3

Reasoning and evidence

In this chapter you will:
consider the inductive method of argument
examine the place of experiments in science
consider what counts as valid science.

In this chapter we shall look at a basic approach to science that

developed from the seventeenth century and which may still be
used to some extent to distinguish between genuine science and
pseudoscience. We will be concerned mainly with the inductive
method of gaining knowledge, and the impact it had on scientific
methodology. The key feature here is the recognition that all
claims to scientific knowledge must be supported by evidence from
observation and/or experiment.
Subsequent chapters will then consider the debates about how
scientific theories are developed, assessed and (if found inadequate)
replaced, and the more general problem of scientific realism – in
other words, whether scientific statements describe reality or just our
experience of reality. A key question in all this is whether scientific
theories can ever be proved to be ‘correct’, in any absolute sense, by
the evidence that supports them, and – if not – how we judge between
competing theories.
The rise of modern science brought with it an ideal about achieving
certainty through reasoning from evidence, but we shall see that,
although for some it may remain an ideal, it is very difficult (perhaps
impossible) to achieve fully in practice.

3. Reasoning and evidence 49

Observation and objectivity
Observation has always been the starting point for scientific enquiry.
Before any theory is put together, before even the basic questions
have been asked, it is the fact that people have observed the natural
world and wondered why it is as it is that has been the impetus
behind science. Fundamental to the philosophy of science is the
discussion of how you move from observations and experimental
evidence to theories that attempt to explain what has been observed.
Caution is a keynote in making scientific claims; everything should be
backed up by sound theoretical reasoning and experimental evidence.
Here, for example, is a statement made by Professor Neil Turok
in 1998, in a newspaper article describing his work with Professor
Stephen Hawking on the early states of the universe. It contains two
very wise notes of caution:
First, the discovery is essentially mathematical, and is formulated in
the language of the theory of general relativity invented by Albert
Einstein to describe gravity, the force which shapes the large-
scale structure of the universe. It is hard to describe such things in
everyday terms without being misleading in some respects – the
origin of our universe was certainly not an everyday event.

The second important warning I have to give is that the theories we

have built of a very early universe before the Big Bang are not yet
backed up by experiment. We often talk as if they are real because
we take them very seriously, but we certainly have no special
oracular insight to the truth. What we are doing is constructing
hypotheses which conform to the very rigorous standard of
theoretical physics. But we are under no illusions that, until our
theories are thoroughly supported by detailed experimental and
observatory results they will remain speculative.
The Daily Telegraph, 14 March 1998

Notice two important points here:

1 It is not always possible to describe things in language which will
enable a non-scientist to get an accurate, imaginative grasp of
what is being discussed. Some things are so extraordinary that
they make sense only in terms of mathematical formulae.

50
 2 Any hypothesis, however carefully put together based on the best
existing theories, must remain provisional until backed up by
observations or experimental evidence.
When Galileo argued in favour of the Copernican view of the
universe, his work was challenged by the more conservative thinkers
of his day, not because his observations or calculations were found to
be wrong, but because his argument was based on those observations
rather than on a theoretical understanding of the principles that
should govern a perfectly ordered world.
The other key difference between the experiments and observations
carried out by Galileo and the older Aristotelian view of reality
was that Galileo simply looked at what happened, not at why it
happened. Observation comes prior to explanation, but it should also
take precedence over any assumptions that the observer may have.
In other words, the act of observing should be done in as objective
fashion as possible.
We have already seen (in Chapter 2) the need for objectivity featured
in the work of Francis Bacon, who argued that knowledge should
be based on evidence. His ‘idols’ of habit, prejudice and conformity,
and his insistence that one should accept evidence even where it did
not conform to one’s expectations, mark a clear shift to what became
established as the scientific method.
In other words, we should try to set aside all personal preferences
and prejudices when observing. But this, of course, is impossible;
everything we observe depends on our senses and their particular
limitations; everything is seen from a particular perspective. The
basic problem with scientific observation is that, as an ideal, it
should be absolutely objective, but in reality it will always be
limited and prejudiced in some way. Nevertheless, the challenges
of the scientific method is to try to eliminate all personal and
subjective influences.

Insight
More controversially, as we shall see later, it may involve attempting to set
aside the whole web of established knowledge, in order to avoid slotting a
new piece of evidence into an existing theoretical mould.

3. Reasoning and evidence 51

 EXPERIENCE AND KNOWLEDGE
Epistemology is the philosophical term for the study of the theory of
knowledge. Some philosophers have argued that all knowledge starts
with the operations of the mind, pointing to the ambiguous nature of
sense experience; others (empiricists) have argued that everything we
know is based on experience.
John Locke (1632–1704) was an empiricist who argued that
everything we know comes from sense experience, and that the mind
at birth is a blank sheet. Locke divided the qualities we perceive in an
object into two categories – primary and secondary:
! primary qualities – these belonged to the object itself, and
included its location, its dimensions and its mass. He considered
that these would remain true for the object no matter who
perceived it.
! secondary qualities – these depended upon the sense faculties
of the person perceiving the object, and could vary with
circumstances. Thus, for example, the ability to perceive colour,
smell and sound depends upon our senses; if the light changes,
we see things as having a different colour.
Science was therefore concerned with primary qualities. These it
could measure, and seemed to be objective, as opposed to the more
subjective secondary ones.

Comment
Imagine how different the world would be if examined only in
terms of primary qualities. Rather than colours, sounds, tastes,
you would have information about dimensions. Music would be
a digital sequence, or the pulsing of sound waves in the air.
A sunset would be information about wavelengths of light and
the composition of the atmosphere.

In general, science deals with primary qualities. The personal

encounter with the world, taking in a multitude of experiences
simultaneously, mixing personal interpretation and the
limitations of sense experience with whatever is encountered as
external to the self, is the stuff of the arts, not of science.

52
 Science analyses, eliminates the irrelevant and the personal,
and finds the relationship between the primary qualities of
objects.
Setting aside the dominance of secondary qualities in
experience, along with any sense of purpose or goal, was
essential for the development of scientific method – but
it was not an easy step to take. The mechanical world of
Newtonian physics was a rather abstract and dull place – far
removed from the confusing richness of personal experience.

The more we look at the way information is gathered and described, the
clearer it becomes that there will always be a gap between reality and
description. Just as the world changes depending upon whether we are
mainly concerned with primary or secondary qualities, so the pictures
and models we use to describe it cannot really be said to be ‘true’, simply
because we have no way to make a direct comparison between the
description and model we use and the reality to which it points. Our
experience can never be unambiguous, but the methods developed by
science aimed to eliminate personal factors as much as possible.

Are instruments objective?

Even instruments can cause problems. For example, using
his telescope, Galileo saw that there were mountains on the
Moon, a discovery that challenged the received tradition that
the heavenly bodies were perfect spheres. However, this is not
simply a triumph of evidence over metaphysical prejudice,
since – from the drawings Galileo made – we know that some
of his observations were wrong. Some of what he perceives
as mountains must have been the result of distortions in the
glass of his telescope.
Hence, the observations or experimental data used by
science are only going to be as good as the equipment and
instruments used to gather them.

3. Reasoning and evidence 53

As we shall see, the recognition that we cannot simply observe and
describe came to the fore in the twentieth century, particularly in
terms of subatomic physics, since it seemed impossible to disentangle
what was seen from the action of seeing it.

Induction
The rise of science was characterized by a new seriousness with
which evidence was gathered and examined in order to frame general
theories. There are two very different forms of argument:
! A deductive argument starts with a general principle and deduces
other things from it. So, for example, if you assume that all
heavenly bodies must be perfect spheres, a logical deduction is
that there cannot be mountains on the Moon.
! An inductive argument starts with observations or experimental
results and on the basis of these sets about framing general
principles that take them into account. Thus, observing
mountains on the Moon, you conclude that not all heavenly
bodies are perfect spheres.
It was the inductive form of argument – generally termed ‘inductive
inference’ – that became a distinguishing feature of modern science.
Bertrand Russell described the ‘principle of induction’ by saying
that the more two things are observed together, the more it is
assumed that they are causally linked. If I perform an experiment
only once, I may be uncertain of its results. If I perform it a
hundred times, with the same result each time, I become convinced
that I will obtain that result every time I perform it. Thus far, this
sounds no more than common sense, but it raises many problems,
for it is one thing to anticipate the likely outcome of an experiment
on the basis of past experience, quite another to say that the past
experience proves that a certain result will always be obtained, as
we shall see later.

54
 The black swan
There is a classic example of induction which makes the
situation so clear that it is always worth repeating…

Someone from Europe, having seen many swans, all of them

white, comes to the conclusion that ‘all swans are white’ and
anticipates that the next swan to appear will also be white.
That generalization is confirmed with every new swan that is
seen. Then, visiting Australia, the person comes across a black
swan and has to think again.
The generalized conclusion from seeing the white swans is
as example of what is termed ‘enumerative induction’ – as
the numbers stack up, so the conclusion seems more and
more certain. But the key thing to recognize is that, while the
evidence suggests that all swans are white, it cannot prove
that all swans are white, as the first encounter with a black
swan shows. Of course, this example is clear because 1) swans
are easily distinguished from other birds and 2) adult swans
come in suitably contrasting colours. In most other situations
we may find that there is doubt about the classification of the
thing we are examining (improbably: ‘Is it a swan or could it be
a duck or a goose?’) and the claim to see an anomaly might
not be so black or white!

THE INDUCTIVE METHOD

The inductive approach to knowledge is based on the impartial
gathering of evidence, or the setting up of appropriate experiments,
such that the resulting information can be examined and conclusions
drawn from it. It assumes that the person examining it will come
with an open mind, and that theories framed as a result of that
examination will then be checked against new evidence.

3. Reasoning and evidence 55

This is sometimes presented as the general ‘scientific method’,
although we need to remember that science works in a number of
different ways. In practice, induction works like this:
! Evidence is gathered, and irrelevant factors are eliminated as far
as possible.
! Conclusions are drawn from that evidence, which lead to the
framing of an hypothesis.
! Experiments are devised to test out the hypothesis, by seeing if it
can correctly predict the results of those experiments.
! If necessary, the hypothesis is modified to take into account the
results of those later experiments.
! A general theory is framed from the hypothesis and its related
experimental data.
! That theory is then used to make predictions, on the basis of
which it can be either confirmed or disproved.

Example
The final step in this process is well illustrated by the key
prediction that confirmed Einstein’s theory of General
Relativity. Einstein argued that light would bend within a strong
gravitational field, and therefore that stars would appear to
shift their relative positions when the light from them passed
close to the Sun. This was a remarkably bold prediction to
make. It could be tested only by observing the stars very
close to the edge of the Sun as it passed across the sky, and
by comparing this with their position relative to other stars
once the light coming from them was no longer affected by
the Sun’s gravitational pull. But the only time when they could
be observed so close to the sun was during an eclipse. Teams
of observers went to Africa and South America to observe
an eclipse in 1919. The stars did indeed appear to shift their
positions to a degree very close to Einstein’s predictions, thus
confirming the theory of General Relativity.

Confirmed scientific theories are often referred to as ‘laws of nature’

or ‘laws of physics’, but it is important to recognize exactly what

56
is meant by ‘law’ in this case. This is not the sort of law that has to
be obeyed. A scientific law cannot dictate how things should be;
it simply describes them. The law of gravity does not require that,
having tripped up, I should adopt a prone position on the pavement –
it simply describes the phenomenon that, having tripped, I fall.
Hence, if I trip and float upwards, I am not disobeying a law, it
simply means that I am in an environment (e.g. in orbit) in which the
phenomenon described by the ‘law of gravity’ does not apply, or that
the effect of gravity is countered by other forces than enable me to
float upwards. The ‘law’ cannot be ‘broken’ in these circumstances,
only be found to be inadequate to give a complete description of
what is happening.

A CLASSIC CRITIQUE OF EMPIRICAL EVIDENCE

The philosopher David Hume pointed out that scientific laws were only
summaries of what had been experienced so far. The more evidence that
confirmed them, the greater their degrees of probability, but no amount
of evidence could lead to the claim of absolute certainty.
Hume argued that the wise man should always proportion his belief
to the evidence available; the more evidence in favour of something
(or balanced in favour, where there are examples to the contrary),
the more likely it is to be true. He also pointed out that, in assessing
evidence, one should take into account the reliability of witnesses,
and whether they had a particular interest in the evidence they give.
Like Francis Bacon, Hume sets out basic rules for the assessment of
evidence, with the attempt to remove all subjective factors or partiality,
and to achieve as objective a review of evidence as is possible.
What Hume established (in his Enquiry Concerning Human
Understanding, section 4) was that no amount of evidence could,
through the logic of induction, ever establish the absolute validity of
a claim. There is always scope for a counter-example, and therefore
for the claim to fail.

Insight
This gets to the heart of the ‘problem of induction’ and raises the most
profound problems for science since it challenges the foundations of the
scientific method. Many of the later discussions about how to deal with
competing theories, or the limitations of scientific claims, stem from this basic
problem – evidence cannot yield absolute certainty.

3. Reasoning and evidence 57

With hindsight, that might seem a very reasonable conclusion to draw
from the process of gathering scientific evidence, but in Hume’s day –
when scientific method was sought as something of a replacement for
Aristotle in terms of a certainty in life – it was radical. It was this apparent
attack on the rational justification of scientific theories that later ‘awoke’
the philosopher Kant from his slumbers. He accepted the force of Hume’s
challenge, but could not bring himself to deny the towering achievements
of Newton’s physics, which appeared to spring from the certainty of
established laws of nature. It drove Kant to the conclusion that the
certainty we see in the structures of nature (particularly in the ideas of
time, space and causality) are there because our minds impose such
categories upon the phenomena of our experience.
In many ways, the distinction Kant made between the ‘phenomena’
of our experience and the ‘noumena’ of things as they are in
themselves, with the latter unknowable directly, continues to be
relevant. I cannot know an electron as it is in itself, but only as it
appears to me through the various models or images by which I
try to understand things at the subatomic level. I may understand
something in a way that is useful to me, but that does not mean that
my understanding is – or can ever be – definitive.
John Stuart Mill (1806–73), a philosopher best known for his work
on freedom and on utilitarian ethics, gave an account of how we
go about using inductive reasoning in his book A System of Logic,
Ratiocinative and Inductive (1843), using the principles of similarity
and difference. Broadly, the argument works along these lines:

Suppose I want to examine why it is that people contract a

particular illness…
I look at all the evidence about that incidence of that illness to
see if there are any common antecedent factors that might have
been its cause. Do they all eat a particular diet? Do they smoke?
Do they come from a particular part of the world? Do they all use
the same source of drinking water? In other words, I am looking for
similarities in the background of the cases I am examining.
But not all of those similarities will be relevant. The fact that they
are all human beings need not be taken into account, because that’s
equally shared by those who do not have the illness. But perhaps

58
 one might look at their racial group or their age. If a factor is not
common to the group as a whole, it is unlikely to be relevant.
Equally, I can examine differences. Given a number of people, only one
of whom has the illness I am examining, I can look for differences in
their background. If I find something about the person with the illness
that does not apply to all of those who have not contracted it, that
becomes a likely cause. If all the circumstances except one are held in
common, then that one is the cause of the illness.

Insight
The problem, of course, is that you seldom have a situation where you can be
sure that there is only one difference in circumstances, and therefore that you
have found the cause of what you are examining. The result may be brought
about by a factor you have not yet thought of checking, or by a particular
arrangement of otherwise common circumstances.

It will be clear by now that this kind of reasoning can never give
certainty, but only an increasingly high degree of probability. There is
always going to be the chance that some new evidence will show that
the original hypothesis, upon which a theory is based, was wrong. Most
likely, it is shown that the theory only applies within a limited field,
and that in some unusual set of circumstances it breaks down. Even
if it is never disproved, or shown to be limited in this way, a scientific
theory that has been developed using this inductive method, is always
going to be open to the possibility of being proved wrong. Without that
possibility, it is not scientific. This is the classic problem of induction –
no amount of evidence will ever be enough to prove the case.
In an example in his Problems of Philosophy (1952), Bertrand
Russell gives a characteristically clear and entertaining account of the
problem of induction. Having explained that we tend to assume that
what has always been experienced in the past will continue to be the
case in the future, he introduces the example of the chicken which,
having been fed regularly every morning, anticipates that this will
continue to happen in the future. But, of course, this need not be so:
The man who has fed the chicken every day throughout its life at last
wrings its neck instead, showing that more refined views as to the
uniformity of nature would have been useful to the chicken.
Bertrand Russell, Problems of Philosophy (1952)

3. Reasoning and evidence 59

 GOODMAN’S ‘NEW RIDDLE’
An important modern discussion of the problem of induction was
set out by Professor Nelson Goodman of Harvard in 1955, in his
influential book Fact, Fiction and Forecast, and the examples he gave
(e.g. ‘All ravens are black’ and the colour ‘grue’) are frequently cited
in other books.
Goodman takes Hume’s view that there are no necessary connections
between matters of fact. Rather, experiencing one thing following
another in a regular pattern leads us to a habit of mind in which
we see them associated and therefore to claim that one causes the
other. Everything is predicted on the basis of past regularity, because
regularity has established a habit.
We establish general rules on the basis of particulars that we
experience, and those rules are then used as the basis for inference –
in other words, observation of particular events lead to a rule, and
the rule then leads to predictions about other events. The important
thing is to realize that the past can place no logical restrictions on the
future. The fact that something has not happened in the past does not
mean that it cannot happen in the future.
Notice the circularity in the way induction is used – rules depend on
particulars and the prediction of particulars depends on rules. We
justify the ‘rules of induction’ by saying that they are framed on the
basis of successful induction. That’s fine for practical purposes, but
it does not give any independent justification for predictions about
future events. It works because it works; but that does not mean that
it has to work. Goodman comments:
A rule is amended if it yields an inference we are unwilling to
accept; an inference is rejected if it violates a rule we are unwilling
to reject.
Nelson Goodman, Fact Fiction and Forecast (4th edn), page 64

The only justification therefore lies in the apparent agreement

between rules and inferences: if a rule yields acceptable inferences, it
is strengthened. The crucial question, according to Goodman, is not
how you can justify a prediction, but how you can tell the difference
between valid and invalid predictions.
He makes the important distinction between ‘law-like’ statements
and accidental statements. If I use a particular example in order

60
to support an hypothesis, that hypothesis must take the form of a
general law (whether it is right or not is another matter). To use his
examples:
! I can argue from the fact that one piece of copper conducts
electricity to the general principle that all copper conducts
electricity.
! But I cannot argue from the fact that one man in a room is a
third son to the hypothesis that every man in the room is a third
son. Being a third son in this situation is just something that
happens to be the case in this instance – it is not a general feature
of humankind, in the way that conducting electricity is a general
feature of copper.
Here is the famous problem of ‘grue’:
! All emeralds examined before time ‘t’ are green – therefore you
reach the conclusion that all emeralds are green.
! But suppose you use the term ‘grue’ for all things examined up to
time ‘t’ that are green, and all other things that are blue.
! In this case, up to time ‘t’, all emeralds are both green and grue;
after ‘t’ an emerald could only be grue if it was in fact blue.
! Now the problem is that, up to time ‘t’, our usual approach to
induction confirms ‘all emeralds are green’ and ‘all emeralds are
grue’ equally – and yet we know that (after time ‘t’) the first is
going to be true and the second false. How, up to that point, can
we decide between them?

In other words
From the standpoint of the inductive method, there is, prior
to time ‘t’, no way of deciding between emeralds being green
and emeralds being ‘grue’ – both, on the evidence, are equally
likely. But we know, of course, that one is very soon going
to be wrong and the other right. Hence, there is a major
weakness in the use of induction in order to predict what will
be the case in the future.

Now the key feature here is that an ‘accidental hypothesis’ (unlike a

law-like hypothesis) has some restriction in terms of time or space.

3. Reasoning and evidence 61

In other words, it cannot be generalized. The problem with ‘grue’ is
that it has a temporal restriction, in that it means one thing before
a particular time and something else after it. The new riddle of
induction is not so much Hume’s problem about how you justify
general laws in terms of individual cases, but how you tell those
hypotheses that can correctly be generalized from particular instances
and those which cannot.
Let us consider one final example to illustrate the problem of
induction:
! Can induction prove the statement ‘All planets with water
flowing on their surface are likely to support life’?
! We know, in the case of Earth, that it is correct. But is that a
general feature of planets of a certain size and distance from their
suns, or is it simply an accidental feature of our own planet?
The big issue is that science looks for general features and
principles, which have to be abstracted out of the particulars in
which we encounter them. We have encountered life on only one
planet – our own. But we cannot yet know whether that is an
accident, and therefore possibly unique, or whether it is a general
feature of planets of certain types. If we discover water in liquid
form on another planet, but do not discover life there, the statement
is disproved; if we do also find life, the statement is strengthened,
but only to the extent that there are two actual examples, not that
all such planets support life.

A mathematical universe
It is one thing to observe nature, another to explain it, and one of
the key components in the explanations given by scientist in the
seventeenth and eighteenth centuries was mathematics. Galileo
thought that the book of nature was written in the language of
mathematics, but this was not a new idea, for Pythagoras (570–497
BCE) had argued that everything could be given an explanation
in terms of mathematics. Even the title of Newton’s most famous
book is Philosophiae naturalis principia mathematica – an attempt
to understand the workings of nature on mathematical principles.
Work in mathematics thus provided the background to much of the
advancement of science in the seventeenth and eighteenth centuries.

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 ABSTRACTING FROM NATURE
It is important to recognize the nature of mathematics and the very
radical abstraction that it involves. Galileo, Descartes, Huygens and
Newton all produced formulae. In other words, they were seeking
to create a mathematical and abstract way of summing up physical
phenomena, using mathematics to express patterns seen in nature.
That it should be possible for an abstract formula to correspond
to nature was a fundamental assumption made by those involved
in the emerging sciences. Beneath it lay the deeper assumption that
the world is a predictable and ordered place. Escaping from the
earlier era of crude superstition and magic, they saw themselves
emerging into a world where reason and evidence would triumph.
But reason, in its purest form, is seen in logic and mathematics,
and it was therefore natural to expect that the world would be, in
principle, comprehensible in terms of ‘laws of nature’ which, with
mathematical precision, would determine the movement of all things.
The result of this was that the science produced in this period was
not about what is experienced – with all its mixtures of sensations,
beauty, sounds, etc. – but the abstract formulae by which such things
could be understood and predicted. Phenomena were thus ‘reduced’
to their mathematically quantifiable components.
We have already explored this briefly in looking at John Locke’s
distinction between primary and secondary qualities. Fully aware
that colour, sound and taste were obviously linked to the human
sense organs, he called them ‘secondary’ qualities. The primary
ones were mass, location and number – exactly those things that
can be measured and considered mathematically. By the end of
the seventeenth century science thought of ‘real’ nature as silent,
colourless and scentless, an interlocking network of material bodies,
whose activities could be quantified, analysed and expressed in the
form of scientific and mathematical laws.
Notice how abstract the very concept of number is. I see three
separate objects before me and describe them as being ‘three’. Yet
there is nothing in the description of each of them that has the
inherent quality of ‘threeness’. ‘Three’ is a purely abstract term, used
in order to sum up a particularly useful feature of that experience.
Thus, if I am receiving money, it is the number on the banknote that
is of prime importance; its colour or the quality of its paper is of

3. Reasoning and evidence 63

less significance. On the other hand, in a collection of green objects,
a dollar bill might be quite in place, its numerical value of little
significance.
The key thing to remember here is that mathematics is an abstraction,
not a reality. A key feature of seventeenth-century science was
that the whole scheme of highly abstract reasoning was mistaken
for reality itself. Hence it was given an ‘objectivity’ that led to the
assumption that, once all ‘laws’ had been formulated, there would
be nothing left to discover. With the twentieth century and the
recognition of the validity of different and even conflicting theories,
the attempt to ‘objectify’ this abstraction process was recognized to
be limited.

Insight
Once you identify ‘reality’ with mathematical formulae or the theories
that science abstracts from experience or experimental data, then the
world appears to be a mathematically controlled and determined machine.
But reality is not science; reality is what science seeks to explain, and our
explanations will always be limited, open to be challenged by new ideas and
theories.

Experiments
At several points so far we have recognized that scientific evidence
comes from experiments as well as from observations. In particular,
once a theory has been formulated, it is important to set about
finding experiments that will either confirm or refute it.
There are two fundamentally important features of scientific
experiments:

1 THE ISOLATION OF SIGNIFICANT VARIABLES

Experiments create an artificial situation in which, as far as possible,
all extraneous influences are eliminated, so that the investigator can
focus on and measure a single or small number of variables. The
more delicate the thing that the experiment is to measure, the more
stringent are the safeguards to eliminate external factors. Thus, for
example, the experiment to test the presence of the most elusive
neutrinos passing through the Earth was conducted using a tank of

64
absolutely pure water buried deep below the surface of the Earth, far
from all possible sources of interference.
To illustrate the importance of isolating significant variables, let us
take as an example the experimental testing of a new drug. Suppose
only those patients who are most seriously ill are given the new
drug, and those with a milder condition are given more conventional
treatment. The results might well show that, statistically, more
people die after taking the new drug. This would not be a valid
experiment however, because there is the obvious intrusion of an
unwanted variable – namely the severity of the illness. In order for
the experiment to be accurate, it would be necessary to make sure
that two groups of patients were identified, each having the same mix
in terms of age, sex and severity of illness. One group could then be
given the new drug and the other would receive either no drug at all,
or some more conventional treatment.
The result of that experiment might be to say that the new drug
produced X per cent increase in life expectancy. In other words,
all other things being equal, this is the benefit of the drug. If it is
subsequently found that there were all sorts of other factors of which
those conducting the experiment were unaware, then the value of the
experiment would be severely reduced.

Insight
No experiment can ever show the whole situation; if it did, it would have to
be as large and complex as the universe. Experimental evidence is therefore
highly selective, and may reflect the assumptions of the scientist. This, as we
shall see later in this book, is the root cause of much of the debate about the
status of scientific theories.

2 THE ABILITY TO REPRODUCE RESULTS

If something is observed just once, it could be a freak occurrence,
caused by an unusual combination of circumstances. It would
certainly not be an adequate basis on which to frame a scientific
hypothesis. The importance of carefully defined experiments is that
they enable other people to reproduce them, and thus confirm or
challenge the original findings. Once the result of an experiment is
published, scientists in the same area of research all over the world
attempt to reproduce it in order to see if they get the same results,
or to check whether all extraneous variables have in fact been

3. Reasoning and evidence 65

eliminated. If the results cannot be reproduced, they are regarded as
highly suspect.
Hence, the devising of suitable experiments plays a hugely important
part in the overall activity of science. Planning and organizing an
experiment, creating the right conditions and devising and refining
measuring equipment, checking that all other variables have been
eliminated – these very often constitute the bulk of the work done in
many areas of science, compared with which the actual running of
the experiment itself may be relatively easy.
Can there be crucial experiments which are decisive in saying which
of a number of competing theories is correct? Early scientists (e.g.
Francis Bacon) thought this possible, but others (e.g. Pierre Duhem,
a physicist writing at the end of the nineteenth century and the
first years of the twentieth) have argued that they are impossible,
since you can never know the sum total of possible theories that
can be applied to any set of experimental results. Hence, even
if the experiment is run perfectly, that does not guarantee that
there is one and only one possible theory to be endorsed by it. For
practical purposes, however, some experiments (e.g. the Eddington
observations that confirmed Einstein’s theory of General Relativity –
see Chapter 3) do appear to be decisive in saying that, of existing
theories, one is superior to the others.

Hypothesis and confirmation

So far we have looked at the way a scientist can argue from
individual bits of information or experimental results towards a
generalized statement, but that is not the only way in which theories
are developed and tested against evidence. The hypothetico-deductive
method operates in this way:
! Start with an hypothesis
! Deduce from it a prediction
! Check whether that prediction is correct
! If it is correct, the hypothesis is confirmed.

This is the opposite way round from induction, since it starts with a
general idea and then devises means of getting information that can
confirm that the idea is correct. The important thing, however, is that

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it should not impose an hypothesis upon the evidence, rather it uses
evidence to test out the hypothesis.
However, when it comes to testing out an hypothesis against
evidence, there is a problem with knowing what can count for
its confirmation. Carl Hempel (1905–97) gave an example that
has troubled many other philosophers, it is known as the ‘raven
paradox’:

All ravens are black.

This statement predicts that, if you find a raven, it will be black, so
every black raven you find will confirm it. So far so good.
However, ‘All ravens are black’ is the logical equivalent of ‘All non-
black things are not ravens.’ In other words, if the first of these
statements is true, the second must also be true – if it’s not black,
then obviously it’s not a raven.
This produced a problem. Suppose I say ‘All bananas are yellow’
(ignoring, for this argument, that they will eventually go brown). This
confirms the statement that all non-black things are not ravens,
since the banana is not black and it is not a raven. But, logically, if it
confirms that second statement, then it must also confirm the first,
since they are logically equivalent. Hence we arrive at the crazy idea
that statements about bananas being yellow, or leaves green, or
shoes brown, will confirm our original claim that all ravens are black.

One way of trying to get round this problem is to say that all those
other statements do indeed confirm the original claim that all ravens
are black but that they do so only very weakly. Imagine you go
looking for something. As you hunt, you keep discarding everything
that is not what you are looking for, so that everything you discard
brings you – in theory at least – one step nearer finding that searched-
for thing. The yellow banana does confirm the black raven, but only
in so far as that yellow thing is not, after all, a raven!

TESTING AGAINST EXPERIENCE

Induction, as a method, may have been fine for some problems, but
in dealing with relativity and in assessing quantum theory, Einstein

3. Reasoning and evidence 67

recognized that there was no way of arguing from experience
to theory. His method was to start with logically simple general
principles, develop a theory on the basis of them, and then test that
theory out against experience.
Einstein’s wonderful early thought experiments – for example,
a flashbulb going off in a railway carriage, illuminating clocks
simultaneously (from the perspective of someone in the carriage) or
not (from a stationary observer outside the carriage) – present puzzles
of a practical sort the answers to which illuminate his general theory
of relativity.
Given the theory, the implications for observing clocks in railway
carriages gives practical confirmation; but no amount of observing
passing trains is ever (on a basis of inductive inference) going to
generate the theory of relativity.

Abductive reasoning
We have looked at induction (where evidence is used to support a
theory) and deduction (where we examine the logical consequence
of a theory), but very often what we are trying to do is find the best
possible explanation for something, and use a form of reason that is
called abduction. Consider this example:

I see an unopened letter on the pavement early in the morning and

reckon that the best explanation is that the postman dropped it.
I infer, from the letter on the pavement, that the postman dropped
it because, if the postman dropped it, it would be there on the
pavement. In other words, I am working from a consequence back
to a precondition.
Of course, it is possible that someone else dropped it, but of the
infinite number of possible reasons for the letter being there, I have
attempted to narrow down the possibilities in order to test out
and see if the one I have inferred is correct. Science often works by
seeking the ‘inference to the best explanation’, using this kind of
abductive reasoning.

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What counts as science?
Blind commitment to a theory is not an intellectual virtue: it is an
intellectual crime.
Imre Lakatos, 1973

Science always requires a healthy measure of scepticism, a willingness

to re-examine views in the light of new evidence, and to strive for
theories that are based on objective facts that can be checked and
confirmed. As we saw earlier, it was the quest for objectivity, loyalty
to the experimental method, and a willingness to set aside established
ideas in favour of reason and evidence, that characterized the work of
Francis Bacon and others. There were disagreements about the extent
to which certainty was possible, and some (e.g. Newton) were willing
to accept ‘practical certainty’ even though recognizing that ‘absolute
certainty’ was never going to be possible.
The assumption here is that, if you want to explain a phenomenon,
you need to show the conditions that have brought it about, along
with a general ‘law of nature’ that it appears to be following.
This is sometimes referred to as the ‘Covering Law’ model. That
would be fine, except that the general law is framed on the basis of
evidence that is never going to be complete, and the phenomenon
you are attempting to explain may well be a bit of evidence that will
eventually show your ‘law’ to be inadequate.
In the twentieth century there was considerable debate, as we shall
see in Chapter 4, about the process by which inadequacies in a theory
are examined, and the point at which the theory should be discarded.
No scientific theory can be expected to last for all time. Theories may
be falsified by new and contrary evidence (Popper) or be displaced
when there is a general shift in the matrix of views in which they are
embedded (Kuhn).
On this basis, we cannot say that good or effective science provides
knowledge that will be confirmed as true for all time, whereas bad or
ineffective science yields results that have been (or will be) proved false.
After all, something that is believed for all the wrong reasons may
eventually be proved correct, and the most cherished theories in science
can be displaced by others that are more effective. What distinguished
science from other methods of enquiry is to do with the nature of the
claims it makes, and the methods by which it seeks to establish them.

3. Reasoning and evidence 69

 KEEP IN MIND…
1 Reasoning from evidence was a key feature of the rise of modern
science.

2 We cannot be absolutely certain about any theory that is

based on evidence, since new evidence may always appear to
undermine it.

3 The inductive method argues from evidence to theory, not vice

versa.

4 Hume argued that belief should always be proportional to

evidence.

5 Goodman pointed to the problem of ‘grue’ where evidence

confirms two contradictory claims.

6 Newton saw the world as operating on rational and

mathematical principles.

7 Experiments seek to provide measurable data with a limited

number of variables.

8 An abductive argument infers a reason in order to explain a

present phenomenon.

9 Science is defined by its methodology rather than its content.

10 The willingness to allow evidence to confirm or challenge

theories is a mark of genuine science.

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