INTRODUCTION TO PHILOSOPHY OF SCIENCE
Book I Page 2
Thesis III: Ontological relativity.
In his discussions about Einstein’s special theory of relativity in Physics and Philosophy (1958) and in Across the Frontiers (1974) Heisenberg describes the “decisive step” in the development of special relativity. That step was Einstein’s rejection of 1902 Nobel-laureate Hendrik Lorentz’s (1853-1928) distinction between “apparent time” and “actual time” in the Lorentz-Fitzgerald contraction. Lorentz took the Newtonian concepts to describe real space and time. But in his relativity theory Einstein took Lorentz’s “apparent time” as physically real time, while altogether rejecting the Newtonian concept of absolute time as real time. In other words the “decisive step” in Einstein’s special theory of relativity consisted of Einstein’s taking the relativity theory realistically, thus letting his relativity theory characterize the physically real, i.e., physical ontology.
Heisenberg imitated Einstein’s practice for making his interpretation of his Copenhagen interpretation of quantum theory. In “History of Quantum Theory” in his Physics and Philosophy Heisenberg describes his imitation of Einstein in his discovery experience for quantum theory. There he states that his development of the indeterminacy relations involved turning around a question: instead of asking himself how one can express in the Newtonian mathematical scheme a given experimental situation, he asked whether only such experimental situations can arise in nature as can be described in the formalism of his quantum mechanics. The new question is an ontological question with the answer supplied by his quantum theory.
Again in “Remarks on the Origin of the Relations of Uncertainty” in The Uncertainty Principle and Foundations of Quantum Mechanics (1977) Heisenberg explicitly states that a Newtonian path of the electron in the cloud chamber does not exist. And still again in “The Development of the Interpretation of the Quantum Theory” in 1945 Nobel-laureate Wolfgang Pauli’s Niels Bohr and the Development of Physics (1955) Heisenberg says that he inverted the question of how to pass from an experimentally given situation to its mathematical representation. There he concludes that only those states that can be represented as vectors in Hilbert space can exist in nature and be realized experimentally. And he immediately adds that this conclusion has its prototype in Einstein’s special theory of relativity, when Einstein had removed the difficulties of electrodynamics by saying that the apparent time of the Lorentz transformation is real time. Like Heisenberg in 1926, the contemporary pragmatist philosophers let the scientist rather than the philosopher decide ontological questions. And the scientist decides on the basis of empirical adequacy demonstrated in his empirically tested explanations. Many years later in his Ontological Relativity (1970) Quine called this thesis “ontological relativity”, as it is known today.
Ontological relativity did not begin with Heisenberg much less with Quine. Copernicus (1473-1543) and Galileo practiced it when they both interpreted heliocentrism realistically thus accepting the ontology it describes – to the fateful chagrin of Pope Urban VIII (1568-1644). Heisenberg’s Copenhagen interpretation still prevails in physics today.
The contemporary pragmatist concepts of the four functional topics may now be summarized as follows:
Aim of science:
The successful outcome (and thus the aim) of basic-science research is explanations, which are made by developing theories that satisfy empirical tests and are thereby made scientific laws, which can function in scientific explanations and test designs.
Wherever possible the explanation should enable prediction of either future events or evidence of past events. And it is beneficial furthermore for the explanation to enable control of explained nonlinguistic reality by applied science thus enabling new engineering technologies, new medical therapies and new social policies.
Discovery is the construction of new and empirically more adequate theories.
Contemporary pragmatism is consistent with computerized discovery systems, which aim to proceduralize and then to mechanize new theory construction, in order to advance contemporary science.
In the “Introduction” to his magisterial Patterns of Discovery: An Inquiry into the Conceptual Foundations of Science (1958), Yale University philosopher of science Hanson wrote that earlier philosophers of science like the positivists had mistakenly regarded as paradigms of inquiry finished systems like Newton’s planetary mechanics instead of the unsettled, dynamic research sciences like contemporary microphysics. Hanson explains that the finished systems are no longer research sciences, although they were at one time. He states that distinctions applying to the finished systems ought to be suspect when transferred to research disciplines, and that such transferred distinctions afford an artificial account of the activities in which Kepler, Galileo and Newton were actually engaged. He thus maintains that ideas such as “theory”, “hypothesis”, “law”, “causality” and “principle” if drawn from what he calls the finished “catalogue-sciences” found in undergraduate textbooks will ill prepare one for research science.
Both romantics and positivists define “theory” semantically, while contemporary pragmatists define “theory” pragmatically, i.e., by its function in basic-research science.
Contemporary pragmatists define both theory and observation language pragmatically instead of semantically. The pragmatics of both uses of language in basic science is empirical testing.
Theories are universally quantified statements that are proposed for testing.
Test-designs are universally quantified statements that are presumed for testing, to characterize the subject of the test and to describe procedures for execution of the test. They also include universal statements that are semantical rules for the test-outcome statements, which are asserted with particular quantification, when the test outcome is produced and known.
Observation language is particularly quantified test-design and test-outcome statements with their semantics defined in the universally quantified test-design language.
The semantics of newly constructed theories reveal new perspectives and ontologies.
Scientific laws are former theories that have been tested with nonfalsifying test outcomes.
Unlike positivists, pragmatists do not recognize any natural observation semantics. For believers in a theory, the theory language may also contribute to the observational semantics, but that semantical contribution cannot operate in reporting the test outcome without violating the test’s contingency.
Contemporary pragmatists individuate theories semantically: Two theory expressions are different theories either (1) if the expressions has a different test design so they identify different subjects, or (2) if the expressions make contrary claims about the same subject as defined by the same test design.
Contemporary pragmatists recognize the empirical criterion as the only valid decision criterion that yields scientific progress.
On the pragmatist thesis of relativized semantics and ontological relativity, semantics and ontologies can never trump the empirical criterion for criticism, because acceptance of ontologies is based upon empirical adequacy of a theory especially as demonstrated by empirical test outcomes. Thus contrary to romantics, pragmatists permit description of subjective mental states in social-science theories and explanations, but never require such description as a criterion for criticism. Or as Popper said, science is “subjectless”.
Pragmatists recognize the nontruth-functional hypothetical-conditional heuristic schema for expressing proposed theories.
Pragmatists recognize the modus tollens falsifying argument for empirical testing of the theories.
Unlike the logical positivists, pragmatists do not recognize the truth-functional conditional logic for scientific criticism, because the logic of empirical testing is not truth-functional.
Explanation describes the occurrence of individual events and conditions as caused by the occurrence of other described events and conditions related in law statements.
Pragmatists recognize the modus ponens nontruth-functional deductive logical argument with the hypothetical-conditional heuristic schema that includes universally quantified statements expressible in conditional form that are scientific laws. Whenever possible the explanation is predictive.
Laws are said to be “explained” in the sense that a set of logically related laws may form a deductive system.
CHAPTER 3. Philosophy of Language
Many and probably most of the central concepts and issues in philosophy of science involve philosophy of language. Therefore the following selected elements of contemporary pragmatist philosophy of language are discussed in relation to philosophy of science.
3.01 Synchronic and Diachronic Analysis
To borrow some terminology from Ferdinand de Saussure’s (1857-1913) classic Course in General Linguistics (1959) language analyses may be either synchronic or diachronic.
The synchronic view is static, because it exhibits the state of a language at a point in time like a photograph. And to borrow some terminology from Carnap’s Meaning and Necessity (1947) with revised meaning for computational philosophy of science, the state of the language for a specific scientific problem is displayed synchronically in a semantical state description. In the pragmatist’s semantical state description statements – both theory language and the law language in the relevant test design – function as semantical rules that describe the meanings of their constituent descriptive terms.
The diachronic view on the other hand exhibits two chronologically successive states of the language for the same problem as defined by a single test design, and it shows semantical change over the interim period. Then the view is a comparative-static semantical analysis like “before” and “after” photographs. And if a transitional process between the two successive language states is also described, as in the computer code for a discovery system, then the diachronic view is dynamic like a motion picture.
For more about Carnap the reader is referred to BOOK III at www.philsci.com or in the e-book Twentieth-Century Philosophy of Science: A History.
3.02 Object Language and Metalanguage
Many philosophers of science such as Carnap in his Logical Syntax of Language (1937) distinguish two levels of language, object language and metalanguage.
Object language is used to describe the nonlinguistic real world.
Metalanguage is used to describe language, either object language or metalanguage.
The language of science is typically expressed in the object-language perspective, while much of the discourse in philosophy of science is in the metalinguistic perspective. Terms such as “theory” and “explanation” are examples of expressions in metalanguage.
3.03 Dimensions of Language
The metalinguistic perspective includes what may be called dimensions of language, which serve well as an organizing framework for philosophy of language. Four dimensions may be distinguished for philosophy of language. They are A. syntax, B. semantics, C. ontology and D. pragmatics.
Syntax is the structure of language, semantics is the meanings associated with syntax, ontology is the real world as described by semantics, and pragmatics is the uses of semantically interpreted syntax.
Most philosophers of science ignore the linguists’ phonetic and phonemic dimensions. And most linguists ignore the ontological dimension.
3.04 Syntactical Dimension
Syntax is the system of linguistic symbols considered in abstraction from their associated meanings.
Syntax is the most obvious part of language. It is residual after abstraction from pragmatics, ontology, and semantics. And it consists only of the forms of expressions, so it is often said to be “formal”. Since meanings are excluded from the syntactical dimension, the expressions are said to be “semantically uninterpreted”. And since much of the language of science is usually written, the syntax of interest consists of visible marks on paper or more recently linguistic displays on computer monitor display screens. The syntax of expressions is sometimes called “inscriptions” or “code”. Examples of syntax include the sentence structures of colloquial discourse, the formulas of pure or formal mathematics, and computer source codes such as FORTRAN or LISP.
3.05 Syntactical Rules
Syntax is a system of symbols. Therefore in addition to the syntactical symbols and structures, there are also rules for the system called “syntactical rules”. These rules are of two types: formation rules and transformation rules.
Formation rules are procedures described in metalanguage that regulate the construction of grammatical expressions out of more elementary symbols.
Formation rules order such syntactical elements as mathematical variables and operator signs, descriptive and syncategorematic terms and the user-defined variable names and reserved words in computer source codes. Expressions constructed from the symbols in compliance with the formation rules for a language are called “grammatical” or “well formed formulas”, and include the computer instructions called “compiler-acceptable” and “interpreter-acceptable” source code.
When there exists an explicit and adequate set of syntactical formation rules, it is possible to develop a type of computer program called a “mechanized generative grammar”. A generative grammar produces grammatical expressions from inputs consisting of more elementary syntactical symbols. The generative-grammar computer programs input, process, and output object language, while the source-code instructions constituting the computer system are therefore metalinguistic expressions.
A mechanized generative grammar is a computer system that applies formation rules to more elementary syntactical symbols inputted to the system, and that outputs grammatically well formed expressions.
When a mechanized generative grammar is used to produce new scientific theories in the object language of a science, the computer system is called a “discovery system”. Typically the system also contains an empirical test criterion for the selection for output of a subset of the numerous theories generated.
A discovery system is a mechanized generative grammar that constructs and also may empirically test scientific theories as its output.
Transformation rules change grammatical sentences into other grammatical sentences.
Transformation rules are used in logical and mathematical deductions. But logic and mathematical rules are intended not only to produce new grammatical sentences but also to guarantee truth transferability from one set of sentences or equations to another to generate theorems, usually by the transformation rule of substitution that makes logic extensional.
Transformation rules are of greater interest to linguists, mathematicians and logicians than to contemporary philosophers of science, who recently have been more interested in mechanizing formation rules for generative-grammar discovery systems.
In 1956 Herbert Simon developed an artificial-intelligence computer system named LOGIC THEORIST, which operated with his “heuristic-search” discovery system design. This system developed deductive proofs of the theorems in Alfred N. Whitehead and Bertrand Russell’s Principia Mathematica. The symbolic-logic formulas are object language for this system. But Simon correctly denies that the Russellian symbolic logic is an effective metalanguage for the design of discovery systems.
3.06 Mathematical Language
The syntactical dimension of mathematical language includes mathematical symbols and the formation and transformation rules of the various branches of mathematics. Mathematics applied in science functions as object language for which the syntax is supplied by the mathematical formalism. Whenever possible the object language of science is mathematical rather than colloquial, because measurement values for variables enable the scientist to quantify the error in his theory, after estimates are made for the range of measurement error, usually by repeated execution of the measurement procedure.
3.07 Logical Quantification in Mathematics
Mathematical expressions in science are universally quantified when descriptive variables have no associated numerical values, and are particularly quantified when numeric values are associated with any of the expression’s descriptive variables either by measurement or by calculation.
Like categorical statements, mathematical equations are explicitly quantified logically as either universal or particular, even though the explicit indication is not by means of the syncategorematic logical quantifiers “every”, “some” or “no”. An equation in science is universally quantified logically when none of its descriptive variables are assigned numeric values. Universally quantified equations may contain mathematical constants as in some theories or laws. An equation is particularly quantified logically by associating measurement values with any of its descriptive variables. A variable may then be said to describe an individual measurement instance.
When a numeric value is associated with a descriptive variable by computation with measurement values associated with other descriptive variables in the same mathematical expression, the variable’s calculated value may be said to describe an individual empirical instance. In this case the referenced instance has not been measured but depends on measurements associated with other variables in the same equation.
Individual empirical instances are calculated when an equation is used to make a numerical prediction. The individual empirical instance is the predicted value, which makes an empirical claim. In a test it is compared with an individual measurement instance, which is the test-outcome value made for the same variable. The individual empirical instance made by the predicting equation is not said to be empirical because the predicting equation is correct or accurate, but rather because the predicting theory makes an empirical claim, which may be falsified by the empirical test.
3.08 Semantical Dimension
Semantics is the meanings associated with syntactical symbols.
Semantics is the second of the four dimensions, and it includes the syntactical dimension. Language viewed in the semantical metalinguistic perspective is said to be “semantically interpreted syntax”, which is merely to say that the syntactical symbols have meanings associated with them.
3.09 Nominalist vs. Conceptualist Semantics
Both nominalism and conceptualism are represented in contemporary pragmatism, but nominalism is the minority view. Contemporary nominalist philosophers advocate a two-level semantics, which in written language consists only of syntactical structures and the ontologies that are referenced by the structures, or as Quine says “word and object”. The two-level semantics is also called a referential thesis of semantics, because it excludes any mid-level mental representations variously called ideas, meanings, significations, concepts or propositions. Therefore on the nominalist view language purporting to reference nonexistent fictional entities is semantically nonsignificant, which is to say it is literally meaningless.
On the alternative three-level view terms symbolize universal meanings, which in turn signify such aspects of extramental reality as attributes, and reference ontologies that include individual entities. When we are exposed to the extramental realities, they are distinguishable by the senses in perceived stimuli, which in turn are synthesized by the brain, and in due course are registered in memory. The sense stimuli deliver information revealing similarities and differences in reality. The signified attributes are similarities found by perception, and the referenced entities manifesting the attributes are recognized by invariant continuities found in perceived change. The signification is always more or less vague, and the reference is therefore always more or less indeterminate or what Quine calls “inscrutable”. The three-level view is called a conceptualist thesis of semantics.
The philosophy of nominalism was common among many positivists, although some like the logical positivist Carnap maintained a three-level semantics. In Carnap’s three-level semantics descriptive terms symbolize what he called “intensions”, which are concepts or meanings effectively viewed as in simple supposition. The intensions in turn signify attributes and thereby reference in personal supposition what he called “extensions”, which are the individual entities manifesting the signified attributes.
While the contemporary pragmatism emerged as a critique of neopositivism, some philosophers carried the positivists’ nominalism into contemporary pragmatism. Pragmatist philosophers such as Quine opted for nominalism. He rejected concepts, ideas, meanings, propositions and all other mentalistic views of knowledge due to the notational conventions of the Russellian predicate calculus, a logic that Quine liked to call “canonical”. However, in his book Word and Object (1960) Quine also uses a phrase “stimulus meaning”, which he defines as a disposition by a native speaker of a language to assent or dissent from a sentence in response to present stimuli. And he added that the stimulus is not just a singular event, but rather is a “universal”, which he called a “repeatable event form”.
Nominalism is by no means essential to or characteristic of contemporary pragmatism, and most contemporary pragmatist philosophers of science such as Hanson, Feyerabend and Thomas S. Kuhn (1922-1996), and most linguists except the behaviorists have opted for the three-level semantics, which is also assumed herein. Behaviorism is positivism in the behavioral sciences. Also, computational philosophers of science such as Simon, Langley and Thagard, who advocate the cognitive-psychology interpretation of discovery systems instead of the linguistic-analysis interpretation, reject both nominalism and behaviorism.
Cognitive scientists recognize the three-level semantics, and furthermore believe that they can model the mental level with computer systems. Thus in his book Mind: Introduction to Cognitive Science (1996) Thagard states that the central hypothesis of cognitive science is that the human mind has mental representations analogous to data structures and cognitive processes analogous to algorithms. Cognitive psychologists claim that their computer systems using data structures and algorithms applied to the data structures can model both the mind’s concepts and its cognitive processes with the concepts.
3.10 Naturalistic vs. Artifactual Semantics
The artifactual thesis of the semantics of language is that the meanings of descriptive term are determined by their linguistic context consisting of universally quantified statements believed to be true.
This implies that ontology, semantics and belief are mutually determining.
The contemporary pragmatist philosophy of science is distinguished by a post-positivist philosophy of language, which has replaced the traditional naturalistic thesis with the artifactual thesis of semantics. The naturalistic thesis affirms an absolutist semantics according to which the semantics of descriptive terms is acquired ostensively and is fully determined by perceived reality and the processes of perception.
Thus on the naturalistic view descriptive terms function effectively as names or labels, a view that Quine ridicules with his phrase “myth of the museum” and “gallery of ideas”. Then after the meanings for descriptive terms are acquired ostensively, the truth of statements constructed with the descriptive terms is ascertained empirically.
On the artifactual semantical thesis sense stimuli reveal mind-independent reality as semantically signified ontology. Sense stimuli are conceptualized as the semantics that is determined by linguistic context consisting of a set of beliefs that by virtue of its belief status has a defining rôle for the semantics. When the beliefs function as test-design statements, they may occasion falsification of a theory.
The artifactual semantical thesis together with the ontological relativity thesis revolutionized philosophy of science by relativizing both semantics and ontology to belief, especially empirically warranted belief. The outcome of this new linguistic philosophy is that ontology, semantics and belief are all mutually determining and thus interdependent.
3.11 Romantic Semantics
On the romantic view the positivist semantics may be acceptable for the natural sciences, but it is deemed inadequate for understanding “human action” in the sociocultural sciences. “Human action” considered by the romantic cultural sciences has subjective meaning for the members of a group or society, because it is purposeful and motivating for the members’ social interactions.
Therefore the semantics for social-science explaining human action must include description of the culturally shared subjective meanings and motivations that the human actions have for the social-group members.
Romantics call the resulting subjective meaning “interpretative understanding”. The social member’s voluntary actions are controlled by this interpretative understanding, i.e., by the motivating views and values that are internalized and shared among the members of a social group by the social-psychological “mechanisms” of socialization and social control. This understanding is accessed by the social scientist in the process of his research. Furthermore if the researcher is a member in the society or group he is investigating, the validity of his empathetically based and vicariously imputed interpretative understanding is enhanced by his personal experiences as a participant in the group or society’s life.
3.12 Positivist Semantics
For positivists the semantics of observation language is causally determined by nature and acquired ostensively by perception. Positivists maintain the naturalistic semantics, and the descriptive terms used for reporting observations are primitive and simple. Positivists thus maintain a naturalistic semantics. These meanings were variously called “sensations”, “sense impressions”, “sense perceptions”, “sense data” or “phenomena” by different positivists. For these often called “phenomenalists” the sense perceptions are the object of knowledge rather than constituting knowledge thus making positivism solipsistic.
In the case of a term such as “black” the child’s ostensive acquisition of meaning might involve the child pointing his finger at a present instance of a perceived black object. And then upon hearing the word “black” in repeated experiences of several other black objects, he associates the word “black” with his various experienced perceptions of the color black. Furthermore from several early experiences expressible as “That raven is black” the young learner may eventually infer intuitively by natural inductive generalization that “Every raven is black.” However, solipsistic phenomenalism makes sharing such experiences philosophically problematic.
Positivists maintain three characteristic theses about semantics:
- Meaning invariance.
- Analytic-synthetic dichotomy.
- Observation-theory dichotomy.
3.13 Positivist Thesis of Meaning Invariance
What is fundamental to the naturalistic philosophy of semantics is the thesis that the semantics of observation terms is fully determined by the ostensive awareness that is perception. Different languages are conventional in their vocabulary symbols and in their syntactical structures and grammatical rules. But according to the naturalistic philosophy of semantics nature makes the semantics of observation terms the same for all persons who have received the same perceptual stimuli that occasioned their having acquired their semantics in the same circumstances by simple ostension. Thus the natural semantics of a univocal descriptive term used to report observations is invariant through time and is independent of different linguistic contexts in which the semantics may occur; it is primitive and simple. Positivists viewed this meaning invariance as the basis for objectivity in science.
3.14 Positivist Analytic-Synthetic Dichotomy
In addition to the descriptive observation terms that have primitive and simple semantics acquired ostensively, the positivist philosophers also recognized the existence of certain terms that acquire their meanings contextually and that have complex semantics. An early distinction between simple and complex ideas can be found in his Essay Concerning Human Understanding (1689) by the British empiricist philosopher John Locke (1632-1704). The positivist recognized compositional meanings for terms occurring in three types of statements: the definition, the analytic sentence and the theory:
The first type of term having complex semantics that the positivists recognized occurs in the definition. The defined subject term or definiendum has a compositional semantics that is exhibited by the structured meaning complex associated with the several words in the defining predicate or definiens. For example “Every bachelor is a never-married man” is a definition, so the component parts of the word “bachelor” are “never-married” and “man”.
The second type occurs in the analytic sentence, which is an a priori or self-evident truth, a truth known by reflection on the interdependence of the meanings of its constituent terms. Analytic sentences contrast with synthetic sentences, which are a posteriori, i.e., empirical, and are thus deemed to have independent meanings for their terms. The positivists view the analytic-synthetic distinction as a fundamental dichotomy between the two types of statements. A similar distinction between “relations of ideas” and “matters of fact” can be found in An Enquiry Concerning Human Understanding (1748) by the British empiricist philosopher David Hume.
An example of an analytic sentence is “Every bachelor is unmarried”. The semantics of the term “bachelor” is compositional and is determined contextually, because the idea of never having been married is by definition included as a component part of the meaning of “bachelor” thus making the phrase “unmarried bachelor” redundant. Contemporary pragmatists such as Quine in his historic paper “Two Dogmas of Empiricism” (1952) reject the positivist thesis of a priori truth. Quine, a pragmatist, maintains that all sentences are empirical.
3.15 Positivist Observation-Theory Dichotomy
Positivists alleged the existence of “observation terms”, which are terms that reference observable entities or phenomena. Observation terms are deemed to have simple, elementary and primitive semantics and to receive their semantics ostensively and passively. Positivists furthermore called the particularly quantified sentences containing only such terms “observation sentences”, if stated on the occasion of observing. For example the sentence “That raven is black” uttered while the speaker of the sentence is viewing a present raven, is an observation sentence.
In contrast to observation terms there is a third type of term having complex semantics that the positivists called the “theoretical term”. The term “electron” is a favorite paradigm for the positivists’ theoretical term. The positivists considered theoretical entities such as electrons to be postulated entities as opposed to observed entities like elephants. And they defined “theory” as sentences containing any theoretical terms. Many positivists view the semantics of the significant theoretical term as simple like the observation term even though its semantics is not acquired by observation but rather contextually. Carnap was a more sophisticated positivist. He said that the definition determines the whole meaning of a defined term, while the theory determines only part of the meaning of a theoretical term, such that the theoretical term can acquire more meaning as the science containing the theory develops.
Nominalists furthermore believe that theoretical terms are meaningless, unless these terms logically derive their semantics from observation terms. On the nominalists’ view terms purporting either unobserved entities or phenomena not known observationally to exist have no known referents and therefore no semantical significance or meaning. For example the phrase “tooth fairy” is meaningless, since tooth fairies are deemed mythical and thus never to have been observed. For nominalists theoretical terms in science receive their semantics by logical connection to observation language by “correspondence rules”, a connection that enables what positivists called “logical reduction to an observation-language reduction base”. Without such connection the theory is deemed to be meaningless and objectionably “metaphysical”
Both the post-positivist Popper and later the logical positivist Carl Hempel (1905-1997) have noted that the problem of the logical reduction of theories to observation language is a problem that the positivists have never solved, because positivists cannot exclude what they considered to be metaphysical and thus meaningless discourse from the scientific theories currently accepted both by the neopositivists and by contemporary scientists.
In summary the positivists
recognized the definition, the analytical sentence and the
theory sentence as exhibiting composition in the semantics of
their constituent subject terms.