Hempel's Critique of Analyticity  

          Carl G. Hempel (1905-1997) was one of Carnap's more sympathetic colleagues, and had been Carnap's assistant just after immi­grating to the U.S. from Nazi Germany.  In the New York Times (23 November 1997) obituary for Hempel, Quine was quoted as describing Hempel as a “moderate Logical Positivist”, and as saying that Hempel’s views had been succeeded by relativist doctrines, which would make science a matter of fads, and which Quine are “anti-scientific.”  In his later years Quine concluded that his wholistic view of observation statements implies a relativistic theory of truth, and he retreated from the implications of his “Two Dogmas of Empiricism” (1952).  After reading Quine's "Two Dogma's of Empiricism" in which Quine criticized Carnap's concept of analyticity, Hempel gave serious reconsideration to Carnap's analyticity thesis.  Hempel does not reject Carnap's concept of L-truth.  His disagreement is only with the concept of A-truth, the truth that Carnap calls meaning postulates, which are known to be true by virtue of the meaning relations among the descrip­tive terms in the sentence.
          Hempel's critique of A-truth is set forth in "Implica­tions of Carnap's Work for the Philosophy of Science" in Schilpp's The Philosophy of Rudolf Carnap (1963) and rele­vant comments are to be found in his earlier work, "Theore­tician's Dilemma" in Minnesota Studies (1958).  Firstly Hempel considers problems of empirical significance presen­ted by analyticity.  After contrasting Carnap's concept of reduction sentences with the idea of definition, taking note that the reduction sentence offers convenient schema for a partial operational meaning, Hempel states that contrary to Carnap the reduction type of sentence does not eliminate all dependency on general empirical laws in these sentences.  He says that Paul W. Bridgman had advocated operational defini­tions with one definition for every method of measurement, because defining any measurement concept by more than one method of measure incurs the risk of an invalid empirical generalization, even if the different methods yield the same measurement value.  The reduction type of sentence elimin­ates this risk, because in it only one generalization is used. However, Hempel says that an inductive risk is still incurred even for reduction sentences, since even if only one operational criterion is used any application of a term requires a generalization.  Therefore reduction sentences "fuse" together two functions of language, which had traditionally been thought to be totally different.  These are firstly the specification of meanings and secondly the description of contingent fact.  He maintains that the fruitful introduction of new concepts in science is always intimately bound up with the establishment of new laws.
          Hempel then generalizes on his thesis that reduction sentences have the two functions of meaning specification and empirical law, to produce his own general conception of a semantical or "interpretative" system.  Firstly he distin­guishes an observational and a theoretical vocabulary.  Then he states that a theory T characterized by a set of postu­lates with primitive theoretical terms constituting the theoretical vocabulary, is made an interpreted system by the set of sentences J satisfying three conditions: (1) J is logically compatible with T; (2) J contains no extralogical (descriptive) terms that are not an element of the observational or theoretical vocabulary; (3) J contains elements of the observational and theoreti­cal vocabulary in an essential way, i.e. in a manner that does not make J logically equivalent to some set of sentences in which neither the observational or the theoretical terms occur.  Interpretative systems so conceived share the same two char­acteristics that distinguish reduction sentences from defin­itions.  Firstly they give only partial definitions of the theoretical terms they specify, and secondly they are not purely stipulative in character, but imply certain state­ments containing only observational terms.  However unlike Carnap's concept of a semantical system with reduction sen­tences, Hempel's general concept of an interpretative system does not provide an interpretation, complete or incomplete, for each theoretical term individually in the whole system.  Therefore in the interpretative system J the theoretical terms are not dispensable, and Hempel argues that in his definition of an interpretative system, the distinction between the theory and its interpretative sentences is arbitrary, because these two types of sentences have the same status and function.  It is only in conjunction with the interpretative sentences that the theory can imply observational sentences, and the interpretative sentences no less than the theory may be theoretical laws.  Furthermore, when discrepancies between predictions and experimental data call for modification of the predictive apparatus, suitable adjustments may be made not just by changing the theory but alternatively by chang­ing the interpretative sentences.  Therefore interpretative sentences must have the same status as the sentences constituting the theory, thus making it diffi­cult to identify either theory or interpretative sentences as analytic. Following a similar line of argument Hempel rejects Carnap's proposal of introducing predicates by means of meaning postulates, which purport to separate the meaning specification function from the empirically descriptive function.  Hempel questions the rationale for separating these two functions.  He asks what distinctive status is conferred on a meaning postulate, since any statement once accepted in empirical science may conceivably be abandoned for the sake of resolving a conflict between theory and the stated body of available evidence.  He says that apart from logical and mathematical truths, there can be no scientific statements that satisfy conditions for analytic meaning postulates.
          In addition to discussing problems for empirical signi­ficance of analytical sentences, Hempel also discusses prob­lems of empirical testing.  He references Carnap's Logical Syntax of Language, where Carnap references Poincare and Duhem, saying that no statement accepted in empirical sci­ence is taken to be immune from criticism and revision. Carnap furthermore stated that a statement in a scientific theory cannot be tested in isolation, but must be tested with other accepted statements, such that it is the entire theoretical system that is tested.  And this is what Quine also maintains in his "Two Dogmas", which Hempel references in this context. Hempel relates that on Carnap's view of a semantical system, in which theoretical terms are viewed as being introduced by reduction sentences based on an observation vocabulary, it is possible to speak of individual sentences containing theoretical terms as being confirmable by refer­ence to observation sentences.  But Hempel notes that in his general concept of an interpreted theory, this idea has no useful counterpart, because one would have to say that the experimental import of a sentence relative to an interpreted theory is expressed by the class of nonanalytic observation sentences implied by the sentences and the theory.  His view renders the notions of testability and experiential signifi­cance relative to a given theory, assigning all sentences of the theory the same experiential import represented by the class of all observation sentences implied by the theory.  This is because testability and empirical significance are attributable not to scientific statements in isolation, but only to interpreted theoretical systems.  Furthermore, as Kuhn notes in The Road Since Structure (1993), a few years after writing "Theore­tician's Dilemma" Hempel began speaking of “antecedently available terms” instead of “observation terms”, thus implicitly adopting what Kuhn describes as a developmental or historical view of science.
          Hempel concludes that these considerations make it doubtful that the basic tenants of Positivism and empiricism can be formulated in a clear and precise way.  The circum­stance that empirical significance and testability require­ments are applicable to entire theoretical systems, make these requirements extremely weak.  For the Positivist that weakness permits the disturbing possibility of adding to contemporary physical theory an axiomatized metaphysics of Being and Essence that would be an empirically significant system.  One alternative is to exclude theoretical terms altogether, but Hempel invokes the criterion of simplicity.  He concludes that the problem of giving a precise explica­tion of this aspect of scientific theories presents a new and challenging task for the philosophy of science.

Carnap's Reply to Hempel

          Carnap replies to Hempel's attack on the analytic-synthetic distinction both in the Schilpp volume containing Hempel's critique and in the concluding two chapters of his Philosophical Foundations of Physics (1963).  He maintains that the analytic-synthetic distinction is of supreme impor­tance for philosophy of science.  The theory of rel­ativity could not have been developed had Einstein not re­cognized the sharp dividing line between pure mathematics, in which there are many logically consistent geometries, and physics, in which only experiment and observation can deter­mine which of these mathematical geometries can be applied most usefully to the physical world.  This reply made late in Carnap’s career reveals how influential Einstein’s development of relativity theory was on Carnap’s philosophical thinking.
          Firstly however Carnap takes up the identification of the analytic-synthetic distinction in natural language. He notes that natural language is sufficiently imprecise that not everyone understands every word in the same way, such that some sentences may be ambiguous as to whether they are analytic or factual.  The division depends on what charac­teristics described by the predicate terms are taken to be essentially or definitively related to one another.  For example does red colored head plumage define a redheaded woodpecker?  If not, then a green headed bird may be classified as a redheaded woodpecker, if it has other characteristics deemed definitive of the species.  Carnap maintains that while certain statements may be ambiguous due to the vagueness of the predicates, the analytic-synthetic distinction as such is not therefore problematic for the same reason.
          Carnap next turns to the analytic-synthetic distinction in an artificial observation language.  In this case the distinction is determined by laying down precise rules, which are the meaning postulates or A-postulates.  These rules determine what characteristics described by predicate constants are essential to their subjects.  To the extent that these rules are vague, there will be sentences that are vague with respect to the analytic-synthetic status.  But Carnap says that in such cases the distinction between analytic and synthetic is not as such vague.
          Then he turns to the determination of the distinction in an artificial theoretical language, where the fact that theoretical terms cannot be given complete interpretations causes special difficulties.  He takes as an example the track in the Wilson cloud chamber, which can be observed and can be explained in terms of an electron passing through the chamber.  Such observations provide only a partial and indirect empirical interpretation of the entity referenced by the theoretical term "electron", to which the observed track is linked by correspondence rules.  The problem is to find a way to distinguish in the linguistic network of correspondence postulates and theoretical postulates, those sentences that are analytic and those that are synthetic.  It is easy to identify the L-true sentences, because des­criptive terms are not involved in determining L-truth.  But A-truth, the truth of analytic sentences, is problematic in this case. To recognize analytic statements in a theoretical language, it is necessary to have A-postulates that satisfy the meaning relations holding among the theoretical terms.  But the theoretical postulates alone cannot serve as A-pos­tulates, since without the correspondence rules the theore­tical postulates have no interpretation at all.  Yet the theoretical postulates together with the correspondence postulates cannot be analytic, because then the theory would have no empirical content.
          Carnap notes Hempel's proposal that there is a double role for the theoretical and correspondence postulates, that defies the analytic-synthetic distinction, such that these postulates both stipulate meaning and also make empirical assertions.  But Carnap proposes another way that preserves the empirical content of scientific theories while admitting the analytic-synthetic distinction.  His proposal utilizes the Ramsey sentence, but without Ramsey's final step of eliminating the theoretical terms from the semantical sys­tem, since he believes that eliminating theoretical terms is too inconvenient for the scientists, who find that theoreti­cal terms simplify their work enormously.  Instead of split­ting an interpreted theory into theoretical postulates and correspondence rules, Carnap proposes splitting it into analytic and factual sentences with the factual part consisting of a Ramsey sentence equivalent to the empirical content of the interpreted theory.  The Ramsey sentence therefore implies the whole interpreted theory, and this implication is itself analytic; it is the analytic part of the theory.  Carnap maintains that this analytic implication provides a way to distinguish between analytic and synthetic statements in the theoretical language, because the analytic implication is that if there exist entities, that are referenced by the existential quantifiers of the Ramsey sentence, that are of a kind bound together by all the relations expressed in the theoretical postulates of the theory, and that are related to observed entities by all the relations specified by the correspondence postulates of the theory, then the theory itself is true.
          In his "Theoretician's Dilemma" Hempel had criticized the Ramsey sentence as avoiding reference to theoretical entities only in Greek variables rather than in spirit.  The Ramsey sentence still asserts the existence of certain entities of the kind postulated by a physical theory without guaranteeing any more than does the physical theory that those entities are observable or at least are fully characterizable in terms of observables.  Therefore, the Ramsey sentence provides no satisfactory way of avoiding theoreti­cal concepts.
          In his replies to Hempel in Schilpp's book Carnap says that he agrees with Hempel that the Ramsey sentence does refer to theoretical entities by the use of abstract varia­bles.  But he argues that these entities are not unobservable physical objects like atoms or electrons, but rather are purely logicomathematical entities such as natural num­bers, classes of such numbers, or classes of classes.  The Ramsey sentence for a physical theory is a factual statement that says that the observable events in the world are such that there are natural numbers, classes of such numbers, or classes of classes, that are correlated with the events in a prescribed way, and which have among themselves certain relations.

Quine's Pragmatist Critiques

          Willard Van Orman Quine (1908-2000) was born in Akron, Ohio.  In 1930 he graduated summa cum laude in mathematics from Oberlin College, and then entered Harvard University's graduate school of philosophy.  He wrote his doctoral dis­sertation under the direction of Alfred North Whitehead, the co-author with Bertrand Russell of the Principia Mathematica, and he published it as A System of Logistic in 1934.  Quine became a faculty member of Harvard's department of philosophy in 1936, where he remained for the duration of his long career.  He enjoyed traveling, and wrote an autobiographical travelogue as The Time of My Life in 1985.  Quine described his long acquaintanceship with Carnap in "Homage to Rudolf Carnap" (1970), a memorial article pub­lished in the year of Carnap's death, and reprinted later in Quine's Ways of Paradox (1976).  Quine met Carnap during his European travels in the 1930's, and their dialogues continued after Carnap relocated to the United States in 1935.  While Quine might be regarded as Carnap's principal protagonist, their philosophies are much more similar than different.  In the memorial article Quine refers to Carnap as a towering figure, who dominated philosophy in the 1930's as Russell had in previous decades, and he also refers to Carnap as his greatest teacher.  Their private correspon­dence has been published under the title Dear Carnap, Dear Van (ed. Creath, 1990), which reveals nothing about their philosophical views that is not already known from their published works, but exhibits their enduring friendship notwithstanding their widening philosophical differences.
          Quine's best known criticism of Carnap's philosophy is his rejection of the analytic type of statement.  This criticism together with several others has their basis in Quine's Pragmatist view of empiricism.  Quine published a brief statement of his own doctrine of empiricism as "The Pragmatist's Place in Empiricism" (1975), later appearing in his Theories and Things (1981) as "Five Milestones of Empir­icism.”  This paper is ostensibly a history of empiricism in terms of five historical turning points, but the five historical milestones also happen to be the central theses of Quine's own Pragmatist philosophy.  He summarizes these five historical turning points as follows:  

 1.   The shift from ideas to words

 2.   The shift of semantic focus from terms to sentences

 3.   The shift of semantic focus from sentences to systems of sentences

 4.   The abandonment of the analytic-synthetic distinction

 5.   The abandonment of any first philosophy prior to natural science

          Quine's several criticisms of Carnap's Positivist ver­sion of empiricism may be viewed as having a basis in these five distinctive aspects of his Pragmatist version of empir­icism.  The first two of the five points are the basis for Quine's criticism of Carnap's doctrine of intensions, as well as a critique of the idea of propositions.  The third point, sometimes known as the Duhem-Quine thesis, is the basis for Quine's critique of logical reductionism and for his wholistic thesis of semantical indeterminacy and his thesis of ontolo­gical relativity.  The fourth is his rejection of analyti­city, which follows from the third point.  And the fifth and final point is Quine's critique of Carnap's doctrine of "frameworks" and of the distinction between "internal" and "external" questions.  Each of these criticisms is consi­dered in greater detail below.