Second, there is the question of what is meant by "knowledge." People claim

to know that the stick is really straight even when it is half-submerged in

water. But, as indicated earlier, if this claim is correct, then knowledge

cannot simply be identical with perception. For whatever theory about the

nature of knowledge one develops, the theory cannot have as a consequence

that knowing something to be the case can sometimes be mistaken or


Third, even if knowledge is not simply to be identified with perception,

there nevertheless must be some important relationship between knowledge

and perception. After all, how could one know that the stick is really

straight unless under some conditions it looked straight? And sometimes a

person who is in pain exhibits that pain by his behaviour; thus there are

conditions that genuinely involve the behaviour of pain. But what are those

conditions? It seems evident that the knowledge that a stick is straight or

that one is in great pain must come from what is seen in certain

circumstances: perception must somehow be a fundamental element in the

knowledge human beings have. It is evident that one needs a theory to

explain what the relationship is--and a theory of this sort, as the history

of the subject all too well indicates, is extraordinarily difficult to


The two problems also differ in certain respects. The problem of man's

knowledge of the external world raises a unique difficulty that some of the

best philosophical minds of the 20th century (among them, Bertrand Russell,

H.H. Price, C.D. Broad, and G.E. Moore) spent their careers trying to

solve. The perplexity arises with respect to the status of the entity one

sees when one sees a bent stick in water. In such a case, there exists an

entity--a bent stick in water--that one perceives and that appears to be

exactly where the genuinely straight stick is. But clearly it cannot be;

for the entity that exists exactly where the straight stick is is the stick

itself, an entity that is not bent. Thus, the question arises as to what

kind of a thing this bent-stick-in-water is and where it exists.

The responses to these questions have been innumerable, and nearly all of

them raise further difficulties. Some theorists have denied that what one

sees in such a case is an existent entity at all but have found it

difficult to explain why one seems to see such an entity. Still others have

suggested that the image seen in such a case is in one's mind and not

really in space. But then what is it for something to be in one's mind,

where in the mind is it, and why, if it is in the mind, does it appear to

be "out there," in space where the stick is? And above all, how does one

decide these questions? The various questions posed above only suggest the

vast network of difficulties, and in order to straighten out its tangles it

becomes indispensable to develop theories.



In accordance with a proposal made above, epistemology, or the logic of

scientific discovery, -should be identified with the theory of scientific

method. The theory of method, in so far as it goes beyond the purely

logical analysis of the relations between scientific statements, is

concerned with the choice of methods—with decisions about the way in which

scientific statements are to be dealt with. These decisions will of course

depend in their turn upon the aim, which we choose from among a number of

possible aims.

Methodology or a scientific method is a collective term denoting the

various processes by the aid of which the sciences are built up. In a wide

sense, any mode of investigation by which scientific or other impartial and

systematic knowledge is acquired is called a scientific method.

What are the rules of scientific method, and why do we need them? Can

there be a theory of such rules, a methodology? The way in which one

answers these questions will largely depend upon one’s attitude to science.

The way in which one answers these questions will largely depend upon one's

attitude to science. Those who, like the positivists, see empirical science

as a system of statements, which satisfy certain logical criteria, such as

meaningfulness or verifiability, will give one-answer. A very different

answer will be given by those who tend to see the distinguishing

characteristic of empirical statements in their susceptibility to

revision—in the fact that they can be criticised,-and superseded by better

ones; and who regard it as their task to analyse the characteristic ability

of science to advance, and the characteristic manner in which a choice is

made, in crucial cases, between conflicting systems of theories.

Such methods, as it was mentioned above, are of two principal types—

technical and logical. A technical or technological method is a method of

manipulating the phenomena under investigation, measuring them with

precision, and determining the conditions under which they occur, so as to

be able to observe them in a favourable and fruitful manner. A logical

method is a method of reasoning about the phenomena investigated, a

method of drawing inferences from the conditions under which they occur, so

as to interpret them as accurately as possible. The term "scientific

method" in the first instance probably suggests to most minds the technical

methods of manipulation and measurement. These technical methods are very

numerous and they are different in the different sciences. Few men ever

master the technical methods of more than one science or one group of

closely connected sciences. An account of the most important technical

methods is usually given in connection with the several sciences. It would

be impossible, even if it were desirable, to give a useful survey of all,

or even of the most important, technical methods of science. It is

different with the logical methods of science. These methods of reasoning

from the available evidence are not really numerous, and are essentially

the same in all the sciences. It is both possible and desirable to survey

them in outline. Moreover, these logical methods of science are in a very

real sense the soul of the technical methods.

In pure science the technical methods are not regarded as an end in

themselves, but merely as a means to the discovery of the nature of the

phenomena under investigation. This is done by drawing conclusions from the

observations and experiments, which the technical methods render possible.

Sometimes the technical methods make it possible for the expert

investigator to observe and measure certain phenomena, which otherwise

could either not be observed and measured at all, or not so accurately.

Sometimes they enable him so to determine the conditions of their

occurrence that he can draw reliable conclusions about them, instead of

having to be content with unverified conjectures. The highly speculative,

mainly conjectural character of early science was no doubt due entirely to

the lack of suitable technical methods and scientific instruments. In a

sense; therefore, it may be said that the technical methods of science are

auxiliary to the logical methods, or methods of reasoning. And it is these

methods that are to be considered in the present article. The technical

methods of science, as ought to be clear from the preceding remarks, are of

first rate importance, 'and we have not the remotest desire to underrate

them; but it would be futile to attempt to survey them here.

Some Mental Activities Common to All Methods.

There are certain mental activities, which are so absolutely

indispensable to science that they are practically always employed in

scientific investigations, however much these may vary in other respects.

In a wide sense these mental activities might consequently be called

methods of science, and they are frequently so called. But this practice is

objectionable, because it leads to cross division and confusion. What is

common to all methods should not itself be called a method, for it only

encourages the effacing of important differences; and when there are many

such factors common to all the methods, or most of them, confusion is

inevitable. When the mental activities involved are more or less common to

the methods, these must be differentiated by reference to other, variable

factors—such as the different types of data from which the inferences are

drawn, and the different types of order sought or discovered in the

different kinds, of phenomena investigated— the two sets of differences

being, of course, intimately connected. The mental activities referred to

are the following: Observation (including experiment), analysis and

synthesis, imagination, supposition and idealisation, inference (inductive

and deductive), and comparison (including analogy). A few words must be

said about each of these; but no significance should be attached to the

order in which they are dealt with.

Observation and Experiment.

Observation is the act of apprehending things and events, their

attributes and their concrete relationships. From the point of view of

scientific interest two types of observation may be distinguished, namely:

(1) The bare observation of phenomena under conditions which are beyond the

control of the investigator, and (2) experiment, that is, the observation

of phenomena under conditions controlled by the investigator. What

distinguishes experiment from bare observation is control over what is

observed, not the use of scientific apparatus, nor the amount of trouble

taken. The mere use of telescopes or microscopes, etc., even the selection

of specially suitable times and places of observation, does not constitute

an experiment, if there is no control over the phenomenon observed. On the

other hand, where there is such control, there is experiment, even if next

to no apparatus be used, and the amount of trouble involved be negligible.

The making of experiments usually demands the employment of technical

methods, but the main interest centres in the observations made possible

thereby. The great advantage of experiment over bare observation is that it

renders possible a more reliable analysis of complex phenomena, and more

reliable inferences about their connections, by the variation of

circumstances, which it effects. Its importance is so great that people

commonly speak of "experimental method." The objection to this is that

experiment may be, and is, used in connection with various methods, which

are differentiated on other, and more legitimate, grounds. To speak of a

method of observation is even less permissible, seeing that no method can

be employed without it.

Analysis and Synthesis.

The phenomena of nature are very complex and, to all appearances, very

confused. The discovery of any kind of order in them is only rendered

possible by processes of analysis and synthesis. These are as essential to

all scientific investigation as is observation itself. The process of

analysis is helped by the comparison of two or more objects or events that

are similar in some respects and different in others. But while comparison

is a necessary instrument of analysis, analysis, in its turn, renders

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


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.


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.


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


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


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.

6. As soon as an experimental result comes out against the prediction and

we arc satisfied that it is not a blunder we decide to consider the theory

falsified, but only tentatively so.

7. With this we gain a deeper understanding of our problem and proceed to

invent our next hypothetical theory for solving it, which we treat again in

the same way.

8. The concatenation of all these conjectures and refutations constitutes

the dynamics of scientific progress, moving ever closer to the truth, but

never reaching certainty.

In summary, the Popperian deductivist believes that science moves from

the general to the particulars and back to the general— a process without

end. Let me inject a metaphor. I might liken the Popperian view of science

to that of a carriage with two horses. The experimental horse is strong,

but blind. The theoretical horse can see, but it cannot pull. Only both

together can bring the carriage forward. And behind it leaves a track

bearing witness to the incessant struggle of trial and error.

The Deductive-inductive Method.

Just as money makes money, so knowledge already acquired facilitates the

acquisition of more knowledge. It is equally evident in the case of the

method, which will now engage our attention. The progress of science, and

of knowledge generally, is frequently facilitated by supplementing the

simpler inductive methods by deductive reasoning from knowledge already

acquired. Such a combination of deduction with induction, J. S. Mill called

the "Deductive Method," by which he really meant the "Deductive Method of

Induction." To avoid the confusion of the "Deductive Method" with mere

deduction, which is only one part of the whole method, it is better to

describe it as the "Deductive-Inductive Method" or the "Inductive-Deductive

Method." Mill distinguished two principal forms of this method as applied

to the study of natural phenomena, -namely, (1) that form of it in which

deduction precedes induction, and (2) that in which induction precedes

deduction. The first of these (1) he called the "Physical Method"; the

second (2) he called the "Historical Method."

These names are rather misleading, inasmuch as both forms of the method are

frequently employed in physics, where sometimes, say in the study of light,

mathematical (i.e., deductive) calculations precede and suggest physical

experiments (i.e., induction), and sometimes the inductive results of

observation or experiment provide the occasion or stimulus for mathematical

deductions. In any case, the differences in order of sequence are of no

great importance, and hardly deserve separate names. What is of importance

is to note the principal kinds of occasion, which call for the use of this

combined method. They are mainly three in number: (1) When an hypothesis

cannot be verified (i.e., tested) directly, but only indirectly; (2) when

it is possible to systematise a number of already established inductions,

or laws, under more comprehensive laws or theories; (3) when, owing to the

difficulties of certain problems, or on account of the lack of sufficient

and suitable instances of the phenomena under investigation, it is

considered desirable either to confirm an inductive result by independent

deductive reasoning from the nature of the case in the light of previous

knowledge, or to confirm a deductive conclusion by independent inductive


An example of each of these types may help to make them clear. (1) When

Galileo was investigating the law of the velocity of falling bodies he

eventually formed the hypothesis that a body starting from rest falls with

a uniform acceleration, and that its velocity varies with the time of its

fall. But he could not devise any method for the direct verification of

this hypothesis. By mathematical deduction, however, he arrived at the

conclusion that a body falling according to his hypothetical law would fall

through a distance proportionate to the time of its fall. This consequence

could be tested by comparing the distances and the time of falling bodies,

which thus served as an indirect verification of his hypothesis. (2) By

inductions from numerous astronomical observations made by Tycho Brahe and

himself, Kepler discovered the three familiar laws called by his name,

namely, (a) that the planets move in elliptic orbits which have the sun for

one of their foci; (6) that the velocity of a planet is such that the

radius vector (i.e., an imaginary line joining the moving planet to the

sun) sweeps out equal areas in equal periods of time; and (c) that the

squares of the periodic times of any two planets (that is, the times which

they take to complete their revolutions round the sun) are proportional to

the cubes of their mean distances from the sun. These three laws appeared

to be quite independent of each other. But Newton systematised them all in

the more comprehensive induction, or theory, of celestial gravitation. He

showed that they could all be deduced from the one law that the planets

tend to move towards each other with a force varying directly with the

product of their masses, and inversely with the square of the distances

between them. (3) H. Spencer, by comparing a number of predominantly

industrial States and also, of predominantly military States, ancient and

modern, inferred inductively that the former type of State is democratic

and gives rise to free institutions, whereas the latter type is

undemocratic and tends to oppression. As the sparse evidence hardly

permitted of a rigorous application of any of .the inductive methods,

Spencer tried to confirm his conclusion by deductive reasoning from the

nature of the case in the light of what is known about the human mind. He

pointed out that in a type of society, which is predominantly industrial,

the trading relations between individuals are the predominant relations,

and these train them to humour and consider others. The result is a

democratic attitude in all. In a State, which is predominantly military,

the relations which are most common among its members are those of

authority, on the one part, and of subordination on the other. The result

is the reverse of a democratic atmosphere.


In conclusion, I would like to discuss the relation of epistemology to

other branches of philosophy. Philosophy viewed in the broadest possible

terms divides into many branches: metaphysics, ethics, aesthetics, logic,

philosophy of language, philosophy of mind, philosophy of science, and a

gamut of others. Each of these disciplines has its special subject matter:

for metaphysics it is the ultimate nature of the world; for ethics, the

nature of the good life and how people ideally ought to comport themselves

in their relations with others; and for philosophy of science, the

methodology and results of scientific activity. Each of these disciplines

attempts to arrive at a systematic understanding of the issues that arise

in its particular domain. The word systematic is important in this

connection, referring, as explained earlier, to the construction of sets of

principles or theories that are broad-ranging, consistent, and rationally

defensible. In effect, such theories can be regarded as sets of complex

claims about the various matters that are under consideration.

Epistemology stands in a close and special relationship to each of these

disciplines. Though the various divisions of philosophy differ in their

subject matter and often in the approaches taken by philosophers to their

characteristic questions, they have one feature in common: the desire to

arrive at the truth about that with which they are concerned--say, about

the fundamental ingredients of the world or about the nature of the good

life for man. If no such claims were asserted, there would be no need for

epistemology. But, once theses have been advanced, positions staked out,

and theories proposed, the characteristic questions of epistemology

inexorably follow. How can one know that any such claim is true? What is

the evidence in favour of (or against) it? Can the claim be proven?

Virtually all of the branches of philosophy thus give rise to

epistemological ponderings.

These ponderings may be described as first-order queries. They in turn

inevitably generate others that are, as it were, second-order queries, and

which are equally or more troubling. What is it to know something? What

counts as evidence for or against a particular theory? What is meant by a

proof? Or even, as the Greek Sceptics asked, is human knowledge possible at

all, or is human access to the world such that no knowledge and no

certitude about it is possible? The answers to these second-order questions

also require the construction of theories, and in this respect epistemology

is no different from the other branches of philosophy. One can thus define

or characterise epistemology as that branch of philosophy, which is

dedicated to the resolution of such first- and second-order queries.


1. A preface to the logic of science, by Peter Alexander, Sheed and Ward,

London and New York, 1963.

2. Popper selections, edited by Dawid Miller, Princeton University press,


3. The critical approach to science and philosophy, edited by Mario Bunge,

The free press of Glencoe Collier- Magmillan limited, London, 1964.

4. Britannica encyclopaedia, 1948.

5. Logic without metaphysics, by Ernest Nagel, Glencoe, Ill..: Free Press,


6. "Epistemology, History of,", by D.W. Hamlyn. The Encyclopaedia of


7. Introduction to Objectivist Epistemology, expanded 2nd ed., by Ayn Rand,

New York: Penguin Group, 1990.

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