This chapter presents a review of some of those basic ideas of scientific
method which are involved in practically every investigation. Only elementary
views will be expressed here; more elaborate treatments of some of the topics
will be given later. Nevertheless it is obviously important to have a clear
understanding of the nature of observation, cause and effect, hypothesis,
deduction, models, mathematics, and various kinds of fallacies. Even the mature
scientist can profit by reconsidering these items in the light of his own
experience. To some readers most of the statements of this chapter may appear
rather obvious, but they are, after all, the basis on which more complicated
procedures are founded.
3.1. Authority in Science
Science begins with the observation of selected parts of nature. Although
the scientist uses his mind to imagine ways in which the world might be
constructed, he knows that only by looking at reality can he find out whether
any of these ways correspond with reality. He rejects authority as an ultimate
basis for truth. Though he is compelled by practical necessity to use facts and
statements put forward by other workers, he reserves for himself the decision as
to whether these other workers are reputable, whether their methods are good,
and whether in any particular case the alleged facts are credible. He further
considers it his privilege and sometimes his duty to repeat and test the work of
others wherever he feels that this is desirable.
The collective judgment of scientists, in so far as there is substantial agreement, constitutes the body of science. The fact that there are very large areas of agreement, in spite of the individualistic, antiauthoritarian nature of science, is partial evidence for the validity of scientific methods. However, there are cases where universal agreement has been attained for an untruth, though this has more often been the case with sweeping generalizations than with the basic observations. Each generation of scientists has to decide for itself what it will believe, using the best available evidence and the most careful methods of interpretation. With the best luck in the world, some of these decisions will later be proved wrong, but there is no other way.
3.2. Observation and Description
Observation implies selection. A forest can be observed as a forest, but
not easily as ten thousand trees. A tree can also be observed as a whole, but
not easily as thousands of leaves, twigs, platelets of bark, etc. The powers of
man are limited, and it is necessary to limit what is to be observed to a
portion of the universe small enough to be encompassed. An unwise choice yields
items so r motely connected that no amount of study would ever determine their
interrelations. Observation leads to description. Precise definitions are
adopted so that a specific word carries the same meaning to all scientists. The
botanists have probably carried scientific description to its highest peak.
Consider, for example, the following botanical descriptionl of the leaves of a
white oak tree:
The leaves are conduplicate in the bud, obovate-oblong and gradually narrowed and wedge-shaped a the base; they are divided into terminal lobes, and from three to nine but usually three pairs of lateral lobes by wide sinuses, which are rounded at the bottom, and are sometimes shallow and sometimes penetrate nearly to the midribs; the terminal lobe is short or elongated, obovate and three-lobed, or occasionally ovate, entire and acute or rounded; the lateral lobes are oblique, broad or narrow, entire or auriculate, and increase in size from the base to the apex of the leaf; or on vigorous shoots or small branches developed from the trunks of old trees, the leaves are often repand or slightly sinuately lobed or occasionally entire below and threelobed at the broad apex; when they unfold they are bright red above, pale below, and coated with soft pubescence; the red colour fades at the end of a few days, and they become silvery white and very lustrous; their covering of tomentum then gradually disappears, and when fully grown the leaves are thin, firm and glabrous, bright green and lustrous or dull on the upper surface, pale or glaucous and glabrous below, and from five to nine inches in length, with stout bright yellow midribs, conspicuous primary veins running to the points of the lobes, lateral veins forked and united near the margins, conspicuous renticulate veinlets and stout pale petioles flattened and grooved on the upper side and enlarged toward the base. 1 C. S. Sargent, The Silva of North America, Houghton Mifflin Company, Boston, 1891-1902, Vol. VIII, p. 17.
Pedantic-sounding, perhaps, but every word means something, and to those who know the language it is a concise and precise record of careful observations. It is worth looking at an oak leaf with the above description at hand.
Many nonscientists are excellent observers, but there are certain points emphasized more in scientific observation. One of the most important of these is the immediate recording of the data in a notebook. An experimental scientist without his notebook is off duty. Human memory is entirely too fallible to be trusted in such matters. There is a well known law professor who annually stages a mock trial and calls witnesses to testify concerning some event previously enacted before all his students. The disagreements of the differen.t witnesses are always vivid evidence of the fallibility of human memory. Some remarks on the requirements of a good notebook are given in Sec. 6.2.
The second point involves the question of bias. It is probably impossible for anyone to free himself completely from preconceived prejudices, and in a certain sense this is not desirable. It is important to have some hypothesis in mind before making an observation; if this were not so, how would one know what to observe? On the other hand, it is equally important to arrange the conditions of observation so that the observer's bias will not distort the observations. This is far less easy than it sounds, and often elaborate strategems must be devised to enable the observer to outwit his own bias and get the true facts recorded in his notebook.
A scientific observer is never afraid to allow others to view the phenomena in which he is interested. He should welcome checks and repetitions of his work as adding to their certainty. Some events, such as eclipses, cannot be reproduced at will and occur naturally rather rarely. These especially need multiple independent observers and in addition instrumental methods of recording portions of the phenomena for later study, as, for example, by photography.
A feature of scientific observation is a tendency to be quantitative. Numbers are used as part of the description where possible. Even rather intractable qualities like hardness are given numerical scales, even if of a somewhat arbitrary nature. Thus the mineralogist rates hardness according to a scale with diamond 10, topaz 8, quartz 7, orthoclase 6, etc. If B scratches C but A scratches B, then B lies between A and C. The use of numerical measures permits a more precise description and ultimately may make possible the application of mathematics.
Of course not all science is numerical; qualitative statements playa very large role which should not be belittled. It all depends upon the object of the investigation; if "green" is sufficient for the purpose in mind, it is foolish and wasteful to give a table of wavelengths.
Another distinguishing characteristic is the use of instruments as aids to the senses. Much of nature can be observed with the naked eye, but far more becomes accessible when microscopes, telescopes, measuring instruments, and all the vast and formidable array of scientific paraphernalia can be used. Even very simple instruments such as a meter stick, stethoscope, or test tube help considerably. In spite of the arrival of the age of the super billion-volt synchro-cyclotron, there still must be a good deal left worth observing with simple instruments.
3.3. Cause and Effect
Strictly speaking, every event is surely unique and therefore not to be
observed again. From a practical viewpoint, though, some events do show
similarities, and if certain features are selected for study, it becomes proper
to speak of similar events or even, as a figure of speech, identical events. It
is further obvious that in this sense certain events occur in pairs, in that if
the first occurs, the second accompanies or follows it. Sometimes the first
event is said to be the cause of the second, but usually the definition of cause
and effect has other restrictions as well. Thus it is often felt that one event
is the cause of the other only if suppressing it also always suppresses the
effect. Otherwise both events may be effects of some third event.
A great deal has been written about the philosophy of cause and effect, much of which is based on redefining the terms in one way or another. Here, however, a rather prosaic viewpoint will be adopted. A practical aim of science is to control nature or, failing that, to predict important. events. These aims are closely allied to that of explanation, a complex notion. If a scheme of connections between events has been uncovered such that when one event is made or allowed to occur, another necessarily follows, whereas if the first is not allowed to occur, the second will not happen, then the first event will be said to be the cause of the other. This definition requires that the first event be sufficiently fully specified, a limiting idea in itself since in principle it probably requires an infinite number of specifications. Fortunately, in practice a finite number usually suffices with a high, but not complete, degree of certainty. Some events seem to be capable of arising from several alternative causes. This can be put down either as a defect of the above definition or as a result of insufficiently precise specification of the exact nature of the effect. In practice, again, events often are specified so loosely that several causes are possible. Then the definition given above is conveniently broadened to include such cases.
An explanation that does not increase man's power over nature may be psychologically useful, but it is not to be considered in the same class as one which does lead to an increased ability to predict or control future events. Prediction and control are important aimfs of science. This is true even in such sciences as geology, where little can be done at present to control the larger forces molding the earth, but where progress is being made in learning to predict their consequences.
3.4. Analysis and Synthesis
Even the most restricted portions of the real world are too complex to be
comprehended in complete and exact detail by human effort. For one thing, under
increasingly refined observation it is found that it is impossible to neglect
interactions with the rest of the universe. As a consequence it is necessary to
ignore most of the actual features of an event under study and abstract from the
real situation certain aspects which together make up an idealized version of
the real event. This idealization, if successful, provides a useful
approximation to the real situation, or rather to certain parts of the real
Even then, it is usually convenient to break the idealization into a number of parts for separate treatment, i.e., to analyze the problem. The possibility of doing this rests on the question of whether or not there exist parts approximately independent of one another or mutually interacting in simple ways. Thus, the study of the way in which the body of an animal functions can be analyzed, at first, into separate studies of the respiratory, circulatory, digestive, etc., systems, even though these are not completely independent.
Closely related to the above steps is the practice of simplification. Not only are certain features abstracted from real events to create idealized events, but also certain aspects of these idealized events are then often altered so as to produce simplified idealized events. These simplifications may be such that they could approximate possible, though not necessarily existing, real situations, or they may be quite impossible of actual realization. The latter type are often invoked as a stage in the solution of more realistic cases. For example, the solution of the effect of an alternating electrical field on a polar molecule in solution was first set up and solved in two dimensions because this relatively easy problem showed most of the features of the three-dimensional case and served as a useful pilot problem before attacking the spatial one.
When the parts of a problem have been solved, the application of this knowledge, or perhaps of the consequences of some set of hypotheses, to an observable situation may require that various of the parts be put together. In other words, an approximation to a real situation may be constructed by synthe. is from relatively simple parts. This may be the only situation capable of experimental or observational test, or it may represent some case of practical utility for which a prediction is desired. In applying this technique two warnings are important. It is necessary that the parts used be the correct ones and also that the effects of their interaction be sufficiently closely taken into account. The artificial insect which some students constructed by joining the body of a bee, the wings of a grasshopper, and the legs of a spider, and which was immediately identified by their professor as a specimen of species "humbug," is an example of the first error. The difficulties with current treatments of the electronic structure of atoms and molecules stem largely from the difficulty of accounting properly for interactions of the parts.
After the selection of part of nature and its observation, the next
stage is the construction of a hypothesis, or trial idea concerning the nature
and connection of the observations. In fact, this stage often begins during the
observational one. Hypotheses differ in their subtlety and consequently in the
obscurity of their origins. A simple one may be a mere generalization of the
observations. More complex hypotheses may postulate connections between events,
or elaborate chains of cause and effect. Analogy is a very powerful tool in the
construction of hypotheses, but imagination is of the utmost importance. People
differ enormously in their power to construct useful hypotheses, and it is here
that true genius shows itself.
The possibility of constructing hypotheses rests on the assumption that there is some order in nature. This is not the same as the assumption that all parts of nature are ordered. The fact is that many parts of nature have been found to have an approximate order, but many other parts have so far defied the attack of scientists. The usual viewpoint is that this is a difference of degree only, but if a given set of phenomena is sufficiently complicated, it is certainly possible that it is beyond human powers to unravel it within the foreseeable future. However, it is usual to assume that some degree of order can be ascertained even if a more complete solution does not appear.
If two different hypotheses fit the observed facts and if one is clearly simpler than the other, it is customary to accept the simpler until further evidence causes its rejection. It has often been questioned whether this is justifiable; but it is always done, and it is certainly hard to justify the opposite course. There is, however, little to support the assumption that a simple hypothesis can always be found.
The most important feature about a hypothesis is that it is a mere trial idea, a tentative suggestion concerning the nature of things. Until it has been tested, it should not be confused with a law. Unfortunately, in many fields, especially on the border lines of science, hypotheses are often accepted without adequate tests. Plausibility is not a substitute for evidence, however great may be the emotional wish to believe. An amusing illustration is provided by a British anthropologist who states that the absence of doors between rooms of American houses is due to the fact that loneliness is intolerable to Americans. Aside from the question of whether or not American homes do in fact have fewer doors, this fiat statement is a mere hypothesis masquerading as a law. An alternative hypothesis would be that doors are expensive, make a small room seem smaller, interfere with traffic, and serve no useful purpose in a house with central heating, as contrasted with an essentially unheated British home with the inhabitants huddled around an open fire in one room. The difficulty of testing hypotheses in the social sciences has led to an abbreviation of the scientific method in which this step is simply omitted. Plausible hypotheses are merely set down as facts without further ado. To a certain deplorable extent this same practice occurs in medicine as well. Induction. The basic method of science is generalization, or induction. This is the process of drawing inferences about a whole class from observations on a few of its members. .When a botanist describes a new plant, he is not primarily interested in the properties of the actual specimens he observed but in those properties which he has reason to believe are shared by all other specimens of the same species. The inductive method of reasoning is difficult to justify philosophically, but every human being uses it continually in his daily life. It often fails, but there appears to be no substitute. Thus few people worry about the possibility that tomorrow they may be thrown off the earth because of the failure of the law of gravity. It works today, it worked yesterday, and it has worked for a long time, so that even most philosophers act on the assumption that it will continue to be obeyed.
In Secs. 7.3 to 7.5 this method of constructing hypotheses will be discussed at greater length, including some of its pitfalls.
When a hypothesis has been devised to fit the observed facts, it becomes
possible to apply the rules of formal logic and deduce various consequences.
Logic does not enter science until this stage is reached.
In recent years the study of the principles of deductive logic has led to a revival of interest in this long-dormant subject. These new ideas have been most concisely expressed by means of a symbolic notation; hence the name symbolic logic. This is briefly discussed in Sec. 10.5.
Mathematics and logic are closely related, and in many branches of science forms of mathematics are available which are suitable for the deduction of the consequences of hypotheses. When this is so, much more elaborate and far-reaching deductions become possible because of the great power of mathematical notation and methods, which permit deductions to be made that would be overwhelmingly complex if argued in ordinary language. Nevertheless a sacrifice is usually made when reliance is placed on mathematics, because the existing forms of mathematics are adequate only for simplified cases. For example, much of organic chemistry has been developed with little assistance from mathematics. A13 a consequence the methods of argument which have developed in this field are not exact and certain, but they are applicable to a very wide range of problems quite beyond the reach of more formal procedures.
3.7. The Testing of Hypotheses
In many cases hypotheses are so simple and their consequences so obvious that
it becomes possible to test them directly. New observe......
Si quieren seguir leyendo el libro, se encuentra en la biblioteca del CCMC, o lo pueden adquirir en la editorial Dover .
Regresar al inicio