MIND

A   QUARTERLY  REVIEW

OF

PSYCHOLOGY   AND PHILOSOPBY

!.-STUDIES IN THE LOGIC OF CON­ FIRMATION  (IJ;).

BY   CARL  G. HEMPEL.

7.  The Predi.ction-<Yriterion of Conformation and its Short­ oomings.-W e are now in a position to analyze a second conception of confirmation which is reflected in many methodological dis­ cussions and  which can claim  a great  deal  of plausibility.                    Its basic idea  is very simple:   General  hypotheses  in science as  well as in everyday usage are intended to  enable  us  to  anticipate future events ; hence, it seems reasonable to count any prediction which is borne out ,by subsequent observation as confirming evidence for the hypothesis on which it is based, and any predic­ tion  that  fails  as disconfirming  evidence.    To  illustrate :   Let H1 be the hypothesis that all metals, when heated, expand; symbolically:  ' (x) ((Metal (x) . Heated  (x)) :::, Exp(x)) '.                          If we are  given  an  observation  report to the effect that a certain  object a is a metal and is heated, then by means of H1 we can derive the prediction that a expands. Suppose that this is borne out by observation and described in an additional observation statement. We sb.oulq. then have -the total observation report. {Metal(a), Heated(a),  Exp.(a)}.1                                      This  report  would  be  qualified  as  con­ firming evidence for H1 because its last sentence hears out  what could  be  predicted,  or derived, from the first  two  by means  of

Hi; more explicitly: because the last sentence  can  be derived  from the first two in conjunction with Hi.-Now let H2 be the hypothesis that  all swans  are white ;  symbolically :   ' (x) (Swan

10. :,  White(x)) ';   and consider the observation report {Swan(a),

,_, White(a)}.   This  report  would  constitute disconfirming evi­ dence for H 2 because the second of its sentences contradicts (and thus fails to bear out) the prediction 'White(a)' which can be deduced from the first sentence in conjunction with H2 ; or, symmetrically, because the first sentence contradicts the conse­ quence ',_, Swan(a)' which can be derived from the second in conjunction  with H2•                                        Obviously,  either  of these formulations implies that H2  is incompatible  with the given observation report.

These illustrations suggest the following general definition of confirmation as successful prediction  :

Prediction-criterion of Confirmation : Let H be a hypothesis, B

an observation report, i.e. a class of observation sentences.   Then

1. Bis said to confirm H if B can be divided into two mutually exclusive subclasses Bi and B2 such that B2 is not empty, and every sentence of B2 can be logically deduced from Bi in conjunction with  H,  but  not from  Bi alone.
   2. Bis   said to disconfirm H if H logically contradicts  B.i
3. Bis said to be neutral with respect to H if it neither con­ firms nor disconfirms H.2

But while this criterion is quite sound as a statement of suffi­ cient conditions of confirmation for hypotheses of the type illus­ trated above, it is considerably too narrow. to serve as a general definition of confirmation.    Generally  speaking,  this  criterion would serve its purpose if all scientific hypotheses could be con­ strued as asserting regular connections of observable features in the  subject-matter  under  investigation ;  i.e. if  they  all  were of

the form "Whenever  the observable  characteristic  P  is  present in an object or a situation, then the observable  characteristic  Q will also be present." But  actually,  most  scientific  hypotheses and laws are not of this simple type; as  a  rule,  they  express regular connections  of characteristics which are not  observable  in the sense of direct observability, nor even in a much more liberal sense. Consider, for example, the following hypothesis : "Whenever plane-polarized light of wave length ,\  traverses  a layer  of quartz  of  thickness d, then  its  plane  of  polarization is

rotated  through an  angle  oc which is proportional  to i-"-Let us

assume that the observational  vocabulary,  by  means  of  which our observation reports have to be formulated, contains exclus­ ively terms referring to directly  observable  attributes.  Then, since the question of whether a given ray of light is plane­ polarized and has the wave length,\ cannot  be decided  by means of direct observation, no observation report of the kind here admitted could include information of this  type.  This in itself would not be crucial  if  at  least  we could  assume  that  the fact that a given ray of light is plane-polarized, etc., could be logically inferred  from some  possible  observation  report;  for  then,  from a suitable report of this kind, in conjunction with the given hypothesis, one would be able to  predict a  rotation of the plane  of polarization ; and from this prediction, which itself is not yet expressed in  exclusively observational  terms,  one might  expect to derive further predictions in the form of genuine observation sentences. But  actually,  a  hypothesis to the efiect that  a given ray of light is plane-polarized has to be considered as .a general hypothesis which entails an unlimited number of observation sentences; thus it cannot  be logically  inferred  from, but at  best be confirmed by, a suitable set of observational findings. The logically essential  point can  best  be exhibited  by reference  to a

. very  simple abstract  case:  Let  us  assume that  Ri and  R2   are

two relations of a kind accessible to direct observation, and that the field of scientific investigation contains infinitely  many objects.   Consider  now the hypothesis

(H)                         (x)((y)Ri(x,  y) :,  (Ez)R2(x, z)),

i.e. :  Whenever an object  x stands in R1  to  every  object  y, then it stands in R2 to at  least  one object  z.-This simple  hypothesis has the following property: However many observation sen­  tences may be given, H does not enable us to derive any new observation  sentences  from  them.   Indeed-to  state  the  reason in  suggestive  though  not  formally  rigorous  terms-in   order to

make a prediction concerning some specific object a, we shoqjd first have to know that a stands m R1 to every object; and this necessary inforw.ation  clearly Gannot  be contained in any finite

number, however large, of observation sentences, because a finite set of observation sentences can tell us at  best for a finite number of  object&  th11,t a  stands  in  Rt to  them.    Thus an observa­

tion report, which always invQlves only a finite number of ob­ servation sentences, can never provide a 1,uffi.ciently broad basis for a prediction  by means  of  H.1-Besides,  even if  we did know

that a stood in  Ri to  every object, the prediction  derivable   by

means of H would not be an observation  sentence ;  it  would assert that a stands in R2 to some objeot,  without  specifying which, and whel'fl to find it. Thus, H would be an empirical hypothesis, containing, besides purely logical terms, only ex­ pressions belonging to the observational vocabulary, and yet the predictions which it  renders  possible neither start from nor lead  to  observation repo,:ts.

It is, therefore, a considerable over-simplification to say t4at scientific hypotheses and  theories enable us to derive predictions of future experiences from descriptions of past ones. Unquestion­ ably, scientific hypotheses  do  have  a  predictive  function;  but t4e way in which they perform this function, the  manner  ip.  which they establish logical connections between observation reports, is logically more complex than a deductive  inference. Thus, in the last illustration, the predictive use of  H may assume the following form : On the basis of a number  of  in,diviq.ual tests,  which show that  a doef! stand  in  R1   to  three objects  b, c,

and  d, we may accept  the  hypothesis  that  a stands in  Ri to all

objects; or, in terms of our formal mode of speech:  In  view 0£ the observation report {Ri(a, b), R1 (a, c), Ri(a,d)}, the hypothesis that (y)Ri_(a, y) is accepted as confirmed by, though-not logically

inferable from, that report.2 This process might be referred to as  quasi-induction.3       From  the  hypothesis  thus established  we

can then proceed to derive, by means of H, the prediction that a stands in  R2  to  at  least  one object.  This again,  as was pointed out above, is not an observation sentence ; and indeed no ob­ servation sentence can be derived from it ; but it can, in turn, be confirmed  by a suitable observation sentence, such as ' R2(a , b) '.

-In     other  cases,  the   prediction   of  actual observation  sentences may be possible ; thus if  the  given  hypothesis  asserts  that (x)((y)Ri_(x, y) :, (z) R2( x, z)), then after quasi-inductively accept­ ing, as above, that (y)R1 (a , y), we can  derive,  by  means  of  the given hypothesis, the sentence that a stands in R2  to  every object, and thence, we can deduce special  predictions  such  as 'Ria, b) ', etc.,  which  do  have  the  form  of  observation. sentences.

Thus, the chain of reasoning which leads from given observa" tional findings to the" prediction" of new ones actually involves, besides deductive  inferences,  certain quasi-inductive steps  each of which consists in the acceptance of  an  intermediate statement on the basis of confirming, but usually not logically conclusive, evidence. In most scientific predictions,  this  general  pattern occurs in multiple re-iteration;  an analysis of  the  predictive  use of the hypothesis mentioned a ove, concerning plane-polarized light, could serve as a:h illustration. In the present  context, however, this general account of the structure of scientific pre­ diction is sufficient : it shows that a general definition of con­ firmation by reference to successful prediction becomes circular ; indeed, in order to make the original formulation of the predic­ tion-criterion of confirmation sufficiently comprehensive, we should have to replace the  phrase  " can  be logically  deduced " by "can be obtained by a series of steps of deduction and quasi­ indu:ction " ; and the definition of  "  quasi-induction "  in  the above sense presupposes the concept of confirmation.

Let us note, as a  by-product  of  the  preceding consideration, the fact that an adequate analysis of scientific prediction (and analogously, of scientific explanation, and of the testing of empirical hypotheses) requires an analysis of the concept of confirmation. The reason for  this  fact  may  be  restated  in general terms as follows: Scientific laws and theories, as a rule, connect terms which lie on the level of abstract theoretical constructs rather than on that of direct observation ; and from observation sentenc,es, no merely deductive logical inference leads

to statements about those theoretical constructs which are the starting  point  for  scientific  predictions ;  statements   about logical constructs,  such  as  " This  piece  of  iron  is  magnetic " or "Here, a plane-polarized ray  of  light  traverses  a  quartz crystal" can be confirmed, but not  entailed,  by  observation reports, and thus, even though based  on general scientific laws, the "prediction" of new observational findings on the  basis  of given ones is a process involving confirmation in addition to logical deduction.1

8. Conditions of Adequacy for any Definition of Confirmation.­ The two most customary conceptions  of  confirmation,  which were rendered explicit in Nicod's criterion and in the prediction criterion, have thus been found unsuitable for a general definition of confirmation. Besides this negative result,  the  preceding analysis has also exhibited certain logical characteristics of scientific prediction, explanation, and  testing,  and it  has led to the establishment of certain standards which an adequate de­ finition of confirmation has to satisfy.  These standards include  the equivalence  condition and the requirement that the definition of confirmation be applicable to hypotheses of any degree  of logical complexity, rather than to the simplest type of universal conditional only. An adequate definition of confirmation, how­ ever,  has to satisfy several further logical requirements,  to which

.we  now turn.

First of all, it will be agreed that any sentence which is entailed by-i.e. a logical consequence of-a given  observation  report  has to be considered as confirmed by that report : Entailment  is a special case of confirmation. Thus, e.g., we want to say that the observation report " a is black " confirms the sentence (hypo­ thesis) " a is black or grey " ; and-to refer to one of the illustra­ tions given in the preceding s ction-the observation sentence '  R2(a, b)' should  certainly  be  confirming  evidence  for  the sentence '(Ez)Ria, z) '. We are  therefore  led  to  the  stipulation that any adequate definition of confirmation must insure the fulfilment of the

(8.1) Entailment condition: Any sentence which is entailed by an observation  report is confirmed  by it.1

This conditipn is suggested by  the  preceding  consideration, but of· course not proved by it.  To  make  it  a  standard  of adequacy for the definition of  confirmation  means to  lay down the stipulation that a proposed definition of confirmation will be rejected as logically inadequate if it is not constructed  in such a way that (8.1) is unconditionally satisfied. An analogous remark applies to the subsequently proposed further standards of adequacy.-

Second, an observation report which  confirms  certain  hypo­ theses would invariably be qualified as  confirming  any  conse­ quence  of those hypotheses.                                Indeed  :   any  such consequence  is but an assertion of all or part  of  the  combined  content  of  the original hypotheses and  has therefore  to  be regarded  as confirmed by  any  evidence  which  confirms  the   original  hypotheses.                                This suggests the  following  condition  of adequacy  :

(8.2) Consequence Condition:  If  an  observation  report  con­ firms every one of a  class K  of  sentences,  then  it  also  confirms any  sentence  which is a logical consequence  of  K.

If (8.2) is satisfied, then the same is true of the following two more special conditions :             ·

(8.21) Special Consequence Condition: l£ an observation report confirms a hypothesis  H, then it  also confirms  every  consequence of H.

(8.22)  Equivalence Condition:  If  an observation report confirms

a hypothesis H, then it also confirms every hypothesis which is logically equivalent with H.

(This follows from (8.21) in view of the fact that equivalent hypotheses are mutual consequences of each other.) Thus, the satisfaction  of  the  consequence  condition  entails  that  of  our earlier equivalence condition, and the latter loses its status of an independent   requirement.

In view of the apparent obviousness of these conditions, it is interesting to note that the definition of confirmation in terms of successful prediction, while satisfying the equivalence condition, would violate the consequence condition. Consider, for example, the  formulation  of  the  prediction-criterion  given  in  the earlier

part  of  the  preceding  section.  Clearly,  if  the  observational findings  B2  can  be  predicted  on  the  basis  of  the  findings  B1   by

/means of the hypothesis H, the same prediction is obtainable by means of  any  equivalent hypothesis,  but not generally by means

of  a weaker one.

On the other hand,  any  prediction  obtainable  by  means  of  H caii obviously also be established by means  of  any  hypothesis which is stronger than H, i.e.  which  logically  entails  H.  Thus, while the consequence  condition  stipulates  in  effect  that  what­ ever confirms a given hypothesis also confirms any weaker hypothesis, the relation of confirmation defined in  terms  of successful prediction would satisfy the condition that whatever confirms· a  given hypothesis,  also  confirms  every  stronger one.

But is this " converse consequence condition ", as it might be called, not reasonable enough, and should it not even be included among our standards of adequacy for the definition of confirma­ tion ? The second of these two suggestions  can  be  readily disposed of : The adoption of the  new condition,  in addition  to (8.1) and (8.2), would have the consequence that any observation report B would confirm any  hypothesis  H  whatsoever.  Thus, e.g., if Bis the report" a is a raven" and His Hooke's law, then, according  to  (8.1), B confirms the sentence" a is a raven",  hence B would, . according to the converse consequence condition, confirm the stronger sentence "a is a raven,  and  Hooke's  law holds " ; and finally, by virtue of (8.2), B would confirm H, which is a consequence of  the  last sentence.   Obviously, the same type of  argument  can  be applied in all other cases.

But is it not true, after all, that  very  often  observational  data which  confirm  a  hypothesis  H  are  considered  also as  confirming a stronger hypothesis ? Is it not true, for example, that those experimental findings which  confirm  Galileo's  law,  or  Kepler's laws, are considered also as confirming  Newton's  law  of  gravita­ tion ? 1 This is indeed the case, but  this  does  not  justify  the acceptance  of  the  converse  entailment  condition   as   a   general rule of the logic of  confirmation  ;  for in the  cases  just  mentioned, the weaker hypothesis is connected with the  stronger  one  by  a logical bond of a particular kind : it is essentially a substitution instance of the  stronger one;  thus, e.g., while the  law  of  gravita­ tion refers  to  the  force  obtaining  between  any  two  bodies, Galileo's law is a  specialization referring  to  the  case  where one of

the bodies is the  earth, the other  an object  near its  surface.  In the preceding case, however,  where  Hooke's law was shown  to be confirmed by the observation report that a is a raven, this situation  does not  prevail;  and  here, the  rule that whatever con­

:finns a given hypothesis  also confirms any  stronger  one  becomes an entirely absurd principle. Thus, the converse consequence con­ dition  does  not  provide a sound  general condition  of  ad  equacy.1

A third  condition  remains to be stated: 2

(8.3) Consistency Condition: Every logically consistent observa­ tion report is logically compatible with the class of all the hypotheses which it  confirms.

The two most important implications of this requirement ate the  following :

(8.31) Unless  an  observation  report  is  self-c ontradictory, 3  it does not confirm any hypothesis with which it is not logically compatible.

(8.32)  Unless  an   observation  report  is  self-contradictory, it

does not confirm any hypotheses  which contradict  each other.

The first of these corollaries will readily be accepted ; the second,  however,-and  consequently   (8.3) itself-will  perhaps be

felt  to  embody  a  too  severe  restriction.   It   might   be  pointed out, for example, that a finite set of measurements concerning the variation of one physical magnitude, x,  with  another,  y,  may conform to, and thus be said to confirm,  several  different  hypo­ theses  as  to  the  particular  mathematical  function  in  terms  of which the relationship 0£ x and y can be expressed ; but su h hypotheses are incompatible because  to  at  least  one  value  of  x, they  will assign different  values  of y.

No doubt  it  is possible  to  liberalize  the  formal standards  of

.adequacy in line with these considerations. This would amount to dropping (8.3) and (8.32) and retaining only (8.31). One of the effects of this measure would be that when a logically consistent observation report B confirms each of two hypotheses, it does not necessarily confirm their conjunction ; for the hypotheses might he mutually incompatible, hence their conjunction self-contra­ dictory;  consequently,  by (8.31), B could not confirm it.-This

.consequence is intuitively rather awkward, and one might there­ fore feel inclined to suggest that while (8.3) should be dropped and

{8.31)  retained,  (8.32)  should  be  replaced  by  the requirement

{8.33): If an observation sentence confirms each of two hypo­ theses, then it also  confirms  their  conjunction.  But  it  can readily be shown that by virtue of (8.2) this set of  conditions ntails  the fulfilment  of  (8.32).      ·

If, therefore, the condition (8.3) appears to be  too  rigorous,  the most obvious alternative  would  seem  to  lie in replacing  (8.3) and its  corollaries  by the  much weaker  condition  (8.31)  alone;   and  it is an  important  problem  whether  an  intuitively  adequate  defini­ tion of confirmation can  be constructed  which satisfies  (8.1), (8.2) and (8.31), but  not  (8.3).-0ne  of  the  great  advantages  of  a definition which  satisfies  (8.3)  is that  it  sets a  limit, so  to  ijpeak, to the  strength  of  the  hypotheses  which  can  be  confirmed  by given    evidence.1

The remainder of the present study, therefore, will be con­ cerned exclusively with the problem of establishing  a definition  of confirmation which satisfies the more severe formal conditions represented  by (8.1),  (8.2), and  (8.3) together.

The fulfilment  of  these  requirements,  which may be regarded

.as general laws of the logic of confirmation, is of course only a necessary, not a s fficient, condition for the adequacy  of  any proposed  definition  of  confirmation.    Thus,  e.g., if  "B  confirms

H "· were defined as meaning " B logically entails H ", then the above three conditions would clearly be satisfied ;  but  the definition  would not be adequate  because confirmation  has to  be a more comprehensive  relation than entailment  (the latter might be referred to as the special case of conclusive confirmation). Thus, a definition of confirmation, to be acceptable, also has to be materially adequate: it has to provide a reasonably close ap­ proximation  to that conception of confirmation  which is implicit in scientific procedure and methodological discussion. That conception is vague and to some extent quite unclear, as I  have tried  to show in earlier  parts of  this paper;  therefore,  i_t would be too much to expect full agreement  as to the material adequacy of a proposed definition of confirmation ;  on  the  other  hand, there will be rather general  agreement  on certain  points ;  thus, e.g., the identification of confirmation with entailment, or  the Nicod criterion of confirmation as analyzed above, or any defini­ tion of confirmation by  reference  to  a  '· sense  of  evidence ", will probably now be admitted not to be adequate approximations to_ that concept of confirmation which is relevant for the logic of science.

On the other hand, the soundness  of  the  logical  analysis (which, in a clear sense, always involves a logical reconstruction) of a theoretical concept cannot be gauged simply by our feelings  of satisfaction at a certain  proposed  analysis ;  and if there  are, say, two alternative proposals  for defining a term on  the  basis  of a logical analysis, and if both appear to come fairly close to the intended meaning, then the choice has to be made largely by reference to such features as the logical properties of the two reconstructions, and the comprehensiveness and simplicity of the theories to  which they lead.

9. The Satisfaction Criterion of Confirmation.-As has been mentioned before, a precise definition of confirmation requires reference to some definite " language of science ", in which all observation reports and all hypotheses under consideration are assumed to be formulated, and whose logical structure  is sup­ posed   to   be  precisely  determined.             The   more  complex  this language, and the richer its logical means of expression, the more difficult it will be, as a rule, to establish an adequate definition of confirmation for it.      However,  the  problem has been  solved at least for certain cases : With respect to languages of a compara­ tively simple logical structure, it  has been  possible  to  construct an explicit definition of confirmation which satisfies all of  the above logical requirements, and which appears to be intuitively rather  adequate.     An exposition  of  the  technical  details of this

definition has been published  elsewhere; 1  in  the  present  study, which is concerned with the general logical and methodological aspects of the problem of confirmation rather than with technical details, it will be attempted to characterize the definition of con­ firmation thus obtained as clearly as possible with a minimum of technicalities.

Consider  the  simple  case  of  the   hypothesis  H:   '(x)(Raven(x)

:, Black(x)) ', where 'Raven' and 'Black' are supposed to be­ terms of our observational vocabulary. Let B be an observation report to the effect that Raven(a) . Black(a) . ,...,_, Raven(c) . Black(c). ,...,_, Raven(d). r-;., Black(d). Then B may be said  to confirm H in the following sense : There are three objects al­ together mentioned in B, namely a, c, and d ;  and as far as these are concerned, B informs us that all  those which ar  ravens (i.e. just the object a) are also black.2 In other words, from the­ information contained in B we can infer that  the hypothesis  H does hold true within the finite class of those objects which are mentioned  in B.

Let us apply the same  cbnsideration  fo  a  hypothesis  of  a logically   more   complex   structure.     Let   H   be   the   hypothesis "  Everybody likes somebody  "  ;  in symbols :  '  (x)(Ey)Likes(x, y)',

i.e. for every (person) x, there exists at least one (not necessarily different person) y such that x likes y. (Here again, 'Likes' is aupposed to he a relation-ter which occurs in our observational vocabulary.)   Suppose  now that  we are  given an observation

report  B in  which the  names of  two  persons,  say  ' e '  and 'f ',

occur. Under what conditions shall we say that B confirms H 1 The previous illustration suggests the answer: If from B we can infer that H is satisfied within the finite class {e, f}; i.e. that within {e, f} everybody likes somebody. This in turn  meaw, that e likes e.or f, and f likes e or f. Thus, B would be said to confirm H if B entailed the statement " e likes e or f, and f likes e or f ". This latter statement will be called the development of H for the finite class {e,J}.-

The concept of development of a hypothesis, H,for a finite cl,ass of individuals, C, can be defined in a general fashion ; the de­ velopment of H for O states what H would assert if there existed exclusively  those  objects  which  are  elements  of 0.-Thus, e.g.,

the   development   0£  the   hypothesis  H1  = '(x)(P(x) v Q(x))'

(i.e. "Every object has the property P or the property Q ") for the class {a, b} is '(P(a) v Q(a)) . (P(b) v Q(b))' (i.e. "a has the property P or the property Q, and b has the property P or the property Q ") ; the development of the existential hypothesis H2 that   at least  one object  has the  property P, i.e. '(Ex)P(x) ', for

{a, b} is 'P(a) v P(b)'; the development of a hypothesis which contains no quantifiers, such as  H3  :  'P(c) v Q(c) '  is  defined as that hypothesis itself, no matter what the reference class of individuals is.

A more detailed formal analysis based on considerations 0£ this type leads to the introduction of a general relation of con­ firmation in two steps; the first consists in defining a special relation of direct confirmation  along  the  lines  just  indicated ; the second step then defines the general relation of confirmation by reference to direct confirmation.

Omitting minor details, we may summarize the two definitions as  follows:

(9.1 Df.) An observation report B directly confirms a hypo­ thesis H if B entails the development of H for the class of those objects  which are mentioned  in  B.

(9.2 Df.) An observation report B confirms a hypothesis H if H is entailed by a class of sentences each of which is directly con­ firmed  by B.

The criterion expressed in these definitions might be called the satisfaction criterion of confirmation because its  basic  idea consists  in  construing  a   hypothesis  as  confirmed   by  a given

observation report if the  hypothesis is satisfied in the  finite class of those individuals which are mentioned  in the report.-Let  us now apply the two definitions to our last examples : The observa­ tion  report  B1  :  'P(a) . Q(b)'  directly  confirms  (and  tlierefore also confirms) the hypothesis H1, because it entails the develop­ ment of H1 for the class {a, b}, which was given above.-The hypothesis H3 is not directly confirmed by B, because its develop­ ment-i.e.  H3  itself-obviously is  not  entailed  by  B1.        However, H3  is entailed  by H1,   which is directly  confirmed  by  B1  ;   hence, by virtue of (9.2), B1 confirms H 3.

Similarly, it  can readily  be seen that B1   directly  confirms  H 2•

Finally, to refer to  the  first  illustration  given  in  this  section  : The  observation  report  'Raven(a)  .  Black(a)  .  ,-..,  Raven(c)  . ,-.....,

Black(c) . ,..._, Raven(d) . ,..._, Black(d) ' confirms (even directly) the hypothesis' (x)(Raven(x) :) Black(x)) ', for it  entails  the  develop­ ment of the latter for the class {a, c, d}, which can be written as follows:  '(Raven(a)   :)   Black(a)).  (Raven(c)   :)   Black(c)). (Raven

4. :)  Black(d)) '.

It  is now easy  to  define  disconfirmation and  neutrality :

(9.3 Df.) An observation  report B disconfirms a hypothesis  H if  it  confirms the  denial of H.

(9.4  Df.)  An  observation  report  B  is  neutral  with   respect   to a  hypothesis  H if  B  neither  confirms nor disconfirms H.

By virtue of the criteria laid down in (9.2), (9.3), (9.4), every consistent observation report, B, divides all possible hypotheses into three mutually exclusive classes : those confirmed by B, those disconfirmed by B, and those with respect to which B is neutral. The definition of confirmation here proposed can be shown to satisfy all the formal conditions of adequacy embodied in (8.1), (8.2), and (8.3) and their consequences; for the condition (8.2) this is  easy to  see ;  for  the  other  conditions  the  proof  is more

complicated.1

Furthermore, the application of the above definition of con­ firmation is not restricted to hypotheses of universal conditional form (as Nicod's criterion is, for example), nor to universal hypo­ theses in general ; it applies, in fact, to any hypothesis which can be expressed by means of property and relation terms of the observational vocabulary of the given language, individual names, the customary connective symbols for  'not',  'and', 'or',  'if­ then ',  and any number  of  universal  and  existential  quantifiers.

Finally, as is suggested by  the  preceding illustrations  as weU as by the general considerations which underlie the establishment of the above definition, it seems that we have obtained a definition

-0f confirmation which also is materially adequate in the sense of being a reasonable approximation to the intended meaning of onfirmation.

A brief discussion of certain special cases of co firmation mig:t,.t

jerve  to shed further  light on tlµs latter aspect  of our analysis.

10. The P,el,ative anii the Absolute Concepts of Veriji,cQ,tiori and, Falsification.-If an observation report entails  a  hypothesis  If, then, by virtue of (8.1), it confirms H. This is in good agreeIQ.ent with the customary conception of confirming  evidence ;  in fact, we have here an extreme case of confirmation, the case where B conclusively confirms H ; this case is realized if, and only if, B entails H. We shall then also say that B verifies H.  Thus, verification is a special case of confirmation ; it is a logical relation

between sentences ;  more specifically, it is simply the relation of

-entailment with its domain restricted to observation sentences. Analogously,  we shall say that  B conclusively  disconfirms H,

or B fq,lsifies H, if and only if B is incompatible with H ; in this case, B entails the denial of H and therefore,  by virtue  of  (8.1) and (9.3), confirms the denial of H and disconfirms H. Hence, falsifi ation  is a special case of disconfirmation ;  it  is the logical

:relation· of incompatibility  between  sentences,  with its domain

:restricted  to  observation sentences.

Clearly, the concepts of veriji,cQ,tion and falsification as here defined are relative; a hypothesis can be said to be verified or falsified only with respect to some observation report; and a hypothesis may be verified by one observation  report  and  may not be verified by  another.  There  are,  however,  hypotheses which cannot be verified and others which cannot be falsified by any  observation  report.  This  will  be  shown  presently.   We shall say that a given hypothesis is verifiable (falsifiable) if it is possible to construct an observation  report  which  verifies (falsifies) the hypothesis. Whether a hypothesis is verifiable, or falsifiable, in this sense depends exclusively on its logical form. Briefly, the following  cases may be distinguished:

1. If   a   hypothesis   does  not   contain   the quantifier   terms " all " and " some " or their symbolic equivalents, then it is both verifiable and falsifiable. Thus, e.g., the  hypothesis  "Object  a turns  blue or green "  js entailed  and thus verified  by  the report " Object a turns blue " ; and the same hypothesis is incompatible with, and thus falsified by,  the  report  "Object  a  turns  neither blue nor green ".
2. A purely existential hypothesis (i.e. one which can be symbolized by a formula consisting of one or more existential quantifiers   followed   by   a   sentential   function   containing no

quantifiers) is verifiable, but not falsifiable, if-as is usually assumed-the universe  of  discourse  contains  an  infinite  number of objects.-Thus, e.g., the hypothesis "There are blue roses" is verified. by the observation report "Object  a is a  blue rose",  but no finite observation report can  ever contradict  and  thus falsify the  hypothesis.                                       _

3. Conversely, a purely universal  hypothesis  (symbolized  by a formula consisting of one or more universal quantifiers followed by a sentential function  containing  no quantifiers)  is falsifiable but not verifiable for an  infinite  universe  of  discourse.  Thus, e.g., the hypothesis " (x)(Swan(x) :> White(x)) " is completely falsified by the observation report {Swan(a), ,..._, White(a)} ; but no finite observation report can entail and thus verify the hypothesis  in question.
4. Hypotheses which cannot be expressed bysentences of one of the three types mentioned so far, and which in this sense require both lilliversal and existential quantifiers  for  their formulation, are as a rule neither verifiable nor falsifiable.1 Thus, e.g., the hypothesis " Every substance is soluble in some solvent " - symbolically ' (x)(Ey)Soluble(x, y) '-is neither entailed by, nor incompatible with any observation report, no matter how many cases of solubility or non-solubility of particular substances in particular solvents the report may list. An analogous  remark applies to  the  hypothesis  " You  can  fool  some  of  the  people all of the time", whose symbolic formulation '(Ex)(t)Fl(x,t) ' contains  one  existential  and  one universal quantifier.                                                               But of course, all of the hypotheses belonging to this fourth class are capable of being confirmed or disconfirmed by suitable observation reports; this was illustrated early in section 9 by reference to the hypothesis ' (x)(Ey)Likes(x, y) '.

This rather detailed account  of  verification  and  falsification has been presented not  only in the  hope of further  elucidating the meaning of confirmation and disconfirmation as defined above, but also in order to provide a basis for a sharp differentia­ tion of two meanings of verification (and similarly of falsification) which have not always been clearly separated in recent discussions of the character of empirical knowledge. One of the two meanings of verification which we wish to distinguish here is the relative concept  just  explained;   for  greater .clarity  we shall sometimes

refer to it as re"lative verification. .The other meaning is what may be called a.hsolute or definitive verification. This latter concept of verification does not belong to formal logic, but rather to prag­ matics 1  :  it  refers  to  the  acceptal!,ce  of  hypotheses  by "observers 1' or "scientists",  etc.,  on  the  basis  of  relevant evidence.   Generally speaking,  we may distinguish  three phases in the scientific test of a given hypothesis (which do not neces­ sarily occur in the order in which they are listed here). The first phase consists in the performance of suitable experiments or observations and the ensuing acceptance of observation sen­ tences,or of observation reports, stating the results obtained ; the next phase consists in confronting the given hypothesis with the accepted observation reports, i.e.  in  ascemining  whether  the latter constitute confirming, disconfirming or irrelevant evidence with respect to the hypothesis; the final phase.consists either in accepting or rejecting the hypothesis on the strength of the con­ firming or- disconfirming evidence constituted by the accepted observation reports, or in suspending judgment, awaiting the establishment  of further  relevant evidence.

The present study has been concerned almost exclusively with the second phase; as we have seen, this phase is of a  purely  logical character ; the standards of evaluation here  invoked­ namely the criteria of confirmation, disconfirmation and neu­ trality-can be completely formulated in terms of  concepts belonging to the field of  pure  logic.

The first phase, on the other hand, is of a pragmatic character ; it involves no logical confrontation of sentences with other sentences. It consists in performing certain experiments or systematic observations and noting the results. The latter are expressed in sentences which have the form of observation reports, and their acceptance by the scientist is connected  (by causal, not by logical relations) with experiences  occurring  in  those  tests. (Of course, a sentence which has the form  of  an  observation report may in certain cases be accepted not on the basis of direct observation, but because it is confirmed by other observation reports which were previously established; but this process is illustrative of the second phase,  which  was. discussed  before Here we are considering the case where a sentence is accepted directly "on the basis of  experiential  :findings"  rather  than because it  is supported  by previously  established statements.)

The third phase, too, can be construed as pragmatic, namely as consisting in a decision  on the part of the scientist  or a  group of

scientists to accept (or reject, or leave in suspense, as the case  may be) a given hypothesis after ascertaining what amount of confirming or of disconfirming evidence for the hypothesis is contained 'in the totality of the accepted observation sentences. However, it may well  be attempted  to give a  reconstruction of this phase in purely logical terms. This- would require the establishment of general " rules of  acceptance "  ;  roughly speaking, these rules would state how well a given hypothesis has to be confirmed by the accepted observation reports to be scien­ tifically  acceptable  itself  ; 1  i.e.  the  rules  would  formulate criteria for the acceptance or rejection of a hypothesis by reference to the kind and amount of confirming or disconfirming  evidence for it embodied in the totality of accepted observation reports; possibly, these criteria would also refer to such additional factors as  the  " simplicity "  of  the  hypothesis  in  question,  the  manner in which it fits into the system  of  previously  accepted  theories, etc. It is at present an open question  to  what  extent  a  satis­ factory system of such rules can be formulated in purely logical t erms.2

At any rate, the acceptance of a hypothesis on the basis of a sufficient body of confirming evidence will as a rule be tentative, and will hold only " until further notice ", i.e. with the  proviso that if new and unfavourable evidence should turn up (in other words, if new observation reports should be accepted which dis­ confirm the hypothesis in question) the hypothesis will be aban­ doned again.

Are there any exceptions to this rule ? Are there any empirical hypotheses which are capable of being established definitively, hypotheses such that we can be  sure  that  once  accepted  on  the basis. of experiential evidence,  they  will. never  have  to  be  re­ voked ? Hypotheses of this kind will be called absolutely or definitively verifiable ; and the concept of absolute or definitive falsifiability  will  be construed  analogously.                                                                                  .

While the existence of hypotheses which are relatively veri­ fiable or relatively falsifiable is a simple logical fact, which was illustrated in the beginning of this section, the question of the existence of absolutely verifiable, or absolutely falsifiable, hypo­ theses is a highly controversial issue which has received a great deal of attention in recent  empiricist  writings.1                                                                                                                              As the  problem

is only loosely connected with the subject of this essay, we shall restrict  ourselves  here  to  a  few general observations.                                                              ·

Let it be assumed that the language of science has the general structure characterized and presupposed in the previous discus­ sions, especially in section 9.  Then  it  is reasonable  to  expect that only such hypotheses can  possibly  be absolutely  verifiable as are relatively verifiable by suitable observation reports ; hypotheses of universal form, for example, which are not even capable of relative verification, certainly cannot be expected  to  be absolutely verifiable : In however many instances such a hypothesis  may  have  been  borne  out  by experiential  findings, it is always possible that new evidence will be obtained which disconfirms the hypothesis. Let us, therefore, restrict our search for absolutely verifiable hypotheses to the class of those hypo­ theses which  are relatively verifiable.

Suppose now that H is a hypothesis  of  this  latter  type,  and that it is relatively verified, i.e. logically entailed, by an observa­ tion report B, and that the latter is accepted in science as  an account of the outcome of some experiment or observation.  Can we then say that His absolutely confirmed, that it will never be revoked 1 Clearly, that depends on whether  the  repoi:t  B  has been accepted irrevocably, or whether it may conceivably suffer the fate of being disavowed later. Thus the question as to the existence of absolutely verifiable hypotheses leads back to the question of whether all, or at least some, observation reports become irrevocable parts of the system of science once they have been accepted in connection with certain observations or experi­ ments. This question is not simply one of fact ; it  cannot adequately be answered by a descriptive account of the research behaviour of scientists. Here, as in all other cases of logical analysis of science, the problem calls £or a "rational reconstruc­ tion " of scientific procedure,·i.e. for the construction of a con­ sistent and comprehensive theoretical model of scientific inquiry, which is then to serve as a system of reference, or a standard, in the   examination   of   any   particular   scientific   research.  The

construction of the theoretical model has, of course, to be oriented by the characteristics of actual scientific procedure, but it is not determined by the latter in the sense in which a  descriptive account of some scientific study would be. Indeed, it is generally agreed that scientists sometimes infringe the standards of sound scientific procedure; besides, for the sake of theoretical compre­ hensiveness and systematization, the abstract model will have to contain certain idealized elements which cannot possibly be determined in detail by a study of how scientists actually work. This is true especially  of  observation  reports:  A study  of  the way in which laboratory reports, or descriptions of other types of

,observational findings, are formulated in the practice of scientific research is of interest for the choice of  assumptions  concerning the form and the status of  observation  sen ences in the model  of a "language of science" ; but clearly, such a study cannot completely determine what form observation sentences are  to have in the theoretical model, nor whether they are to be con­ sidered as irrevocable  once they are accepted.

Perhaps an analogy may further elucidate this view concerning the character of logical analysis : Suppose that we observe two persons whose language we do  not  understand  playing a  game on  some· kind  of  chess  board ;   and  suppose  that  we  want  to " reconstruct " the rules of  the  game.  A  mere  descriptive account of the playing-behaviour of the  individuals  will  not suffice to do this;  indeed,  we should not even necessarily  reject a theoretical reconstruction of the game which did not always characterize (tCcurately the actual moves of the players:  we should allow for the possibility of occasional violations of the rules. Our reconstruction would  rather  be guided by the object­ ive of obtaining a consistent and comprehensive system of rules which are as simple as possible, and to which  the  observed playing behaviour  conforms at  least to  a large extent.   In terms of the standard thus obtained, we may then describe and critically analyze any concrete performance of the game.

The  parallel  is obvious;  and it  appears  to  be clear,  too, that in both cases the decision about various features of the theoretical model will have the character of a convention, which is influenced by considerations of simplicity, consistency, and comprehensive­ ness, and not only bY, a study of the actual procedure of scientists

.at work.1

This remark applies· in particular to the specific question under consideration, namely whether "there are" in science any irrevocably accepted observation reports (all of whose conse­ quences would then be absolutely verified empirical hypotheses). The situation becomes clearer when we put the question into this form: Shall we allow, in our rational reconstruction of science, for the possibility that certain observation reports may be accepted as irrevocable, or shall the acceptance of all observation reports be subject to the "' until further notice" clause 1 In comparing the merits of the alternative stipulations, we should have to investigate the extent to which each of them is capable of elucidating the structure of scientific inquiry in terms of a simple, consistent theory. We do not propose to enter into a discussion of this question here except for mentioning that various considerations militate in favour of the convention that no observation report is to be accepted definitively and irrevoc­ ably.1 If this alternative is chosen, then not even those hypo­ theses which are entailed by accepted observation reports are absolutely verified, nor are those hypotheses which are found incompatible with accepted observation reports thereby abso­ lutely falsified: in fact, in this case, no hypothesis whatsoever would be absolutely verifiable or absolutely falsi.fi_able. If, on the other hand, some-or even all-observation sentences are declared irrevocable once they have been accepted, then those hypotheses entailed by or incompatible with irrevocable observa­ tion sentences will be absolutely verified, or absolutely falsified, respectively.

It should now be clear that the concepts of absolute and of relative verifiability (and falsifiability) are of an entirely different character. Failure to distinguish them has caused considerable misunderstanding in recent discussions on the nature of scientific knowledge. Thus, e.g., K.  Popper's  proposal  to  admit  as scientific hypotheses exclusively sentences which are (relatively) falsifo1ble by suitable observation reports has been criticized by means of arguments which, in effect, support the claim that scientific hypotheses should not be construed as being absolutely falsifiable-a point that Popper had not denied.-As  can  be seen from our earlier discussion of relative falsifiability, however, Popper's proposal to limit scientific hypotheses to the form of (relatively) falsifiable sentences involves a very severe restriction

of the possible forms of scientific hypotheses 1 ; in particular, it rules out all purely existential hypotheses as well as most hypo­ theses whose formulation requires both universal and existential quantification ;  and  it  may  be  criticized  on  this  account;   for in terms of this theoretical reconstruction of science it seems difficult or altogether impossible to give an adequate  account of the status and function of the more complex scientific hypotheses and   theories.-

With these remarks let us conclude our study of the logic of confirmation.   What   has  been  said   above  about   the   nature   of the logical analysis of science in general, applies to the  present analysis  of  confirmation  in  particular:   It   is  a  specific  proposal for a systematic and comprehensive logical reconstruction of  a concept which  is  basic  for  the  methodology  of  empirical  science as well as for the problem area customarily called"  epistemology". The need for a theoretical clarification  of  that  concept  was evidenced by the fact that no general theoretical account of confirmation has been available so far, and that certain  widely accepted  conceptions  of  confirmation  involve  difficulties  so serious that  it  might  be  doubted  whether  a  satisfactory  theory  of the   concept  is at  all attainable.

It was found, however, that the problem can be solved:  A general definition of confirmation, couched in purely  logical terms, was developed for scientific languages of a specified and relatively simple logical character. The logical model  thus obtained appeared to be satisfactory in the  sense of  the  formal and material standards of adequacy that had been set up previously.

I have tried to state the essential features of the  proposed analysis and reconstruction of confirmation  as  explicitly  as possible in the hope of stimulating a critical discussion and of facilitating further inquiries into the various issues  pertinent  to this pr.oblem area. Among the open questions which seem to deserve careful consideration, I should like to mention the ex­ ploration of concepts of confirmation which fail to satisfy the general consistency condition ; the extension of the definition of confirmation to the case where even observation sentences con-. taining quantifiers  are permitted ;  and finally the development of