The NATURE and ORGANIZATION of SCIENTIFIC KNOWLEDGE R. H. WRIGHT University of New Brunswick, Fredericton, New Brunswick, Canada
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REQUENT references to "a scientifically adjusted
tarW or "a scientific income-tax schedule" on the part of political speakers reflect the faith of the common man in "science" to give him what he wants. The word "science" popularly signifies physics, chemistry, geology, and biology and their various subdivisions, and i t is the success of these sciences in meeting the material wants of men that is responsible for the popular
faith in the power of science to cope with our political and economic problems. Most of the "science courses" in our schools and colleges have as their announced object the training of future citizens in scientific methods and habits of thought. This is particularly true of nonprofessional general courses. Unfortunately the usual textbooks used in such courses give only a very hazy notion of the pattern of scientific
knowledge so that their transfer-value to problems of everyday life is all too slight. In what follows an attempt will be made to pick out the underlying pattern which is common to the several branches of physical and biological science. It may be that restricting the name "science" to these branches of knowledge unjustly excludes such things as history and political economy, but to begin by arguing this point would serve no useful purpose and would probably lead to a definition so all-embracing as to be quite useless. The proper course in an enquiry of this sort is to examine a number of authentic samples and then to see how far the doubtful cases conform to the established type. It is better and easier to enlarge where necessary a toonarrow definition than to attempt the limitation of an indefinitely broad one. Natural science deals with phenomena, a phenomenon
being some object or ment (or combination of them) which we perceive with our senses. For scientific purposes i t is essential that a phenomenon be perceptible and if possible actually perceived by more than one observer. If one man, standing in the midst of a crowd, should alone declare that the sun is green, the phenomenon would he regarded as pbysiological or perhaps psychological-certainly not as astronomical. If, however, he should return from a desert island and report a green sun, the statement would be placed on record for what it might be worth. If subsequently other Robinson Crusoes made similar reports, the attention of science would be drawn either to the peculiar atmosphere of the island or to a possible correlation between solitude and visual hallucinations. Hunger belongs to a class of phenomena which are perceived subjectively and which from their nature are not perceptible to more than one observer. Physiologists meet this situation by picking out what is common to the independent accounts of differentobservers. "For the same two normal human beings the organs of sense are also machines of thg same type and thus within limits only capable of conveying the same sense impressions to the brain. Herein consfsts the similarity of the Universe for all normal human beings." (Karl Pearson, "The Grammar of Science.")
of the exact meaning of each word used, for thoughts must eventually be cast into words. The coining of new terms and the growth of a scientific terminology ("scientific jargon") are the natural outcome of this necessity for clarity and precision in scientific writing. Care, impartiality, and honesty in the gathering of data are the very comer-stone of science, for without reliable data no sound superstructure can be erected. Realization of this has enabled science to draw its greatest strength from its distrust of its own data! Experiments and observations must be checked, rechecked, and cross-checked. One must ever be on the watch for error and misunderstanding. Darwin is reported to have said that Nature will tell you a direct lie if she can! Sometimes i t is said that science deals with facts. Whether this is correct depends on the meaning attached to the word "fact." To the average person, "Fact" implies "Truth." Very little experience with either the making of experiments or the construction of sentences is enough to show that every measurement has a residuum of error and every sentence is but an approximation to the thought of the writer. It is therefore better to say that science deals with datadata which are almost certainly not true but which are the best obtainable approximation to it. The truth can only he hinted at. When data have been collected, sorted, arranged, and classified (and, if need be, checked), then certain regularities may appear. That is, it may be possible to correlate one set of observations with another, or the appearance of one kind of behaviour with the incidence of one set of influences. An obvious example is the well-known copelation of the positions of the sun and moon with the height of the tide. On the basis of such a correlation a generalization or law may be formulated.
A generalization or "Law of Nature" is merely a statement that under given circumstances certain phenomena can generally or always be obsemed. Many, if not all,
scientific laws are statistical, that is, they hold accurately for large assemblages of atoms or animals, but are no more than statements of probability when applied to individuals or small groups. Recognition of When a phenomenon is carefully examined and the ob- this is most important in biology and in physics when servations are recorded, these records are called data. we seek to formulate or apply laws relating to the beData may be obtained in either of two ways: by hare haviour of individual orgaiiisms or particles. The observations and by experimental observations. A phenomena of chemistry usually involve such large bare obsemation is one made by an obsemer who has no numbers of atoms or molecules that the statistical control over the influences acting on the phenomenon ob- aspect of chemical laws can generally be overlooked. The purpose of a generalization is to enable observaserved. Selection of a particularly favonrable time or place for making the observation does not constitute tions to be transferred from one case to another. The control. Neither does the simple act of measurement transfer is naturally attended by some uncertainty at unless the conditions of measurement (temperature for fist, and i t is an essential part of the scientific method instance) are controlled. An experimental obsewation to subject every generalization to the widest possible is one made by an observer who does exercise some control test of experiment and observation. Such testing almost always leads to the discovery of definite limitaooer the influences acting on his material. To be of value, either kind of observation must be tions on the applicability of the generalization. Few made carefully and impartially, and i t must be re- laws are always, absolutely, and universally exact; the simple gas laws of Boyle and Charles are valid only corded. Accurate description requires a clear understanding a t relatively high temperatures and low pressures.
modified or abandoned or overthrown, it means that the discovery of new generalizations or the amendment of old ones has required some change in the current set of assnmptions and attendant reasoning in order that the new knowledge may be fitted to the old. Logic, which is an integral part of all theories, is of two kinds, qualitative and quantitative. "Common logic" is qualitative logic, mathematics is quantitative logic. This reveals the true relation of mathematics to science, a relation that is often misunderstood. Quantitative, mathematical logic is needed as soon as the technic of observation has advanced to a point where servations or experiments is culled a working hypothesis. quantitative data and quantitative generalizations are Working hypotheses are among the most useful tools of possible. To say that a study is not scientific until science when properly used. this stage is reached is to miss the whole point of the When data have been accumulated, and a number of scientific method. It is logical thinking of whatever generalizations formulated, an attempt may be made to sort which is essential to science, and attempts to rerelate them by means of a theory. That is, certain as- duce qualitative generalizations to mathematical form sumptions are made and it is shown that these assump- in the hope of being thereby more scientific, are merely tions enable one set of generalizations to be deduced pathetic--or funny. from another apparently unrelated set of generaliza"Mathematics has no symbols for confused ideas." tions. For example, the Daltonian atomic theory by Logic consists of certain rules for reasoning from premmaking certain assnmptions about atoms enabled the ises to conclusions which normal and civilized men have laws of definite, of multiple, and of reciprocal propor- agreed to adopt. "The same type of physical organ retions to be deduced from the laws of the conservation ceives the same sense impressions and forms the same of mass and immutability of elements. 'constructs.' Two normal perceptive faculties couIt is sometimes supposed that a theory explains a struct practically the same Universe. Were this not set of generalizations. In the sense that- a theory true, the results of thinking in one mind would have no makes coherent an otherwise incoherent body.of knowl- validity for a second mind. The universal validity of edge, this is true. It is popularly supposed, for ex- science depends on the similarity of the perceptive and ample, that the atomic theory affords an explanation reasoning faculties in normal, civilized men." (Karl of the basic facts of chemistry. Actually, so long as Penreon the law of mass-conservation remains unexplained, It is necessary to draw a-'clear and sharp distinction the basic facts of chemistry remain "nnexplainednbetween hypotheses on the one hand and simplifying although made much more intelligible by the atomic assnmptions and restrictions on the other. theory which gives a concise description of them. A A simplifying assumption i s a simplification of an hytheory may be likened to a map whicb provides a bird'spothesis madefor reasons of logical expediency. For exeye view of a complicated terrain and enables the relaample, in the kinetic theory of gases, we may assume tion of one part to another to be discerned. (as an hypothesis) that the molecules occupy a finite It is the existence of classific$ion and generalization, and above all, of theory that enables science to be volume. For purposes of mathematical computation, we may suppose that the molecules are spheres of asdescribed as an organized body of knowledge. signed radius. Attributing a spherical form to gas We are now in a position to frame a clear definition molecules is a simplifying assumption which may or of the terms theory and hypothesis, and to draw a rather simple distinction between them. An hypothesis may not be justified. If i t fails to lead to verifiable is a more or less plausible assumption used in constructing deductions, i t is the simplifying assumption rather than a theory. (This is, of course, distinct from the concep- .the hypothesis which is discredited. A restriction is an assumption concerning the condition of a working hypothesis already defined.) A When, as knowledge increases, it is found necessary thus to modify or restrict apparently well-established laws, this means simply that their limitations have been more clearly recognized, and our confidence in what remains is proportionately increased. Whiie it is true that generalizations are formulated on the basis of data, very often generalizations are suspected by the observer before he has the data on which to establish them. This is perfectly legitimate, and the observer is no less competent or scientific, so long as his preconceptions do not affect the integrity of his data. A preconception wed as a guide in making ob-
theory is a whole body of knowledge, data, generalizations, and assumptions, knit together by a train of logiuzl reasoning. The majority of textbooks fail to draw a clear distinction between the words theory and hypothesis, and leave only an impression that hypotheses are &found theories and theories no more than hypotheses not quite so ill-found. The proposed definitions are more clear-cut and afford a better idea of the organization of scientific knowledge. It is essential that the number of assnmptions used in constructing a theory be kept a t a minimum. When we hear that some well-known theory has been
tions under which a system is to be examined. or a generalization applied. In working out the theory of a chemi-
cal reaction, we may postulate that the substances concerned occupy a constant volume. The data used to verify the predictions of the theory must conform to this restriction or the test is not a fair one. Reviewing what has been said, a few points require special emphasis. Science takes for granted the existence of an enduring external world with things in it. Science readily admits that these things (phenomena) are known to us only through our senses, and does not worry much about
"reality." It is content if the impressions received are consistent (that is, reproducible and uncontradictory) and coherent (that is, capable of being related one to another). Science therefore excludes from its scope all knowledge obtained from other than sensory impressions (from intuition or revelation, for example) unless such knowledge is capable of being tested in the ordinary way-when the intuition becomes a working hypothesis. Recorded observations constitute the data from which generalizations are drawn, concerning which assumptions are made and around which theories are constructed. The important thing about science is its impartial and critical attitude to its own data which demands the checking of observations by diierent observers. The individual can only be scientific when he is one of a group. While a science may be born out of purely observational data, history shows that the fullest and most fruitful development has been attained only when both observational and experimental data are available. Theories serve a threefold purpose. In constrncting them the aim is always to link together generalizations that are as far apart as possible. The more farreaching a theory is the more useful it is. In this way theories weld science into a compact whole. Again, a good theory in addition to linking generalizations that are already known will usually suggest hitherto unsuspected generalizations. The search,for data to prove or disprove these predictions serves both to enlarge the general body of knowledge and to test the usefulness of assumptions embodied in the theory. The great difference between a scientific theory and a pseudo-scientific one is this: that a scientific theory stands or fallsby the correctness of its predictions, while a pseudo-scientific theory is upheld because its logic is sound or its assumptions plausible. Finally, by providing links between generalizations, theories often enable us to bridge the gap between a field where experiment is possible and vne where only observational data are available. This is beautifully illustrated by modern astrophysics. Perhaps some day economics will advance to this stage. Let us now see what practical value there is in the foregoing analysis. Fist, it emphasizes the nature of scientific data and the attitude of science toward its data. Second, i t is a reminder that generalizations are founded in data and derived from data. They are tested by gathering more data. They can only be attacked by adducing conflicting data. The question of what "ought" to be does not enter, i t is purely and simply a matter of what "is."
Third, it shows that a theory combines the three elements, generalizations, hypotheses, and logic. Therefore, any theory can be examined as to the soundness of these three ingredients, but the criteria of their soundness are quite different. A generalization is justified or discredited by data. Logic consists of agreed rules for reasoning. Hypotheses are justified by, first (and least important) their success in correlating generalizations, and second (and critically important) their success in leading to verifiable predictions. A theory that only lets us be wise after the event is useless. It is not necessary that a theory should predict everything-but what predictions a theory does make must be correct. This criterion of utility is the only criterion of an acceptable hypothesis. Plausibility is not important. (Compare relativity and wave mechanics.) Bound up with the criterion of utility is the question of simplicity. That theory is the most useful which is the simplest, which means capable of linking the most generalizations with the help of the fewest assumptions. The criterion of an hypothesis is its usefulness The criterion of a simplifying assumption is its fairness and convenience. The criterion of a restriction is its applicability in a particular case. In conclusion, we may add a word concerning definitions. A definition is a form of words stating the meening of a word. There are two sorts of wofds to be defined: the words used in describing phenomena are of one kind; some of the words used in framing hypotheses are of the other. A word used in describing phenomena must be defined in such a way as to enable +ny person possessed of the necessary skill and facilities to recognize the thing defined. Every technical word used in a generalization must be de6ned in this way. The word "element" is sometimes defined as indicating a substance composed of one kind of atom only. As a definition this is worthless-unless i t be taken as defining the word "atom!" The word element' should rather be defined somewhat as follows (at any rate for chemical purposes). An element is a pure substance (previously defined) which cannot he separated into parts having diierent chemical properties (previously defined) by the use of ordinary physical and chemical methods. The second kind of word is'that used to designate something hypothetical. Atoms, molecules, valence bonds, electrons, and so forth, are whatever we choose to say they are, they have whatever properties it may be useful to assign to them. Definitions of words of this kind may be altered almost a t will. Definitions of words of the other kind can only he altered if it becomes evident that the previous definition was incomplete or ambiguous.
PITTSBURGH SUMMER ANNOUNCEMENTS Professor Wojciech Swietoslawski, formerly Head of the Physico-Chemical Institute in the University of Warsaw and the present Chairman of the Committee on Physico-Chemical Stand-
a d s of the International Union of Chemistry, will offer lectures in the Department of Chemistry, University of Pittsburgh, on calorimetry and ehulliometry, from July 2nd to July 30th.
