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
situation.
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.
3.5. Hypothesis
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.
3.6. Deduction
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......
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