RUDOLF CARNAP ON SEMANTICAL SYSTEMS AND
W.V.O. QUINE'S PRAGMATIST CRITIQUE
BOOK III - Page 5
The Philosophy of Science
Aim of Science
Carnap’s explicit statement of the aim of science is set forth in his Aufbau. The aim of science consists in finding and ordering true propositions firstly through the formulation of the constructional system – the introduction of concepts – and secondly through the ascertainment of the empirical connections among the concepts. This is a characterization of the products of science. And it is completely programmatic, saying nothing about the activities of scientists in their research practices. For contemporary philosophers a discussion of the aim of science is a discussion in the pragmatics of science, that is, what the scientist does as a user of scientific language when he does successful basic research. But Carnap identifies the pragmatics of language with the empirical investigation of historically given natural languages. He always constructs his own languages usually using Russell’s symbolic logic, and then uses these contrived artificial languages to address the philosophical problems of interest to the positivist program for philosophy, namely, the logical reduction of theoretical terms to demonstrate their meaningfulness and the logical reduction of the vocabulary of science to a common observational basis to advance its unification.
Carnap also has explicit views on scientific explanation: He says it always involves laws, and he classifies scientific laws as either empirical laws or theoretical laws. Empirical laws explain facts, which are statements that describe individual instances. The explanation has the logical structure of a deduction. The premises of the deduction consist of at least one law together with statements of fact that describe individual instances in the same terms as those occurring in the laws. The conclusion is also a factual sentence that describes the individual instances in the same terms as those in the law. In this manner empirical laws explain observed instances described by factual statements.
Theoretical laws are related to empirical laws in a way that is analogous to the way that empirical laws are related to facts. The theoretical law is more general. It helps to explain deductively empirical laws that are already known and to permit the derivation of new empirical laws, just as the empirical laws help to explain facts that have been observed and to predict new facts. Furthermore the theoretical law puts several empirical laws into an orderly pattern, just as the empirical generalization puts many facts into an orderly pattern. The supreme value of theory is its power to predict new empirical laws; explaining known laws is of minor value. Carnap claims that every revolutionary theory in the history of science has predicted new empirical laws that are confirmed by empirical tests.
Unlike Duhem, Carnap does not stratify the semantics of physics. To say that theoretical laws explain empirical laws is not for Carnap to say as Duhem did, that the theory is an axiomatic system with conclusions that are statements which parallel the empirical laws, and that has its own semantics that in turn refers to the empirical laws. In Carnap’s view the theoretical terms receive all their semantics from the observation terms by means of reduction sentences that he calls “correspondence rules.” When Carnap says that theoretical laws explain empirical laws, he means that a deductive relationship is established between the axioms of the theory and the empirical laws, and that the relationship is mediated by the correspondence rules. The postulated axioms, which are the theoretical laws, together with the correspondence rules enable the physicist to explain empirical laws by logical deduction.
In Carnap’s philosophy the numerical approximation that Duhem saw existing between the solution sets for the equation deduced from the axioms on the one hand and the solution sets for the equation the empirical laws on the other hand, has no semantical implications and is not philosophically problematic. The post-positivist philosophers agree with Duhem, and maintain that while the numerical difference between theoretical and empirical laws are experimentally indistinguishable due to measurement error, nonetheless the solution sets from the two types of laws are logically distinguishable, such that it is incorrect to say that experimental laws are logically derived from theoretical postulates. In Popper’s phraseology the derived theoretical laws (such as Newton’s) “correct” the experimental laws (such as Kepler’s) purporting to describe the same phenomena.
Carnap’s philosophy of scientific criticism is his thesis of confirmation. Both theoretical and empirical laws may be more or less confirmed, but empirical laws are confirmed directly by observation or measurement, while theoretical laws are confirmed indirectly through the confirmation of the empirical laws deductively derived from them. Both empirical and theoretical laws may be classified as either universal or statistical laws, and most of Carnap’s discussion of this distinction is in the context of empirical laws. All empirical laws are statements expressing observed regularities as precisely as possible. If a certain regularity is observed at all times and in all places, then that regularity is expressed in the form of a universal law. But if the law asserts that an event or the relation of one event to another occurs in only a certain percentage of cases, then the statement is called a statistical law. Both types of laws occur in the object language of science, and both are empirical statements. Statements about both universal and statistical laws occur in the metalanguage that refers to the object language of science in which the law and theory statements are expressed, and for both types the statements in the metalanguage may refer to the degree of confirmation of the laws.
Statements of the degree of confirmation are statements of logical probability associated with both universal and statistical laws. Logical probability is an estimate of the long-term relative frequency stated by the statistical laws, and takes values between zero and one inclusively. The statements associating the degree of confirmation to a statement in the object language are statements in the metalanguage. The metalanguage is a language of the philosopher of science, and philosophy is not in Carnap’s view an empirical or factual science. Philosophy of science is the logic of science, and the statements in the metalanguage are L-true or analytic. Logical probability is the logical relation similar to logical implication. By a logical analysis of a stated hypothesis h and the stated evidence e, one may conclude that h is not deductively implied but is partially implied by e to the degree r. For any pair of sentences e and h inductive logic assigns a number giving the logical probability of h with respect to e. In this way Carnap views the metalanguage to consist of analytic statements as opposed to the synthetic statements in the object language consisting of laws of nature.
Carnap’s philosophy of scientific discovery gives different accounts for the discovery of empirical laws and the discovery of theoretical laws. His philosophy of discovery of empirical laws is inductivist; induction is the measurement of the degree of regularity in observed instances known either passively by casual observation or actively by experimentation. His philosophy of discovery of theoretical laws recognizes the rôle of the creative imagination. He presciently gives consideration to the use of computers. But he pessimistically expresses doubts that rules can be established to enable a scientist to survey millions of sentences giving various observational reports, and then by a mechanized procedure applying these rules to generate a general theory consisting of a system of theoretical laws that would explain the observed phenomena. This is because theories deal with unobservables and use a conceptual framework that goes far beyond the framework used for the description of observations. Creative ingenuity is needed to create theories. Therefore Carnap concludes that there cannot be an inductive machine, a computer system into which the scientist can input all the relevant observation sentences, and then get an output consisting of a system of laws that explain the observed phenomena. He only believed that given observation e and hypothesis h, there could be an inductive machine, which will mechanically determine the logical probability or degree of confirmation of h on the basis of e.
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 said are “antiscientific.” 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 that of A-truth, which Carnap calls meaning postulates that 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. Hempel 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. It may be noted parenthetically that Hickey’s concept semantical rule echoes Hempel’s rejection of separating meaning specification from empirical description.
In addition to discussing the empirical significance of analytical sentences, Hempel also discusses empirical testing. He references Carnap’s Logical Syntax of Language, where Carnap cites Poincare and Duhem, saying that no statement accepted in empirical science is 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. This is also what Quine maintains in his “Two Dogmas”, which Hempel cites 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, individual sentences that contain theoretical terms are confirmable by reference to observation sentences.
But Hempel notes that in his general concept of an interpreted theory, his interpretative system J, 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 those sentences and the theory. His view renders the notions of testability and experiential significance relative to a given theory, thus 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 challenging task for 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 as such is not 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 rôle 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, (1) that are referenced by the existential quantifiers of the Ramsey sentence, (2) that are of a kind bound together by all the relations expressed in the theoretical postulates of the theory, and (3) 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.
The issues between Carnap and Hempel about analytical sentences, the semantics of theoretical terms and the value of the Ramsey sentence will be made moot by Quine’s pragmatist critiques of Carnap and his pragmatic reconceptualization of language.