RUSSELL HANSON, DAVID BOHM AND OTHERS ON THE SEMANTICS OF DISCOVERY

BOOK VII - Page 6

Hesse on Models and Analogy

Quanta and Reality (1962) is a collection of discourses initially broadcast as a radio series by the BBC in 1961.  It includes a dialogue involving Bohm, a “Postscript” commentary by Hanson and a commentary titled “Models and Matter” by the Cambridge University philosopher of science, Mary B. Hesse.  Hanson’s comments are generally critical of Bohm; Hesse’s are more sympathetic.  This alignment among the participants is not limited to the specifics about the contemporary quantum theory; it divides along issues about the semantics of scientific theories in general and also about the rôle of semantics in scientific discovery.  All participants have much to say about the semantics involved in scientific discovery.

On Hanson’s view the semantics of a theory is determined completely by the mathematical formalism and the measurement concepts that the equations of the formalism relate.  The relations expressed by the theory including its grammatical/mathematical form determine the conceptual gestalt, which constitutes the semantics of the theory.  And in the case of quantum theory the Copenhagen semantical interpretation with its duality thesis is integral to the mathematical formalism of the quantum theory.  Furthermore the semantics of the quantum theory so understood is strategic to the further development of microphysics, as evidenced by the fact that Dirac said he relied on it for his development of his field quantum theory.  Hanson does not deny that there may also be other language about the microphysical domain explained by the equations of the quantum theory, language that does not contradict the quantum theory.  But he views such supplementary language as mere philosophy, and not as part of the theory.  He places Bohr’s naïve epistemology in this category of supplementary philosophical language.

Opponents to the Copenhagen interpretation agree with Hanson that semantics has a strategic rôle in scientific discovery.  But they do not agree that the Copenhagen interpretation is integral to the formalism of the theory.  They are motivated to disagree not only because some of them propose alternatives to the duality thesis, but also because in general they maintain that there is more that determines the semantics of theories than just the mathematical formalism and measurement concepts.  The source of this additional semantics, which they say is found in many if not all theories, is the nonliteral figurative and often imaginative language that they find in the history of physics.  This figurative language involves analogies and metaphors, and this distinctively additional semantics is often called a “model”.  This is one of several common meanings for the term “model”, and in the present context the term functions to articulate the different views on the issue at hand.

Unlike Hanson, Hesse views the ideas of waves and particles as models for quantum theory.  Her former mentor at Cambridge, R.B. Braithwaite, a positivist philosopher of science influenced Hesse’s views about the semantics of theories.  Their views are similar but not the same.  Both Hesse and Braithwaite are positivists, and thus dichotomize observation and theoretical terms, although Hesse’s views evolved beyond positivism late in her career.   The distinction between observation and theoretical terms produces for positivists the peculiar problem as to how theoretical terms contained in a semantically uninterpreted formal calculus can be meaningful instead of meaningless or “metaphysical”.  In his Scientific Explanation (1953) Braithwaite distinguishes two sources of semantical interpretation for an uninterpreted formal calculus containing theoretical terms:

Firstly the formal calculus may receive a semantical interpretation that makes it a meaningful scientific theory containing theoretical terms, when the implied consequences, i.e., the observation sentences, determine the meaning of the theoretical terms in the calculus of the premises, i.e., the theory statements.  Theoretical terms are thus said to receive indirect meaning, since their meanings are determined by their contexts both in relation to one another in the statements of the theory, and in relation to the sentences expressing the directly testable observable outcomes that the experimentalist can logically derive from the theory statements.  In other words the meanings of the theoretical terms are indirect, because they receive all their semantics contextually and not ostensively, as do observation terms.  Therefore Braithwaite labeled this source “contextualism”.  Yet Braithwaite also maintains that a good theory is capable of growth, such that it must be an alternative way of describing the empirical observation statements upon which it is based.  Consequently he admits that the meanings of the theoretical terms need not be limited to being contextually defined explicitly, because the indirect contextual interpretation does not satisfy this growth criterion for theories.

Secondly therefore Braithwaite additionally states that a theory may furthermore receive an interpretation from another source called a model.  A model is supplementary language that contributes meaning both to the terms in the premises and to those in the conclusions, i.e., both to the theoretical terms and the observation terms.  Most notably, unlike the contextual source the model is not a literal interpretation for the domain explained by the theory.  Thus Braithwaite says that theories and models have different epistemological structures, even when they have the same calculus.  It might also be said that the introduction of the model makes the theoretical terms equivocal with one meaning a literal one defined in context and another a nonliteral one defined by the model language. 

For example according to Braithwaite the solar system may serve as a model for the hydrogen atom, even though it is understood that the atom is not literally to be understood as a planetary-stellar system.  Braithwaite says that thinking of theories by means of models is always “as-if” thinking, e.g., thinking of the atom as if it were a solar system.  But he makes an exception for quantum theory.  He says that for the physicist, Schrödinger’s wave function is exhaustively interpreted in terms of its use in the calculus of the quantum theory, and he adds in a footnote that no one supposes that Schrödinger’s wave function denotes a wave in any ordinary sense of the term “wave”. Therefore in Braithwaite’s view modern quantum theory does not have any model.

Hesse’s semantical theory is set forth in her Models and Analogies (1953) and also in her article “Models and Analogies in Science” in The Encyclopedia of Philosophy (1967).  There she compares two earlier conflicting protagonists in the issue of models and the semantical interpretation of theories.  One is Pierre Duhem and the other is Norman Campbell.  In his Aim and Structure of Physical Theory Duhem had argued a view similar to Hanson’s that the semantics of a physical theory is determined only by the equations and measurement concepts, and that even if models based on analogy with more familiar phenomena have served some heuristic value for developing the new theory, nonetheless these models are not part of the theory itself and may be discarded after the theory is constructed.

But Hesse’s views on the semantics of theories are more like Campbell’s than Braithwaite’s.  In his Physics, The Elements (1920) the Cambrian philosopher Norman R. Campbell argued that analogically based models are not merely dispensable aids, but rather are indispensable to a theory, because they assist in the continuous extension of the theory.  He argued that the positivists’ hypothetico-deductive form of explanation alone is insufficient to account for the rôle of theory in science.  He maintained that in addition to the three elements typically admitted by positivists – (1) the formal deductive system of hypothesized axioms and theorems, (2) the dictionary for translating some of the descriptive terms in the formal system into experimental terms, and (3) the experimental laws such as the gas laws, which are confirmed by empirical tests and also can be deduced from the system of hypothesis plus dictionary – there is a fourth element in theories, namely (4) the analogical model, such as may be exemplified in gas theory by the model of point particles moving at random in the vessel containing the gas.  The motivating intent behind this view is that scientific theories are not static museum artifacts, but rather are always growing as an integral part of the growth of science.  This much, which might be called the Cambrian thesis of theoretical terms, is accepted by both Braithwaite and Hesse.

But Hesse’s views are not identical with Braithwaite’s.  Most notably unlike Braithwaite, Hesse does not distinguish the semantics of theoretical terms from the semantics of models.  In fact for Hesse it is the models that supply the indirect meaning for the theoretical terms.  And since extrapolation on the basis of the models explains how the theories grow, Hesse’s interest in the semantics of theoretical terms leads her into the topic of scientific discovery.  Hesse also differs with Braithwaite about the interpretation of quantum theory.  She believes that the concepts of wave and particle supply modern quantum theory with two contrary models.  In her examination of analogical models Hesse distinguishes three parts to an analogy, which she calls the “positive analogy”, the “negative analogy”, and the “neutral analogy”.  The positive analogy consists of those aspects of some familiar phenomena, which are known to apply to the phenomenon explained by the theory.  These include the similarities that have occasioned recognition of the analogy in the first place.  The negative analogy consists of those aspects of the familiar phenomena that are known not to apply or are known to be irrelevant to the phenomenon explained by the theory, and the theorist ignores them. 

Hesse views the neutral analogy as strategic for scientific discovery.  The neutral analogy consists of those aspects of the familiar phenomena whose relevance to the problematic phenomena in the domain of the theory is presently unknown, and therefore whose explanatory potential for further development of the theory is not yet known.  She calls the semantics supplied by the neutral analogy – the concepts and conceptual relations not present in the empirical data alone – the “surplus” meaning.  She also uses the phrase “open texture property” of meaning without referencing any previous usage of the phrase in the literature. The neutral analogy guides further theoretical exploration of the problematic phenomena.  Exploitation of the model for scientific discovery consists in investigating this neutral analogy, because it suggests modifications and developments of the theory that can be subsequently tested empirically.  Such in Hesse’s view is how neutral analogies facilitate discovery and enable theories to grow.

In “Models and Matter” Hesse says that in quantum theory the wave and particle models are such that what is positive analogy in the one model is negative analogy in the other.  She also says without elaboration that in the two models there are still features that physicists cannot classify as either positive or negative, and that it is due to these features that the particle and wave models are yet essential.  Like Bohm, Hesse claims that if physicists were forbidden to talk in terms of models at all, then they would have no expectations, and would be imprisoned forever inside the range of existing experiments.

In her discussion of subquantum theories in the chapter “Modern Physics” in her Forces and Fields: The Concept of Action at a Distance in the History of Physics (1962) she expresses agreement with Bohm’s thesis that a new quantum theory postulating a subquantum order of magnitude is possible.  Specifically she rejects the Copenhagen thesis that current formulations of quantum theory and current models of physical reality are unalterable.  She says that if the wave and particle models each turn out to be unsatisfactory in isolation but usable when regarded as complementary to each another, it is curiously conservative to assert that no other models can be conceived and to elevate the principle of complementarity to a quasimetaphysical status, when it should instead be regarded as a consequence of the poverty of our imagination.  She adds that it may be very difficult to conceive new models, especially when it is remembered that they cannot be entirely abstract formalisms, because they must be tied to the observable at some level.  But difficulty does not entail logical impossibility.

Hesse on Metaphor

The thesis that analogically created models supply nonliteral interpretation for theoretical explanations leads Hesse to consider the semantics of metaphorical language.  In her “Explanatory Function of Metaphor” in Logic, Methodology and Philosophy of Science (ed. Bar-Hillel, 1965) she states that her views are significantly influenced by the interactionist concept of metaphor proposed by her Cambrian colleague Max Black in his Models and Metaphors (1962).  Black opposes his interactionist view to the comparison view.  On his rendering of the comparison view the metaphorical statement is nonliteral for two reasons: Firstly if it is taken literally, it is a false statement.  Secondly it can be restated as an exhaustive list of similes, which are literal statements expressing the similarities implied in the metaphor.  In other words in rejecting the comparison view Black rejects the thesis that metaphors are elliptical similes. 

In her paper on the function of metaphor in theoretical explanation Hesse distinguishes a primary system and a secondary system, where both systems may be taken as real or physical systems that are described literally. In a scientific theory the primary system is the domain of the statements that describe the explained phenomenon in an observation language, while the secondary system is the domain of the statements constituting the explanation and containing either observation language or a familiar theory from which the explanatory model is taken.  Then the explanation of the primary system consists of statements that use vocabulary describing the secondary system and that are applied metaphorically to the primary system on the basis of some similarity or analogy.

In his statement of his interactionist thesis Black lays down a criterion for the literal equivalence of a metaphor: the metaphor can be re-expressed as an exhaustive list of statements expressing all the similarities in the metaphor as literal similes.  Then he rejects the possibility of reducing the metaphor to such a list of similes, because such a list can never be exhaustive.  This inexhaustibility is especially important to Hesse, because the possibility of indefinitely extending and explaining the metaphor constitutes the fruitfulness of the explanatory model containing the metaphorical language. 

But the thesis that metaphor cannot be reduced to literal language is not all there is to Black’s interactive view of metaphor.  The interactive thesis is called “interactive”, because the metaphorical use of language is seen as changing the literal meanings of the words that are used metaphorically; there is an interaction of the meanings of the words in their descriptions of both the primary and secondary systems.  For example he says that the metaphorical statement “Man is a wolf” makes wolves seem more human and men seem more lupine.  This is contrasted with the comparison thesis, which purportedly assumes that the literal description of both primary and secondary systems is unaffected by the metaphor, such that the meanings of the terms remain semantically invariant. 

In Hesse’s view the semantical variance postulated by the interaction view of metaphor is relevant to scientific explanation, because metaphor changes the semantics of the observation language.  This thesis distances Hesse from the positivists, for whom the observation language must remain completely uncontaminated by theoretical language.  Hesse sees this meaning variance in the observation language as contrary to the assumptions of the hypothetico-deductive account of explanation, in which it is assumed that descriptive laws pertaining to the domain of the explanandum remain empirically independent and semantically invariant through all changes of explanatory theory.  She therefore advances the view that the deductive model of explanation should be modified and supplemented by a view of theoretical explanation as metaphoric redescription of the domain of the explanation.

The interactive view of metaphor advanced by Black and used by Hesse, is not the prevailing view.  Conventionally metaphor is construed as an elliptical simile containing implicitly the idea of an underlying similarity that can be explicitly and literally expressed by a simile with the words “like” or “as”.  For example in his Philosophy of Language (1964) William P. Alston sets forth what may be taken as the comparison thesis of metaphor.  Like Black and Hesse, Alston maintains that metaphor has an indeterminacy in it that is inexhaustible.  But he also maintains that it is a mistake to believe that metaphorical and literal languages are different kinds of meaning.  On Alston’s view the difference between metaphorical and literal language is one of degree, where literal language may be identified with established usage and metaphor is a new usage that is derived from established usage.  All meanings are literal meanings, and the derived and unconventional usage in a metaphor may be expressed literally with greater or lesser extent of explanation.  When the new usage is forgotten, the metaphor becomes a dead metaphor in the sense that it is no longer recognized in the linguistic system.  But when it has become part of the established usage, then the metaphor has become a dead metaphor in the sense that it has become part of the conventional literal language, and explanation of its derivation from the original established usage becomes an exercise in etymology. 

Furthermore unlike Black or Hesse, Alston does not say that metaphor must be capable of being reduced to an exhaustive list of similes, in order to be reduced to literal use, because there is indeterminacy in literal language as well as in metaphor.  Alston references Friedrich Waismann’s “Verifiability” in Logic and Language (1952) stating that literal words denoting physical objects have an inexhaustible vagueness which remains even after all attempts at clarification.  This vagueness remains because in addition to actual cases of indeterminacy of application, one can think of an indefinite number of possible cases in which one would not know whether or not the term applies.  For example is a certain plant a tree or a bush?  Waismann calls this inexhaustible vagueness the “open texture” of descriptive language.  Quine called it “empirical underdetermination”.  Alston denies that metaphor is simply vagueness, but he says that in both metaphorical and established language there is an inexhaustible indeterminacy due to the fact that it is impossible to decide in advance on every possible usage of a word. 

The conclusion to be drawn from this is that Black’s criticism for the reduction of metaphor to literal language by means of an exhaustive list of similes is not a feasible criterion, because it would demand more determinateness of nonliteral language than of literal language.  A weaker criterion therefore is in order.  It would seem sufficient to require only that a metaphor be re-expressible with at least one simile that makes explicit an implicit underlying similarity, presumably but not necessarily the similarity that is intended by the speaker or writer initiating the metaphor.  Furthermore semantical variability or meaning variance must therefore be a property of both metaphorical and literal language, or it must be a property of neither, since the former is merely the elliptical expression of the latter.

These considerations are relevant to Hesse’s thesis about metaphor in theoretical explanation in science.  Her tacitly assumed premise is that meaning variance does not occur in literal language, i.e., in the absence of metaphor.  On this premise the nonreducibility of metaphor to literal language is strategic to her rejection of the adequacy of the hypothetico-deductive thesis of theoretical explanation, and it is strategic to her reliance on metaphor to account for semantical change or meaning variance in the language for description of observed phenomena.  On the other hand if as Alston says metaphor is reducible to literal language, then semantical variability must be a property of both metaphorical and literal language, or it must be a property of neither.  And it is clearly a property of metaphor; otherwise there would be no dead metaphors indicating that the new metaphorical use has either been forgotten or has become a new alternative literal use.  Thus the reducibility of metaphor to conventional literal language implies that metaphor cannot satisfactorily be used as a general explanation of semantical change in science, even if it can serve to indicate that semantical change has occurred relative to currently established meaning.  The theory-laden character of observation discourse resulting from theory revision is a much more general aspect of the semantics of language than just its metaphorical usage.  The explanation of semantical change or meaning variance demands a general theory of semantical description for all literal language.  At the same time metaphor seems clearly to have a rôle in occasioning semantical change, and it may have a strategic utility for the development of new theories in science.

Two decades after these 1960’s-vintage papers on analogy, metaphor, and models Hesse finally reconciled herself to the artifactual thesis of the semantics of language and the phenomenon of pervasive meaning variance in the semantics of descriptive terms.  But her pathway was a circuitous one.  In her Construction of Reality (1986), co-authored with Michael A. Arbib, she says that her starting point is Max Black’s interaction theory of metaphor as modified in the light of Wittgenstein’s family-resemblance theory of meaning.  At the end of her philosophical trek she is not consistent with Black’s irreducible separation of literal and metaphorical meanings, although she continues to advocate it.  Firstly she rejects literal meaning understood as invariant meaning, and announces (placing her own words in quotes) that “all language is metaphorical”, phraseology that she says some will find “shocking.”  It might better have been described as “mocking” the meaning of literal.  Her thesis is that the use of general terms is always metaphorical in the sense of relying on perceived similarities and differences between various individuals, similarities that are family resemblances for which a term has been acceptably used in the past.  She dichotomously opposes Wittgenstein’s family-resemblance thesis to the Aristotelian natural-kinds thesis.  She says that either the world is really Aristotelian, such that objects really fall into sharply discriminated species; or in practice we allow that language works by capturing approximate meanings, such that degrees of similarity and difference are sufficiently accessible to perception to avoid confusion in ordinary usage. 

Hesse believes that the second option is more realistic.  She adds that it implies that we lose potential information every time we use a general descriptive term – either information that is present to perception but neglected for purposes of the description (e.g., no one discriminates every potential shade of red), or information present in reality but below the level of conscious perception.  In the latter case the information may later be made accessible by instrumental aids such as a spectrometer.  Understood in terms of the family-resemblance analysis, metaphorical shifts of meaning depending on similarities and differences between objects are pervasive in language – not deviant – and some of the mechanisms of metaphor are essential to the meaning of any descriptive language whatsoever.  She explains that this is what she means by her thesis that all language is metaphorical.  This peculiar outcome is due to her identification of the naturalistic thesis of the meaning of terms, which she calls semantical naturalism, with the concept of literal meaning, and is also due to her earlier conclusion that metaphor enables a nonliteral redescription of observed phenomena in scientific explanation.

Yet she does not abandon altogether the intuitively recognized distinction between literal and metaphorical usages in language.  Having firstly rejected the meaning-invariant idea of literalness she then secondly redefines the meaning of “literal” by making the distinction between literal and metaphoric pragmatic instead of semantic.  And it is here that Black’s interactionist thesis would seem to serve her no longer, because what now distinguishes metaphor from the literal is not Black’s semantical irreducibility but rather conventionality. 

Rejecting Black’s irreducibility thesis would seem implied by a pragmatic distinction, because she says that her new definition of “literal” merely enshrines the use that is most frequent in familiar context – the use that least disturbs the network of conventional meanings.  It is the meaning often placed first in dictionary lexical entries, where it is followed by comparatively dead metaphors.  And metaphor denotes particular forms of literary expressions that depend on explicit recognition of similarities and analogies.  For example “Richard is a lion” is a metaphor, because it based on elaborate analogy between particular human and animal dispositions, in which the obvious differences between human beings and lions are consciously discarded.  A metaphor in this sense is usually recognized only when it is newly minted.  When metaphors become entrenched in a language, they become a new literal usage.  Such is often the internment of dead metaphors.

Hesse says scientific language conforms closely to her metaphorical model of meaning.  Not only is theoretical explanation a metaphoric redescription of the domain of the phenomena, as she said in the 1960’s, but more recently she says that scientific revolutions are metaphoric revolutions.  In her earlier years as a positivist, Hesse had been critical of Kuhn often referring to his views pejoratively as “historicist”, an idea she refused to explain when once asked personally by Hickey.  Now using the Kuhnian terminology and referencing Kuhn she says that in the development of science a tension always exists between normal and revolutionary science: normal science seeks to reduce instability of meaning and increase consistency and to evolve logically connected theories.  Revolutionary science makes metaphoric leaps that create new meanings and applications and that may constitute genuine theoretical progress.  Ironically in his later writings Kuhn rejected Hesse’s thesis that all meaning is metaphorical, and he actually embraced Black’s interactionist view.

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