Edward A. Remler

Department of Physics

Williamsburg VA 23185

May, 1998

The subject of this paper is the image of physics as it appears to the educated public, and in particular, the question of how that image should be introduced to that public via courses given to non-science oriented students. Students should learn the purpose as well as a bit of the content of physics. Pedagogical practice generally assumes that purpose is either already obvious from content or becomes so, but in contrast to the other sciences, and due to the unique position of physics as the cornerstone of science, this is not so. The cornerstone of science is set on a metaphysical grounds, and the vast majority of students start out, metaphysically, as Aristotelians at best. This paper emphasizes the improbability that students will come to understand, on their own, much less adopt, the metaphysical assumptions of physics. The message then is that in such introductory courses, it is at least as important to teach some metaphysics as to teach some physics.

Physicists, as teachers, are generally aware of relevant issues, but they are not sufficiently aware of their potency if only because, as physicists, they come from the minority of students for whom metaphysical issues were not potent. Their awareness will be raised by presenting major issues from two perspectives. The first is that of the Church at the time of Galileo’s inquisition. Issues puzzling to the Church’s chief theologian, Cardinal Bellarmine, and to Pope Urban VII, both well educated men of their time, will be seen to be the same as those which puzzle well educated people today. The second perspective is that of modern post-positivist philosophers of science such as Thomas Kuhn. These thinkers quite literally confess to not understanding the laws governing physics’ development. They have felt forced, as a result, to come to some remarkably negative conclusions about science.

Thus, church history and modern philosophy both testify to the fact that few people outside the profession understand physics’ inner dynamics. That dynamics is an expression of the purpose of physics as perceived by its practitioners, and that in turn is based on metaphysical assumptions common to the physics community. In the same vein, modern physics pedagogy can testify to widespread student confusion about metaphysical issues similar to those affecting popes as well as philosophers. The conclusion seems to be that in their introductory courses for non-scientists, physicists must undertake explaining themselves–explaining their attitudes and not only their subject matter. Some tentative suggestions for how this may be done are given.

Introductory College Physics tries to teach physics to a typically pre-scientific mind. In the course of this, it presumably converts the student’s outlook upon the natural world from (at best) Aristotelian to (at least) Newtonian. The student is to duplicate the worldview transformation of the Scientific Revolution. Intellectual ontogeny is to recapitulate phylogeny: the student’s mind is to change in a way which recapitulates that of science in the century between Galileo and Newton. This rarely occurs.

Some students manage the jump, or they have managed it before entering the course. We know this because in each generation some of them become physicists. Their ability is a question of talent which pedagogy may help but not create. I will not be discussing helping such talent.

Neither will I be discussing the more common problem of simply getting basic facts and skills across to science-oriented students: physics as a service to other professions. Here, pedagogy clearly makes a difference, and most of its current R&D seems to be in this area.

My subject is the understanding of physics given to the majority of educated people as conveyed through introductory courses given to non-science oriented students. In contrast to the other types of students mentioned, these will rarely have more than this one opportunity to get a feeling for what physics is about. This includes more than learning content; it includes getting a sense of the purpose of physics, and a sense of its position in the spectrum of human knowledge.

The following all-too common opinions and beliefs are well-known examples of not knowing what physics is about:

• A sense of theories in physics being regularly ‘disproved’ or ‘overthrown’ (as in Einstein disproved Newton) which reveals a basic misunderstanding of the purpose and meaning of such theories.
• A belief, on this basis, in the respectability of alternative sciences.
• A critique of physics as an ideal or abstract study somehow disconnected from much of reality.
• A belief, on this basis, that the study of physics offers little beyond its subject matter proper; in effect, the separation of physics from most human and humane concerns.
• An associated further set of critiques clustered around the buzzwords of reductionism, holism, emergence, etc. as these appear in discussions of physics and are extended elsewhere.

Its position as the cornerstone of science makes dealing with the large issues behind such misperceptions uniquely important in the context of physics–at least as important educationally as teaching subject matter itself–and its position also makes this educational goal uniquely difficult. This uniqueness is not generally appreciated. Sensitive teachers of all subjects commonly feel let down by how little they seem to get across to students. What sets physics apart?

And even assuming this uniqueness, where does a recognition of it get us? Enthusiastic and innovative teachers are always creating new ways to improve subject matter presentation–to get around mathematical difficulties, to simplify explanations, to illuminate wider relevance, and so on. What else can one do but continue to do such things and hope for the best?

I contend that answers to both these questions–why is physics pedagogy uniquely difficult, and what new sorts of things can be done to improve it–lie beyond physics; they are rooted in metaphysics. The common misperceptions about physics noted above, the unique problems physics pedagogy has in dealing with them, and their educational importance, all require answers based in metaphysics.

Originally ‘metaphysics’ merely designated the placement of the written material given that name after physics (then the study of most of nature) in compilations of Aristotle’s works. Metaphysics did not designate material intellectually ‘beyond’ or ‘transcending’ science. Nevertheless, this is what metaphysics came to mean, and it is a good starting point for defining how the word will be used here.

It focuses attention on metaphysics’ relation to science rather than on the subject matter under its domain. This is appropriate because this domain was reduced as part of the creation of physics. Thus, prior to Newton, a physical theory was considered unacceptable if it was metaphysically unacceptable. In contrast, most physicists would maintain that now, even though hypotheses based at least in part on metaphysical preconceptions necessarily enter into any physical theory, metaphysics is never decisive; it never determines a theory’s ultimate acceptance. I would maintain that this is true not only as an ideal but, since Newton, as an historical fact^.

Many historians and philosophers of science, however, contend that this is merely an "historical fact", that this nearly universal belief of the physics community is merely a fiction. Their rationale will be touched upon later in this article but the existence of this divergence of beliefs is what is most important here. For one thing, it suffices to show that the issue is not something most non-science students can be expected to solve on their own. It is not enough to just teach students the facts of physics and assume that the physicists’ view of the matter (or the philosophers view for that matter) will automatically reveal itself to them. They must be led to it, and that job, as the divergence of beliefs also demonstrates, is difficult, and one which physicists must do themselves.

As long as one is not a physicist, historian or philosopher the issue just discussed (really, that of the role of metaphysics in the minds of physicists, and its effect on their actions) is important, but only indirectly. In particular, of direct importance to non-science students is their perception of physics’ standing in their worldview: what physics is about in the sense of its purpose and position in the spectrum of knowledge. And even more, how the study of physics might inform and change their metaphysics, and how it might through that, change their worldviews.

Ontology, the study of what exists, is the central concern of metaphysics. In what sense do atoms exist? In what sense can unperceived, or indirectly perceived, or logically inferred things (such as quarks) be said to exist? What does it mean to say something exists? Such questions, in turn, naturally involve Epistemology, the study of how we gain knowledge: How do we gain the knowledge that something exists? Because of its cornerstone position, physics is where such questions arise most directly and demandingly–not so much to the enthusiastic doer of physics as to the critical viewer. An appreciation of physics is a vigorous exercise in applied metaphysics, and this should be accounted as one of the main reasons for its cultivation, and its position in a liberal education.

Physicists share common views about metaphysics as it applies to their work. Their views are implicitly learned during a long professional training. They do not need to be explicitly taught; and being understood, they need not be discussed. But non-science students, and the population at large they represent, do not generally share these views. They share pre-scientific ones. Examples will be discussed throughout this paper but as a quick preview, consider the common student complaint that physics only deals with idealized situations. From this it is easy to conclude that, even though physics is obviously useful, it not necessarily true. One result is the belief that physics is probably not true when it conflicts with common sense or previously cherished beliefs. The metaphysical basis of this complaint is a conception of reality (is it or should it be taken to be what is directly perceived by our senses?) and a conception of truth (how is it identified?).

In a similar vein, students commonly expect physics to provide commonsense, reasonable explanations (it is too ‘abstract’), to explain what matter ‘really is’ (essences), and to explain why things happen (true causes) not merely how. The metaphysical assumptions behind these expectations are ancient and multifaceted. They can be addressed in this essay only peripherally. How such questions are addressed in a physics course, however, will deeply influence how all of that course’s factual material is perceived. And because of physics special position in science, it will also determine the value placed on the whole scientific enterprise. Students’ discouraging discovery that physics does not conform to these expectations encourages misconceptions such as those listed previously.

Few physicists remember being overly concerned with such matters as students (probably a pre-requisite for becoming a physicist) so that, even if as teachers they recognize that their students do have such concerns, the problem does not seem as important as it is being made out to be here. The curriculum assumes that such problems vanish if and when students learn to appreciate more of the content of physics. Students presumably will then be won over by physics’ beauty, its utility, its logical structure, and so on. In the end they will understand, if not share, the metaphysical outlook of science.

Of course this rarely happens, certainly within the course of a year, but the problem is generally attributed to the innate difficulty of physics itself–its subject matter and especially its use of mathematics–rather than to the difficulty of metaphysical issues. I contend that this is incorrect and leads to much misplaced effort. I believe that physicists’ lack of personal experience struggling with metaphysics lowers their consciousness of the difficulty others have with it. Therefore, a major purpose of this paper is simply consciousness raising.

Both consciousness and the issues themselves will be raised in this essay by describing major issues that professional metaphysicians, past and present, have raised contra science. There can be no better source of the issues and no more dramatic proof of their difficulty.

The next section describes issues raised by Church theologians–major metaphysicians of their era–just prior to the trial of Galileo, almost four centuries ago. I indicate how these issues are close to those of concern to modern post-positivist philosophers, and, albeit less coherently and consciously, close to those underlying the concerns of modern students.

The paper then discusses the uniqueness of physics, specifically its uniquely deep level of explanation as achieved through mathematics. The purpose of this is to try to explain the origin of the unique difficulty of physics pedagogy. The main point here is that the mathematical symbols appearing at such deeper levels of explanation are only indirectly tied to language. They can be talked about but not really understood through language. Their meaning is not to be explained. Their meaning is the set of rules governing their use. It is something learned through use over time. This is a great barrier to any real comprehension of physics by non-professionals. This point will be especially brought out by a discussion of post-positivist criticisms of science.

The paper concludes with some pedagogical suggestions.

A portion of a letter written by Bellarmine, to Foscarini a supporter of Galileo goes as follows:

Here Bellarmine distinguishes between on the one hand speaking hypothetically as a mathematician and on the other hand speaking absolutely when affirming heliocentrism in very truth. He understood heliocentrism as phenomenology: a convenient reduction of many data to relatively few parameters. The data were the ephemeredes and the parameters were quantities like orbital radii and speeds.

Phenomenology is implied, in the usage of his time, by calling heliocentrism a hypothesis: under this hypothesis, the data can be organized in this way, under that hypothesis, in that way. It was associated with the idea of ‘saving the phenomena’: what new hypotheses could save the utility (under the impact of new and more accurate data) of the ancient Platonic/Ptolemaic scheme for parametrizing the ephemeredes. Whatever the new hypotheses might be, they were merely mathematical expedients, not assumed to provide an understanding of ‘true causes’.

Since Plato, astronomers had become history’s first pure phenomenologists, and although their work was very useful, they rarely imagined that its meaning could transcend its immediate practical purpose. Enlightened opinion believed that there was no more to astronomy than phenomenology, and in particular, it believed that astronomers did not speak absolutely or in very truth. Bellarmine knew of three main astronomical systems, the Ptolemaic, the Tychonic, and the Copernican systems, each based on different hypotheses, and knew that each provided approximately equally successful descriptions of the same data. Could they all be the very truth of the matter? It seemed more likely that none were.

Today we are familiar and comfortable with the idea that all our theories are provisional, but neither Bellarmine nor Galileo thought about physical theories in this way. They both talked as if they knew what absolute truth meant, and Galileo talked as if absolute truth was what his physics was about. Most people still assume physics establishes some kind of absolute truths.

In contrast, philosophers conceive of truth in general as a murky issue. A corollary to this is a break or at least loosening in any necessary connection between physics and absolute truth, and to many philosophers, this implies philosophic relativism; they connect loss of absoluteness to loss of uniqueness. Thomas Kuhn, in the course defending himself from being mislabeled as a relativist by fellow philosophers, noted:

If successive theories grow ever closer to, or approximate more and more closely to, the truth then clearly astronomers could speak absolutely or in very truth and say that heliocentrism is absolutely more true than geocentrism. But if a philosopher believes that successive theories do not, does that mean she denies the absolute supremacy of heliocentrism? Kuhn tells us that many philosophers assumed this was the case when judging him.

In summary, Bellarmine knew of multiple ways to save the phenomena, believed they were equivalent, and was thus a de facto philosophic relativist. Kuhn tells us that some modern philosophers used doubts he expressed about concepts such as what is "really there" to infer that he was a philosophical relativist.

Bellarmine can be related to modern philosophical relativism in another way. There is an epistemological view which is often expressed today by the so-called Duhem-Quine thesis. One version of it, according to Larry Laudan, is

The only observational basis for such a statement would seem to be as follows. Just as sufficiently clever mathematical astronomers known to Bellarmine were able to pile on epicycles, equants, and so on as needed to fit theory to new observations, so also sufficiently clever modern phenomenologists can attach bells and whistles to their theories as needed to fit new experimental data. This seems to lead some to believe in the existence of multiple physical theories of equal explanatory value. This is at least in part a problem of not having the experience necessary to distinguish between multiple usages of the word ‘theory’. The word is used in many different ways: as in Newton’s gravitational theory, as in Quantum theory, as in String theory, and as in the theory of the liquid drop (model of the nucleus). All make very different epistemological claims.

In these examples we see how over a span of four hundred years, similar metaphysical issues concerning the nature of truth, have led educated people–popes and philosophers–to similar basic misperceptions. Students should be expected to share them. Thoughtful students and philosophers both have perceptions of truth which are not those of physics, and the fact that the former cannot yet consciously formulate and coherently express them does not mean that they are not deeply troubled by them.

Pythagoras famously said that All is Number. Plato, his intellectual descendant, suggested even more when he talked about trying to understand how the many could come from the One. The modern scientific version of Plato’s goal would be Unified Theory of Everything: a simple, comprehensive, universal, and mathematical theory of everything. Pythagoras and Plato knew so little about natural law and how it could be discovered that their visions can only be called religious. People of common sense have little patience with such visions, and Aristotle is their prophet. The idea that all the complexity of nature is just the unfolding of simple law, and that it is mathematical law, has always seemed absurd to most people. Common sense and Aristotle tell us to stick to the obvious facts: nature is a complex mix of concepts, causes, motions, sensations, and so on, and, by and large, knowledge consists in their categorization.

People are natural Aristoteleans. They try to not confuse categories: quantity with quality, cause with effect, matter with motion, space with time, animate with inanimate, mind with brain, human with machine intelligence, and apples with oranges. Neither do they confuse natural realms; they keep separate laws and methods of investigation proper to each realm. It was apparent in Galileo’s era that, in the celestial realm, change has a constancy, order, simplicity, and serenity which is qualitatively distinct from the generation, decay, complexity, and chaos which characterizes change in the terrestrial realm. Because of this, Galileo’s attempt to connect them seemed patently absurd (as absurd, say, as a connection between human and machine intelligence); it appeared to be the improper extension of methods used for the study of the celestial to the terrestrial. In a similar vein today, many disdain measurement, objectivity, and logic in the study of humanities, considering that, though these are methods appropriate to the physical science, their application beyond its borders is arrant ‘scientism’.

Students should be made aware of the fact that common sense opinion of what is beyond science has shifted continually. For example, since the scientific revolution, one boundary of the realm of science has shifted from the location of the Moon’s orbit to a metaphysical sphere separating brain and mind. Whether or not shifts continue is of course unknown, but any apriori exclusion of the physical sciences from large swathes of human culture is just Aristotelianism revisited.

The domain of mathematics is very broadly conceived and still in flux, but it has always centered on number and quantity, concepts people have always found difficult to categorize. "What is number?" is as an old and familiar question. This in turn has made it difficult for people to really believe Galileo’s dictum that the book of Nature is written in the language of mathematics. Examples will be discussed in this and the next sections.

Quantity is apparently ontologically deficient: it does not seem to be made of the right stuff to serve as the basis for physics. In the terminology of Galileo’s era, mathematics is concerned not with substance but with "nude quantity" alone. Quantity is a concept abstracted from substance. How can anything fully describe that from which it is abstracted? When quantity is used to describe substance it seems that it must leave behind qualities with names like ‘essences’, ‘natures’, and ‘quiddities’. And mathematics apparently cannot describe causal relations between things either, in the sense that it describes quantitative relations between cause and effect but not why things change.

Physicists may dismiss such concerns as metaphysical, vague, meaningless, and quaint, but pedagogues may not. Concepts like causes and essences are vague in proportion to their metaphysical content. Concepts like existence and truth are even vaguer for being even more metaphysical, and certainly they are not easily dismissed. Metaphysics imbues concepts with more not less importance to those concerned with it, and makes those concepts more not less difficult to handle. These concerns about mathematics were prominent before the scientific revolution, and, remain so in pre-scientific minds. That quantity is not equivalent to substance, that it cannot even fully describe substance, and that it cannot explain why causes cause, all seem to be obviously true. The conclusion, to which Cardinal Bellarmine would agree, is that mathematical physics cannot fully describe physical reality.

The preceding comments addressed deficiencies inferred on general grounds, but Galileo’s era also had direct evidence of deficiencies. Algebra, in the sense of manipulation of non-numeric symbols, was just being discovered. Bellarmine could have known nothing about such things; his understanding of mathematics could only have been at the level of arithmetic (itself not so old at that time). Neither could he have had much understanding of the concept of a function. Thus he could not have conceived of mathematics as a general science of relations. Furthermore, he could not have seen how relations between numbers (let alone variables) related to geometric form since analytic geometry did not yet exist. Having no conception of the relation between algebra and geometry, he could not have imagined the immense variety of curves and surfaces describable by mathematics.

Taking all this into account, he understandably had difficulty believing that a language seemingly limited to little more than arithmetic, trigonometry, and geometry was the language in which God wrote the book of Nature. This required a leap in faith which overtaxed even the chief theologian of the Church.

But are modern students much better prepared than Bellarmine in this respect? Their understanding of mathematics is such that they also must make a great leap of faith? For example, few of them will have ever seen anything beyond the simplest algebraic relations plotted as curves so that even the descriptive power of classical mathematical functions is unknown to them.

Another perceived deficiency of mathematics is illustrated by one of Zeno’s paradoxes. To move from 0 to 1 along the real line I must first move to 1/2, then to 3/4, then to 7/8, and so on. I must do an infinite number of things. Everyone now knows how to add up an infinite series and so can prove that the motion can be completed in a finite amount of time, but there remains the problem of how an unending number of tasks can end. How do you reach the end of a series which has no end. This appeared as a logical inconsistency entering into the application of mathematics to physical reality.

Zeno’s paradox appeared to demonstrate that mathematics was fundamentally unable to describe motion. Today people hear about other apparent deficiencies of mathematics such as Godel’s discovery of arithmetical truths unprovable as theorems. Apparently then, all truths may not be eventually derivable from the basic laws of physics.

Matteo Barberini, though originally a friend of Galileo, eventually, as Pope Urban VIII, had him tried before the Inquisition. The two are reported to have privately discussed Copernicanism. Barberini’s words were reconstructed by Santillana as follows.

However this is interpreted, it questions reason’s power to connect phenomena to some sort of unique truth. Similar critiques of rationality are central to postmodernism, the deconstructionist and social constructivist branches of which are leading sources of anti-science diatribes. The constructivist philosopher, Paul Feyerabend, for example, when discussing the Church’s role in the trial of Galileo, connects the constructivist program with the ideas of the Pope as follows:

He claims that science seeks to inhumanely impose a unified vision of truth uniformly everywhere, and that this drive towards intellectual hegemony must be tempered by other equally valid systems of truth. The Church sought to temper science with Scripture. Feyerabend elsewhere suggests both Astrology and Aristotelianism for this purpose.

The pope, and Feyerabend and other postmodernists, all devalue science’s search for basic truths by their belief that there are none. The pope points out that God is not bound by natural law and that reality is not uniquely tied to phenomena. The philosopher does not believe laws of physics are universally or even widely applicable. Both views diminish the scope and meaning of physics. It becomes little more than an handmaiden to technology.

Students who have absorbed such worldviews will be impervious to even the best science pedagogy. They will remain unimpressed by even the best presentation of (say) the careful and elegant reasoning underlying Special Relativity. For, applying another quotation from Feyerabend, they will see Special Relativity as merely a point of view, valid in its area, but inapplicable outside. The instructor sees in Special Relativity a great and astounding truth; the student is underwhelmed by this curiousity of physics. This student attitude may well not appear in the physics classroom; it will appear, however, when science is seriously challenged elsewhere.

Such direct connections are felt to be necessary. We are convinced that water vapor exists in large part because we feel that liquid water must turn into something when it evaporates, and similarly, that something must be turning into a cloud when that appears. Both beliefs–as strong as any we have–are rooted in the naive metaphysical feeling that matter can neither vanish into nor appear out of nothing.

Positivist concepts also include electricity, heat, light rays, radio waves, and infra-red and ultra-violet radiation. They are close to the phenomena; they are necessary to use, relatively easy to use, and often used in qualitative reasoning about phenomena; these properties are what transform such concepts into realities in peoples’ minds. No one labels physics as especially abstract or difficult because it uses them, and they present no metaphysical problems to anyone. Most of the hard sciences are built almost entirely of similar positivist concepts.

Positivism, the school of thought which held that physics should be limited to such concepts, lost its last battle at the start of the 20^th century. That battle was over atomism. Until then, atomism was opposed by a significant number of physicists because classical macroscopic phenomena did not require explanation in terms of atoms. The phenomena of everyday life, cannot by themselves convince anyone that atoms necessarily exist, that they are as real as, say, electricity, heat, or water vapor. And although most people today, if asked, will easily profess a belief in atoms, it is really a matter of faith based on the authority of science.

To see that atoms are really necessary components of the microscopic world requires knowledge about that world which non-physicists neither have nor are ever likely to have. Reasoning convincingly about evaporation at the atomic level, for example, requires knowing something about molecular velocities, sizes, shapes, distances, and internal, kinetic, and interaction energies, energy transfer, diffusion rates, temperature energy relations, entropic effects, … . Generally, only a physicist has and knows how to use such information.

Because of this, atoms attain only academic reality to students. They can reason about them, but only inconclusively, just as they already reason about concepts in the arts, humanities and the social sciences. They may be atomists under ordinary circumstances, but nothing holds them firmly to it. An atom is only as real to them as a current theory of literary criticism. It then becomes entirely possible for philosophers to convert them, for example, to a belief that the atomic structure of matter is a conceptual tool of Western Imperialism.

The reality of many physics concepts from atoms to quantum mechanical wave functions is often questioned. This is a problem almost unique to physics; no one doubts the reality of a chemist’s acid, a biologists bacterium or a geologist’s rock. Thus it is necessary to explain to students the operational meaning of reality in physics.

One way to do this is by analogy to virtual reality: artificially created reality produced by computer programmed instruments coupled to the senses. When experiencing virtual reality, we remember how it got there; otherwise we would be convinced that what we senses is real. Something appears to be real because of innumerable correlations of sensations. Its motion in a field of vision is correlated with that of other objects, with muscular sensations, and with the sense of touch. We reach out to touch it and we do touch it. These correlations make things real; they define what is normally meant by reality, whether it be virtual or real.

Scientific instruments extend sensations, and theories extend our understanding of correlations between sensations. In this way physicists sense an extended world with a sense of reality comparable to that which is provided by the technology of virtual reality. In the case of physics, the input to instruments is programmed by Nature, but the word reality retains its meaning. An object in physics is real because of innumerable correlations between measurements of it and of other objects–correlations which allow us to function in an otherwise uncorrelated chaos.

That such extensions of the senses could be achieved and such extensive correlations could be discovered through mathematical analysis was unimaginable prior to the scientific revolution. It remains unimagined by most people to this day. As a result, most people think the normal world is in some sense ‘more real’ than the supersensible world of the physicist. This is only natural since they have no experience with this extended world. Students must somehow be made aware of the fact that there is no essential difference in the criteria that are used to define reality in either world.

Language is often almost identified with thought–how can we even think about something without a word for it?--yet of course unconscious and therefore non-verbal thought not only exists but is the brain’s preponderant activity. Original ideas (certainly some, possibly most) in physics, as in many (probably most) fields, are generated without (or at least without much) conscious verbal reasoning–without the use of language. In most fields, however, language is used for afterthought–to explain one’s conclusions, after having reached them, to one’s self and to others. This is understandable on the assumption that language originated for communication as opposed to generation of thought.

The arts provide exceptions to language’s powers of communication. An explanation of a symphony is appreciated mainly by the musically deaf. We are accustomed to this and may think of it as being peculiar to great art. Certainly we do not normally find language inadequate in the sciences. The construction and function of a kidney, of a rock formation, or of an ecosystem, are well described by language. That is why it may be difficult to recognize that the problem does occur in physics. Physics is exceptional amongst the sciences and the reason, as just discussed, is simply that it describes parts of reality beyond that for which language was created.

A statement such as "An electron is both a wave and a particle" helps illustrate language’s limited utility in physics. To someone who knows quantum mechanics, the statement’s meaning is clear–but only because quantum mechanics is already clear. To someone who does not know quantum mechanics, the words communicate only a paradox. It is an unnecessary paradox created by the attempt to use ordinary language to describe a quantum mechanical object. For by themselves, the operational rules within quantum mechanics, which serve to define electrons, are internally consistent and straightforward.

Although language’s use in physics is limited, it is, of course, also necessary. First of all, It is necessary to relate physics to sensation. Communications concerning phenomena directly observed by the senses, be they lightning strokes or the output of measuring instruments, are the original motivation for ordinary language. We have no means of communicating and describing directly observed phenomena other than through ordinary language. This communication remains the necessary use of language in physics; it forms its interface with the sensible world.

But this interface is only part of physics. Beneath it lies various levels of abstraction, and as depth increases, ordinary language’s effectiveness decreases. It fails

1. as an instrument of reasoning. Mathematical reasoning is unique in its internal consistency, the logical certainty of its deductions, and the depth of logic–the sheer number of steps between assumptions and theorems–it enables to us to reach.
1. as a descriptor of mathematical reasoning. Mathematical reasoning proceeds via symbolic manipulation. Even describing such manipulation in words, which is effectively how such reasoning was performed before the techniques of symbolic manipulation were invented, is a mind-numbing exercise. The sheer verbosity of a completely verbal description of just a typical physical formula obscures the relations it expresses. These relations, immediately apparent in their symbolic representation and therefore easily accessible to conscious thought, are the basic structural elements of a physical theory. People who cannot ‘read’ mathematical symbols easily and directly, are always focussed on translating relations into words, and consequently have great difficulty seeing the forest–the large structure of a theory–for the trees.
1. as a descriptor of the results of mathematical reasoning. Mathematical reasoning takes us ever deeper beneath the surface of things, away from the directly sensible world of phenomena, and we encounter (as in the abyss) creatures with ever stranger properties. Whatever else they may be, in an ontological sense, these creatures are mental structures. The structure which is the electron has a phenomenological level associated with things such as static electricity, household current, hot cathodes, gas discharges. Their common association to the electron, within the conceptual structure it represents, interconnects them. The electron similarly interconnects a host of parameters (mass, charge, spin,...,); they must be used in conjunction in calculations. Finally, this mental structure also includes an algebraic symbol–the field operator for the electron–which has itself a host of associated properties such as its anticommutation relations and its coupling to other fields.

These latter attributes of the electron are purely mathematical and operational in character; they have physical consequences but not physical meaning. The Pauli exclusion principle which can be basically understood with words relating it to phenomena, is a consequence of anticommutation relations, but not their meaning. Anticommutation relations have algebraic meaning which are meaningless to mathematically untrained people.

Yet further from physics interface with the sensible world, beyond the electron, the situation exacerbates–creatures become even stranger. The electron had a phenomenological level for which words were necessary, but the supersymmetric string has none at all. Such objects have only operational meaning within mathematics.

These deficiencies of language significantly influence elementary physics pedagogy. The example just discussed, the quantum mechanical electron, of course does not play an important role the elementary physics taught non-science students; it was chosen as a very extreme and therefore clear example of a general problem. On the other hand, Newtonian dynamics is (or should be) an important part of elementary pedagogy, and verbal descriptions of it suffer from similar problems, though less visibly. For example, part of Newton’s great accomplishment was his conversion of the ideas surrounding the concept of force from the qualitative to the quantitative, and to the extent that the latter is ignored, so is the real meaning of the scientific revolution.

This problem cannot be adequately discuss here. It is easier to make the point indirectly by examining similar but more obvious and well documented consequences of the deficiencies of language–their effects on philosophers.

Philosophers of science focus attention on physicists’ verbal description of the world. In doing so they project upon physics the same primacy of language which holds for philosophy and for themselves. This section illustrates this focus on language and indicates its consequences

Thomas Kuhn views the adoption of successive paradigms by the whole of a community of scholars in a scientific discipline as an outstanding characteristic of modern science . Taking the early history of electricity as an example, he notes that,

Given this importance, physics’ major steps should be manifest in changeovers to ever better paradigms, but philosophers of the post-positivist school (Kuhn, Feyerabend, Latakos, Quine,…) claim that this is untrue or at least not demonstrable. Descriptions of two paradigm changeovers illustrating their claims are as follows.

General problems these examples illustrate are that (1) different paradigms cannot be measured against one another ("incommensurability"); (2) they are not uniquely determined by the evidence ("underdetermination"); and consequently (3) scientific revolutions and are settled irrationally ("anything goes"). These will be very briefly discussed.

Scientists generally believe that their newer theories encompass their older ones–they explain everything their older ones do and more. This property would provide a rational criterion for accepting a new theory. But according to their critics, example 2 above is typical of many which show that this criterion is not met; new phenomena are explained with a new paradigm but, quite generally, other phenomena become no longer explained.

If rational criteria were applied for paradigm replacement, the philosophers of science believe that scientists should have been able in the past to choose between competing paradigms quickly and without controversy. They point out that historically this has not the case, and this leads them to the belief that all sorts of irrational forces determine–"anything goes" to determine–the outcome of scientific revolutions.

Incommensurability is directly illustrated by example 1 where the very question of the force between heat particles becomes meaningless. Similarly, questions about properties of light corpuscles become meaningless in the context of classical wave theory. This apparently explains why rational criteria for deciding between paradigms may actually be impossible to formulate:

Underdetermination implies that more than one theoretical construction can always be placed upon a given collection of data. Thus at any stage in physics’ development, there is no paradigm uniquely determined by its data. This again seems to imply that particular choices of theories are contingent on extra-scientific factors–factors similar to those which, for example, determine reigning theories of literature or philosophy.

Kuhn and others critics cannot find any criteria which would supply coherent reasons for physicists’ choice of one paradigm over another. They cannot identify a measure of progress. Kuhn can, however, explain why there is nonetheless always an appearance of progress.

These remarks have indeed given rise to Orwellian conclusions. Some of them noted by Laudan are as follows.

Most physicists would be amazed at such conclusions. The physics they know is a vast interlocking edifice of data and theory; it starts with Newtonian mechanics and grows from it to embrace all types of phenomena. There is also a vast technology proving (in the original sense of testing) this theory in a common-sense way anyone can understand.

Of course, critics of science are well aware of all this but find it unconvincing. They appear to believe that similarly successful intellectual edifices meaningfully different than currently accepted physical theory could have, and would have, been built had paradigm choices gone other ways at innumerable junctures in history. Apparently, had phlogiston been retained, the wave nature of light denied, even the Aristotelian worldview been maintained, all with sufficient vigor when challenged by alternative paradigms, physics would have developed with equal success, but very differently.

Physicists and philosophers seem to be living in different worlds. They might use the same terminology, but they would typically mean fundamentally different things by it. I am repeating Laudan’s description of incommensurability and applying it to physicists’ and philosophers’ concepts of what physics is about. I believe that much of this inability to communicate is due to the fact that philosophers are mainly aware of ordinary language while physicists think and decide on the basis of mathematical language.

To illustrate this point, I will propose a somewhat simplified measure of progress in physics: one which would supply critics with a coherent reason for physicists’ choice of one paradigm over another.

In virtually all philosophical discussions of this issue, there is barely any mention of physics’ reduction of vast quantities of experimental data to very few simple analytic formula. Random examples of such reductions are:

1. Kepler’s planetary laws
1. Boyle’s gas law
1. Planck’s radiation law.
1. Rydberg’s atomic spectra law.

Every entry in a complete list of such laws is a simple analytic expression which applies directly to a very large number of experimental data points. Formula must reduce these data into a simple expression. There has surely never been a case in the history of physics in which such a formula has been discarded as a result of a change in paradigm. People do not squander utility of this magnitude for any reason.

This list can be thought of as the ‘product line’ of physics. It is what its ‘consumers’, the other sciences and the engineering professions, use themselves, and ultimately use to judge the productivity and social utility of physics. What goes on in the factory, the physicists’ business practices, the machines they use–theories, words, paradigms,…,--to manufacture their product, all these they change so as to minimize their costs of production.

Words are especially easy for physicists to change. Kepler, for example, thought the Sun special, and this presumably inspired his belief in its special attractive force, and in turn gave rise to a dynamic as opposed to geometric conception of planetary orbits. But his belief served a purely inspirational purpose. His formula remain, impervious to paradigm changes, because they are unique, irreplaceable facts–solid products of physics.

Even aposteori, and as an academic exercise, it is virtually impossible to think up a replacement for any of the simple analytic expressions noted above. The formula are hard, durable facts and are no less true in the observational sense than any of the thousands of data points which they express and replace.

An ever expanding list of analytic reductions of experimental data is by itself sufficient, as a measure, to demonstrate that the progress of physics is objectively cumulative. But the formula on this list are only the most apparent truths of physics. Deeper formula–more basic equations of physics–are deeper truths. Together, they define truth in physics.

This idea of truth (which includes the methods for achieving it demonstrated by Galileo and Newton) is a part of the paradigm shift we call the scientific revolution. Its discovery was the birth of physics. Its discovery liberated natural philosophy from not the influence but the rule of metaphysics. The purpose of physics became the pursuit of this truth, this encapsulation and reduction of data–without which reams of data are of little use, and with which they are of great use–and the meaning of physical concepts, which are mathematical objects comprising these formula expressed truths, are identical with their mathematical rules of use.

The preceding was a vision of what physics is about, and something of this nature is in the possession of every practicing physicist. Student being given an idea of what physics is about deserve to be exposed to some physicist’s version of it. Otherwise, they will have little chance of ever learning how physicists view their own field.

Students cannot learn this on their own. The existence of the post-positivist critique of physics demonstrates that the facts do not speak for themselves even to highly informed and intelligent people. The facts, must be spoken for. Indeed, even physics’ experimental facts are merely "facts" to its critics (preconditioned by a theory/paradigm). What is a fact, what is truth,...–these are classic questions of metaphysics.

A view of Cardinal Bellarmine, a great metaphysician of the past, reappears in modern post-positivist form. It proposes multiple equivalently valid descriptions of phenomena (as in Ptolemaic, Tychonic, and Copernican astronomy); thus the relativity of truth; thus the social determination of all truth (if this is true even of physics, the erstwhile paragon of objective science); thus the unwarranted nature of the modern hegemony of Western science. Responses may seem painfully obvious to physicists but they are not so to others. They are in any case not to be found within physics; they must transcend physics if they are to determine its position within a worldview. To go beyond physics is to be metaphysical. No amount of clear and inspired teaching of physics itself will solve this problem.

This problem, unique to physics for reasons discussed, points to a vision of what should be physics’ unique place in a liberal arts curriculum. For just as physics probes the simplest systems in nature, it probes metaphysics in the simplest context. In the context of physical truth, what is truth is a question relatively free of emotional, moral, and aesthetic, complexities whereas the same question asked in, say, literature is not. Physics is like an x-ray which reveals the bare bones of the issue without the red meat of emotion. And just as geometry has been the classic introduction to logical thought, so also physics should become the classic introduction to metaphysical thought. Indeed, I am maintaining that it must become so for non-scientists, in order that they gain any idea of what physics is about. Thus a course which truly engages the metaphysics of physics, will evoke a clear and uncluttered recognition of the most basic assumptions we make in all areas of thought.

The main message–that physics pedagogy has a deep, difficult, subtle problem with metaphysics, one which cannot be solved by just teaching physics–has now been sufficiently emphasized. The question then is what, in a practical sense, is to be done about it.

Here are tentative ideas for topics and themes based on the views put forward in this essay.

• Physicists cannot and should not try to teach metaphysics as a discipline, but they can and should explain how metaphysics impinges on their discipline. They should not hope to effect a ‘conversion’ of students to a scientific worldview, but they can and should teach an awareness of both the pre-scientific and scientific worldviews which the typical student and physicist, respectively, bring with them to the study of natural law.
• They should teach that physics, at its most basic level, is about the reduction of vast amounts of data to simple laws–data reduction in an extended sense of the word;
• that physics’ has an operational sense of the meaning of truth and reality. How and why physics’ extended world–extended through instrumental perception and mathematical thought–has the same claim to reality, and is as uniquely determined–and as ‘underdetermined’!--as their ordinary world;
• an enlarged view of mathematics so that students do not automatically assume that, since physics is writ in the language of mathematics, it necessarily provides an intrinsically impoverished or unnatural view of nature;
• the grand concept of the world evolving according to universal law or as Whitehead put it, the world as the evolution of an idea, the grand scheme of physics of equations of propagation plus initial conditions–something remarkably few students, in my experience, have either heard of or comprehend.

Again and finally, as things stand, only physicists can tell students and the public at large, about such things. Physicists, in their introductory courses, have little more than this one shot at making their unique enterprise, the foundation of all science and technology, intellectually reasonable to the educated non-scientific public. We must of course also tell students about the physical world as we now see it; but if that is all they are told, physics becomes to them, as it now is to its philosopher-critics, only one out of many possible equivalently valid stories about the world.