The Postmodern Critique
The general public tends to view science as progressive, as able to steadily accumulate truth. It starts calling something a science to suggest that it is at a stage of development at which it too can steadily accumulate truth. And science is said to possess the surest method for the gathering of truth.
Critics, on the other hand, claim that this progressiveness, even that of the hard sciences, is an illusion. They point to a history of conceptual revolutions in physics--light changed from particle to wave, and then to something that is both particle and wave, electricity and magnetism changed from distinct forces acting instantaneously at a distance to a single field propagated at the speed of light, heat changed from a particle to a form of energy transfer,…--that does not appear to be progressing towards any particular vision of the world. They have launched a comprehensive critique of the knowledge claims of all the sciences associated with the postmodern movement in philosophy. This chapter discusses this critique, and then relates it to the ancient battle between paganism and monotheism.
Paradigms, Models, and Theories
The term paradigm originally designated an example of a standard grammatical structure (e.g. a sample declension or conjugation); its meaning was then extended to structure in all fields. The Hydrogen atom, and the Harmonic Oscillator, are names of paradigms found in quantum mechanics texts. They show how quantum theory works when applied to important kinds of systems. Kuhn, interested in how communities of scientists behaved, noted that each community shared a set of paradigms that operationally defined its shared ideas and methods. He extended the use of paradigm to denote these ideas and methods.
But Kuhn also used paradigm loosely, and others after him, even more so, and its meaning has become diluted and ambiguous. Comparing 'paradigm' to 'model' and 'theory', words more commonly used in physics, all three vary widely and overlap in meaning. Their differences are tied mainly to context: something can be called all three depending on context. It will be useful to begin by explaining and then respecting these differences in what follows.
I shall use the word theory to focus attention on sets of equations encompassing relatively large ranges of phenomena. Thus we have the theories of Classical Electrodynamics, Quantum Electrodynamics, Classical Mechanics, Quantum Mechanics, Newtonian Gravitation, and so on. Theories can also divide into a number of smaller range sub-theories. The equations defining a theory act like a set of mathematical axioms; the laws derived from them are then analogs of mathematical theorems.
Kuhn uses this word differently. For example, he talks about electrical research in the 18th century when there were numerous concepts concerning the nature of electricity, all of whom he labels components of real scientific theories, of theories that had been drawn in part from experiment and observation and that partially determined the choice and interpretation of additional experiments. Thus, here he uses theory to denote any set of ideas providing the basis for research in accord with the scientific method of hypothesis, explanation, and testing.
The electrical 'theories' Kuhn mentions that match this definition, each explained a few electrical phenomena, often barely and always qualitatively, and left unexplained many other phenomena for which there were other theories. There is virtually no area of physics since the mid 19th century to which this is applicable, and consequently the primary meaning of theory has shifted to the very different, large, mathematically based structures to which I have restricted the word.
The word 'model' has two meanings in normal usage, both of which also apply to physics. First it means a version simplified in order to more easily be able display certain features of an original; and since the equations governing any real physical system must always be simplified to be solved, applications of theory are always models. When an application covers a large or important enough range of phenomena it is apt to be called both a model and a theory. Thus, for example, we hear of the Ptolemaic and Copernican theories as well as models of the solar system, and the Bohr model as well as theory of the atom. On the other hand, there is a "billiard ball" model of gases in which atoms interact like hard spheres that bounce off of one another. This assumption of hard sphere interaction simplifies the mathematics describing a gas enough (at the expense of restricting the model's range of validity) so as to make the designation model more appropriate than theory.
In every day language we also talk about various models of products like cars and airplanes. The word here does not indicated a simplification but rather a version. Every theory has multiple versions. Newtonian mechanics tells us that there is empty space, time, mass, position, velocity, acceleration, force,…, but what kind of mass (discrete or continuous), how much mass, and what force law, and so on, needs to be specified in each physical circumstance. Each version is often called a model.
Models are human inventions. Each is an hypothesis, an intuition, a work of art, and an interpretation of theory, bounded by human imagination, which in turn is bounded by human experience. We have, in fact, limited experience and relatively few classes of models at our disposal. The most well known classes fall under labels of particles and fields (discrete and continuous entities), and we have discovered in the 20th century that ultimately, neither is sufficient, everything has properties of both.
The words theory and model attend mainly to the mathematical and physical, whereas paradigm, mainly to social, historical, and developmental considerations. This is as the origin of word paradigm suggests, and how I will use it when discussing physics. It is useful, for example, when dealing with unformed fields of physics--fields as yet organized and described by no set of basic equations, no coherent theory or model at all. This describes most of physics before the mid 19th century when optics, heat, electricity, magnetism, and chemistry, all could be said to be fought over by competing paradigms.
Paradigm is similarly useful when describing research in areas in which rough and as yet poorly established models are competing with one another. During the last half century, particle physics has seen various models of field theory based on different particles and groups, S-matrix theory, Regge theory, the parton model, string theory, and so on. All had their competing communities of advocates and all could be described as paradigms. In cases such as these, factors other than physical evidence come into play, many of them social, that determine different research communities, their membership, and relative strengths.
To summarize, a term such as string theory is most useful when contemplating relations between a certain set of axioms and their consequences, all functioning as part of (hopefully) comprehensive physical theory. The term string model shifts attention to these equations as comprising one possible form of a quantum theory of field. Calling this approach a paradigm calls attention to its provisional status, and to the existence of a community who share a research program dedicated to its development.
Underdetermination
Underdetermination is the name of a key component of the postmodern critique, and is the thesis that science has no way to uniquely prefer any one theory or model over another. It states that any theory can be elaborated or patched up by a clever enough theoretician to describe a given body the data, and that this and further criteria typically used to compare theories are too ambiguous to decide on a uniquely best one. The proponents of this thesis generally feel that social forces actually determine which theories gain dominance in physics, i.e. that physical theory is primarily a 'social construct'.
This claim will be discussed in terms of a model of the process of discovery itself. The process is modeled as the discovery of a curve (or set of curves) passing a through a set of physical data points on a graph. Since most physical theory is judged by the fitting of curves to data, this is a rather realistic model.
A small enough number of data points can always be described by many types of simple mathematical curves or families of curves. At the top of the Figure 1, a few such points are plotted. The next two pictures show them described by two sets of simple curves. These sets represent, in our model, different approaches to describing the same small set of phenomena. These approaches would be competing paradigms.
The last picture models the experience of physics: the fact that, sufficiently large numbers of data have always resolved the situation in favor of one paradigm which then becomes dominant. This is one part of the miracle Wigner pointed out in the essay referred to earlier as follows.
The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend....perhaps also to our bafflement, to wide branches of learning.
What exactly is it that is miraculous? An appreciation of miracles requires an understanding of what is not miraculous. This can be illustrated by non-miraculous curve-fitting, as follows.
The formula for a straight line graph contains a pair of constants–parameters–determining, say, its slope and its intercept with the horizontal axis. Each pair corresponds to a unique straight line. One pair can always be found so that the line runs through any two specified points such as A and B in Figure 2. Thus, two data points, can always be fitted using one pair of parameters. Such a fit is non-miraculous.
Figure 2: Data points A and B can be fit by a unique straight line because it has two adjustable parameters. A,B, and C can be fit by infinitely many kinds of curves having three adjustable parameters of which two examples, the parabola and the circle, are shown. On the right we have a kind of curve (here a cubic) having more than three adjustable parameters. The figure shows how infinitely many curves of one kind can fit three points if that kind has more than three adjustable parameters.
If a third data point C is measured, then unless there is a law constraining it to fall on straight line through A and B, the statistical chance that it will do so is essentially zero. If it does, that will appear to be miraculous, at least unless you get used to it.
In order to fit three points in the absence of such a law, curves require at least three adjustable parameters. The left side of Figure 2 shows two examples–a circle and a parabola–out of an endless variety of three-parameter curves.
The same rule holds for any number of points. Any number of points can be fit by an endless variety of curves as long as each has at least as many adjustable parameters as there are points to be fit. The more parameters, the more twists and turns the curve can have. If there are more parameters than the necessary minimum, then many curves of the same kind can fit the points. This is illustrated on the right side of the figure where different curves of one kind–four parameter cubics–all run through the same three points.
If any set of data points can be connected by an endless variety of smooth, mathematically well-defined curves, then certainly no set determine any one them. This corresponds to the idea underlying the thesis that theories are radically underdetermined by data.
This thesis would maintain, for example, that had physicists tried hard enough, the Newtonian paradigm could have been adjusted so as to describe characteristically quantum phenomena such as black body and molecular spectra, and the stability of the atom. The rationale underlying this thesis is that there are an unlimited number of kinds of forces and particles existing within the Newtonian paradigm, all available, like parameters, to be adjusted to describe data.
Our model can clarify this idea. If more physical data points are added to the three shown in the previous picture, two sorts of things can happen. The left side of Figure 3 shows what to expect when you need to use a number of adjustable parameters about equal to the number of data; the right is typical of needing far fewer parameters than data. The shape on the left comes about because a set of data enlarged by one newly measured point generally requires a correspondingly enlarged set of parameters in order to be fit. This, in turn, generally changes the whole shape of the curve. With each new parameter the curve accumulates a new kind of twist. In the other case, one new point after another would fall on the same fixed curve: a circle defined by three parameters.
Figure 3: Two ‘theories’ describing the same data. The one on the left does not provide comprehension, that on the right, does. The one on the left provides no prediction, that on the right does. The principle of underdetermination counts them as equivalent. The one on the left provides no data reduction, that on the right does.
Curve fitting has two goals: the comprehension and the prediction of data. The circle on the right fulfills both whereas the curve on the left fulfills neither. The circle organizes many otherwise unrelated points into a structure that is a single, easily comprehensible, object of thought that also can predict where future measurements will fall. Both goals are achieved to the degree that data is reduced to a few parameters.
These same goals apply to physical theories. Any numbers of forces and particles are available within the Newtonian paradigm to describe data. Adding to them to describe new data is the analog of adding new parameters. Doing so leads to theories analogous in structure and utility to the curve on the left of Figure 3. Thus, for example, physicists became convinced in the years prior to the ascendancy of quantum mechanics, and after strenuous effort, that even if sufficiently many forces and particles could be cleverly added the Newtonian paradigm so that it would fit quantum phenomena, they would get the theoretical equivalent of such a curve.
There are considerations touching on the charge of underdetermination such as the so-called corrigibility of data that have yet to be addressed, but its key deficiency should now be clear. The charge ignores the goals of theory and model making in the mathematical sciences. These goals go beyond a mere description or explanation of data, they require a highly reduced one.
Consider the goal of theory in a non-mathematical discipline such as history. The historian looks for reasons for historical events so that they become intelligible. Such reasons are the normal ones given for our actions, and we have a vast store of them. One historian finds one set of reasons that seem sufficient to motivate an historical event while another finds another. Historians attempting more than minimal intelligibility, seek reasons that are key to whole sets of related events. A well known example is economic advantage, which is typically found to be a key component of national policy decisions.
Of course, there is never a single reason for any of our decisions; anyone can name many, each with its own weight. A probabilistic interpretation of such weights would lead to a kind of quantification of history that could be related to our model. The reasons that such a probabilistic historical theory would propose for an event would be parameters and the weights like parameter values. The probability given to the occurrence of an event would be a theoretical prediction: a sharp prediction would be like a sharply drawn curve.
But such an historical theory does not exist and the reason is in the nature of historical data. Historical circumstances never exactly repeat and even if many similar ones are collected and treated as more or less the same, there are still relatively few of them. When a statistical theory as outlined here, makes a prediction, a single datum is useless, and a few approximately similar data are almost so. Many data are needed to confirm a statistical prediction.
All non-quantifiable theories must similarly remain vague and poorly tested; vague because without quantitative comparisons, a given reason for an event can only be judged as more or less important; poorly tested because objective tests of theory must be replaced by subjective appeals to judgement.
In addition, if attempts to estimate (even subjectively) data reduction were made in order to choose, as in science, between theories, they would fail because theories such as those in history, require comparatively many parameters to explain few data. As a result, they can at best achieve only modest and unconvincing reductions of the data. In contrast, as discussions have already suggested and we shall see later in more detail, reductions achieved in the hard sciences are dramatic and completely convincing.
Non-quantitative theories outside of the hard sciences are comparable to the paradigms used to explain electrical phenomena in the 18th century; but because they are non-quantifiable, they can never evolve beyond that stage. They remain split into communities of scholars following different paradigms for reasons underdetermined by the facts. For them, the Nietzschean claim that all is interpretation is hard to dispute. And it is quite understandable that people from such a background, without any or adequate experience with quantitative theory, should imagine that beneath it all, physics is really no different than history or literary criticism. All their theories are non-miraculous, and so they can neither experience nor appreciate the miracle Wigner talked about.
The objectivity and certainty of scientific experiments are vouchsafed by their reproducibility: if you perform a series of concrete operations A, the result will always be B. A is made up of commands which say build according to these specs, read this meter, throw this switch, and so on. B is made up of statements predicting what you will read off your instruments. These commands and statements do not depend on whether you think light is a corpuscle, wave, or even a god. They are in the theory-independent ordinary language that describes everyday phenomena.
Miracles aside, precisely the same acts under precisely the same conditions always produce precisely the same results. But some thinkers use language which seems to categorically deny this. Mary Hess writes
Most empiricist accounts of science have been based, usually tacitly, on the notion of a comparatively unproblematic observation language. It matters little how this is construed - whether in terms of hard sense data, operational definitions, ordinary language, or what not - the essential point is that there are statements of some kind whose meaning as descriptions of states of affairs is supposed to be transparent, and whose truth-value is supposed to be directly and individually decidable by setting up the appropriate observation situations. It is a long time since anyone seriously claimed that the truth of such statements can be known incorrigibly…
This statement seems to be attacking the possibility of all experiential knowledge, not merely that gained from scientific experiment. If there are no statements of experimental science whose truth…is directly and individually decidable by setting up the appropriate observation situations, then there are none at all, within or outside of science. For surely things repeat their behavior under similar situations whether or not they are parts of scientific experiments. If this were not so, there would be no experiential knowledge whatsoever.
Of course, it is certainly possible to deny experience as our source of certain knowledge (as certain as man can have). And in fact, as we shall discuss, this denial has a long history: one that can be credited with having blocked the development of science for about two millennia. This aside, however, I take this sort of statement as a rhetorical exaggeration that is necessary to dispense with before continuing.
Corrigibility was more carefully discussed by the late 19th century physicist Pierre Duhem when he emphasized the influence of theory upon data. He discussed a galvanometer, an instrument used to measure weak electric currents, as follows:
Here, for instance, is an instrument called a tangent galvanometer. On a circular frame is wrapped a copper wire covered by silk insulation; in the center of the frame a very small bar of magnetized steel is suspended by a silk thread; an aluminum needle carried by this small bar moves over a circle divided into degrees. This permits one to report with precision the direction in which the small bar is oriented. When the two ends of the copper wire are connected to the poles of a battery, the magnet is deflected with a deviation that can be read on the divided circle; the deviation is, for instance, 30°. The mere perception of this fact does not imply any commitment to physical theories, but neither does it suffice to constitute an experiment in physics.
A galvanometer constructed in a precisely specified way, connected to a precisely specified kind of cell, has only one response, independent of physical theory. But a simple report of this response does not suffice to constitute an experiment in physics:
The physicist...does not aim to know the deviation experienced by the magnet, but rather to measure … the current going through the copper wire. Now, in order to calculate …[current] agreeing with the value, 30°, of the observed deviation, he must bring this latter value into a certain formula… a consequence of the laws of electromagnetism…
The formula relating the directly perceived angle of deviation with current comes from a theoretical model of the galvanometer. Current itself is only indirectly perceived via a theory; and an instrument, like any physical system, can also only be related to theory via a model.
.....Hence, when a physicist does an experiment, two very distinct representations of the instrument on which he is working fill his mind: one is the image of the concrete instrument that he manipulates in reality; the other is a schematic model of the same instrument, constructed with the aid of symbols supplied by theories; and it is on this ideal and symbolic instrument that he does his reasoning, and it is to it that he applies the laws and formulas of physics.
But this holds for sensual as well as instrumental perception. Consider the visual system's use of templates that include, at basic levels, the line segments, patches of texture, orientations, color mixtures, and so on. All images are built out of them. A certain network of neurons combine data input from the retina into the perception of a line segment; this can be compared to a network of ideas that combine data ( e.g. the number of windings in the magnet, the deviation of the magnet) to form a measurement of current. Note that a network of ideas represents a physical network of neuronal connections somewhere within the brain.
Both line segments and currents are corrigible perceptions because both are model dependent. Different neuronal wirings of visual systems can create different images out of the same retinal data. Similarly, a different theoretical model of a galvanometer can create a different current inferred from the same input. Changes in theory also lead to new galvonometers which provide more accurate and precise values for measured current.
Line segments and currents are both theoretical concepts. The theory used by the visual system is embodied in structures in it, biologically developed in the course of evolution, and genetically passed on to us. Other structures in higher cognitive centers embody other kinds of theory, for example, the electromagnetic theory used to analyze galvanometric signals. The visual system's theory is used unconsciously, electromagnetic theory, consciously; the development and transmission of one is biological, the other, social.
On the basis of these origins, physics' vision of the world is no less 'real' than that we associate with our everyday perceptions: the one that identifies ‘raw sensory data’ with ‘the real world’. On the basis of its results, there is greater reason to trust in the truth of physics' perception--true here taken in its meaning of trustworthiness and constancy under trial. There are two kinds of trials we put to physics, and these are not of the constancy of measurement itself, as assumed by the corrigibility argument, but rather of the constancy of relations, between measurements and between phenomena.
The latter of these relates to the opening remarks of this section concerning experiential learning which does not involve any scientific theory. Because scientific experiments taken in this sense, in contrast to ordinary experience, are either exactly repeatable or else not acceptable, they are even more trustworthy that the ordinary experiences we learn by. Of course, it is just this trustworthiness--translating into that of everything derived from scientific technology from bridges to medicines,--which ultimately ensures public admiration and support of science.
But this sort of truth is insufficient for deeper concerns regarding the effect of theory on worldviews, and hence on the measurements that underlie theory. Contrary to the expectations of its critics, however, the corrigibility of measurements highlights a strength rather than a weakness of physics. The corrigibility of measurements means that although measurements are always subject to change, such changes always leave essentially invariant the mathematical equations that reduce and relate measurements to one another. Relations between measurements remain incorrigibly true under the test of changes in measurement. If this were not so, none of the quantitative laws discovered one, two and three centuries ago, before numerous and dramatic advances in instrumentation and theory would still be valid and useful, and yet virtually all of them are.
Elsewhere, the invariant truth and utility of the equations of mathematical physics under radical changes in physical interpretations of theory (verbal interpretations which model the equations, creating physical pictures of them in our minds) has been emphasized. Here, that invariance is just being extended to include changes in measurement induced by changes in instrumentation and in theoretical analysis.
Also appearing under the heading of corrigibility is the idea that theory not only alters data, but also decides what data it will and will not explain-- what is worth explaining. Two theories cannot be completely compared–are incommensurable–when they ask different questions of nature and explain different data. It is then no longer a case of being able to compare them by the same objective standard of how well they explain the same facts since they take the facts which suit them best.
Kuhn describes the different data Aristotle and Galileo took from observing pendulums and free falling bodies as follows:
Seeing constrained fall [a stone tied to a string as a pendulum], the Aristotelian would measure (or at least discuss–the Aristotelian seldom measured) the weight of the stone, the vertical height to which it had been raised, and the time required for it to achieve rest. Together with the resistance of the medium, these were the conceptual categories deployed by Aristotelian science when dealing with a falling body. …, Galileo saw the swinging stone quite differently…[he] measured only weight, radius, angular displacement, and time per swing,
…and the same differences of vision are apparent [for the case of free fall]. For [Aristotle] the relevant measures of a motion were … total distance covered and total time elapsed…. Similarly, because the stone was impelled by its nature to reach its final resting point, Aristotle [observed]… the distance to the final end point rather than … that from the origin of motion.
Aristotle asks why objects fall, and answers that they seek their natural resting place in the universe. Galileo does not ask why, and does not believe that objects ‘seek’ anything. Aristotle observes free fall in its natural surroundings in which air resistance plays a complicating role. Galileo sets up and observes an artificially simplified situation–an experiment. Aristotle thinks that the distance of an object to its goal, its resting place, is important to consider. Galileo does not bother measuring it. It seems that a paradigm chooses what it will explain, and inhibits us from noticing what it chooses not to explain.
The response to this is, first of all, that everything on Kuhn’s list of Aristotelian questions and observations that could be described by measurable quantities has been subsequently described by the physics created by Galileo and his successors, and this has been true of all changes in physics. Contrary to the impression one often gains from reading such critiques, questions about measurable quantities do not lie around forever unanswered. They all get answered sooner or later, almost always sooner.
This being said, however, what about other than quantitative kinds of questions, like those of the Aristotelians, which for so long had seemed so reasonable? Do they remain unanswered just because the new paradigm does not recognize them as valid? And what happens with Aristotelian answers which, whatever their faults, had also seemed so reasonable and satisfactory to so many for so long? Are not discarded theories and paradigms, like Aristotelianism, examples of the many possible useful ways available to us for understanding the world?
Kuhn discusses this elsewhere in the context of the 18th century phlogiston paradigm. He points out that it gave order to a large number of physical and chemical phenomena, listing these as follows:
…[it] gave order to a large number of physical and chemical phenomena. It explained why bodies burned–they were rich in phlogiston–and why metals had so many more properties in common than did their ores. The metals were all compounded from different elementary earths combined with phlogiston, and the latter, common to all metals, produced common properties. In addition, the phlogiston theory accounted for a number of reactions in which acids were formed by the combustion of substances like carbon and sulphur. Also, it explained the decrease of volume when combustion occurs in a confined volume of air–the phlogiston released by combustion "spoils" the elasticity of the air that absorbed it, just as fire "spoils" the elasticity of a steel spring.
As in his previous comment, this again indicates Aristotelian standards of explanation. The whole abandonment of Aristotelianism and creation of modern science was prompted by dissatisfactions–religious, metaphysical, and practical–with such questions and the answers they produced.
The quantity and quality of pre-scientific explanations are inadequate by modern scientific standards. The quantity of loose correlations established by phlogiston cannot have been more than a few hundred at most; and whereas a theory of the cause of a war that would correlate this many facts would perhaps gain commanding respect, it would not in the hard sciences. For in the latter, not only are thousands of exact measurements typically reduced to a few parameters, but also tight correlations are established with all physical observations. Phlogiston could have no such tightly quantitative correlations. It eventual competitor, the theory of oxidation, could, and it was the realization of this possibility that caused the changeover from one paradigm to the other.
And yet again, another favorite example of postmodernist critics is Descartes ‘explanation’ of the fact that all the planets move in the same circular sense about the sun: an explanation they point to as having been lost in the transition to the Newtonian paradigm. Descartes explanation, however, amounted to no more than a statement that planetary motion was a form of vortex motion. Unfortunately, all motion in his theory, is vorticular, and we are given only the vaguest of qualitative ideas as to why it is that everything about us–not only the planets–does not appear to move in similar vortices. In fact, a real explanation would require some kind of hypothesis about interactions between neighboring vortices concerning which he had at best only wildly incorrect qualitative opinions. Virtually all Cartesian explanation is of this nature. It is no explanation in any modern sense of the word.
One can go through all the examples given by Kuhn and his followers–all supposedly showing how the idea of scientific progress fails–and find the same fundamental problem. None distinguish pre-scientific from scientific standards of explanation, and most deal with the former. None can point to a successor theory which does not include within it all the data reducing power of its predecessor. Humanity never lets go of data reducing formula; they are the solid gold achievements of physics that it consistently and continually mines and accumulates.
Its Metaphysical Basis
The first part of this chapter has discussed recent epistemological criticisms of physics. Underdetermination is the claim that physical theory is undetermined by experimental data. Corrigibility, attacks the factual basis of science, saying that its data is theory dependent. Incommensurability states that there is no rational way to compare and choose between theories. I have argued that these criticisms ignore the mathematical nature and hence misunderstand the purpose of physics and physical theory.
Critics such as Kuhn are well aware of this nature and of the nature of the progress claimed by physics. Why then do they not take it into account? There are undoubtedly many causes, but the primary one must be metaphysical. For just as it takes total blindness to bump into a wall, not merely imperfect vision, so also it takes the total blindness arising from insensitivity to a totally different worldview to cause an otherwise subtle mind to come up with what appear as gross errors in the eyes of that worldview. And the missteps made by postmodern critics do cause them to be seen, from the other side, to bump into walls.
Critics simply cannot see giving philosophical weight to an idea such as that paradigm choice in physics is determined by data reduction. The following discussion ties these non-overlapping worldviews to those of philosophical monotheism and paganism.
Incommensurable Worldviews
Kuhn's analysis can be turned upon itself by analyzing not scientific communities, but communities which study these communities. Kuhnians themselves comprise a community built about one paradigm--a community within the field of the history of physics--while another is that of physicists themselves. As both Kuhn's analysis would suggest and the preceding analysis has attempted to demonstrate, the paradigms each use are incommensurable. Because they are, their respective followers talk past one another; each miss the other's point entirely; each appears wrongheaded to the other; each appear to be blind to what is obvious to the other, to bump into walls.
Is each paradigm therefore equally valid? If you apply the rhetoric Kuhn used to compare paradigms within physics, to paradigms about physics, you would say that the postmodernist's is 'as good as' the physicist's view. Both offer an explanation of the inner dynamics of the physics community. If there are no mutually agreed upon standards by which to compare explanations, the relativist should maintain that one can say no more than that each is equally valid relative to its own standard.
But Kuhn did not analyze himself as he did differing paradigms in physics. He did not say that physicists have their standards of explanation and I have mine. He said quite clearly that the understanding of the physics community of itself was wrong and that his was better.
Ontology versus Puzzle Solving
Underlying Kuhn's critique was a concept of what constitutes knowledge. Only when he began to re-evaluate his ideas in the face of criticism and to correct for ideas he claimed were falsely attributed to him, did he begin to question this idea. He began his re-evaluation in a Postscript to his book as follows:
It has now been almost seven years since this book was first published. In the interim both the response of critics and my own further work have increased my understanding of a number of the issues it raises. On fundamentals my viewpoint is very nearly unchanged, but I now recognize aspects of its initial formulation that create gratuitous difficulties and misunderstandings. … some of those misunderstandings have been my own….
….scientific development is, like biological, a unidirectional and irreversible process. Later scientific theories are better than earlier ones for solving puzzles…. That is not a relativists position, and it displays the sense in which I am a convinced believer in scientific progress.
Of course, to be convinced that progress exists, the progress must be measurable, and if that is so then successive paradigms cannot be incommensurable, they must be comparable. Kuhn compares them in terms of what he calls their "puzzle solving" ability--a phrase he uses throughout his book to denote the normal science done within a paradigm.
For example, according to one paradigm, heat was a substance called caloric whereas according to another, it was a form of motion. Work normally done within the caloric paradigm sought to explain phenomena in terms of this substance. Similarly, workers within the other paradigm normally pursued their explanations in terms of molecular motion. Each group tried to explain--to solve the puzzles offered by the phenomena--in its own way. Puzzle solving means working completely within a paradigm.
How can you compare a solution in terms of caloric to one in terms of motion? Which is better if both can explain the phenomena? That is the question of incommensurability. In his re-evaluation Kuhn admits that paradigms are comparable in terms of their puzzle solving abilities. His intuition of the measure of these abilities is described earlier in the last quoted passage, as follows:
….it should be easy to design a list of criteria that would enable an uncommitted observer to distinguish the earlier from the more recent theory time after time. Among
Nevertheless, when writing his book he did not seriously consider this view--a diffuse version of the one I am proposing here. Had he done so, he would not have been left to wondering how decisions between paradigms were made and would not have effectively concluded that the process was political.
He describes why he did not seriously consider using this standard to compare paradigms:
Compared with the notion of progress most prevalent among both philosophers of science and laymen, this …[standard]… lacks an essential element. A scientific theory is usually felt to be better than its predecessors not only in the sense that it is a better instrument for discovering and solving puzzles but also because it is somehow a better representation of what nature is really like. One often hears that successive theories grow ever closer to, or approximate more and more closely to, the truth. Apparently generalizations like that refer not to the puzzle solutions and the concrete predictions derived from a theory but rather to its ontology, to the match, that is, between the entities with which the theory populates nature and what is "really there"
Thus, most philosophers and laymen look for more than the ability to answer to any question of nature in the form in which mathematical physics provides. They look for more than merely the ability to predict the results of experiment. They also look for an ontology, ... the match… between the entities with which the theory populates nature and what is "really there". For example, according to ancient atomists, little balls floating in space are really there as fundamental existents. This is the sort of knowledge--ontological knowledge--philosophers and laymen generally seek from physics. Instead, they get from it an ever changing and non-convergent ontology.
Again, it is important to remember that this is an old complaint and the general outlines of the answer given is also old. It was discussed a century ago by the great physicist Henri Poincare as follows:
The ephemeral nature of scientific theories takes by surprise the man of the world. Their brief period of prosperity ended, he sees them abandoned one after another; he sees ruins piled upon ruins; he predicts that the theories in fashion to-day will in a short time succumb in their turn, and he concludes that they are absolutely in vain. This is what he calls the bankruptcy of science.
His scepticism is superficial; he does not take into account the object of scientific theories……. No theory seemed established on firmer ground than Fresnel's, which attributed light to the movements of the ether. Then if Maxwell's theory is to-day preferred, does that mean that Fresnel's work was in vain ? No; for Fresnel's object was not to know whether there really is an ether, if it is or is not formed of atoms, if these atoms really move in this way or that; his object was to predict optical phenomena.
This Fresnel's theory enables us to do to day as well as it did before Maxwell's time. …
If the [mathematical] relations are known to us, what does it matter if we think it convenient to replace one image by another ?
In the same passage previously quoted, Kuhn indicates that he is changing his idea of what science is about to that of physicists such as Poincare--that he is switching paradigms:
Perhaps there is some other way of salvaging the notion of 'truth' for application to whole theories, but this one [i.e. truth is a match between the entities with which the theory populates nature and what is "really there"] will not do. There is, I think, no theory-independent way to reconstruct phrases like 'really there'; the notion of a match between the ontology of a theory and its "real" counterpart in nature now seems to me illusive in principle.
The notion of progress most prevalent among both philosophers of science and laymen that human understanding of the basic laws of nature can and must go beyond mathematics, mere 'recipe', is natural, normal, and intuitive. Only working experience pushes a person to abandon it. This abandonment resembles the change in the meaning of number signaled by the change in status of zero. Thinkers pointed out that zero was not a number; its meaning did not conform to the current definition of number, but practice then created a new definition. That took a few centuries to establish itself and the present transition will do so also. On the other hand, those not working with the basic laws of physics may never feel compelled to change.
Models of Postmodern Paganism
A great lesson of theoretical physics is the necessity to abandon the idea of a universe centered on humanity. The famous example was the abandonment of geocentrism, but there are at least two extensions of this still in the making: the abandonment of two more forms of anthropocentrism. One is associated with phenomena, the other with ideas.
The first is typified by the tendency to confuse the apparent size of an effect with its importance. The scientist is often faulted for an obsessive interest in small details, unawareness of the big picture, and narrowness of vision. But all these judgements are relative to human scales and senses; what is small on a human sensory scale is not necessarily small in the nature of things and a narrow window may lead to the widest of views. Thus the small details have very often been at the center of large of discoveries: a slight deviation in the path of Mars, a slight shift in the spectrum of hydrogen (keys to Newtonian mechanics and quantum electrodynamics respectively), and so on.
Something can be barely seen if it is also too large on our sensory scale; here, large includes especially the idea of the all encompassing and the all too familiar. The rotation of the earth was hard to see because everything nearby rotated as well. Our submersion in an ocean of air was unknown until recently because everything about us is also submerged. The night sky excites wonder but its darkness is taken as no special mystery. We often wonder about the meaning of our life but rarely about why there is anything at all.
Only physics forces on us this necessity to abandon the idea of a universe centered on our parochial concerns; all the other sciences are centered either on man-sized, or earth-bound, or human and social phenomena. A move beyond parochial phenomena naturally drives a corresponding movement of ideas and of vocabulary. It forces us to move beyond a vocabulary created to communicate ideas about anthropocentric phenomena, and this again brings up the question of the proper vocabulary for a description of the universe.
Responses to the expansion from the parochial to the universal separate the pagan from the monotheist: the latter embraces, the former resists the process. Anthropocentrism arises from the impulse to deify man and chaos that I have previously associated with the pagan tradition.
Just as philosophical monotheism comes in a variety of forms--e.g. with and without an avowed belief in a Creator--so also does paganism. One form, that of the original Kuhn (i.e. before he wrote his Postscript), is composed of ideas that gained him his popular following. It is based on the idea that there is an external reality (objective and really there) that is humanly accessible and verbally describable, and that to know reality is to know its true ontology. This is a form of knowledge that goes beyond mathematics. Formula express relations between things, but ontologies tell you what these things actually are. Kuhn believed that the philosophically meaningful goal of physics is to discover true ontology.
In contrast, modern physics thinks of ontologies merely as models: changeable human creations that aid conceptualization. When it was young, its first successful models were imagined to be unique and really out there, but experience has it taught otherwise. Only the reduction of ever increasing data to ever fewer simple mathematical expressions has permanence; only it survives all revolutions. The original Kuhn and his popular following cannot accept that this is all there is to human knowledge.
In his Postscript, as quoted above, the later Kuhn realized that a true ontology was unattainable, but failed to then suggest that the miraculous mathematical edifice created by physics may the best form of truth humans can hope for: the closest we can get to reality. Instead, he suggested and others have insisted, that if the human mind cannot see what is really there--real in ontological terms--then there is nothing really there; and that physics is therefore a creation of mind unguided by anything beyond social forces. They cannot accept any real limitations on human language and the power of mind.
It feels a bit strange calling a scholar like Kuhn a pagan. He would have been taken aback by it just as he was when others took his analysis and used it to draw radical conclusions, systematically based on strong and consciously pagan worldviews. Kuhn was really an accidental pagan and more an historian than a philosopher. Nietzsche was the completely postmodern, completely pagan philosopher. Between the two--one accidental and unknowing, the other deep and purposeful--one can locate most postmodern critics of physics. Their thoughts seem to result from historical analyses, often inspired by Kuhn, ignited by sparks from the psychological and philosophical bonfire set by Nietzsche. When their passions are allowed to show, the whole religious connection becomes blazingly apparent.
Thus, consider the popular postmodern philosopher Paul Feyerabend who attacks monotheism rather explicitly as follows :
… The assumption that there exists universally valid and binding standards of knowledge and action is a special case of a belief whose influence extends far beyond the domain of intellectual debate. This belief… may be formulated by saying that there exists a right way of living and that the world must be made to accept it.
Moral authority is crammed down people's throats. For the origin of this practice, he quotes from the historian Eric Voegelin:
The Law of Moses abounds with bloodthirsty fantasies concerning the radical extermination of the goyim in Canaan ….The conception of war as an instrument for exterminating everybody in sight who does not believe in Yahweh is an innovation of Deuteronomy.
Jewish fanatical monotheism
propelled… Moslem conquests …the Crusaders in their bloody battles, …lubricated the guillotine, …[and is responsible for] the libertarian and/or Marxist defenders of Science, Freedom, and Dignity.
These, Feyerabend finally associates with:
… social groups who prepared what is now known as Western rationalism and who laid the intellectual foundations for Western science… denied that the world was as rich and knowledge as complex as… commonsense … seemed to imply.
[These elitist social groups] distinguished between a ‘real world’ and a ‘world of appearances’. As they presented the matter, the real world was simple, uniform, subject to stable universal laws and the same for all.… From the very beginning, intellectuals claimed to possess insights unavailable to ordinary mortals.
….An enormous amount [of the work of philosophers] (and of the work of scientists from Descartes and Galileo up to and including our own Nobel prizewinners) consisted in combating, ridiculing and, if possible, eliminating ideas and practices which, though well established, successful, and advantageous for many people, did not conform to their idiosyncratic standards.
Feyerabend links a belief in (simple, uniform, subject to stable universal laws and the same for all) universal natural law, a belief in universal standards of morality (there exists a right way of living and that the world must be made to accept it), and Judaism, which can be taken here, generously, to mean monotheism. He protests the modern hegemony of science and monotheism which demand unique, universal moral as well as natural law. Man is thus presumably outside of natural law.
Feyerabend represents a part of the pagan tradition manifest today in widespread and diverse movements in the West associated with New Age and Eastern religions, and hostile to the Western ‘religions’ associated with monotheism and science, dual hegemonies, both organized about ideas of unity and universality. Its roots are in polytheism: multiple independent gods have simply become multiple independent forces, both intellectual and physical.