechend den empirischen Gegebenheiten gedeutet werden. Der Autor des vorliegenden Buches stellt sich zur Aufgabe, die Beziehungen der formalen Elemente der physikalischen Beschreibung zu ihrer inhaltlichen, d.i. semantischen, Deutung zu untersuchen. Er geht dabei yon der zweifellos richtigen Ansicht aus, dab diese semantischen Probleme in der klassischen wie in der modernen Physik im Prinzip yon gleicher Art sind, auch wenn in der neueren physikalischen Forschung die Gegentiberstellung yon Formalismus und Interpretation wegen der hier aufgetretehen besonderen Deutungsschwierigkeiten in erh/Shtem MaBe in Erscheihung tritt. Ein bedeutender Vorzug des Buches liegt in der klar verstfindlichen Darstellung der logischen Analyse yon Beispielen und Modellen, an denen Schleichert seine Untersuchungen verdeutlicht. Die sehr einleuchtende Voraussetzung, dab das Fundament jeder physikalischen Deutung in der M~Sglichkeit yon Messungen und Experimenten zu suchen sei, erm~Sglicht Schleichert zu zeigen, dab schon die Ausdrticke der klassischen Physik wirklich mel3baren Zust~tnden bzw. Zustands~inderungen nur zum Teil zugeordnet werden k~Snnen. Auch kann er weiter zeigen, dab bereits in der klassischen Physik den angewandten logischmathematischen Operationen keineswegs in allen F~illen empirische Prozesse bzw. Beziehungen zwischen empirischen Zustiinden entsprechen. Vielmehr k~Snnen nur bestimmten Operationen und auch ihnen nur unter bestimmten, meist relativ einfachen Bedingungen empirische Korrelate zugeordnet werden. Oberdies werden die mathematischen Operationen, wie Addition, Differenzieren, Integration, je nach den empirischen Be107

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dingungen oft in verschiedener Weise gedeutet, oder auch nur als formale Umformungsverfahren beniitzt. Vielfach sttitzt sich die Interpretation yon Ausdrticken auf Analogien, zu denen man durch Extrapolation von Wertverl/iufen der Messungen gelangt. Noch bedeutungsvoller ist der vom Autor erbrachte und an zahlreichen Beispielen erl/iuterte Beweis, dab die Gewinnung neuer Naturgesetze durch Ableitung aus gegebenen Pr~imissen niemals eine rein analytisch-formale Deduktion ist. Vielmehr werden bei solchen "Ableitungen" entweder Bedeutungs/inderungen an den in den Pr/imissen vorkommenden Ausdriicken vorgenommen oder es werden den "abgeleiteten" Ausdriicken neue (erweiterte oder auch ganz neue) Bedeutungen zugeordnet. In jedem Falle verliert die "Ableitung" durch solche semantische ~nderungen ihren analytisch-formalen Charakter. Der Autor zeigt dies in besonders illustrativer Weise am Beispiel der "Ableitung" des Energieerhaltungssatzes aus dem Newtonschen Kraftgesetz. Als weiteres semantisches Kriterium zur Bestimmung des empirischen Aussagegehaltes einer physikalischen Gleichung ftihrt Schleichert die Bedingung an, daB die Ausdriicke zu beiden Seiten einer Gleichung durch von einander unabh/ingige MeBverfahren in ihren Einzelwerten bestimmbar sein mtissen. Gibt es z.B. mlr ftir den aufder einen Seite der Gleichung stehenden Ausdruck ein eigenes MeBverfahren zur Bestimmung der Einzelwerte, dann wird die Gleichung zu einer aussageleeren analytischenFormel. Vollst/indig deutbar sind nach Schleichert physikalische Ausdriicke dann, wenn alle Argumente eines fu.nktionalen Ausdrucks (Pr~idikatenausdrucks) deutbar sind. Den Pr/idikatzeichen kommt nach seiner Meinung immer nur die Bedeutung formaler Relationen zu. Dies aber, glaube ich, gilt nur ftir einfache physikalische Formelzusammenh/inge. Denn abgesehen davon, dab Pr/idikate selbst wieder Argumente komplizierterer Funktionen sein k6nnen, kommt es auch zuweilen vor, daB Pr~tdikate mit den gleichen, vollst/indig als Messungsgr/SBen deutbaren Argumenten in verschiedenen Zustandsbereichen inhaltlich verschieden gedeutet werden. Es sei nur an die diversen Energieprgdikate erinnert, die alle Masse und Geschwindigkeit zu Argumenten haben. Eine Ftille neuer Deutungsprobleme bieten die relativistischen Transformationsformeln und die aus ihnen ableitbaren Ausdrticke. Hier stiJtzen sich die semantischen Deutungen vielfach auf bloB als m/Sglich angenommene, abet praktisch nicht durchfiihrbare experirnentelle Verfahren, 108

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wobei nicht selten fiir den gleichen Ausdruck mehrere "experimentelle" MSglichkeiten beri.icksichtigt werden. Dem Autor gelingt es zu zeigen, dab die neuere physikalische Forschung in steigendem MaBe "unvollsgindig" gedeutete Ausdriicke, bzw. Ausdriicke mit variierender Interpretation bentitzt. Feste Regeln, wie die Deutungen der formal angesetzten bzw. abgeleiteten Ausdrticke vorzunehmen seien, gibt es nicht, vielmehr kommt es bier auf "geschickte Ans~itze" an. W~ihrend in der klassischen Physik und den Relativit~itstheorien die Ableitungen immer aus zumindest unvollst~indig gedeuteten Pr~tmissen erfolgen und die Bedeutungs~inderungen, durch die man zu neuen nachprtifbaren Aussagen kommt, die Ausdriicke in den Pr~imissen wie in den SchluBs~ttzen betreffen kSnnen, kommen in der Quantenphysik, wie Schleichert durch Zergliederung der komplizierten Formeln nachweist, h~iufig F~ille vor, wo Ableitungen aus vollst~indig ungedeuteten Formeln stattfinden und man erst nachtr~iglich, yon auBen her, d.h. ganz unabh/ingig von den Pr~imissen und den Deduktionsregeln, die abgeleiteten Ausdriicke zu deuten sucht. Auch der Fall, dab man formale Widersprtiche in Theorien durch hypothetische Deutungen gewisser Ausdrticke zu beheben sucht, wird vom Autor untersucht. Die logische Analyse l~13t solche Versuche yon vorneherein als erkenntnislogisch unzul~issig erkennen. Schleichert zeigt dies an den viel erSrterten relativistischen Paradoxien. Indem er auf den Ursprung dieser Widerspriiche, n/imlich auf die Unvertr~tglichkeit der zwei relativistischen Prinzipien, des Relativit~ttsprinzips und des Prinzips der Konstanz der Lichtgeschwindigkeit, zuriickgeht, kann er darauf hinweisen, dab die aus diesen Thesen formal ableitbaren Widersprfiche allein durch eine entsprechende Ab~inderung der zwei Prinzipien vermieden werden kSnnen. Das Bueh befaBt sich mit Fragen, die systematisch bis heute kaum behandelt wurden, zweifellos jedoch die Grundlagen der exakten Naturwissenschaften betreffen. Schon durch diese Aktualit~tt des behandelten Themas, vor aUem aber auch wegen der klaren, leicht faBlichen Darstellung selbst der kompliziertesten Zusammenh~inge kann das Buch jedem an erkenntnislogischen Grundlagenproblemen Interessierten w/irmstens empfohlen werden. Universitiit Wien

BELA JUHOS

109

REVIEWS Carl G. Hempel, Aspects of Scientific Explanation and Other Essays in the Philosophy of Science, Free Press, New York 1965, x + 505 pp., $12.50. In this extremely interesting book enlivened by style and inventiveness, Hempel has collected many of the articles which he has written during the last twenty years. Most of them are already well-known to students of inductive logic and the philosophy of science. But read together, they give the reader a deeper understanding of the point of view which underlies Hempel's work as well as the opportunity of tracing out implications of his thought which are not nearly so apparent in the individual essays. A clear point of view about science emerges from Hempel's work. Science is an activity whose primary function is the explanation and prediction of phenomena on the basis of beliefs which have already been rationally accepted. 1 The performance of this function is a necessary condition for a set of statements being considered a scientific theory. In fact, the conditions for a set of sentences being accorded the title "scientific" are rather strict. They must be employed in the explanation and prediction of singular statements which contain, in addition to logical constants, observational terms. 2 Such sentences are naturally part of the language of science. But sentences which contain non-observational terms in addition to (or instead of) observational terms are aliens and gain acceptance only when they meet certain conditions. Those conditions are precisely statable in terms of their use in the explanation and prediction of those singular statements mentioned above. For a set of sentences not only to be part of the language of science, but in addition a part of our accepted body of science, even further conditions must be satisfied. The mark of scientific theories is that they possess empirical significance. Because theoretical sentences bear specified relationships to observational sentences, scientific theories do have this characteristic of empirical content. On the one hand, this permits the explanation of singular events by general statements and initial conditions, and even the explanation of general statements by theories. 3 On the other hand it permits the confirmation of scientific theories by singular observational statements. 4 Since i Aspects of Scientific Explanation (cited hereafter as ASE), pp. 173, 333, 396. ASE, pp. 185, 211-17. 3 ASE, p. 248. 4 ASE, chapter I.

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the verification of most scientific theories is possible only at the expense of trivializing them, the relation of confirmation is the basis upon which to accept or reject alternative scientific theories. 5 Furthermore, lawlike statements are an essential ingredient in any scientific explanation, and, alternately, may be an essential precondition for confirmation. Such lawlikeness involves generality but not merely generality. 6 These are the major outlines of Hempel's theory of science. Consonant with it is a set of methodological assumptions. The task of the philosophy of science is the rational reconstruction in the metalanguage of science of the important epistemic concepts by means of which science is best understood. 7 These epistemic concepts include confirmation, empirical significance, rational acceptance, and explanation. The metalanguage employed is primarily semantic in character, though pragmatic notions may be found necessary for the reconstruction of such epistemic notions, s The object-language in which scientific theories are stated is extensional, and the semantic language encompasses only the theory of reference and not that of sense. These latter restrictions are based, I believe, on what Hempel takes to be the unsatisfactory semantical status of most intensional notions. 9 This underlying conception of method disposes Hempel to study the products of scientific activity (scientific statements) and their interrelations rather than the process of scientific activity. This is only natural. The machinery which he employs has as its objects, sentences or propositions. The epistemic relations employed presuppose the prior ascertainment of both terms (sentences or propositions) of the relation. They are temporal only in an implicit sense. The logic in terms of which scientific statements are formulated involves no temporal operators. It is natural under these circumstances for Hempel to claim that the philosophy of science is concerned with science in its context of justification and not in its context of discovery. Roughly speaking in the former one studies science as a set of products; in the latter one focuses on science as 5 ASE, p. 41. 6 ASE, pp. 264-70, 291-3. 7 ASE, pp. 4-70, 270 ft. 8 ASE, Chapter I, postscript to Chapter I (1964), pp. 50-1. 9 Cf. ASE, pp. 270 ft., 'A Purely Syntactical Theory of Confirmation', Journal of Symbolic Logic 8 (1943) 122-43. Hempel shows also his distrust of intensional notions in the metalanguage in various places, e.g. ASE, p. 342.

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a process of activities. It is reasonable to study science in the former way, but it is surely not the only reasonable way. The former way relegates to the domain of the pragmatic (and therefore in general to that of the unformalized) all kinds of interesting problems whose investigation is somehow ancillary to the major task of the philosophy of science. Thus Hempel has many interesting things to say about the pragmatic function of explanation and its part in the genesis of scientific activity as well as about the heuristic role of analogies in scientific theorizing, i0 But he considers them pragmatic questions and accepts the dichotomy: formalized reconstruction (which goes with) semantic distinctions (which go with) a context of justification versus

unformalized reconstruction (which goes with) pragmatic distinctions (which go with) a context of discovery I only raise the question at the present time of whether new tools of inquiry could not be used to treat science in a more unified way and to reduce the grabbag of pragmatic questions to more manageable proportions. Certain consequences follow from Hempel's substantive and methodological assumptions: (1). A dominant concern of Hempel is to show that all the statements of science have empirical significance. That they have such significance is a necessary condition for them functioning in explanations or predictions of singular statements (else we could have metaphysical explanations of events) as well as for them being capable of confirmation. It is not surprising that the search for a characterization of empirical significance should be one of Hempel's major concerns. To give at least a condition of empirical significance becomes an important part of his task. Think for a moment of his system minus even such a criterion of empirical significance. No way of distinguishing science from metaphysics, either in terms of its content or of its function of explaining singular statements, could be provided. The proper logical relationships requisite for explanation might hold between singular statements and statements i0 Especially in the chapter, 'Aspects of ScientificExplanation'. x

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(theories) which are not scientific. This would be disastrous for Hempel's whole program. Yet it is the attempt to characterize a criterion of empirical significance which must be judged the least successful of the projects Hempel has undertaken. He is unable to state necessary and sufficient conditions for the empirical significance of statements and must retreat to a far less ambitious project: the statement of sufficient conditions for characterizing a theory as scientific, n A theory T is scientific if at least one observational statement is a logical consequence of it. But if T is scientific, then, as Hempel admits, so is T' = T ^ M where Mis some metaphysical theory. 1~ So, in principle, scientific theories may always contain as proper sub-sets, metaphysical theories. If Hempel has not met disaster, he has at the least skirted it. What this suggests is that the whole attempt to construct a characterization of scientific statements or theory in terms of their empirical significance is wrong-headed. Scientific statements (and theories) share with statements of other kinds the characteristic of meaningfulness. It is a mistake to take the epistemic relation which some scientific statements bear to others as a basis for assigning meaning to these former statements. (2). Hempel's other concern is the development of a logic of science. A number of epistemic concepts (like confirmation, verification, explanation, acceptance) are studied and as much as is possible their logical properties are described. This involves not only studying them individually but systematically noting their interconnections. These concepts are clearly intertwined in Hempel's account. A necessary condition of an explanation is that the statements entering into it be empirically significant. A necessary condition that a statement be empirically significant is that it be confirmable. Furthermore such epistemic notions bear striking formal similarities to one another. Difficulties which arise in the definition of one concept reappear in the definition of another one. Such structural similarities although noted by Hempel are not systematically attended to by him. Yet they suggest possibilities for study which have as yet not been explored. I propose to discuss in turn these two central concerns of Hempel and u A S E , pp. 116-7. 12 A S E , p. 219.

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attempt to link the problems encountered in each with certain debatable assumptions which are to be found in his substantive and methodological assumptions. For Hempel, empirical significance (of a sentence S) is a relational concept. S is empirically significant if (a) it is an observational sentence or (b) it bears some specified relation R to a set of observational sentences. In this way theoretical sentences are admitted within the class of empirically significant statements. Unfortunately, every sentence which is formulated in the underlying language turns out (on a very plausible definition of R) to be empirically significant. So Hempel abandons the search for the empirical significance of sentences; he shifts to the search for a criterion of the empirical significance of terms, and finally to the search for a criterion for the empirical significance of theories. In all cases, the search for a criterion is unsuccessful and Hempel is finally driven to the suggestion that a notion of "degree of empirical meaning" be substituted for the usual classificatory concept which has been employed. Underlying this search, there seems to me to be a confusion in Hempel's mind between a semantic criterion of meaning and an epistemic notion of empirical content. He grants that all the statements of a putative theory - including the theoretical ones - have specified truth-conditions. But then surely they have meaning. Hempel agrees with this, too, but goes on to claim that this is not enough. 13 They must have empirical significance as well if they are to be acceptable to us. But why? Hempel assumes that sentences containing at least one theoretical term have meaning only if they stand in some specified (and acceptable) relation to sentences which normally are meaningful, i.e. are observational. In other words, a sentence (or theory) is meaningful in the semantic sense if and only if it is significant in the empirical sense. Primafacie, there seems no obvious reason to accept this condition. Terms, sentences, even theories may be meaningful because they fulfil certain semantic conditions, and yet they may bear no relationship to some class of observational terms or sentences. In addition, to require of them that they be empirically significant in order to be meaningful involves difficulties of its own. Suppose a statement could be meaningful in the semantic sense if and only if it za ASE, p. 217-22.

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were empirically significant. Empirical significance, as Hempel characterizes it, is a relational notion; a statement is empirically significant in relation to a set of statements. What about them; are they empirically significant? Either we face an infinite regress, or we must accept some class of statements as primitively empirically significant. The meaningfulness of these statements must be specified by means of a semantic theory which is identical with the one that we have first assumed or with another one. 14 It is unreasonable to assume two semantic theories when one is sutficient, and therefore it is unreasonable to require in the first place that a scientific statement be accorded semantic meaning if and only if it is accorded empirical significance. In the light of these considerations, many of Hempel's objectives seem ill-conceived. He has, it is true, given up the attempt to define the notion of empirical significance. But he is left with the problems which its introduction engendered. Thus he is at pains to discover whether theoretical terms (and sentences) are necessary ingredients of a logical account of science. Why is this the case? Since scientists employ theoretical sentences all the time, this is a good reason to think of them as quite necessary. But if one thinks, as Hempel does, that theories are meaningful only in so far as they logically imply observational sentences, it is easy for him to conclude that their only scientific function is in the derivation of observational sentences. He says this explicitly in many places. 15 Thence, it is another easy step to ask whether or not they are dispensable, i.e. whether there is some alternative theory which does not contain theoretical terms and which is capable in every case of allowing for the derivation of the same set of observational sentences as did the original theory. But the problem arose because theoretical sentences had a kind of derivative meaning and were therefore best gotten rid of. If this notion is given up, there seems an obvious answer to Hempel's question: Are theoretical sentences and theoretical terms eliminable? Of course not. They are 14 In fact, empiricists have frequently argued for a special theory of meaning for a class of base terms; the theory is that the meaning of these terms is identical with their reference. Hilary Putnana in the article 'Craig's Theorem', Journal of Philosophy 62 (1965) has convincingly argued that the theory is at the basis of many empiricist accounts of science. I agree with him in thinking that it is a bankrupt theory. In any case, Hempel does require some non-epistemic theory for such terms, under the assumptions stated above. 15 ASE, pp. 210, 211.

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meaningful, and by means of them other theoretical sentences can be derived. After all, this has traditionally been the task of scientific investigation: the understanding of the unobserved as well as the observed relations in nature. This is merely to say that Hempel's assumption that the function of science is the explanation and prediction of observational sentences is a notoriously narrow one and that it is suspect once we question his assumptions about the basis for attributing meaning to scientific sentences. If this argument is persuasive, other consequences follow from it. The elaborate discussions of the functional replaceability of theories by means of the devices of Craig's theorem or Ramsey sentences only makes sense if it is assumed that the function of science is the prediction and explanation of a class of sentences Ko = {the class of consequences of the axioms of a theory Twhich contain in addition to logical terms only observational terms}. If the class

KT11= {the class of all consequences S, of the axioms such that

S,e {CN(T)- Ko}}

must also be considered in the body of the scientific theory, then short of including in V0 = {the class of observational terms}, the class VT of theoretical terms, i.e. (A)

VT~_Vo,

the use of Craig's results or of Ramsey sentences will only insure that a truncated scientific theory can always be produced. But if condition (A) is satisfied, the devices cannot be applied. For they require for their application that

(B)

VrnVo=0

Put another way, we are faced with a dilemma. If condition (B) is fulfilled, then Ramsey sentences and Craig's results will only insure us that a theory with a truncated class of consequences can replace the original theory. If condition (A) is fulfilled, then the devices are not even formally applicable. In the latter case, it is always possible to formally partition the class into two subsets which fulfill condition (B). But such a partition doesn't serve the purpose of providing us with a functionally equivalent 116

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theory, for the whole notion of "functionally equivalent" no longer has a clear justification; indeed it rests upon an illicit assumption. The whole distinction between observational and theoretical terms is already a questionable one. Hempel himself admits that in practice it is extremely difficult to characterize the set of observation terms Vo and theoretical terms VT, but he claims that at least in theory some nonarbitrary partition of the set V= VTUVo, VTnVo=Ois possible. Reasons have been given already for suggesting that the distinction relies on an implicit division of terms into those that are inherently empirically significant and those whose significance must be earned by showing their relation to the former terms. It rests upon a mistaken notion. Furthermore, from what Hempel himself says about observable predicates, it seems impossible to think of the distinction into two exclusive and exhaustive sets as other than arbitrary. Observability is a property of terms which is relative to techniques, to the logical structure of the language in which the term is expressed, and perhaps to other factors which have not even been mentioned. In application to individual terms, say "3 inches high", it is clear that the distinction can be argued both ways. Wrongheaded metaphysics seems to be at the bottom of the distinction. Why preserve it if it is not needed? What I have said should not be taken to imply that Hempel's investigations are not of value. On the contrary, I think them of great value, but not for the ends which Hempel himself envisions. Much of his effort has been expended in attempting to justify the employment of those parts of scientific theory which need no justification. But along the way he has begun the investigation of many epistemic notions which are peculiarly amenable to formal treatment. Thus Hempel in his search for some weakened alternative to the earlier verifiability theory of meaning has begun the investigation of the relational concept of what can be called the "empirical content" of terms, sentences, and most interestingly, theories. It is wrong to think that having empirical content is a necessary or sufficient condition for a term, sentence, or theory to have a special kind of meaning. But it may well be that in determining whether or not a theory is confirmed, the relationship (or relationships) studied by Hempel will play a role. It is surely possible that Hempel's investigations will be of great value in extending the notion of confirmation to conceptually richer languages than those so far investigated by him and Carnap, i.e. 117

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to what Carnap has called the theoretical language. 16 In fact, Hempel's notion of the criterion for empirical significance of an interpreted theory already bears a family resemblance to a notion of confirmation he has rejected, the predictionist criterion of confirmation. For both notions presuppose the converse consequence condition: I f S 1confirms S2 andS2 ~ CN( S3) (or gives content to T 2 and T 2 ~ CN( T3)), then S 1 confirms S 3 (or gives content to T 3, respectively). This explains why in both cases if $1 bears the designated relationship to S3/T 3 then so does S 1 ^ $2/S~ ^ T2. In fact, the fulfillment of this criterion by both epistemic notions is viewed by Hempel as a positive disadvantage, but this may be an incorrect appraisal of the situation. Especially if the two notions are metricized, as Hempel himself has suggested that they be, there is nothing amiss in the idea. In any case, the notion of empirical content is worth studying on its own account as well as for its relationship to other epistemic notions. We have already noted that another dominant interest of Hempel is the formal characterization of epistemic notions. There is a strong resemblance between the various concepts which Hempel has studied. One way of seeing this is by investigating the various criteria which we come to accept as normative for the notion. Hempel has pioneered in the investigation of such criteria and their mutual relationship, but only in the limited context of the selection of the appropriate criteria for one conception and the determination of the mutual compatability of these criteria. A more systematic study of such criteria reveals characteristics of epistemic notions which are not at first apparent, and permits applications of ideas gained in one area to another one. To some of these questions we now turn. Hempel has most clearly stated the criteria of adequacy for the notion of qualitative confirmation. They are (in slightly different terminology)17: I. Entailment Condition: I f $2 e CN (Sa), then $1 confirms $2. II. Consequence Condition: I f $1 confirms {$2, $3,... S,}, then $1 confirms all Sk, such that Sk~CN {Sz .... , S,}. 16 Hempel himself does not suggest such a use of these notions. 17 These are stated in his essay 'Studies in the Logic of Confirmation', ASE, pp. 5-46. They should be more precisely stated to avoid undesirable consequences.

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(a) Special Consequence Condition: I f S1 confirms

8 2

and Sa ~ CN(S2),

then S1 confirms S 3. (b) Conjunction Condition: I f $1 confirms $2 and S1 confirms $3, then

S 1 confirms ($2 ^ $3). (c) Equivalence Condition: l f S1 confirms S 2 and S 2 is logically equiva-

lent to Sa, then Si confirms $3. III. Consistency Condition: I f $1 is self-consistent and S1 confirms (8 2. . . . . an} , then {S1)u(S2, Sa,..., S,} is consistent. IV. Inverse Equivalence Condition: I f S1 is logically equivalent to $2, and $2 confirms $3, then S1 confirms $3. But he emphatically rejects a condition which he calls the converse consequence condition: V. Converse Consequence Condition: I f $2~ CN (Si) and S 3 confirms

$2, then $3 confirms S1. The reasons that lead Hempel to reject V are the following ones. Si confirms St by the entailment condition. Therefore St confirms St ^ S, for any S, by the converse consequence condition and Si confirms S, by the special consequence condition. It is clear that Hempel must be assuming an additional criterion o f adequacy which I d u b : VI. The Quasi-Completeness Condition: For every Si, there is a sen-

tence Sj, such that it is not the case that St confirms Sj. T h e conditions stated bear resemblances to conditions for other epistemic notions.iS H e m p e l has himself provided a definition o f confirm a t i o n which satisfied I - I V . But it is clear that there m a y be other conceptions o f confirmation which satisfy other criteria. C a r n a p ' s notion is To work out fully the criteria of adequacy for the various other notions would be a task in itself. But even in the literature, some explicit criteria which very much resemble these stated above have been explicitly put forth. Thus, for the notion of 'verifiability', Israel Scheffter has stated a condition of adequacy very much like the quasi-completeness condition. It is found on p. 132 of The Anatomy of Inquiry, New York 1963, and is stated in the following way: "C.A. III. It is not the case that for every sentence S, S is significant." Scheffter fails to recognize the relational character of this concept. For the notion of 'explanation', David Kaplan in 'Explanation Revisited', Philosophy of Science 30 (1961) 429-36 gives versions of the converse consequence condition, special consequence condition, and quasi-completeness conditions. They are, respectively: Converse Consequence R1 : If a singular sentence is explainable by a given theory, then it is explainable by any theory from which the given theory is logically derivable. (Ibid., p. 430.) Special consequence R2: Any singular statement which is logically derivable from 119

REVIEWS o f c o n f i r m a t i o n d o e s satisfy a m o d i f i e d v e r s i o n o f I,

IIc,

v i o l a t e s II, I I a , I I b , a n d III. It also v i o l a t e s V. 19 G o o d m a n

a n d IV. I t accepts IIa,

l i b , I I I a n d a m o d i f i e d f o r m o f V as c r i t e r i a o f a d e q u a c y , b u t his o w n s y s t e m d o e s n o t satisfy e i t h e r I I c o r IV.20 P o p p e r ' s n o t i o n o f c o n f i r m a t i o n satisfies I, I I b , a n d V, b u t it d o e s n o t satisfy I I a o r III. 21 T h e s e r e m a r k s suggest t h a t a s y s t e m a t i c s t u d y o f t h e e p i s t e m i c n o t i o n o f

singular sentences explainable by a theory is itself explainable by a theory. (P. 430.) Quasi-completeness R3 : There is an interpreted language L which contains a fundamental theory T and singular statements E and E ' which are true but not logically provable, such that E is explainable by Tand E ' is not explainable by T. (P. 431.) With regard to 'knowledge', it is clear that most writers accept some version of the consequence condition, although there is vigorous debate about this point. See Jaakko Hintikka, Knowledge and Belief, Ithaca, N.Y., 1962. Many more similarities can be shown by a more careful analysis. These similarities are not accidental; they point to important similarities in the logic of these concepts. 19 Rudolf Carnap, Logical Foundations of Probability, Chicago 1950, pp. 474-76. See also Nelson Goodman, Fact, Fiction, and Forecast, Cleveland 1966, p. 68, fn. 5. z0 Goodman's acceptance of something like VI is shown in his rejection of a putative notion of confirmation because it leads to the following conclusion: "Thus every statement confirms all statements", Fact, Fiction, and Forecast, p. 68. He seems to accept the consistency condition. For in the derivation of the "grue" type paradox, the acceptance of such a condition is surely at the basis of our rejecting the conclusion that (i)

E confirms a is green

(ii)

E confirms a is not-green

(For this version of the paradox, see Israel Scheffier, 'Inductive Inference: A New Approach', Science 127 (1958) 177-81.) Furthermore if such a condition were not imposed, then accepting (i), (ii) and the consequence condition, we could easily show that the quasi-completeness condition was violated. Goodman accepts a special form of the converse consequence condition, i.e. (vi)

if S confirms S ' and S ' is an instance of S", then S confirms S".

(See Fact, Fiction, and Forecast, p. 69.) An instance of a hypothesis is a logical consequence of that hypothesis. Hempel as well accepts this modified version of the converse consequence condition. Goodman does not accept, in his own theory of projection, the inverse equivalence condition. For although for the evidence sets for a, examined before t (1)

E = al is grue and al is an emerald a2 is grue and as is an emerald

an is grue and an is an emerald E ' = al is green and al is an emerald and al is examined before t an is green and a,~ is an emerald and an is examined before t 120

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"confirmation" can be enlarged by a study of the criteria which various candidates for it satisfy. The construction of various characterizations which satisfy different criteria will help us to see the relationships between them and may settle some of the controversies which rage. For example, it is perfectly possible that part of the controversy between Carnap and Popper comes from their constructing different notions which satisfy different criteria. Systematic study of the criteria may reveal certain minimal ones which are acceptable to all serious students of the subject. Furthermore, study may reveal that insufficient attention has been paid to the metalinguistic notions (consequence relation, objects of the epistemic relation, etc.), and this will add new dimensions to the problem. In connection with what has been said, it is interesting to note that Hempel, although he explicitly rejects the converse consequence condition for the notion of "qualitative confirmation", accepts it for the notion of "empirical significance". If, as seems likely, the latter notion will be most fruitfully employed in defining a notion of confirmation for theories, it is hard to see why Hempel is so eager to give up the condition. It is also strange that Hempel should so quickly reject the prediction criterion of confirmation. Whatever its particular form, it embodies a certain interesting notion of confirmation - that statements are confirmed in terms of their consequences - a notion of great importance in the confirmation of theories which do not exemplify the predicates which appear in the it is the case that (2)

E---E' .g

still E' confirms that all emeralds are green but ~ (E confirms that all emeralds are green) since the set E' is not accepted as evidence since it contains the badly entrenched predicate "is grue". 21 Popper defines the qualitative concept of corroboration in the following terms: Let S~ corroborates $1 be symbolized by Co ($1, $2); then Co ($2, $1) iff prob ($2, $1) > prob (S~)

See The Logic of Scientific Discovery, p. 389. For a further discussion of some of the criteria which Popper accepts and rejects, see The Logic of Scientific Discovery, London 1959, pp. 400-2, 372, 119-30. 121

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evidence which confirms them. In fact, Hempel might accept a modified form of the converse consequence condition: V'. I f $1 confirms $2 and Sz is an instance of $3, then S 1 confirms $3 .22 Hempel's notion of the C-development of a statement is supposed to render the intuitive notion of an instance of that statement (trivially if the statement is not a general one). The C-Development of a statement comes close to being a logical consequence of that statement. (It is a logical consequence of the statement and of another statement restricting the individuals of the universe to those with respect to which we are developing the former.) A statement Si confirms a statement Si if it logically implies (and therefore by the entailment condition confirms) the C-development of Sj. It seems to me that Hempel has been much too hasty in his rejection of definitions of confirmation which satisfy the converse consequence condition. There remain a number of possibilities which he has not pursued. Rejection of the consistency condition (which brings with it the rejection of the special consequence condition), restatement of the conditions for confirmation in terms of intensional or pragmatic notions these are some of the possibilities which come to mind. The methods Hempel has developed in his discussion of confirmation may be applied to the other epistemic notions of explanation and verification. Only the surface has been scratched in the investigation of those problems. Hempel's book is a rich and illuminating source of future developments in the field of the logic of science.

C. W. Post College of Long Island University, Brookville, New York

H O W A R D SMOKLER

22 See Goodman, Fact, Fiction, and Forecast, p. 69 and Hempel, ' A Purely Syntactical Definition of Confirmation', Journal of Symbolic Logic 8 (1943) 122-43.

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