possible more exact comparison. After analysing some complex whole into its
parts or aspects, we may tentatively connect one of these with another in
order to discover a law of connection, or we may, in imagination, combine
again some of them and so form an idea of what may be common to many
objects or events, or to whole classes of them. Some combinations so
obtained may not correspond to anything that has ever been observed. In
this way analysis and synthesis, even though they are merely mental in the
first instance, prepare the way for experiment, for discovery and
invention.
Imagination, Supposition and Idealisation.
Such order as may be inherent in the phenomena of nature is not obvious
on the face of them. It has to be sought out by an active interrogation of
nature. The interrogation takes the form of making tentative suppositions,
with the aid of imagination, as to what kind of order might prevail in the
phenomena under investigation. Such suppositions are usually known as
hypotheses, and the formation of fruitful hypotheses requires imagination
and originality, as well as familiarity with the facts investigated.
Without the guidance of such hypotheses observation itself would be barren
in science for we should not know what to look for. Mere staring at facts
is not yet scientific observation of them. Hence for science any
hypothesis, provided it can be put to the test of observation or
experiment, is better than none. For observation not guided by ideas is
blind, just as ideas not tested by observations are empty. Hypotheses that
can be put to the test, even if they should turn out to be false, are
called "fruitful"; those that cannot be so tested even if they should
eventually be found to be true, are for the time being called "barren."
Intimately connected with the processes of imagination and supposition is
the process of idealisation, that is, the process of conceiving the ideal
form or ideal limit of something which may be observable but always falls
short, in its observed forms, of the ideal. The use of limiting cases in
mathematics, and of conceptions like those of an "economic man" in science
are examples of such idealisation.
Inference.
This is the process of forming judgements or opinions on the ground of
other judgements or on the evidence of observation. The evidence may be
merely supposed for the sake of argument, or with a view to the further
consideration of the con-sequences, which follow from it. It is not always
easy to draw the line between direct observation and inference. People,
even trained people, do not always realise, e.g., when they pass from the
observation of a number of facts to a generalisation which, at best, can
only be regarded as an inference from them. But the difficulty need not be
exaggerated. There are two principal types of inference, namely deductive
and inductive. Inductive inference is the process of inferring some kind of
order among phenomena from observations made. Deductive inference is the
process of applying general truths or concepts to suitable instances. In
science inductive inference plays the most important role, and the methods
of sciences are mainly instruments of induction or auxiliaries thereto. But
deductive inference is also necessary to science, and is, in fact, a part
of nearly all complete inductive investigations. Still, marked inductive
ability is very rare. There are thousands who can more or less correctly
apply a discovery for one who can make it.
Comparison and Analogy.
Reference has already been made to the importance of the process of
comparison in the mental analysis of observed phenomena. The observation of
similarities and differences, aided by the processes of analysis and
synthesis, is one of the first steps to knowledge of every kind, and
continues to be indispensable to the pursuit of science throughout its
progress. But there are degrees of similarity. Things may be so alike that
they are at once treated as instances of the same kind or class. And the
formulation and application of generalisations of all kinds are based upon
this possibility of apprehending such class resemblances. On the other
hand, there is a likeness, which stops short of such close class likeness.
Such similarity is usually called analogy. The term is applied to
similarity of structure or of function or of relationship, in fact, to
similarity of almost every kind except that which characterises members of
the same class, in the strict sense of the term. And analogy plays very
important part in the work of science, especially in suggesting those
suppositions or hypotheses which, as already explained, are so essential to
scientific research and discovery.
After this brief survey of various mental activities which are more or less
involved in the pursuit of every kind of knowledge, and consequently from
no suitable bases for the differentiation of the various methods of
science, we may now proceed to the consideration of the several scientific
methods properly so called.
Classification.
This may be described as the oldest and simplest of scientific methods.
The observation of similarities between certain things, and classing them
together, marks the earliest attempt to discover some kind of order in the
apparently chaotic jumble of things that confront the human mind. Language
bears witness to the vast number of classifications made spontaneously by
pre-scientific man. For every common noun expresses the recognition of a
class; and language is much older than science. The first classifications
subserved strictly practical purposes, and had reference mainly to the uses
which man could make of the things classified. They were frequently also
based on superficial resemblances, which veiled deeper differences, or were
influenced by superficial differences, which diverted attention from deeper
similarities. But with the growth of the scientific spirit classifications
became more objective or more natural, attention being paid to the
objective nature of the things themselves rather than to their human uses.
Even now scientific classification rarely begins at the beginning, but sets
out from current classifications embodied in language. It has frequent
occasion to correct popular classifications. At the same time it has
difficulties of its own, and more than one science has been held up for
centuries for want of a really satisfactory scheme or classification of the
phenomena constituting its field of investigation. To recognise a class is
to recognise the unity of essential attributes in a multiplicity of
instances; it is a recognition of the one in the many. To that extent it is
a discovery of order in things. And although it is the simplest method of
science, and can be applied before any other method, it is also the
fundamental method, inasmuch as its results are usually assumed when the
other methods are applied. For science is not, as a rule, concerned with
individuals as such, but with kinds or classes. This means that the
investigator usually assumes the accuracy of the classification of the
phenomena, which he is studying. Of course, this does not always turn out
to be the case. And the final outcome of the application of other methods
of science to certain kinds of phenomena may be a new classification of
them.
Inductive and deductive methods.
Below is the summary of contrasts in the major tenets of inductivism and of
Popper's deductivism.. I begin with a caricature of inductivism in the form
of eight theses:
1. Science strives for justified, proven knowledge, for certain truth.
2. All scientific inquiry begins with observations or experiments.
3. The observational or experimental data are organised into a hypothesis,
which is not yet proven (context of discovery).
4. The observations or experiments are repeated many times.
5. The greater the number of successful repetitions, the higher the
probability of the truth of the hypothesis (context of justification).
6. As soon as we are satisfied that we have reached certainty in that
manner we lay the issue aside forever as a proven law of nature.
7. We then turn to the next observation or experiment with which we
proceed in the same manner.
8. With the conjunction of all these proven theories we build the edifice
of justified and certain science.
In summary, the inductivist believes that science moves from the
particulars to the general and that the truth of the particular data is
transmitted to the general theory.
Now we will observe a caricature of Popper's theory of deduc-tivism,
again in the form of eight theses:
1. Science strives for absolute and objective truth, but it can never reach
certainty.
2. All scientific inquiry begins with a rich context of background
knowledge and with the problems within this context and with metaphysical
research programmes.
3. A theory, that is, a hypothetical answer to a problem, is freely
invented within the metaphysical research programme: it explains the
observable by the unobservable.
4. Experimentally testable consequences, daring consequences that is, are
deduced from the theory and corresponding experiments are carried out to
test the predictions.
5. If an experimental result comes out as predicted, it is taken as a value
in itself and as an encouragement to continue with the theory, but it is
not taken as an element of proof of the theory of the unobservable.
