“THE TRUTH OF SCIENCE: Physical Theories and Reality,” Roger G. Newton, Harvard University Press, Cambridge, MA, 1997.

p. 65: Chapter 4 – Explanatory Devices

“The phenomenological constructs I discussed in the last chapter are often regarded as models rather than theories, implying a certain amount of skepticism about both the reality and the completeness of what is being proposed: ‘Don’t take my proposal too seriously; it’s only a model.’… Some carry this agnosticism so far as to refer to all theories as models – most physicists tend to be philosophically somewhat timid – but I will make a distinction, occasionally blurred, between the less weighty models, on the one hand, and laws and theories assumed to come closer to an exhaustive description of Nature or a part of it, on the other.”

“For more than two centuries, elaborate attempts were made in physics to construct images that would account for phenomena difficult to understand without the help of concrete representations.”

p. 68: “While certainly the most successful theories in physics are those that are able to make very precise numerical predictions agreeing with experimental results, in other situations even the most sophisticated mathematical tools lead only to a qualitative understanding of observations – a reminder that the power of mathematics in theoretical physics goes far beyond the use of numbers. In quantum field theory and particle physics, theorists will often attempt to solve the relevant equations or study their properties in systems with fewer dimensions than are needed for the description of Nature, simply because the realistic case is too difficult.”

p. 69: “One point about the use of models seems quite clear: there is an enormous amount of leeway in their invention, and there can be many different models serving similar purposes. Individual scientists may feel very comfortable with some models and reject others for a variety of reasons….”

“The manner in which simplified versions sometimes help us understand the implications of a theory is by analogy, a powerful general mode of reasoning that may eventually even be successfully incorporated in computer programs.”

p. 71: “A form of analogy of a vaguer and more suggestive kind are the metaphors, which abound in ordinary speech. Beyond the conventional usage, which is almost impossible to avoid, metaphors are used in physics primary at an exploratory stage in the genesis of theory, for pedagogical purpose, or for endowing abstractions with a richer, intuitive context. The suggestive nature of such figures of speech makes them useful for the gestation of new ideas but not for the precision usually needed even in a qualitative explanation.”

p. 73: “There is a long tradition among philosophers – famous for their reluctance to get their hands dirty by handling real pieces of apparatus – to use thought experiments as a means of convincing opponents or disciples of the correctness of their point of view. These devices are also often used to great effect in science, even though real experiments play a greater role.”

p. 76: “All three primary examples of scientific theories of past events – cosmogony, geogony, and biogony—are beset with controversy because they conflict with the accounts offered by various religions, based on authority or individual revelations.”

p. 77: “It is important to note that the physicist’s mode of explanation for the development of a system is always ultimately mathematically based on the use of differential equations, requiring the specification of the system’s initial conditions. The differential equation embodies the underlying law and thus the essence of the explanation, while the initial conditions are contingent and left unexplained. Therefore physics does not attempt to explain the state of the universe as it is – it only claims to be able to predict the entire course of the universe, past, present, and future, provided we know its initial state at the time of the ‘big bang.’”

RESPONSE: I take the preceding to be an outrageous statement. During the time of Isaac Newton a physicist might have been willing to make such a claim. Any physicist who makes such a claim today in my opinion is grossly misinformed about the nature of physics, mathematics, the universe, and human nature. Knowing the universe’s initial state at the time of the “big bang” and thereby being able to predict the entire course of the universe is a nonsensical statement in my mind.

p. 78: “The history of plate tectonics serves as a cautionary tale about the length of time it may sometimes take for an incorrect theory to be driven out and a competing one accepted.”

RESPONSE: In other words to see how science really works as opposed to how students are often taught that it works.

p. 80: “The anthropic principle is a rather unusual explanatory tool put forth by some respectable physicists, though it is regarded as unscientific by many others, as an attempt to deal with a perplexing question concerning the most fundamental constants in particle physics and cosmology.”

“Fundamental particle physics, as mentioned earlier, is at this point (and may always remain) unable to explain the numerical values of a large number of basic constants of Nature, such as the electric charge of the electron, the strengths of the strong and weak nuclear forces, the strength of the gravitational force, and the masses of the elementary particles, numbers that determine many properties of the universe and of its constituents.”

p. 81: “The anthropic principle makes the extraordinary assertion that because this is so, [the specific values possessed by the strong force and the gravitational constant] the existence of intelligent life explains these particular numerical values of the constants. ‘Since it would seem that the existence of galaxies is a necessary condition for the development of intelligent life, the answer to the question “why is the Universe isotropic?” is “because we are here,”’ conclude the physicists C.B. Collins and S.W. Hawking. This strange bit of reasoning clearly needs some explication; there are various interpretations of its logic, each of which has its adherents.”

p. 81: “The first formulation of the anthropic principle interprets it as a purpose: the existence of humans constitutes the purpose of the universe, and the constants determining the strengths of the fundamental forces were given the values they have so that humans could exist. This reading, which is essentially religious, is not accepted by many physicists, though it has followers among some nonscientists. The second formulation asserts that without intelligent observers, the universe would not exist. It is, in effect, a restatement of the idealism of Bishop Berkeley and has supporters among some physicists who interpret quantum mechanics idealistically. The third formulation, based on a peculiar interpretation of quantum mechanics called the ‘many-worlds interpretation,’ states that there are infinitely many different universes, all with different values of the fundamental constants but only one of them hospitable to human intelligence. It is therefore no accident, all three forms of the anthropic principle imply, that we find ourselves in a world in which the constants have the value required for our existence.”

RESPONSE: And of course the fact that if the values were different such that we could not exist and would therefore not be here to raise the question must appear too obvious to be discussed by such sophisticated thinkers.

p. 81-82: “A weaker form of the principle declares that the values of the fundamental physical constants are restricted and therefore can be explained by ‘the requirement that there exist sites where carbon-based life can evolve and by the requirement that the Universe be old enough for it to have already done so.’ This formulation, though less powerful, is subject to the same basic criticism as the stronger version.”

p. 82: “All of these interpretations and uses of the anthropic principle as an explanatory tool have evoked hostility in many scientists, including me. The teleological version of the principle is neither verifiable nor falsifiable and cannot be accepted as a scientific mode of explaining anything; the other versions stand on its head what we mean by an explanation – instead of accounting for the possible development of intelligent life by the structure of the universe, they try to explain this structure by our existence…. But the fact that some serious scientists are willing to make use of it shows that even the question of what constitutes a scientific explanation does not have a simple, clear-cut answer, agreed to by all scientists.”

RESPONSE: To me all of these answers are elements of the “God of the gaps” way of thinking. If we don’t understand it then there must be a mystical purpose behind it. It seems much too early in examining this issue to justify the deus ex machina solution.

p. 83: “We must… conclude that in its scientifically meaningful form, the anthropic principle is contradicted by the available evidence.”

p. 84: Chapter 5 – The Role of Facts

“In the minds of many, the word science conjures up images of ever more facts ever more precisely stated, and the collection of these facts is thought to be the rock bottom on which the infallibility and un-assail ability of science is based. The laws and theories constitute the intellectual framework erected on this factual basis to explain and understand the workings of Nature, or to conquer it. Beyond the theories, in the unfinished upper stories of the building, there are speculations, which the inhabitants indulge in to grasp for new and grander theories, hoping for further understanding.”

“This picture is, of course, a caricature. Positivists believed they could avoid building the house of science on sand by searching for the simplest statements of fact for the foundation, perhaps admitting nothing but individual sense impressions or readings of measuring instruments: they would design the building on the Bauhaus style, austere and unadorned as an obelisk. This ideal, however, was destroyed by the realization that the ground was full of termites and the atmosphere corrosive. The structure of science is not so simple.”

p. 84-85: “There are facts, and then there are facts. Some of them I will call individual…. Others I will call general…. Individual facts are generally of no interest at all to science.”

p. 85: “For the most part, the only facts of interest to science are those I call general, that is, repeatable and reproducible: these form the touchstones of theories and laws. In order to establish general facts, of course, we have to rely on many individual facts. Measurements must be repeated, and each result constitutes a particular fact, but these are not to be regarded as individual occurrences that are of scientific interest in their own right.”

“There are some individual facts that are of interest to science, however, in those areas that have the character of history – cosmogony, geogony, and biological evolution—and in the fields that deal with establishing the constitution of the universe – astronomy, astrophysics, and cosmology.”

p. 86: “The general lack of interest that scientist have in individual facts carries consequences that are rarely discussed…. Because [a strange, unique event]… cannot be repeated, it has the status of an individual fact that has no scientific significance and therefore is of no interest to physics.”

p. 86-87: “The difference between saying something cannot happen and saying its probability is extremely small does become significant, however, when there are many repetitions of the occasions on which it might happen…. You can see from this example [forming the first RNA] that the occurrence of an event of extremely small probability does not always have the status of an individual fact with no scientific interest.”

p. 87: “Scientists often group a number of similar and apparently related facts into an empirical law…. Such laws have a character that places them on the borderline between general facts and theories; they are local laws expressing relations among facts established purely empirically…. They usually are not universally valid but may be of great practical importance in many applications.”

p. 88: “I have mentioned before that there are relatively young areas of science relying primarily on establishing and classifying facts, concerned more with taxonomy than with explanation.”

“What makes one fact more interesting than another is its relation to some explanatory scheme: either it fits into a theory and corroborates it, or it contradicts a theory and leads to an ‘anomaly.’ If it does neither, nor promises to, it remains a ‘mere fact’ and is quickly forgotten…. Finding and establishing an important new fact that can be situated in a theoretical context constitutes a discovery…. Discovering a fact – designing the successful apparatus for making a discovery and convincing the scientific community of its validity – takes great ingenuity and a concerted effort.”

p. 93: “The facts upon which scientific laws are based are almost never established in pristine isolation; rather, in one way or another, they usually depend on these very laws: they are intertwined with them. As philosophers of science have frequently noted, many so-called facts are ‘theory-laden,’ which is to say that the way in which they are demonstrated, and even their very meaning, depend on theoretical interpretations.”

p. 97-98: “The extent to which the facts of science are theory-laden varies greatly. Some facts are relatively pure and independent of theoretical assumptions, others are heavily ‘contaminated.’”

p. 98: “In general, it is fair to say that almost every experimental result used to corroborate or disprove a theory can serve that purpose only after being interpreted by means of either another local theory or another part of the same general theory. In most instances, the daily work of experimental scientists consists of playing off one local theory against another, in the sense that one of them is utilized for the interpretation of the outcome of the experiment, and the resulting ‘fact’ is held up against the other.”

p. 98-99: “One may well argue that the dividing line between facts and theories is not always sharp. Furthermore, in addition to the blurring of the line between theories and ‘data,’ experiments are also subject to influences that may be irrational. After all, their interpretation always has to be guided by ideas based on previous thoughts and knowledge. To perform and evaluate experiments without preconceived ideas, Poincare noted, ‘is impossible. Not only would it make all experiments barren, but that would be attempted which could not be done. Everyone carries in their mind their own conception of the world, of which they can not so easily rid themselves.’ So the genesis of what we regard as facts is, in many senses, adulterated.”

p. 99: “What, then, of the oft-repeated assertion that the imaginative theories of science are subject to the ultimate test of having to be anchored in facts and experimentally verifiable evidence? If these facts are generated by experiments that are full of preconceived ideas, and if they depend on the very theories they are to corroborate, are we to conclude that science is nothing but a vast conspiracy or myth in which the theories are used to fabricate their own facts? Do the results of experiments have no more cognitive value than folklore? There are, alas, supposedly intelligent people who contend just that, but such a conclusion would be quite foolish.”

p. 100: “While it is a great oversimplification to say that theories and laws are finally based on independently verifiable facts, it is nevertheless the case – and this needs emphasizing – that in physics and in most other areas of science the combination of laws and facts, theory-laden though many of the latter may be, has an enormous amount of stability.”

p. 101: Chapter 6 – The Birth and Death of Theories

“As the last chapter indicated, the line that separates the laws and theories of science from the factual evidence is not sharp. Nevertheless, we need to ask what is the relationship between the two? For that matter, what are the origins of theories and what determines their status? Do they emanate from these somewhat contaminated facts? Are the laws ultimately proved by them?”

“To begin with, it is important to make a clear distinction between the origin of a theory and its confirmation. The contention of some philosophers and sociologists of science notwithstanding, the germination of a law in the mind of a scientist – its psychological origin – has very little relation to the evidence on which the law rests. That is why the professional writings of scientists tend to be so impersonal – to the despair of biographers and historians. Scientists screen out all the internal wrestling they went through and the doubts that had to be overcome before they present their theories in a shape they deem suitable for inspection and testing by the world. ‘The success of science as a shareable activity,’ the science historian Gerald Holton rightly observes, ‘is connected with the conscious downplaying of the private struggle.’”

p. 101-102: “Scientists seldom arrive at a theory by pouring over a mass of experimental data and following some systematic method of induction, an image of the ‘scientific method’ that Karl Popper was instrumental in helping to demolish once and for all. We have abundant testimony from scientists themselves that the invention of a theory is almost always an act of imagination and a flash of inspiration. In fact, in may cases, the sudden insights have no relation at all to anything we would call evidence, especially since these intuitions are sometimes based more on subconscious thoughts than on rational reflections.”

p. 104: “Scientists are well aware of the fact that the first proposal of an important new insight is often based on flawed reasoning; this is why science textbooks are usually written in an historical style, substituting an idealized and anachronistic description for the actual course of events that led to a discovery.”

RESPONSE: In my mind this may be an acceptable practice particularly at the introductory level of a science. But somewhere in the science curriculum the student needs to be made aware of the true history of science. If this were done, more scientists might be able to realize that although work in science is a noble calling, what makes it so is the tremendous benefits humanity derives from science. Continuing to teach them that the true value of science is to show us what the universe is like not only misleads them, but misrepresents what actually happens.

“There are times when the intellectual climate in which scientists find themselves is conducive to productive new ideas in a certain area, and other times when it is hostile. Furthermore, scientists with different temperaments naturally react in different ways to their environment. Not only may individual scientists thus suggest divergent answers, but they may ask disparate questions. The very selection of what needs an explanation may be subject to influences that are not always scientific or even rational. From many directions, it seems, varieties of style enter the arena of scientific reasoning.”

p. 105: “Some scientists are more comfortable conceiving of theories by unifying masses of data; others choose on the basis of the manifest beauty of a solution of a puzzle.”

p. 106: “Science is a conservative enterprise with a revolutionary escape clause, like a sturdy steam kettle with a well-functioning safety valve.”

p. 107: “The same constraint on the imagination that exist for scientists also exist for mathematicians, but in their case, of course, these constraints originate from the rigorous demands of logic and the whole body of mathematics rather than from the external world. But great mathematical insights leading to important new theorems often occur and, as is true for scientists, mathematicians sometimes have epiphanies that are not always traceable to rational cogitation. In both cases they appear as sudden solutions to puzzles or problems.”

RESPONSE: And it seems to me this is a universal feature of how the human brain works. When an individual is deeply immersed in a problem our brains work on it independent of conscious direction, and if we are lucky comes up with an answer.

p. 107-108: “Since scientific theories often are based on flashes of insight and produced by a fertile imagination, and since, in addition, they are radically underdetermined by the supporting evidence, we should expect to find instances in which several different competing theories are proposed to account for the same group of phenomena, perhaps all equally effective and confirmed by experiments. So it happened in 1925 when Heisenberg proposed his ‘matrix mechanics’ for the quantum theory and Schrodinger his ‘wave mechanics.’ Both theories accounted equally well for the quantum puzzles but were seemingly totally different. It was not long, however, before the two formulations were found to be mathematically equivalent to one another, and they are now seen simply as two versions of the same abstract quantum theory. ‘The contentious issue,’ as the philosopher Brian Ellis sees it, ‘is whether there are genuine, logically incompatible, theories which are empirically equivalent, in the strong sense that no evidence could possibly distinguish between them.’ I know of no case in which two inequivalent theories of equal range were proposed for the same area, which is surely remarkable in view of the fact, emphasized by many philosophers of science, that theories are never logically determined by observational data.”

RESPONSE: However, since they are tested by their ability to satisfactorily deal with the available data the less useful one is rejected if not immediately then after testing by the new crop of scientists constantly entering the field.

The dual nature of matter – both wave and particle, both logically incompatible — seems to me to fit into the above wonderment, with the caveat that its not a matter of selecting one or the other, but currently both must be accepted.

“Given the murky, sometimes irrational psychological origin of theories, it can be no great surprise to find that theorizing in science is often subject to fashions.”

p. 109: “No matter how old a field of research, and how well understood it is in general, there are always many specific, detailed questions that have not been satisfactorily answered; a scientist who spends time and effort to wring an extra drop from a cow that is milked dry will be rewarded neither by fame or monetary support…. Not every change of direction is a veering of fashion, however; sometimes a new orientation is more in the nature of a ‘paradigm shift.’ The area that has been abandoned is not necessarily falsified by the change of focus, but the unanswered questions left in the old research program are no longer thought to be interesting.”

p. 110: “The first thing to be said is that, just as many kinds of nonrational elements play a role in the psychological origins of a theory, so they may in individual scientists’ instant rejection or easy acceptance of it; initial judgments, even by the most astute, are sometimes found to be quite incorrect.”

“Ultimately, to be accepted, any proposed scientific law has to lead to verifiable consequences. As a matter of general philosophy, the positivists insisted that propositions which could not be tested by observation had no meaning. This requirement, however, is much too stringent, especially since the word meaning can signify many different things. Science, particularly the abstract discipline of physics, is full of concepts that are far removed from experimental significance and of meaningful statements that, in and of themselves, have no observational consequences. Nevertheless, there is no question that a law would be unacceptable if none of its implications were subject to experimental testing. A very general law, as I have noted earlier, may sometime spawn local laws which are more likely to lead to directly verifiable propositions – predictions of the results either of future observations or of an appropriate analysis, so far unperformed, of past experiments (these might be called ‘postdictions,’ in the sense that they agree with facts already known).”

p. 110-111: “Generally speaking, scientists put a much higher premium on predictions than on postdictions. The reason is largely psychological. There is a feeling that with sufficient jiggling of adjustable parameters, clever theorists can always come up with a scheme that fits a known set of data; it is in the predictions that even the smartest have to risk being wrong; this is why the greater the number of significant new predictions an announced theory leads to, the more highly it is valued. Predictions also have the virtue of stimulating experiments that might otherwise not have been performed; when asked a new set of questions, Nature may offer up a new set of revealing answers. Of all the potential values of a new theory, this is the most important.”

p. 111: “It was Karl Popper’s great contribution to emphasize that ultimately what matters in giving meaning to a scientific law is its falsifiability rather than its verifiability…. General statements…. can never be completely confirmed, because it would take an infinite number of attempts to do so. They can, however, be disproved by a single negative observation.”

p. 111-112: “There is another reason, as well, why falsifiability rather than verifiability renders a statement scientifically meaningless – a verification of almost anything can be easily accomplished by appropriate selection of the evidence. Even the observational confirmation of a prediction may be based on a fluke…. ‘What makes the criterion of falsifiability so powerful is this,’ Ernest Gellner trenchantly observes,

If you insist that a believer specifies the conditions in which their faith would cease to be true, you implicitly force them to conceive a world in which their faith is sub judice, at the mercy of some ‘fact’ or other. But this is precisely what faiths, [i.e.] total outlooks, systematically avoid or evade…they have little to fear from a requirement that they be ‘verifiable’: generally speaking, they pervade the world they create so completely that verifications abound – here a verification, there a verification, everywhere a verification.”

RESPONSE: I assume what Gellner is discussing above is the grounding concepts of folk religions. Of course since no folk religion has a theoretical foundation supported by empirical data it goes without saying that they are all supported by psychological mechanisms such as Gellner describes.

p. 112: “One of the most telling arguments against psychoanalysis as a science is that its system can easily produce plausible explanations of symptoms or dreams of any kind, but there appears to be no way to show that the explanation is wrong…. Such theories thus have no real explanatory power; it is their non-falsifiability that accounts for their lack of scientific meaning, not their failure of verifiability. There is no scientific proof; there is only disproof.”

“The scientific importance of falsifiability accounts for the stress scientists put on predictions as necessary concomitants of explanations. So long as understanding a process yields no more than an explanation of facts or relations already known, it is safe and cannot be falsified; only when it leads to predictions does it become risky.”

p. 112-113: “Plausible and enticing as the simple and strict criterion of falsifiability may be, it has been subjected to forceful criticism by science philosophers such as Imre Lakatos. For one thing, it is usually possible to construct an ad hoc modification of a theory to account for an observational discrepancy. ‘Some of the most important research programmes in the history of science were grafted onto older programmes with which they were blatantly inconsistent…. For another, the test of any theory must always rely on some demarcation that gauges the outcome of an observation, other things being equal. In most instances, scientists have to make a judgment about what is responsible for a specific aberration.”

p. 113: “’Falsification’ in the sense of naïve falsificationism (corroborated counterevidence) is not a sufficient condition for eliminating a specific theory: in spite of hundreds of known anomalies we do not regard it as falsified (that is, eliminated) until we have a better one.”

“There is no falsification before the emergence of a better theory,’ concludes Lakatos, and he proposes to replace ‘naïve falsificationism’ by ‘methodological falsificationism,’ which ‘uses our most successful theories as extensions of our senses… demarcating the theory under test from unproblematic background knowledge.’”

“In other words, whether an observed discrepancy is regarded as a falsification of a theory depends on the experimental and theoretical context. In many instances, an experimental result that appears to disagree with a theory is regarded as erroneous…. There are more than a few statements by Einstein and Dirac asserting that they would not necessarily consider their theories falsified by a purported experimental result that disagreed with them. A steadfast belief in their theories even in the face of adverse evidence, if not carried too far, is often a virtue in theorists.”

RESPONSE: And when a scientist is carrying a steadfast belief in their theory too far is difficult to get agreement on particularly if the scientist has achieved great power and authority. And the opposite is also true – receiving a hearing for a new theory by an unrecognized and powerless individual. So politics often plays a bigger role than we are led to expect.

p. 114: “The falsification criterion therefore has inherent limitations; moreover, we must admit that ‘confirmation’ also plays a significant role even if this role cannot be quantified and must never be confused with ‘proof.’ There can be no question that when a new observation agrees with a prediction, it constitutes potent support for the validity of the theory to be tested and has a highly persuasive effect on scientists.”

p. 115: “As Max Planck once remarked in a lecture,

A living and flourishing theory does not avoid its anomalies but searches them out, for the stimulus to further development come from contradictions, not from confirmations.”

“The point to keep in mind is that although falsifiability, rather than verifiability, is the most important criterion in determining whether a theory is scientifically meaningful, its usefulness for the greater task of building confidence in a theory is limited. A theory is accepted not simply because it has withstood many attempts at falsification, the need for such tests notwithstanding, but because it leads to predictions that are experimentally verified.”

p. 115-116: “When deciding whether to throw over an old, falsified theory in favor of one that explains what the previous one could not, scientists are faced with still another question. Sometimes the new theory makes no predictions or postdictions about certain phenomena encompassed by the old…. A new theory not only brings with it new predictions contravening its predecessors – these contraventions are the tools by which the old theory can be falsified – but it also often changes the set of questions regarded as worth answering. This change in focus is the essence of a paradigm shift.”

p. 116: “Are there crucial experiments that test two conflicting hypotheses, establishing one and demolishing the other? Though such definitive trials are often cited in textbooks, there are science philosophers who deny their existence.”

p. 118: “There are two kinds of experimenters, those who like designing laboratory tests to corroborate theories, and those who prefer trying to confute them. When a theory is new and on probation, its confirmation brings glory; when it is well established, fame attends the refutation.”

RESPONSE: An interesting point regarding how psychological motivation can guide choices.

“The courage of experimenters who take a big risk of failing is very healthy for science and can only be applauded.”

p. 118-119: “In addition to data that falsify or corroborate a theory directly, there are also facts that serve to increase or decrease our confidence in it more indirectly…. It is clear, therefore, that there is more to what counts as evidence for or against theories than strict falsification or corroboration.”

p. 119: “All that I have described above – the way theories depend on facts, how theories are generated, and how they are confirmed or confuted – is sometimes encapsulated in the phrase the scientific method. Tomes are written defining and refining it, controversies surround it, and its very value is questioned. Textbooks and college courses of psychology and sociology begin by explaining to students what this method is and then exhorting them to follow it: you must rely on evidence and on evidence only; follow a strict procedure and protocol in your laboratory and do not discard data that disagree with your theory or conjecture; always remain objective and do not allow you passionate attachment to a preconceived idea to color your judgment; remain dispassionate and disinterested. Valuable as such advice undoubtedly is, it is futile to attempt to restrain the scientific method by means of a straightjacket and insist that rigid rules be followed always and exclusively.”

p. 119-120: “Feyerabend also maintains that ‘the events, procedures and results that constitute the sciences have no common structure; there are no elements that occur in every scientific investigation but are missing elsewhere.’ While this claim, too, is exaggerated, I want to emphasize that the present book confines itself largely to the physical sciences, and much of what I am saying does not necessarily apply to the disciplines whose structure is less general and abstract. In fact, many of the problems discussed here do not arise in other scientific areas, which have their own kinds of difficulties to contend with. I agree with Feyerabend that the methods of the science differ among one another in many respects and certainly have some components in common with other activities of the mind.”

p. 120: “There can, however, be no question that its general approach and methodology, inadvisable as it may be to define it too narrowly, separates modern science from most other intellectual endeavors, and especially from the ways in which explanations of natural phenomena have been generated in the past (and still are by the vast majority of humanity). The one general theme that runs through all the sciences is that they rely on evidence accessible to others, or as the physicist John Ziman expresses it, on consensible knowledge. How that goal is to be achieved cannot be prescribed in any detail, but the attitude embodied in modern science is by no means what one could call ‘natural,’ as Feyerabend’s or Bridgman’s definition might lead us to believe. Its most important characteristic is to rely neither on authority nor on individual revelation or intuition. That is not to say that scientists and mathematicians never take the word of an authoritative and highly regarded colleague on faith. They often do; no one can go through the details of every mathematical proof or repeat every experiment. Certainly researchers rely on the word of others in the community, but that reliance is not on authority qua authority – a statement is not accepted automatically simply because it is made by a person in command or written in a sacred book; recourse to one’s own reasoning and senses or those of one’s peers is always implied. Here is where the issue of accreditation of experts arises. ‘Nobody knows more than a tiny fraction of science well enough to judge its validity and value at first hand,’ argues Michael Polanyi.

For the rest one has to rely on views accepted at second hand on the authority of a community of people accredited as scientists. But this accreditation depends in its turn on a complex organization. For each member of the community can judge at first hand only a small number of their fellow members, and yet each is accredited by all. What happens is that each recognizes as scientists a number of others by whom they are recognized as such in turn.”

“As for individual intuition and insight, of course scientists and mathematicians make essential use of them in arriving at new ideas, but that is never the end of the matter. Ultimately, the test of the idea is empirical and public.”

p. 121: “What happens to superseded theories? In general, two destinies are possible. In some cases, the old theory, falsified by specific repeated experiments, is replaced by a new one….”

p. 122: “In other cases, the old theory was not completely replaced and discarded, but its realm of validity was reduced.”

p. 123: “The state of physical science is now at a point that makes it unlikely we will ever again see a basic general theory superseded in the sense of being totally abandoned, except perhaps a theory of history such as cosmogony. No doubt many of our present general theories will have to be revised, but they are likely to remain as limiting cases or phenomenological constructs enclosed within future theories. The present theories of physics and chemistry account for too many details with great accuracy to be given up altogether. Even if a future sub-micro theory should supersede it, the quantum theory is likely to remain as an enormously useful framework, valid in its domain of applicability. Some of our local theories, on the other hand, might have to go by the board, just as other sciences that are at a less developed stage may well see some of their present theories totally abandoned.”

“In the course of my description of the role and structure of the general theories of the modern physical sciences, it has become abundantly clear that mathematics plays an enormously important part in the manner in which these theories are formulated and even sometimes in the way they originate. Let us, therefore, now turn to a more detailed examination of the nature of mathematics and learn why it is indispensable for the pursuit of science.”

RESPONSE: While at the same time keeping in mind that human beings are the ultimate reference system, not mathematics, reality, or God.

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