Semantical Systems: Ontological vs. Linguistic Issues

          Meaning and Necessity has a more specific purpose than the earlier Introduction to Semantics.  The former is the development of a new method of semantical analysis, which Carnap calls the method of extensions and intensions, and which is based on the customary concepts of class and property respectively.  Carnap maintains that these concepts of extension and intension should be substituted for the idea of naming of an abstract entity.  In his autobiography he notes that some philosophers [who happen to include Quine and Goodman] reject this way of speaking as the "hypostatization of entities.”  In their view it is either meaningless or at least in need of proof, to say that such entities as classes and properties actually exist.  But Carnap argues that such terms have long been used in the language of empirical science and mathematics, and that therefore very strong reasons must be offered, if such terms as "class" and "property" are to be condemned as incompat­ible with empiricism or as unscientific.  He says further­more that to label the use of such terms as "Platonistic" or as "Platonistic realism", as is done by these philosophers, is misleading, because these labels neglect the fundamental distinction between, say, physical laws containing real num­ber variables, and ontological theses affirming or denying the reality of universals.  Carnap dislikes the term "onto­logy", and he maintains that the issue between nominalists and realists regarding universals is a pseudo problem, which is devoid of cognitive content.
          Carnap says his method of extension and intension is a superior basis for semantical analysis than an alternative method based on the naming relation, because the latter leads to contradictions, when the names are interchanged with one another in true sentences.  He thus refers to the "antinomy of the name relation", which is due to the fact that a predicate viewed as a name is ambiguous, since it can refer either to a class or to a property.  Some systems avoid this ambiguity by rejecting properties, and Carnap rejects this loss.  Others avoid the antinomy by having different names for properties and their correspond­ing classes, thus resulting in a higher degree of duplica­tion of expressions.  In Carnap's method of extension and intension the expressions for properties and for their corresponding classes have the same intension and extension.  Thus both classes and properties are admitted without the inelegant duplication and without the antinomy; only one predicate is needed to speak about both a certain property and about its corresponding class.
          The antinomy can be avoided by Carnap's method of pre­scribing the principle of interchangeability for expressions with the same extension, which is distinctive of extensional contexts.  This prescription is achieved by means of the L-equivalence relation, such that extensions are defined in terms of intensions.  The extension of a given intension is defined as the one L-determinate extension that is equiva­lent to the given intension.  Extensions are thus reduced to intensions.  The result is what Carnap calls a "neutral metalanguage.”  While the metalanguage for an object lan­guage based on the name relation will contain such terms as "the class human" and "the property human", the neutral metalanguage for an object language based on the method of extension and intension contains only the neutral expression "human.”
          In "Meaning and Synonymy in Natural Language" (1955) also reprinted in the appendix to the 1956 edition of Meaning and Necessity Carnap describes how his method of extension and intension is applicable in pragmatics as well as in pure semantics.  “Pragmatic” in Carnap’s lexicon means empirical linguistics.  The purpose of this paper is to give a procedure for determining inten­sion in natural language.  This procedure is problematic, because unlike the construction of an artificial language, in which extension can be defined on the basis of inten­sions, the empirical investigation of an unknown natural language by the field linguist must begin with the identifi­cation of extensions that is not problematic.  On the basis of either spontaneous or elicited utterances of a native speaker of the unknown natural langu­age, the field linguist can ascertain whether or not the native is willing to apply a given predicate to a thing.  By such investigation the linguist determines firstly the ex­tension of the predicate, the class of things to which the native is willing to apply the predicate, secondly the ex­tension of the contradictory class of things to which the native will not apply the predicate, and thirdly the class of things for which the native will neither affirm nor deny the applicability of the predicate.  The size of the third class indicates what Carnap calls the degree of extensional vagueness of the predicate.  Carnap admits that this determination of extension involves uncertainty and possible er­ror, either due to a failure to recognize an individual case or due to a failure to make the correct inductive infer­ence to the intended thing.  But he says that these hazards apply to all concepts in science, and they offer no reason to reject the concepts of the theory of extension.
          Carnap's thesis is that the analysis of intension for natural language is a scientific procedure, which is metho­dologically just as sound as the field linguist's method of determining extension.  And he notes his disagreement with Quine about this thesis.  Carnap postulates the case in which two linguists agree on the extension of a native's use of a predicate, but not on the intension.  Carnap maintains that in pragmatics the assignment of an intension is an empirical hypothesis, which like any other hypothesis can be tested by observation of linguistic behavior.  In the empir­ical investigation of the native speaker's linguistic beha­vior, the linguist looks for what Carnap calls intensional vagueness.  Extensional and intensional vagueness are related such that a decrease in one produces a decrease in the latter.  This search is directed to finding out what var­iations of a given specimen are admitted within the range of the predicate, where "range" in the context of a discussion of natural languages means those possible kinds of objects for which the predicate holds.  These are cases for which the native has never made a decision about the applicability of the predicate under investigation.  The description of these possible cases is the intensional vagueness of the predicate.  The linguist can therefore describe to the native speaker various imaginary cases, until he hits upon one that differentiates the otherwise co-extensive predi­cates.  Carnap adds that rules of intension are necessary for the language of empirical science, because without them intensional vagueness would remain, and therefore prevent mutual understanding and communication.  Carnap apparently believes that all vagueness can be removed from a predicate, when the predicate is taken from everyday discourse into scientific language. Carnap also elaborates his discussion to include inten­sion for a robot.  He maintains that from a logical point of view the pragmatical concept for a robot is the same as that for a human.  If the internal structure of the robot is not known, however, the same empirical method that is used to determine intension for a human speaker can be used for a robot.  In both cases the intension for a predicate for a speaker is the general condition that an object must satisfy for the speaker to apply the predicate to it.  And if the intensional structure of the robot is known, the intension of a predicate can be known even more completely.
          In his "Empiricism, Semantics and Ontology" (1950) also in Meaning And Necessity (1956) Carnap deals further with the problem of classes and properties, which some philoso­phers such as Quine refer to as abstract "entities.”  Again he notes that in the language of physics it is hardly possible to avoid abstract entities, and that using a language referring to them does not imply embracing a Platonistic ontology.  He views such language as perfectly compatible both with empir­icism and with strictly scientific thinking.  In this paper he explains further why this compatibility is possible. Firstly he notes that there are two kinds of questions concerning the existence or reality of entities.  One kind is addressed by creating a system of new ways of speaking, which system is subject to new rules in the construction of a linguistic "framework", i.e. a whole semantical system, for the new entities in question.  This first kind of question pertains to the existence of the entities referenced by the system as a whole, and Carnap calls these "external" questions.  The other kind of question is appropriately called an "internal" question, since it pertains to the existence of a new kind of entity within the framework.  Internal questions can be resolved by either logi­cal or empirical scientific procedures.  The question of the reality of a kind of entity described by a theoretical term might serve as an ex­ample of an internal question.  The problem of abstract en­tities, however, is an external question, and it is this latter type of question that concerns Carnap in this paper. Carnap maintains that the introduction of a new language framework with its new linguistic forms does not imply any assertion of reality, but rather is merely a new way of speaking.  Therefore, the acceptance of a lin­guistic framework containing terms referring to abstract entities does not amount to the acceptance of Platonism, because the new language framework is not a new metaphysical doctrine.  Carnap then invokes his "principle of tolerance", which he had firstly expressed in his Logical Syntax many years earlier.  The criterion he invokes as a semanticist is not an ontological one, but rather is a pragmatical one.  The relevant criterion is whether abstract linguistic forms of variables are expedient or fruitful for the purposes for which the semantical analysis is designed, such as the clarification or construction of languages for the purpose of communication, and especially for communication in science.

Semantical Systems: Physics and the Reduction of Theories

          Even before Carnap had published his Introduction to Semantics, he had formulated his concept of science as a semantical system, and this concept did not change fundamen­tally for the duration of his contributing career.  The early statements of this concept are set forth in his "Logi­cal Foundations of the Unity of Science" and "Foundations of Logic and Mathematics" in the International Encyclopedia of Uni­fied Science (1938).  In these works he asserts that philo­sophy of science is not the study of the activities of sci­entists, i.e. the pragmatics of science, but rather is the study of the results of the activity, namely the resulting linguistic expressions, which constitute semantical systems.  More specifically the philosopher treats the language of science as an object language, and develops a metatheory about the semantics and syntax of this object language.  The metatheory is expressed in a metalanguage.
          A physical theory is an interpreted semantical system.  Procedurally a calculus is firstly constructed, and then semantical rules are laid down to give the calculus factual content.  The resulting physical calculus will usually presuppose a logical mathematical calculus as its basis, to which there are added the primitive signs which are descriptive terms, and the axioms which are the specific primitive sentences of the physical calculus in question.  For example a calculus of mechanics of mass points can be constructed with the fundamental laws of mechanics taken as axioms.  Semantical rules are laid down stating that the primitive signs designate the class of material particles, the three spatial coordinates of a par­ticle x at time t, the mass of a particle x, and the class of forces acting on a particle x or on a space s at time t.  Thus by semantical interpretation the theorems of the calcu­lus of mechanics become physical laws, that constitute phy­sical mechanics as a theory with factual content that can be tested by observations.  Carnap views the customary division of physics into theoretical and experimental physics as cor­responding to the distinction between calculus and interpre­ted system.  The work in theoretical physics consists mainly in the essentially mathematical work of constructing calculi and carrying out deductions with the calculi.  In experimen­tal physics interpretations are made and theories are tested by experiments.
          Carnap maintains that any physical theory and even the whole of physics can be presented in the form of an inter­preted system consisting of a specific calculus, an axiom system, and a system of semantical rules for interpreta­tion.  The axiom system is based on a logicomathematical calculus with customary interpretation for the nondescrip­tive terms. The construction of a calculus supplemented by an interpretation is called “formalization”.  Formaliza­tion has made it possible to forgo a so-called intuitive understanding of the theory.  Carnap says that when abs­tract, nonintuitive formulas such as Maxwell's equations of electromagnetism were first proposed as new axioms, some physicists endeavored to make them intuitive by constructing a "model", which is an analogy to observable macroprocesses.  But he maintains that the creation of a model has no more than aesthetic, didactic, or heuristic value, because the model offers nothing to the application of the physical theory.  With the advent of relativity theory and quantum theory this demand for intuitive understanding has waned.
          A more adequate and mature treatment of physics as a semantical system, and especially of the problem of abstract or theoretical terms in the semantical system, can be found in Carnap's "The Methodological Character of Theoretical Concepts" (1956) and in his Philosophical Foundations of Physics: An Introduction to the Philosophy of Science (1966).  Firstly some preliminary comments about terms and laws: All the descriptive terms in the object languages used in science may be classified as either prescientific or scientific terms.  The prescientific terms are those that occur in what Carnap calls the physicalist or thing-langu­age.  This language is not the same as the phenomenalist language advocated by Mach.  Carnap had earlier in his career attempted to apply constructionalist procedures to the construction of a phenomenalist language in his Logical Struc­ture of the World (1928).  But later he decided to accept a language in which the idea of a physical thing is not lin­guistically constructed out of elementary phenomena, because he came to believe that all science could be reduced to the thing-language.  This thing-language refers to things and to the properties of things; in Russell's predicate calculus things and properties are symbolized as two distinct types of signs: instantiation signs and predicate signs.  But the thing language is also expressible in a natural language such as English.  The predicates or other descriptive signs referring to properties are of two types: observation terms and disposition terms.  Observation terms are simply names for observable properties such as "hot" and "red.”  These words are called "observable thing-predicates.”  Disposition terms express the disposition of a thing to a certain beha­vior under certain conditions.  They are called "disposition predicates" and are exemplified by such words as "elastic", "soluble", and "flexible.”  These terms are not observable thing-language properties, but by use of conditional reduc­tion sentences they are reducible to observation predicates.  Opposed to prescientific terms are scientific terms.  Carnap classified all scientific terms as "theoretical terms" in a broad sense, even though physicists, as he notes, customarily refer to such terms as "length" and "temperature" as observation terms, because their measure­ment procedures are relatively simple.  More abstract theo­retical terms are exemplified by "electron" or "electrical field.”  A discussion of theoretical terms requires some further discussion of semantical rules in physical theory.          There are two types of semantical rules: definitions and conditional reduction sentences.  A reduction sentence for a descriptive sign is a conditional statement that gives for the sign the conditions for its application by reference to other signs.  The reduction sentence does not give the com­plete meaning for the descriptive sign, but it gives part of its meaning.  It is a "method of determination" enabling the user to apply the term in concrete cases.  A definition is a special case of a reduction sentence that gives all of the meaning of a descriptive term, because it is an equivalence or biconditional sentence.  There is never more than one definition for a univocal term, but there may be many reduc­tion sentences for a univocal term, each of which contri­butes to the term a part of its meaning.  Unfortunately Carnap seems never to have elaborated on how the meanings of terms can have parts.  Both types of sem­antical rules - definitions and reduction sentences - introduce new terms into an object language.  If one language is such that every descriptive term in it is expressible by reduction sentences in terms of another language, then the second language is called a "sufficient reduction basis" for the first language.  For all scientific terms the scientist always knows at least one method of determination, and all such methods always either are reduc­tion sentences or are introduced into an axiomatic system of physics by explicit definition in the axiomatic system.
          Carnap states that he disagrees with the philosophy of the physicist Paul W. Bridgman, who stated in his Logic of Modern Physics (1927) that, every quantitative concept must be defined uniquely by the procedures for measuring it.  This principle is called "operationalism", and it implies that there are as many different concepts of temperature or length as there are different ways of measuring temperature or length.  Carnap maintains that these different opera­tional rules for measurement should not be considered definitions giving the complete meaning of the quantitative concept.  He prefers his idea of reduction sentences in which statements of operational procedures are semantical rules giving only part of the meaning of the theoretical term.  In Carnap's philosophy what distinguishes theoretical terms from observation terms is precisely the fact that the meanings of theoretical terms are always partial and incom­plete.  This view distinguishes Carnap from Heisenberg and from other Positivists such as Nagel, who prefer equivoca­tion to partial meanings.  In Carnap's view statements of operational rules understood as reduction sentences together with all the postulates of theoretical physics function to give partial interpretations to quantitative concepts.  These partial interpretations are never final, but rather are continually increased or "strengthened" by new laws and new operational or measurement rules that develop with the advance of physics.  Such in brief is Carnap's taxonomy of terms.
          Consider next Carnap’s views on scientific laws: Carnap classifies scientific laws as empirical laws and theoretical laws.  This division does not correlate exactly to the division between observation terms and theoretical terms in the broader and less abstract sense of his meaning of "theoretical term.”  The distinction is based on how the laws are developed.  Empirical laws are also called empi­rical generalizations, because they are developed by induc­tive generalization, which to Carnap means recognition of regularities by observation of repeating instances.  The empirical laws contain observation predicates or magnitudes that are measured by relatively simple procedures that can be expressed in reduction sentences or definitions.  Empirical laws therefore may contain theore­tical terms, such as "temperature", "volume", and "pressure", as occur in Boyle's gas laws, as well as observation terms as may occur in such universal generalizations as "all ravens are black.”  The scientist makes direct observations or repeated measurements, finds certain regularities, and then expresses the regularities in an empirical law.  Theoretical laws on the other hand cannot be made by inductive generalization, because they contain theoretical terms in the narrower or more abstract sense; these theoretical terms are too abstract for making laws by generalization.  Exam­ples of these terms are "electron", "atom", "molecule", and "electromagnetic field.”  These are the descriptive terms that the physicists also call theoretical and unobservable, and measurements associated with these theoretical terms cannot be acquired in simple or direct ways.  The develop­ment of theoretical laws proceeds by the physicists' imagi­native construction of theories in the object language of their science.
          Having examined Carnap's classification of the types of terms and of scientific laws, it is now possible to discuss the construction of physical theories.  Logically there is firstly a calculus.  Conceivably the calculus might be completely uninterpreted, but most often the calculus is supplied by what Carnap calls the logicomathematical cal­culus with its semantical rules for its logical terms sup­plying the "customary" interpretations.  In other words the physicist seldom develops his own logic or mathematics, al­though he may use a pre-existing mathematics that had never previously been used in physics, e.g. a non-Euclidian geo­metry.  The physicist then postulates certain axioms, and the descriptive terms in the axiomatic system will either be primitive terms or will be completely defined by reference to primitive terms given in the axioms.  In the axiom system the primitive terms may be classified either as elementary terms or as theoretical terms in the narrow or more abstract sense.  Elementary terms are either observation terms, or are simple magnitudes which are theoretical terms in the less abstract sense.  The elementary terms are given their seman­tical interpretation by semantical rules that either define them or give methods of determination by conditional reduction sentences.
          The aim of the early Positivists was to make all the primitive terms elementary terms.  In this way the semantics of the primitive terms would be given by semantical rules that would either designate them as observation predicates, or designate them by reference to experimental measurement procedures.  And since none of the abstract theoretical terms are primitive in the axiomatic system, any such terms would have to be defined by reference to the primitive terms.  This method would completely satisfy the early Positivist requirement that all the semantics in the physical theory be supplied by semantical rules that constitute an effective reduction of the theory to observations or to experimentally based measurements.  This would surely insure that there would be no contamination of science by metaphy­sical "nonsense.”
          However, there is a problem with this approach, even though it would satisfy the requirements of the early Posi­tivists.  The theories actually constructed by physicists contain abstract theoretical terms that cannot be defined by reference to elementary descriptive terms having seman­tical rules directly giving them their empirical meanings.  As Carnap states, what physicists actually do is not to make all the primitive terms elementary terms, but rather to make the abstract theoretical terms primitive in the axiomatic system and to make the axioms of the systems very general theoretical laws.  In this constructional procedure the se­mantical rules initially have no direct relation to the pri­mitive theoretical terms.  Carnap borrows Carl G. Hempel's metaphor­ical language describing the axioms with their primitive terms as "floating in the air", meaning that the theoretical hypotheses are firstly developed by the imagination of the physicist, while the elementary terms occurring in the empirical laws are "anchored to the ground.”  There remains to connect the theoretical laws with the empirical laws.  This is achieved by a kind of reduction sentence that relates the abstract theoretical terms in the theoretical laws with the elementary terms in the empirical laws.  This reduction sentence is called the "correspondence rule.”  It is a semantical rule that gives a partial and only a par­tial interpretation to the abstract theoretical terms.  Thus the axiomatic system is left open, to make it possible to add new correspondence rules when theories are modified and as physics develops, until one day the theory is completely replaced in a scientific revolution by a newer one with dif­ferent axioms.  The new correspondence rules add more empirical meaning to the theoretical terms as theory is devel­oped, and they also enable the physicist to derive empirical laws from the theoretical laws.  The logical connection be­tween the two types of laws enables the theoretical laws to explain known empirical laws, but Carnap maintains that the supreme value of a theory is its power to predict new empir­ical laws; explaining known laws is of minor importance in his view.  He observes that every successful revolutionary theory has predicted new empirical laws that are confirmed by experi­ment.
          But there still remains a problem for the Logical Positi­vist.  In this more complicated relationship between theory and experiment, there is a question of how abstract theore­tical terms can be distinguished from metaphysical "non­sense.”  Many philosophers of science, such as Popper, maintain that this is a pseudo problem that cannot be solved.  But it was resolved to Carnap's satisfaction by the Ramsey sentence.  The Cambridge logician, Frank P. Ramsey, proposed that the combined system of theoretical postulates and correspondence rules constituting the theory be replaced by an equivalent sentence, which does not con­tain the theoretical terms; in the Ramsey sentence the theo­retical terms are eliminated and are replaced by existen­tially quantified dummy variables.  The Ramsey sentence has the same explanatory and predictive power as the original statement of the theory, but without the metaphysical ques­tions that are occasioned by the original formulation with its theoretical terms.  Carnap reports that Ramsey did not intend that physicists should abandon their use of theore­tical terms; theory is a convenient "short hand" that is useful to the physicist.
          Finally mention must be made of another application of the reductionist logic, the unity of science.  Both Mach and Duhem expressed the belief that there is a basic unity to all science.  In the Vienna Circle the principal advocate of using constructional methods for advancing the unity of sci­ence was Otto Neurath, a sociologist who was interested in the sociology of science as well as its linguistic analysis.  In his autobiography Carnap stated that Neurath's interest in this effort was motivated by the belief that the division between natural sciences and sociocultural sciences, a division that is characteristic of the Romantic tradition, would be a serious obstacle to the extension of the empiricologi­cal method to the social sciences.  Neurath expressed a preference for the physicalist or thing language rather than the phenomenalist language, since the former is easier to apply in social sciences.  His own views are given in his "Foundations of the Social Sciences" in the second volume of the International Encyclopedia of Unified Science (1944).  But before Neurath had published his views, Carnap had pub­lished his "Logical Foundations of the Unity of Science" in the first volume of the Encyclopedia (1938), where he set forth the constructionalist procedures for the logical re­duction of the descriptive vocabulary of the empirical sci­ences to the observational thing language.  The use of the thing language presumes in Carnap's view a philosophical thesis called physicalism, the view that the whole of sci­ence can be reduced to the physical language, the language of physical things.  Carnap says that the physiological and behavioristic approaches in psychology and social science are reducible to the observational thing language, but that the introspective method may not be reducible.  The aim of Carnap's constructionalist program is the logical reduction only of the descriptive terms in science to the observational thing language; this effort is not a reduction of the empirical laws of the sciences to one another.  The reduction of laws occurs as a part of the development of the sciences them­selves and is the task of the empirical scientist, not of the philosopher of science.   The constructionalist procedures for the reduction of descriptive terms for the unity of science are the same as those that Carnap had developed for the reduction of theoretical terms.