This paper was originally published, in a different format, as: What are the aims of science? Radical Philosophy, 1976, 13, pp. 7--17, http://www.radicalphilosophy.com/article/what-are-the-aims-of-science Now available as http://www.cs.bham.ac.uk/research/projects/cogaff/aims-of-science-Sloman.html A revised, extended, version including discussion of the relevance of computing and Artificial Intelligence to science, especially the investigation of possible forms of information processing and intelligence, was published as Chapter 2 of The Computer Revolution in Philosophy: Philosophy, science and models of mind (1978) Now online here (html and PDF, including some notes added after digitisation in 2001) http://www.cs.bham.ac.uk/research/projects/cogaff/crp/ Chapter 2 is available, with some notes added in 2001, as http://www.cs.bham.ac.uk/research/projects/cogaff/crp/#chap2____________________________________________________________________________
I suggest that no simple slogan or definition, such as can be found in
textbooks of science or philosophy can capture its aims. Science is a complex
network of different interlocking activities with multiple practical and
theoretical aims and a great variety of methods. I shall try to describe some
of the aims and their relationships in this essay.
Oversimple characterisations, by both scientists and philosophers, have led to
unnecessary and crippling restrictions on the activities of some would-be
scientists, especially in the social and behavioural sciences, and to
harmfully rigid barriers between science and philosophy.
By undermining the slogan that science is the search for laws, and subsidiary
slogans such as that quantification is essential, that scientific theories
must be empirically refutable, and that the methods of philosophers cannot
serve the aims of scientists, I shall try, in what follows, to liberate some
scientists from the dogmas indoctrinated in universities and colleges. I shall
also try to show philosophers how they can contribute to the scientific study
of man, thereby escaping from the barrenness and triviality complained of so
often by non-philosophers and philosophy students.
A side-effect which will be reported elsewhere, is to undermine some old
philosophical distinctions and pour cold water on battles which rage around
them -- like the distinction between subjectivity and objectivity, and the
battles between empiricists and rationalists.
First crude subdivision of aims of science
Science has not just one aim but several. The aims of scientific investigation
can be crudely subdivided as follows:
1 to extend man's knowledge and understanding of
the form and contents of the universe (factual aims),
2 to extend man's control over the universe, and to use this to improve the
world (technological or practical aims),
3 to discover how things ought to be, what sorts of things are good or bad and
how best to further the purposes of nature or God (normative aims).
Whether the third aim make s sense (and many scientists and philosophers would
dispute this) depends on whether it is possible to derive values and norms
from facts. I shall not discuss it as it is not relevant to the main purposes
of this enquiry.
The second kind of aim will not be given much attention either, except when
relevant to discussions of the first kind of aim.
The first kind of aim, like the others, is of course much wider than science.
We all, including infants and children, aim to extend our knowledge and
understanding: science is unique only in the rigour, system, and amount of
co-operation between individuals involved in its methods. For the present,
however, I shall not explore the peculiarities of science, since what it has
in common with other forms of acquisition of knowledge has been too long
neglected, and it is the common features I want to describe.
In particular, notice that one cannot have the aim of extending one's
knowledge unless one presupposes that one's knowledge is incomplete, or
perhaps even includes mistakes. This means that pursuing this aim requires
systematic self-criticism in order to find the gaps and errors. This
distinguishes both science and perhaps the curiosity of young children from
some other belief systems, such as dogmatic theological systems and political
ideologies. But it does not distinguish science from philosophy.
A further subdivision: form and content
The factual aim, extending knowledge and understanding, can be further
subdivided as follows:
1.a Extending knowledge of what sorts of things are possible and impossible in
the world, and how or why they are (the aim of interpreting the world, or
learning about its form)
1.b Extending knowledge of what particular objects, events, processes, or
states of affairs exist or existed in particular places at particular times
(the aim of acquiring 'historical' knowledge, or learning about the
contents of the world).
A similar distinction pervades the writings of Karl Popper, though he would
disagree with some of the things I say below about (l.a). Different branches
of science tend to stress one or other of these aims, though both aims are
usually present to some extent. For instance, physics is more concerned with
aim (1.a), whereas astronomy is perhaps more concerned with (1.b). Geology,
geography, biology, anthropology, human history, sociology, and some kinds of
linguistics tend to be more concerned with (1.b), i.e. with learning about the
particular contents of particular parts of the universe. Chemistry, some
branches of biology, economics and psychology attempt to investigate truths
not so restricted in scope. In the jargon of philosophers, (1.a) is concerned
with universals, (1.b.) with particulars.
However, the two scientific aims are very closely linked. One cannot discover
what sorts of things are possible, nor test explanatory theories, except by
discovering particular facts about what actually exists or occurs. Conversely,
one cannot really understand particular objects, events, processes etc,
except insofar as one classifies and explains them in the light of more
general knowledge about what kinds of things there can be and how or
why.
These two aims are closely linked in all forms of learning about the world,
not only in science.
Notice that I have characterised these aims in a dynamic form: the aim is to
extend knowledge, to go on learning. Some might say that the aim is to arrive
at some terminal state when everything is known about the form and content of
the world, or at least the form. There are serious problems about whether this
suggestion makes sense: for example, how could one tell that this goal had
been reached? But I do not wish to pursue the matter. For the present, it is
sufficient to note that it makes sense to talk of extending knowledge, that is
removing errors and filling gaps, whether or not any final state of complete
knowledge is possible. Some of the criteria for deciding what is an extension
or improvement will be mentioned later.
Many philosophers of science have found it hard to explain the sense in which
science makes progress, or is cumulative. (e.g. Kuhn, 1962, last chapter).
This is because they tend to think of science as being mainly concerned with
laws; and supposed laws are constantly being refuted or replaced by others.
Very little seems to survive.
But if we see science as being also concerned with knowledge of what is
possible, then it is obviously cumulative. For a single instance demonstrates
a new possibility and, unlike a law, this cannot be refuted by new
discoveries, even if the possibility is re-described from time to time as the
language of scientists evolves. Hypotheses about the limits of these
possibilities (laws) lack this security, for they are constantly subject to
revision as the boundaries are pushed further out, by newly discovered (or
created) possibilities. Explanations of possibilities and their limits
constantly have to be refined or replaced, for the same reason. But this is
all a necessary part of the process of learning and understanding more about
what is possible in the world. It is an organic, principled growth, even if
people do sometimes disagree about what is and what is not progress, for
reasons to be described later.
Let us now look more closely at aim (l.a), the aim of extending knowledge of
the form of the world.
The interpretative aims of science
The aims listed below together constitute the aim (l.a) of interpreting the
world, or learning about its form. They are all so closely related that to
treat them as separate aims would be artificial. Similarly, to call some of
them 'scientific' and others 'metaphysical' or 'philosophical', as empiricists
and Popperians tend to do, is to ignore their interdependence. Rather, they
are all aspects of one aim. For convenience I shall talk of them as separate
aims, but this will be qualified by describing their connections. They are:
(a) Development of new concepts and symbolisms making it possible to
conceive of, represent, think about and ask questions about new kinds or
ranges of possibilities (e.g. new kinds of physical substances, events,
processes, animals, mental states, human behaviour, languages, social systems,
etc.). This aim includes the construction of taxonomies, typologies, scales of
measurement and notations for structural descriptions. This extension of our
conceptual and symbolic powers is one of the major functions of mathematics in
science.
(b) Extending knowledge of what kinds of things (including events and
processes) are possible in the world; i.e. what kinds of things are not
merely conceivable or representable but really can exist or occur. Finding out
what actually exists, and trying to make new things exist, are often means to
this end. We can distinguish knowledge of absolute possibility concerning a
phenomenon X (X can exist) from knowledge of relative possibility (X can exist
in conditions C). Extending knowledge of relative possibilities for X is an
important way of extending knowledge of what is possible. All this should be
distinguished from the aim (e) below, of finding out what kinds of things are
most likely, common or frequent, either absolutely or in specified conditions.
The latter is a concern with probabilities not possibilities.
Aim (b) clearly presupposes aim (a), for one can only acknowledge
possibilities that one can conceive of, describe or represent.
(c) Constructing theories to explain known possibilities: i.e. theories
about the underlying structures, mechanisms, and processes capable of
generating such possibilities. For instance, a theory of the constituents of
atoms may explain the possibility of chemical elements with different
properties. 'How is this possible?' is the typical form of a request for this
kind of explanatory theory, and should be contrasted with the question 'Why is
this so?' or 'Why is this impossible?', discussed in (f) below.
(d) Finding limitations on combinations of known possibilities. These
are often called laws of nature: for instance to say that it is a law of
nature that all Xs are Ys is to say that it is impossible for something
to be both an X and not a Y. It is these laws, limitations or impossibilities
which make the world relatively stable and predictable. This aim, like (c),
presupposes aim (b), since one can discover limitations of possibilities only
if one already knows about those possibilities. (This aim of science is the
one most commonly stressed in the writings of scientists and philosophers. It
subsumes the aim of discovering causal connections, since X causes Y if the
occurrence of X makes the non-occurrence of Y impossible.)
(e) Finding regular or statistical correlations between different
possibilities, for instance correlations of the form 'In conditions C, 90% of
all Xs are Ys'. This is a search for probabilities. It presupposes aim (b) for
the same reason as (d) does. Except in quantum physics, the search for such
statistical correlations is really only a stopgap or means towards acquiring a
deeper understanding of the sort described in (d), above.
Alternatively, it may be an aim of a historical science: facts about relative
frequencies and proportions of various kinds of objects, events or processes
are often important facts about the contents of a particular part of the
world. For instance, most of the correlations unearthed by social scientists
are culture-relative. Such information may have practical value despite its
theoretical poverty.
(f) Constructing theories to explain known impossibilities, laws and
correlations. Such theories answer 'Why?' questions, and are generally
refinements of the theories described in (c). That is, explaining limits of
possibilities (i.e. explaining laws) presupposes or refines an explanation of
the possibilities limited. The theory of molecules composed of atoms which can
recombine explains the possibility of chemical change. Further
refinements concerning weights and valencies of atoms explain the observed
limitations: the laws of constant and multiple proportions.
[Picture of Newcomen's beam engine added in original.]
(g) Finding and eliminating inadequate concepts, symbolisms, and laws, about
what is and is not possible, and inadequate explanations of possibilities and
laws. That this is an aim of science is, as already remarked, implied by
saying that an aim of science is to extend knowledge. As many philosophers of
science have pointed out, it is not generally possible to prove
explanatory theories in science: at most they can only be refuted or shown to
be inadequate in some way. Moreover, when several candidates survive
refutation, the most that can be done is to compare their relative merits and
faults, without necessarily establishing the absolute superiority of one over
the other.
It is often assumed that the only kinds of proper tests are empirical (i.e.
observations of new facts, in experiments or in nature). However, we shall see
that many important tests are not empirical. We shall also see that just as
negative instances count against laws, so do positive instances provide
support for theories about possibilities.
If forced to summarise all this in a single slogan, one could say:
A major aim of science is to find out what sorts
of things are and are not possible in the world,
and to explain how and why.
Though too short to be clear, this may be a useful antidote to more common
slogans stressing the discovery and explanation of laws and regularities. Such
slogans lead to an excessive concern with prediction, control and testing,
topics mainly relevant to aims (d) to (g), while insufficient attention is
paid to the more fundamental aims (a) to (c), especially in psychology and
social science. The result is often sloppy research, theorising and
teaching.
More about interpretative and historical aims of science
Unlike the historical scientist, the interpretative scientist is interested in
actual objects, events or situations only insofar as they are specimens of
what is possible. The research chemist is not interested in the fact that
this particular sample of water was, on a certain day, decomposed into
hydrogen and oxygen in that laboratory, except insofar as this
illustrates something universal, such as the possibility of decomposing
water. This possibility refutes the theory that water is a chemical element
and corroborates the alternative hypothesis that all water is composed of
hydrogen and oxygen, and also more general theories about possible kinds of
transformations of matter. Similarly, although an 'historical' biologist may
be interested in recording, for a fascinated public, the flora and fauna of a
foreign isle, or the antics of a particularly intelligent chimpanzee, the
'interpretative' biologist is interested only insofar as they illustrate
something, such as what kinds of plants and animals can exist (or can
exist in certain conditions) , or what kinds of behaviour are possible
for a chimpanzee or for some other class containing the animal in question.
In short, the interpretative scientist studies the form of the world,
using the contents only as evidence, whereas the historical scientist simply
studies the contents.
There is, of course, no reason. why any one science, or scientist, should be
classified entirely as interpretative, or entirely as historical. Different
elements may intermingle in one branch of science. For instance, a linguist
studying a particular dialect is an interpretative scientist insofar as he is
not concerned merely to record the actual set of sentences uttered by certain
speakers of that dialect, but to characterise the full range of sentences that
would or could be intelligible to an ordinary speaker of that dialect, namely,
a range of possibilities. However, insofar as he is interested merely in
finding out exactly what dialect is intelligible to a certain
spatio-temporally restricted group of persons, he is an historical linguist,
as contrasted with a linguist who is interested in this dialect primarily as a
sample of the kinds of language which human societies can develop: the attempt
to characterise this set of possible languages is often called the search for
linguistic universals.
Thus a richer philosophical terminology would be required for a precise
description of hybrid historical and interpretative aims. This is not relevant
to our present concerns and will not be pursued further. Instead, in II-IV
below, I will concentrate mainly upon an analysis of the first three
components of the interpretative aim, outlined above. These three are very
tightly interconnected.
It is very hard to describe the distinctions between them accurately, and I am
sure I do not yet understand these matters aright. Moreover, each of them
could be further subdivided. Detailed historical analysis is required here, so
that similarities and differences between cases can be described accurately
and a more satisfactory typology developed; a contribution to the scientific
study of science. Alas, this will require the help of persons more scholarly
than I.
As new concepts and symbolisms are developed, and the language extended, new
questions become askable. For instance, people who grasp the concepts 'hotter'
and 'longer' can understand the question whether metal rods get longer when
they are made hotter. And they may even be able to grasp crude distinctions
between metals according to which grows longer faster when heated. But in
order to learn to think about whether the change in length is proportional
to the change in temperature, so that they can then use the constant of
proportionality (divided by the length of the rod) to define a numerical
'coefficient of expansion' for each metal, they need to grasp numerical
representations of differences in temperature and length ('hotter by how
much?', 'longer by how much?').
Similarly, although people may have a crude grasp of distinctions between
velocity and acceleration, and may be able to detect gross changes in either,
on the basis of their own experiences of moving things, being moved, and
perceiving moving objects, nevertheless, until they have learnt how to relate
concepts of distance and time to numerical interval scales, they cannot easily
make precise distinctions between different velocities, or between
acceleration and rate of change of acceleration, nor think of precise
relations between these concepts.
These familiar examples show the power of extending scientific language by
introducing numerical concepts and notations corresponding to old
non-numerical concepts. This sort of thing has been so important in physics
that many biological and social scientists have been deluded into thinking it
part of the definition of a scientist that he uses numbers!
The replacement of Roman numerals with the Arabic system is an example of a
powerful notational advance. Another was the Cartesian method of using
arithmetic to represent geometry and vice versa.
However, non-numerical conceptual and notational devices have also been
important, such as concepts used in describing structures of plants and
animals, concepts used for describing structures of mechanical systems and
electrical circuits (geometrical and topological concepts), taxonomies or
typologies, and grammatical concepts (see N. Chomsky, 1957).
All sorts of notations besides numerical and algebraic ones have played an
important role in extending the abilities of scientists to express what they
know and want to find out, for instance pictures, diagrams, maps, models,
graphs, flow charts, and non-numerical computer programs. Examples include the
diagrams used in the study of levers, pulleys, bending beams, and other
mechanical systems, the 'pictures' of molecules used by chemists, for instance
in the following representation of the formation of water from hydrogen and
oxygen
( H-H, H-H, 0-0) ⇒ (H-O-H, H-O-H )
circuit diagrams used in electronics, optical drawings showing the paths of
light rays, plates showing tracks of subatomic particles, and the 'trees' used
to represent deep-structures of sentences.
Concepts may also be used without being represented explicitly by any external
symbol. There are philosophers who dispute that these are cases of the use of
concepts, but in the face of well known facts I can only regard this as verbal
quibbling. We know that young children and other animals can discriminate,
recognise and react intelligently to things which they cannot name or
describe. The consistency and appropriateness of their behaviour shows that
they act on the basis of reasons, even if they cannot articulate them or are
unaware of them.
The same is true of an adult who cannot describe the features of musical
compositions which enable him to recognise styles of composers and appreciate
their music, or the cues which enable him to judge another's mood. No doubt
this is true also of many scientists, especially when they are in the early
phases of some kind of conceptual development. They may then, like children
and chimpanzees, be unable to articulate fully the reasons they have for some
of the decisions they take about interpreting evidence and assessing
hypotheses.
Our minds may use symbolisms which we can only translate into actions, not
spoken or written language -- until we have extended our language. Non
logicians can often distinguish valid from invalid arguments without being
able to say how. They have not learnt the overt language of logicians.
Even after going a stage further and learning how to articulate their reasons,
scientists may not yet have learned how to teach their new concepts to
colleagues and rival theorists. So attempts at rational persuasion break down.
This has misled some philosophers and historians of science into thinking that
there are no reasons, so that the decisions of scientists are irrational or
non-rational. This is as silly as assuming that a mathematician is irrational
simply because he cannot explain a theorem to a four year old child. The child
may have much to learn before he can understand the problem, let alone the
reasoning, and the mathematician may be a poor teacher.
Concepts are not simple things which you either grasp or don't grasp, or which
can be completely conveyed by an explicit definition or axiomatic
characterisation. For instance, as work of Piaget has shown so clearly, and
Wittgenstein less clearly, very many of our familiar concepts, like 'number',
'more', 'cause', 'moral', and 'language', are very complex structures of which
different fragments may be grasped at different times. A child aged four or
five may be able to count flawlessly well beyond 20, and use counting to get
correct answers to simple addition problems, yet be quite unable to count
backwards, or to answer questions like 'What comes before 6?', 'Is 9 after
(bigger than) 5?'. (Yet he succeeds with the numbers on a clock in front of
him, so he understands the questions.) Does he or does he not understand the
concept of number, or of 6? His failure does not prove that he is irrational:
he still has some procedures to invent for himself -- if his parents and
teachers don't destroy his creative abilities.
The more of one's concepts and associated procedures one is able to represent
explicitly in symbols of some sort, the greater one's power to explore
possibilities systematically by manipulating those symbols. For instance, by
explicitly characterising aspects of our intuitive grasp of spatial structures
in the form of axioms and definitions, one becomes able to experiment with
alterations in the axioms and definitions, and thereby invent concepts of
non-euclidean or other new sorts of geometries. In this way one can learn to
think about new sorts of possibilities without waiting to be confronted with
them. (This kind of thing may also happen below the level of consciousness, in
children and scientists, as part of the process of learning and discovery.) Of
course, one may also extrapolate too far, and construct representations of
things which are not really possible in the world, so empirical investigation
of some sort is required to discover whether things which are conceivable or
representable can also exist. For instance, merely analysing the concept of an
element with atomic number 325 will not decide whether such a thing can occur.
This is the reason for distinguishing the first aim of interpretative science,
namely extending concepts and symbolisms, from the second aim, namely
extending knowledge of what is really possible. (I believe many of these ideas
are to be found in Kant (1781)).
It is not always noted in epistemological discussions that there are two
important phases or steps in the acquisition of knowledge. Discovering that P
is true first of all requires the ability to understand the possibility that P
might be true and might be false, which requires grasping the concepts used in
the proposition P. The second phase is finding out that p is true, for
instance by empirical observation, use of testimony, inference from what is
already known, or some combination of these. In the first phase one is able to
ask a question, in the second one has an answer. (There may be primitive kinds
of knowledge-acquisition in which questions are never understood, only
information acquired and used. But science is not like this).
Usually philosophers plunge into discussions of such questions as whether we
can know anything about the future, or rationally believe anything about the
future, without first asking how a rational being can even think about
the future or think about alternative possible future states of
affairs. They are therefore attempting to assess the rationality of certain
decisions on the basis of a drastically incomplete account of the resources
that might enter into the decision-making process. The reason why this has
been shirked is partly because it is so hard to do, partly because of an
unwarranted restriction of rationality to relations between evidence and
belief-contents, and partly because many philosophers (unlike Wittgenstein,
1956), think that the investigation of conceptual mechanisms is a task for
psychologists not philosophers.
However, most psychologists never even think of the important questions, and
those who do usually lack the techniques of conceptual analysis required for
teaching them: so the job does not get done.
(Piaget seems to be an exception. But many of his followers seem capable only
of repeating his experiments, and not of extending his conceptual analyses.)
There is a need for a tremendous amount of research into what it is to
understand various sorts of concepts, and what makes it possible. There is
also a need for some kind of taxonomy of types of conceptual change, whether
in individuals or in cultures.
The efforts made so far by psychologists to produce such taxonomies capture
only a tiny fragment of the range of possible developments. Here are some
examples of possibilities of conceptual change which still require adequate
explanations. Going from grasping a relation like 'hotter' or 'longer' to
grasping that it can be used to define equivalence classes of objects of the
same temperature or length. Going from this to grasping the possibility of
comparing differences in temperature or length (i.e. understanding an
interval scale). Going from grasping some general concept defined in terms of
a structure, or a function, or some combination of structure and function, to
grasping systematic principles for subdividing that concept into different
categories. Learning to separate the structural and functional aspects of a
hybrid concept, like 'knife', or 'experiment'. Changing a concept by changing
the theories in which it is embedded, in the way that the concept of mass was
changed by going from Newtonian mechanics to Einstein's mechanics.
Developing a new more powerful symbolism for an old set of concepts: e.g.
inventing differential calculus notation for representing changes, or using
the concept of a mathematical function to generalise earlier concepts of
regularity or correlation. Coming to see something in common between things
one has never previously classified together, like mass and energy, particles
and waves, straight lines and geodesics on a sphere.
Going from knowing a set of formulae and how to manipulate them to being able
to see their relevance to a variety of new concrete problems, e.g. going from
understanding algebra to being able to apply it in real life. (There are many
other cases not so closely linked to science, e.g. the growth of social, moral
and political consciousness Learning to feel shame, embarrassment, or guilt,
as contrasted with annoyance or regret, requires complex cognitive
development, and the same is true of many other human emotions. Some concepts
e.g. 'impertinent' are only intelligible in certain cultures.)
Until these conceptual changes are better understood, discussion of
'incommensurability' of scientific theories and of the role of rationality in
science is premature. Meanwhile education will continue to be largely a hit
and miss affair, with teachers not knowing what they are doing or how it
works.
To sum up so far. A system of concepts and symbols constitutes a language.
(This statement is grossly inaccurate, but will do for present purposes.) A
language which is used to formulate one theory will usually also contain
resources for formulating alternatives, including the negation of the theory
and versions of the theory in which some predicate, relational expression or
numerical constant is replaced by another. So concepts and symbols are tools
for generating possibilities or questions for investigation. They have greater
generative power than theories. The scientist who usefully extends the
language of science, unlike one who simply proposes a new theory using
existing concepts and symbols, extends the hypothesis-forming powers of the
scientists who understand him. In this sense conceptual advances are more
profound.
The important differences between modern scientists and those of the distant
past therefore concern not merely the statements and theories thought to be
true or false, but also which statements and theories could be thought of at
all. Not only are more answers known now, but more questions are intelligible.
Criticising conceptual systems
Sometimes old questions become unaskable as a result of conceptual change,
like questions about phlogiston or absolute velocity, or perhaps 'medical'
questions like 'What did he do to deserve this affliction?' Modern medical
science contains no means of generating possibilities constituting answers to
this question, though both laymen and some medical men (on Sundays?) may still
formulate them. (Incompatible systems of concepts and theories may coexist in
one mind -- but that's another story.) So science is served not only by
extending and differentiating existing concepts: rejection of a concept or
typology or mode of representation may also serve the aims of science by
reducing the variety of dead-end questions and theories.
Concepts, typologies, taxonomies, and symbolisms can, like theories, be
rationally criticised, and rejected or modified.
There are several ways in which a typology and associated notation can be
criticised. For instance one may be able to show:
(a) that there are some possibilities it doesn't allow for,
(b) that it represents as possible some cases which
are not really possible,
(c) that some of the subdivisions it makes are of no
theoretical importance,
(d) that some category within it should be sub-divided into
two or more categories, because their instances have
different relations to the other categories,
(e) that the principle of subdivision is too vague to decide
all known cases,
(f) that the classification procedure generates inconsistent
classifications for some instances,
(g) that the notation used does not adequately reflect the
structural properties of the typology, or of the instances,
(h) that the concepts used generate questions which apparently
cannot be answered by scientific investigation (like the
question 'How fast is the Earth moving through the ether?')
(i) that more powerful explanatory theories can be developed
using other tools for representing possibilities.
(It may be that some of these criteria are used,
unconsciously of course, not only by scientists, but also
by young children developing their conceptual systems.)
Several of these criteria will remain rather obscure until later. In particular,
This aim is indefinitely extensible: having found out that Xs can exist or
occur, one can then try to find out whether Xs can exist or occur in specified
conditions C1, C2, C3,... Similarly, having found that objects can have one
range of properties which can change (e.g. length) and can also have another
range of properties which can change (e.g. temperature) one can then try to
find out whether these properties can change independently of each other in
the same object, such as a bar of metal, or a particular object in specified
circumstances, such as a bar of metal under constant pressure or tension.
Such further exploration of the limits of combinations of known possibilities
merges into the search for laws and regularities, as explained previously.
We can conceive of, or describe, a lump of wood turning spontaneously into
gold, or a human living unclothed in a vacuum, but it does not follow that
these things really can exist. What is the difference?
First we look at what it is for something to be conceivable, representable, or
describable.
As philosophers well know, the subjective feeling of intelligibility, the
feeling of having understood or imagined something, is no guarantee that
anything consistent was understood, imagined or conceived of. If someone
claims to be able to conceive of the set of all sets which do not contain
themselves, then provided he is using words in the normal way, we can show, by
Russell's well known argument, using steps that he will accept if he is
reasonable, that he was wrong, or that his 'conceiving' amounted to little
more than repeating the phrase, or some equivalent, to himself. A sentence,
phrase, picture, diagram, or other complex symbol will, if intelligible, be
part of a language which includes syntactic and semantic rules in accordance
with which the symbol is to be interpreted. The mere fact that the symbol is
syntactically well-formed does not guarantee that it can be interpreted,
though it may mislead us into thinking it can. More precisely, it may have a
sense but necessarily fail to have any denotation.
Thus the question 'Does the table exist more slowly than the chair?' is
syntactically perfect but we can show that so long as the words are used
according to normal semantic rules there can be no answer to the question.
For, 'more slowly' when qualifying a verb requires that verb to denote a
process or sequence involving changes other than the change of time, so that
the rate of change or succession can be measured against time. Existence is
not such a process, so rates of existence cannot be compared. (For more on
this see Sloman, 1971b. For non-verbal examples see Clowes, 1971)
So we can use the notion of what is coherently describable or representable in
some well defined language or representational system, as an objective
semantic notion. What is conceivable to a person, will be what is coherently
representable in some symbolic system which he uses, not necessarily fully
consciously. It may be very hard, even for him, to articulate the system he
uses, but that does not disprove its existence. These notions are as objective
as the notion of logical consistency, which is a special case. However the
mere fact that something is, in this sense, representable or conceivable does
not mean that it really can exist. Conversely, what can exist need not be
representable or conceivable using the symbolic resources available to
scientists (or others) at any particular time: their language may need to be
extended. Scientists (like children) may be confronted with an instance of
some possibility, like inertial motion, diffraction, or curvature of
space-time, without seeing it as such because they lack the concepts. (Kuhn,
1962, chapter X, has over-dramatised this by saying they inhabit a different
world.)
The word 'possible' as I have used it, and as others use it, tends to slide
between the two cases (a) used as a synonym for 'consistently representable or
describable using some language', as in 'logically possible', and (b) used to
refer to what can occur or exist in the world. But what is the difference
between (a) and (b)?
This is not an easy question to answer completely. The main difference is that
conceivability or representability can be established simply by analysing the
sentence or other symbol used and checking that the syntactic and semantic
rules of the language in question do not rule out a consistent interpretation
(which is not always easy), whereas checking whether something really is or is
not possible requires empirical investigation of some sort.
If an actual example is found, that conclusively establishes the possibility.
The corresponding kind of impossibility is very much harder to establish, and
perhaps can never be conclusively established, though one can often be fairly
sure that something is not possible in the world either because of extensive
and varied attempts to realise it, or on the basis of inference from some well
established theory. (For instance, I am convinced by physical and biological
arguments that it is impossible for a human being to live without clothing in
a vacuum.)
However, possibility is not the same as actual existence. To say that it is
possible for ten drugged alligators to be painted with red and yellow stripes
and then piled on top of one another, is not to say that this ever has
happened or will happen. Similarly, to say that several courses of action are
possible for me, is not to say that I shall actually follow all of them. So,
in saying that one of the aims of interpretative science is to find out which
kinds of things are possible in the world, I do not mean that the aim is to
find out which kinds actually exist, as in historical science. The latter is
just a means, since existence establishes possibility. (See part one for more
on this.)
What other means are there of deciding that something is really possible,
besides finding an instance? Alas, the only answer I can give to this is that
we can reasonably, though always tentatively perhaps, infer that something is
possible if we have an explanation of its possibility. What this amounts to is
roughly the following: (a) we can consistently represent it using symbolic
resources which have already been shown to be useful in representing what is
actual, and (b) it is not ruled out by any well established law or theory
specifying limitations on possibilities. Perhaps an extra condition is
required: (c) it should differ from already realised possibilities only/in
ways which are in some sense well understood. However, it is not clear that
(c) adds anything to (a) and (b).
It is clear that these conditions do not conclusively prove something to be
possible, for they rest on current theories of the limitations of what is
possible and such theories, being empirical, are bound to include errors and
omissions, at any stage in the advance of science. Further, these conditions
do not yield clear decisions in all cases. For instance, is it reasonable to
believe that it is possible for a normal human being to be trained (perhaps
starting from birth) to run a mile in three minutes? It may not be clear
whether we already know enough to settle such a question.
The above conditions for proving unrealised possibilities need to be further
defined and illustrated. For the present, however, my aim is simply to
indicate roughly how something can be shown to be possible without producing
an instance. So I have demonstrated that possibility is a different concept
from conceivability (or coherent representability), and also different from
existence.
But I still have not given anything approximating to a complete analysis: this
would require very much more than describing the criteria for deciding whether
something is possible or not. It would also require analysis of the role of
the concept of possibility in our thinking, problem-solving, deliberating,
regretting, blaming, praising, etc, and its relations to a whole family of
modal words, such as 'may', 'can', 'might', 'could', 'would', etc. A mammoth
task. (For some useful beginnings see Gibbs, 1970).
At any rate, we cannot analyse 'Things of type X are possible' as
synonymous with 'Either things of type X already exist, or else they
are consistently representable in our symbolic system without being ruled out
by known laws', since this would define real possibility in terms of the
current system of concepts and beliefs. We could try a formula like
'Things of type X are possible if and only if they either exist or are
consistently representable in some useful representational system and are not
ruled out by any true laws'.
But this has the disadvantage of presupposing that there exists some complete
set of true laws formulated in some unspecified language which correctly
defines all the limitations on what is possible in the world. It is by no
means clear that such a presupposition is intelligible. Moreover as a
definition it introduces a circularity, since it is notoriously hard to define
the concept of a law without presupposing the concept of possibility or some
related concept.
Despite the remaining obscurities, I hope I have done enough to indicate both
that the first two aims of interpretative science are different, and also that
they are very closely related. Now for a closer look at the third aim - the
aim of explaining possibilities. I feel least satisfied with what I have to
say about this.
Examples of theories purporting to explain possibilities
The examples which follow are not all correct explanations. Some have
already been superseded and others probably will be. The ancient theory of
epicycles used geometry to explain how it was possible for the apparent paths
of planets to exhibit irregularities while the actual paths were constructed
out of regular circular motions. Known forms of motion were compounded in a
representation of new ones.
The atomic theory after Dalton explained how various kinds of chemical
transformations were possible without any change in basic substances. (It also
explained why the range of possibilities was restricted according to the laws
of constant and multiple proportions, so that it was vastly superior to
previous atomic theories.)
The theory of natural selection explained how it was possible for undirected
(' random') mutations to lead to apparently purposive or goal-directed changes
in biological species. The theory of genes explained how it was possible for
offspring to inherit some but not all of the characteristics of each parent,
and for different siblings to inherit different combinations. The theory that
atoms were composed of protons, neutrons and electrons explained many of the
possibilities summarised in the periodic table of the elements, and explained
how it was possible for one element to be transformed into another.
Einstein's theories of relativity explained how it is possible for mass and
energy to be interconvertible, and for light rays to be curved even in a
vacuum. Other possibilities explained before specimens were produced include
lasers and super-conductivity.
The examples given so far are theories which not only explained possibilities,
but also contained enough detail to make prediction and, in some cases,
control, possible. In the case of the human sciences this is rare. Marx's
social theories explained how it was possible for large numbers of people to
collaborate peacefully in social and economic practices against their own
interest. He also explained how it was possible for such systems to generate
forces tending to their own overthrow.
Popper has tried to explain how it is possible for the growth of scientific
knowledge to be based on rational comparisons and assessment of theories, even
though no theory can ever be proved to be right or even probable.
Chomsky's theory that human minds contain representations of generative
grammars explains how it is possible for sentences never before heard or
uttered nevertheless to be part of a person's language. The theory (see T.
Winograd, 1973) that human minds contain certain sorts of procedures or
programs explains how it is possible for new sentences to be produced or
understood.
Freud's theories explained how it is possible for apparently meaningless slips
and aberrations of behaviour to be significant actions. Piaget's theories
about the structure of many familiar concepts explain how it is possible for a
child to show in some behaviour that he has grasped the concept and in others
that he has not.
Known possibilities for which explanations are still lacking include the
following. The possibility of the growth of an oak from an acorn or a chicken
from an egg. Fragments of the mechanisms are of course understood already, but
there is as yet no explanation of how such an apparently simple structure as a
seed or fertilised ovum can control its own development in such a way
as to produce such an apparently complex structure as a plant or animal.
Another unexplained possibility is the evolution of animals with specific
intelligent abilities (like the ability to learn to use tools, or to learn to
use language) from species lacking these abilities, and in particular the
evolution of human beings. In the case of human psychology, there are very
many possibilities taken for granted as part of common sense, yet still
without even fragmentary explanations, for instance the possibility of a
newborn infant learning whatever human language happens to be spoken around
it, the possibility of relating one's actions to tastes, preferences,
principles, hopes, fears, knowledge, abilities, and social commitments, and
the possibility of changing one's moral attitudes through personal experience.
Formal requirements for explanations of possibilities
The explanations listed earlier may not be correct explanations, but
they at least meet formal conditions for explaining certain possibilities, or
perhaps would do if precisely formulated. These conditions will be described
below. They are generalisations and elaborations of the basic idea, familiar
from writings of philosophers like Popper, Hempel and Nagel, that to explain
something by means of a theory is to deduce it from the theory, perhaps with
some additional premisses. As normally formulated, this assumes that both the
theory and what it explains are expressed in the form of sentences, using
natural language supplemented by the technical language of the science
concerned.
It is also normally assumed that the deduction is logical, that is the
inference from the theory to what it explains can be shown to be valid
according to the rules of inference codified by logicians.
(This is sometimes generalised to permit cases where the inference is only
probabilistic.)
This concept of deduction and the related notion of explanation needs to be
generalised in two ways.
First of all, other means of representation besides sentences may be used,
such as maps, diagrams, three-dimensional models or computer programs.
Secondly, the forms of inference include not only the logical forms
(like 'All A's are B's, All B's are C's. Therefore All A's are C's'), but also
the manipulation of other representations (see Sloman, 1971a). An example is
the manipulation of diagrams representing molecular structures, in order to
explain the possibility of chemical reactions, like the production of water
from hydrogen and oxygen.
On this view the use of models and so-called 'analogies' in science is simply
a change of language: one configuration is used to represent another.
All the usual talk about isomorphism of models in this context is as
misconceived as the theory that sentences in natural language must be
isomorphic with things they describe: there are many more kinds of non-verbal
representations than isomorphic models. (See Goodman, 1968; Clowes, 1971; and
Toulmin, 1953. I was helped to see all this by an unpublished paper by Max
Clowes, called 'Paradigms and syntactic models'.)
Further requirements for explanations of possibilities
We now have a minimal requirement for a theory T formulated in sentences or
other symbolic apparatus to be an explanation of some range of possibilities,
namely:
(1) Statements or other representations of the range of possibilities should
be validly derivable from T, according to whatever criteria for validity are
associated with the 'language' of T.
Perhaps one of the most important illustrations of this is the use of the
theory of bonds between atoms (the theory of valencies) to explain the
possibility of a very large number of chemical compounds and transformations.
Knowing the kinds of bonds into which the various atoms can enter, one can
generate representations of large numbers of chemical compounds, and chemical
reactions, using diagrams of the sorts mentioned previously. Here one range of
(relatively primitive) possibilities is used to explain another range. The
possibility of many kinds of atoms with different chemical bonding potentials
was itself explained later on by a more economical theory which assumed atoms
could be made up of a nucleus containing positively charged protons, neutrons
with no charge, and electrons with negative charge. Thus, postulating a small
number of primitive subatomic components and principles according to which
they could be combined into atoms, physicists could generate representations
of a wide range of possible atoms, and therefore of possible molecules and
reactions.
These theories eventually had to be revised and refined of course, but that
does not affect the point that at least part of the scientific function of
those theories while they survived was to explain a range of possibilities
according to criterion (1). While they worked, they provided 'generative
grammars' for known ranges of possibilities.
However, there are additional requirements if T is to be a good
explanation of the possibilities in question. Rival theories are assessed
according to how well they meet these additional requirements, namely:
(2) The theory should be as definite as possible: i.e. there should be
a clear demarcation between what it does and what it does not explain.
(3) T should be general, i.e. it should explain many different
possibilities, preferably including some possibilities not known about before
the theory was invented. This criterion should be used with caution. Insofar
as a theory generates some possibilities not yet established by actual
instances, efforts should be made to find or create instances, and they should
not be types of things thought to be impossible because of some more general
theory. If repeated efforts to find actual instances fail, this does not
disprove the theory, but it does reduce its credit. So a theory should not
explain too many things.
(4) T should account for fine structure: i.e. the descriptions or
representations of possibilities generated by T should be rich and
detailed.
(5) T should be non-circular: i.e. the possibilities assumed in T should not
be of essentially the same character as the possibilities T purports to
explain.
(6) The derivations from T should be rigorous: i.e. within the range of
possibilities explained by T, the procedures by which those possibilities are
deduced or derived should be explicitly specified so that they can be publicly
assessed, and not left to the intuitions of individuals.
(7) The theory T should be plausible: that is, insofar as it makes any
assertions or has any presuppositions about what is the case or what is
possible, these should not contradict any known facts. However, sometimes the
development of a new theory may lead to the refutation of previously widely
held beliefs, so this criterion has to be used with great discretion.
(8) The theory should be economical: i.e. it should not include
assumptions or concepts which are not required to explain the possibilities it
is used to explain. Sometimes economy is taken to mean the use of relatively
few concepts or assumptions, from which others can be derived as necessary.
The latter is not always a good thing to stress, since great economy in
primitive concepts can go along with uneconomical derivations and great
difficulty of doing anything with the theory, that is, with heuristic
poverty.
(9) The theory should be rich in heuristic power: i.e. the concepts,
assumptions, symbolisms, and transformation procedures of the theory should be
such as to make the detection of gaps and errors, the structuring of
problem-solving strategies, the recognition of relevant evidence, and so on,
easily manageable. (See McCarthy and Hayes, 1969 and my 1971a for more on
this)
These criteria therefore indicate ways in which theories explaining
possibilities may be criticised rationally. For instance, one may be able to
show (by a logical or mathematical argument) that the theory does not in fact
generate the range of possibilities it is said to explain.
(Nearly all psychological theories put forward to explain known human
possibilities, such as perception, fail on this point: the theories generate
the required range of possibilities only in the mind of a sympathetic audience
supplying a large and unspecified set of additional assumptions.)
A theory may be criticised by showing that it explains too much, including
things which so far appear to be impossible. The theory may not explain enough
of the known fine structure of the possibilities (like theories of speech
understanding which don't explain how hearers can cope with complex syntactic
ambiguities, or developmental theories in biology which don't explain how a
chicken's egg can grow into something like its mother or father in so many
detailed ways). The explanation may be circular, like theories which attempt
to explain human mental functioning by assuming the existence of a spirit or
soul with essentially all the abilities it is intended to explain. The theory
may be so indefinite that it is not clear what it does and what it does not
explain.
A theory may also be criticised less directly by criticising the specification
of the range of possibilities which it is meant to explain (e.g. criticising
the typology on which it is based).
For instance the specification may describe a set of structures in ways which
are not related to their functions, like describing sentences in terms of
transition probabilities between successive words. Or the set of possibilities
explained may be shown to be only a sub-range of some wider set of
possibilities which the theory cannot cope with.
For instance, a theory which explains how statements are constructed and
understood can be criticised if it cannot be extended to account for
questions, commands, threats, requests, promises, bets, contracts, and other
types of verbal communication which are clearly functionally related to
statements in that they use related syntactic structures and almost the same
vocabulary. If it turns out that a physical theory of the interactions of
atoms and their components can only explain the possibility of chemical
reactions involving relatively simple molecules, then that will show an
inadequacy in the theory. Similarly, if an economic theory can explain only
the possibility of economic processes occurring when there is a very
restricted amount of information flow in a community, then that theory is not
good enough. Finally, if a theory of the function of moral language accounts
only for abusive and exhortative uses of that kind of language, then it is
clearly inadequate since moral language can be used in a much wider range of
ways.
In some cases, whether a theory explaining some specified range of
possibilities satisfies these criteria or not, or whether it satisfies them
better than a rival theory, is not an empirical question. It is a question to
be settled by logical and mathematical investigations of the structure of the
theory and of what can be derived from it.
Sometimes the theory is too complex for its properties to be exhaustively
surveyed. If so, one can only try out various derivations or manipulations in
test cases. This is partly analogous to an empirical investigation in that the
results are always partial and cannot be worked out in advance by normal human
reasoning. Similarly testing a complex computer program may feel like
conducting some kind of experiment. Nevertheless, as already remarked, the
connections so discovered are not empirical, but logical or mathematical in
nature.
(The criteria listed here can be justified by showing how using them is
necessary for furthering the interpretative and practical aims of science
listed in part one.)
Similarly, no techniques may be available for manipulating the mechanisms, so
that the theory provides no basis for controlling the phenomena. For instance,
the theory of evolution explains the possibility of a wide range of biological
developments without providing a basis for predicting them. Similarly, a
theory explaining the possibility of my uttering sentences of particular forms
need not provide any basis for predicting when I will utter anyone sentence,
or for making me utter it, or even for explaining exactly why I uttered the
particular sentence I did utter at a particular time. This is because the
theory may simply postulate a certain kind of sentence-generating mechanism,
available in my mind as a resource to be used along with other resources.
How any particular resource is used on any particular occasion, may be the
result of myriad complex interactions between such factors as my purposes,
preferences, hopes, fears and moral principles, what I believe to be the case
at the time, what I know about the likely effects of various actions, how much
I am distracted and so on. The theory which explains the possibility of
generating and under standing sentences need not specify all the interactions
between the postulated mechanism and other aspects of the mind. So it need not
provide a basis for prediction and control.
This is true of any explanation of an ability, skill, talent or power, in
terms of a mechanism making it possible. The explanation need not specify the
rest of the system of which that resource is a part, nor specify the
conditions under which the resource is used. And even if it does, the
specification need not refer to either observable conditions or manipulable
conditions. So such explanations of possibilities, though they contribute to
scientific understanding, need not contribute to predictions of actual
events.
It is not possible to refute such a theory, if it merely explains possibilities,
and entails or explains no impossibilities. For it is a fact about the logic
of possibility that 'X is possible' does not entail 'X will occur at some time
or other'.
Similarly 'X never occurs' does not entail 'X is impossible'. Newtonian
mechanics entails that it is possible for some very large body passing near
the earth to deflect the earth from its orbit, and it explains this
possibility: but the fact that this never occurs casts no doubt on the theory.
Similarly, a grammatical theory may explain the possibility of the utterance
of a certain rather complex English sentence, and even though nobody ever
utters that sentence naturally, this casts no doubt on the theory. A
psychological theory may imply that it is possible for a human being to count
backwards from 99 to 0 to the tune of 'Silent night, holy night', without
being refuted merely by the fact that nobody ever does this. Only a much more
complex theory, taking into account a rich set of motives and beliefs, could
ever be used to predict such a performance, and perhaps be refuted by its
non-occurrence.
Lack of predictive power, practical utility, or refutability need not prevent
the scientific merits of an explanation of a range of possibilities from being
discussed rationally, and compared with the merits of rival explanations, in
accordance with the criteria listed above. Nor does it prevent such a theory
from giving deep insight, of a kind which provides a firm basis for building
more elaborate theories which do permit predictions and explanations of
particular events, and which are empirically refutable.
I therefore see no reason for calling such theories nonsensical, as some of
the logical positivists would, nor for banishing them from the realm of
science into metaphysics, as Popper does (though he admits that metaphysical
theories may be rationally discussable and may be a useful stimulus to the
development of what he calls scientific theories).
I am not here arguing over questions of meaning: define 'science' as you will,
my point remains that among the major merits of the generally agreed most
profound scientific theories is the fact that they satisfy the above criteria
for being good explanations of possibilities, and therefore give us good
insights into the nature of the kinds of objects, events or processes that can
exist or occur in the universe. If unrefutable theories are to be dubbed
'metaphysical', then what I am saying is that even important scientific
theories have a metaphysical component, and that the precision, generality,
fine structure, non-circularity, rigour, plausibility, economy and heuristic
power of the metaphysical component are among the objective criteria by which
scientific theories are in fact assessed (and should be assessed).
The development of such 'metaphysical' theories is so intimately bound up with
the development of science that to insist on a demarcation is to make a
trivial semantic point, of no theoretical interest. Moreover, it has bad
effects on the training of scientists.
Empirical support for explanations of possibilities
Further, even though a theory explaining only certain possibilities is not
refutable empirically, that does not mean that empirical evidence is wholly
irrelevant to it. For instance, if a kind of possibility explained by the
theory is observed for the first time after the theory was constructed, then
this is empirical corroboration for the theory, even though the theory did not
specify that the phenomenon ever would occur, or that it would occur in the
particular conditions in which it did. Observing an actual instance of a
possibility explained by some theory provides support for that theory at least
to the extent of showing that there is something for it to explain: it shows
that the theory performs a scientific function.
However, the support adds to previous knowledge only if it is a new
kind of possibility. Mere repetition of observations or experiments does not
increase support for a theory: it merely checks that no errors were made in
previous instances.
In those contexts all the normal stress on repeatability of scientific
experiments is unnecessary and has misled many psychologists and social
scientists into making impossible demands of empirical studies of man and
society. Repetition may be a useful check on whether the phenomenon really is
possible (since it permits more independent witnesses to observe it), and it
provides opportunities for more detailed examination of exactly what occurred,
but is not logically necessary. If a phenomenon occurs only once, then it is
possible, and its possibility needs explaining.
Any explanation of that possibility is therefore not gratuitous, and the only
question that should then arise is not whether the explanation is science or
pseudo-science, or metaphysics, but whether a better explanation can be
found for the same possibility, that is, an explanation meeting more of the
criteria (2) to (9) above; or perhaps serving additional scientific aims
besides explaining possibilities.
The frantic pursuit of repeatability and statistically significant
correlations is based on a belief that science is a search for laws. This has
blinded many scientists to the need for careful description and analysis of
what can occur, and for the explanation of its possibility.
Instead they try to find what always occurs -- a much harder task --
and usually fail. Even if something is actually done by very few persons, or
only by one, that still shows that it is possible for a human being, and this
possibility needs explanation, as much as any other established fact. This
justifies elaborate and detailed investigation and analysis of particular
cases: a task usually shirked because of the search for statistically
significant correlations. Social scientists have much to learn from historians
and students of literature -- despite all the faults of the latter.
I have gone on at such great length about describing and explaining
possibilities because the matter is not generally discussed in books on
philosophy of science. But I do not wish to deny the importance of trying to
construct theories which can be used to explain and predict what actually
occurs, or which explain impossibilities and observed regularities. Of two
theories explaining the same range of possibilities, one which also explains
more impossibilities and permits a wider variety of predictions and
explanations of actual events to be made on the basis of observation, is to be
preferred, since it serves to a greater degree the aims of science listed
previously. I think it is quite premature to seek such predictive explanations
in psychology and social science: these sciences still seem too far from
having good explicit descriptions and explanations of possibilities we all
know about, as linguistics was until recently.
This discussion is still very sketchy and unsatisfactory. Much finer
description and classification of different sorts of explanations is required.
But enough for now!
I admit that there are still serious gaps in my discussion: a theory of
concept-formation is still lacking.
Finally, even if it is agreed that science uses rational means to
pursue the aims described here, the question arises: are these aims
rational? Is it rational to pursue them? I believe there is no answer to this.
If someone genuinely prefers the life of a mystic or hermit or 'primitive'
tribesman to the pursuit of knowledge and understanding of the universe, then
that preference must be respected. However, I believe that the aims and
criteria described here are part of the mental mechanism with which every
human child is born -- but for which it would not be possible to learn all
that human children do learn. So one can reject science only after one has
used it, however unconsciously, for some years.
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