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If we ask scientists what science is and what its aims are, we get a confusing variety of answers.
Whom should we believe? Do scientists really know what they are doing, or are they perhaps as confused about their aims and methods as the rest of us? I suggest that it is as hard for a scientist to characterise the aims and methods of science in general as it is for normal persons to characterise the grammatical rules governing their own use of language. But I am going to stick my neck out and try.
If we are to understand the nature of science, we must see it as an activity and achievement of the human mind alongside others, such as the achievements of children in learning to talk and to cope with people and other objects in their environment, and the achievements of non-scientists living in a rich and complex world which constantly poses problems to be solved. Looking at scientific knowledge as one form of human knowledge, scientific understanding as one form of human understanding, scientific investigation as one form of human problem-solving activity, we can begin to see more clearly what science is, and also what kind of mechanism the human mind is.
I suggest that no simple slogan or definition, such as can be found in textbooks of science or philosophy can capture its aims. For instance, I shall try to show that it is grossly misleading to characterise science as a search for laws. 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. 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 to liberate some scientists from the dogmas indoctrinated in universities and colleges. I shall also try in later chapters 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.
An important reason for studying the aims and methods of science is that it may give us insights into the learning processes of children, and help us design machines which can learn. Equally, the latter project should help us understand science. A side-effect of my argument is to undermine some old philosophical distinctions and pour cold water on battles which rage around them like the distinction between subjectivity and objectivity, the distinction between science and philosophy and the battles between empiricists and rationalists.
My views have been powerfully influenced by the writings of Karl Popper. However, several major points of disagreement with him will emerge.
Whether the third aim makes 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 book. The second kind of aim will not be given much attention either, except when relevant to discussions of the first kind of aim, on which I shall concentrate.
These aims are not restricted to science. We all, including infants and children, aim to extend our knowledge and understanding: science is unique only in the degree of rigour, system and 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 science 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. (See chapter 6 for the role of self-criticism in intelligence.) But it does not distinguish science from philosophy. Let us now examine the factual aims of science more.closely.
NOTE: I would now (since about 2002) express the aim of 'extending knowledge of what sorts of things are possible' in terms of 'extending the ontology' we use. This is also part of the process of child development, e.g. as illustrated in this presentation:
'Ontology extension' in evolution and in development, in animals and machines.
And in: http://www.cs.bham.ac.uk/research/projects/cogaff/talks/#glang
Evolution of minds and languages.
What evolved first and develops first in children:
Languages for communicating, or languages for thinking (Generalised Languages: GLs)?
A similar distinction pervades the writings of Karl Popper, though he would disagree with some of the things I say below about (1.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), studying the form of the world, whereas astronomy is perhaps more concerned with (1.b), studying the contents.
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, (l.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. The study of form and the study of content go hand in hand. (This must be an important factor in the design of intelligent machines.)
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 occurrences, even if the possibility is re-described from time to time as the language of scientists evolves.
Hypotheses about the limits of 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 frequently need 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. (This is true of child development too.) It is an organic, principled growth. Let us now look more closely at aim (1.a), the aim of extending knowledge of the form of the world.
All the following types of learning will ultimately have to be catered for in intelligent machines.
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.
A similar aim must motivate intelligent learning machines.
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 subgoals (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 misguided research, theorising and teaching.
I shall say more about these three fundamental aims later. The next two sections contain further general discussion of the relations between these seven interpretative aims, and the previously mentioned historical and technological aims of science.
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 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 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.
Like the interpretative aim, the "historical" aim of finding out about the contents of particular bits of the world must also be built into intelligent machines. Moreover, the pursuit of these two aims by a machine will interact, as in science.
For example, knowing that rain is possible and wanting to stay dry, one can take a waterproof covering whenever one goes out. More generally, one can take precautions to prevent the effects of an unwanted possibility, even if one cannot predict or prevent it.
Similarly, one can take steps to get the best out of possibilities one knows about but cannot predict or produce, like building tanks to catch water in case it rains, which might be worth doing even if one had no idea how often rain fell, provided one needed the water enough and had time and materials to spare.
The discovery of possibilities may have technological significance in less direct ways. Knowing that something is possible can provide a boost to research into an understanding of how and why, so that its occurrence may be predicted or brought about, or new variants produced. Knowledge that it was possible for things heavier than air to fly, namely birds, provoked research into ways of enabling men and machines to do so. That was a case of a possibility demonstrated by actual instances, then extended to a wider range of instances.
Sometimes a possibility is explained by a theory before instances are known, and this again can have great technological importance, as in the case of Einstein's discovery of the possibility of converting mass into kinetic energy, or the theoretical discovery of the possibility of lasers before they were made. Much of engineering design consists of demonstrating that some new phenomenon is possible and showing how, or that some possibility can be produced in new ways or in new conditions. An intelligent planning system may also need to be able to generate types of possibilities before instances are known actually to exist. This is commonplace in engineering design.
Formally this technological activity has much in common with the supposedly purer or more theoretical activity of inventing a new theory to explain some previously known possibility, or using the ideas of one science to explain possibilities observed in another, for instance using physics to explain chemical possibilities, and using chemistry to explain the very complicated possibility of sexual reproduction. (See J. Watson, 1968.) 'Pure' science first discovers instances of possibilities then creates explanations of those possibilities whereas 'applied' science uses explanations of possibilities to create instances. The kinds of creativity and modes of reasoning involved are often similar. More generally, any form of intelligent action requires an understanding of possibilities. One cannot change the world sensibly without first interpreting it, even though attempting to change things is often indispensable for correcting mistaken interpretations and deepening one's understanding. Acting intelligently in a situation requires a survey of possibilities, which requires an understanding of the potential for change in the situation. For example, opening a window requires a grasp of the possibilities for movement in the window and its catch. But this requires interpreting what is actual, i.e. relating it to general knowledge of what sorts of things are possible in what circumstances: so action requires knowledge of the form of the world. Grasping new possibilities often involves inventing new concepts, new languages in which to represent them, a topic discussed later.
Much more could be said about relations between the interpretative aims of science, and the historical and technological aims. Instead, let's take a closer look at some of the interpretative aims of science, the aims concerned with learning about and understanding possibilities. We shall attempt to clarify the similarities and differences between these aims, and then proceed to formulate criteria for assessing some of the achievements of scientists.
The three aims 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. Let's take a closer look at (a).
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 representation 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 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 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. Both involved numbers.
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.
Pictures, diagrams, maps, models, graphs, flow charts, and computer programs, have all been used. 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 by linguists to represent structures or sentences. I shall argue later that these non-verbal forms of representation play a part in valid reasoning, scientific and non-scientific, conscious and unconscious.
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. Non-logicians can often distinguish valid from invalid arguments without being able to say how. They have not learnt the overt language of logicians.
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.
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 (e.g. Kuhn) into thinking that there are no reasons, and inferring 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. In a later chapter I shall illustrate this by analysing some of the complexities children master when they learn to count.
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.
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. (Work in artificial intelligence is beginning to explore these problems.)
Philosophers 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 a study of our ability to think of things 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 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 tackling them: so the job does not get done. (Piaget seems to be an exception.)
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.
Until these and other 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, When we really can model conceptual development, things will be very different.
To sum up so far. We have been discussing subgoal (a), namely developing new concepts and symbolisms making it possible to conceive of, think about and ask questions about new types of possibilities A system of concepts and symbols with procedures for using them constitutes a language. 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.
So the important differences between modern scientists and those of the distant past include 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. The same applies to development of an individual.
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. Any intelligent learning system will need to have procedures for rationally criticising its current conceptual and symbolic resources. (See Winston (1975) for a simple example of a computer program that modifies its own concepts.)
There are several ways in which a typology and associated notation can be rationally criticised. For instance one may be able to make one or more of these criticism:
(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 subdivided into two or more categories, because their instances have different relations to the other categories,
(e) That a principle of subdivision fails to decide all known cases, e.g. because of inapplicable tests,
(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, e.g. when people use diagrams with bogus detail,
(h) That the concepts used generate questions which apparently cannot be answered by empirical investigation (like the question 'How fast is the Earth moving through the aether?'),
(i) That more powerful explanatory theories can be developed using other tools for representing possibilities.
I suspect that some or all of these criteria are used, unconsciously of course, not only by scientists, but also by young children in developing their conceptual systems. They could also play an important role in an intelligent learning machine.
Several of these criteria will remain rather obscure until later. In particular, the first two can only be understood on the basis of a distinction between what is conceivable or representable and what is really possible in the world. We now examine this, in order to explain the difference between the first two interpretative subgoals of science, namely (a) extending what is conceivable or representable and (b) extending knowledge of what is really possible.
This aim is indefinitely extensible: having found out that X's can exist or occur, one can then try to find out whether X's 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.
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 the connection between sense and failure of reference see Sloman (1971b).)
We can use the notion of what is or is not 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 representational system', as in logically possible', and (b) used to refer to what can occur or exist in the world. This is why the first two interpretative aims of science are not always clearly distinguished. But what is the difference between (a) and (b)?
This is not an easy question to answer. 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. The former involves conceptual analysis (see chapter 4), the latter perception, experiments or surveys.
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 into my bath 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 to the former.
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 only tentatively, 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.
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.
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 and White, 1975.) A good analysis would be part of a design for a mind.
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.
Roughly, an explanation of a possibility or range of possibilities can be defined to be some theory or system of representation which generates the possibility or set of possibilities, or representations or descriptions thereof. An explanation of a range of possibilities may be/a grammar for those possibilities. A computer program is a good illustration: it explains the possibility of the behaviours it can generate (which may depend on the environment in which it is executed). In this way Artificial Intelligence provides explanations of intelligent behaviour. There is much to be clarified in these formulations, but first some examples from the history of science.
Some of the theories listed so far not only explained possibilities, but also contained enough detail to make prediction, and in some cases control, possible. This is fairly common in physics, though more difficult in biology. In the case of the human sciences (and philosophy) the ability to predict and control is rare.
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 producing a work of art, the possibility of extending an art form or language, the possibility of using knowledge acquired in one context to solve a problem of a quite different sort, 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.
There are missing explanations of possibilities in physics and chemistry also. As far as I know, the possibility of mechanical utilisation of fuel energy at levels of efficiency achieved in animals is still not explained.
Such philosophers normally assume 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 assumed that the deduction is logical, that is the inference from 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. 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.
I shall explain in chapter 7 exactly what 'valid' means and why this generalisation to non-verbal forms of valid inference should be permitted. Just as the semantic rules of verbal languages guarantee that certain transformations of sentences preserve truth, so can semantic rules of non-verbal representations guarantee that certain manipulations preserve denotation. (This generalisation of the concept of a valid inference is central to the analysis of the elusive concepts of 'cause' and 'mechanistic explanation' but that is another story.)
Typical examples of such non-verbal inference methods are: the use of Venn diagrams in set theory, the 'parallelogram' representation of addition of forces, velocities and other vectors, the use of circuit-diagrams in electronics, the use of a map to select a route, the use of a diagram to show how a machine works. 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'.)
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:
An illustration 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 or models of molecular structures. Here one range of (relatively primitive) possibilities is used to explain another range.
This simple chemical theory had to be revised and refined of course, but that does not affect the point that at least part of its scientific function while it survived was to explain a range of possibilities according to criterion (1). (In AI research, a program can explain a range of possible behaviours. A derivation consists of running the program, or, preferably, reasoning about the program's capabilities.)
So a good explanation of a range of possibilities should be definite, general (but not too general), able to explain fine structure, non-circular, rigorous, plausible, economical, rich in heuristic power, and extendable.
A theory explaining a range of possibilities 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 do not 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 philosophical 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 conceptual, 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. (Compare Pylyshyn 1978, Sloman 1978.)
These criteria for assessing explanations of possibilities could be justified by showing how their use contributes to the interpretative and practical aims of science. They would also have to play a role in the design of an intelligent learning machine, along with the previously listed criteria for assessing concepts and symbolisms. So these criteria are relevant to developmental psychology and AI, as well as to the methodology of the physical sciences.
Although it explains how certain sorts of phenomena are possible, the underlying mechanism or structure postulated may, at the time the theory is proposed, be unobservable, so that observation of its state cannot be used to predict actual occurrences of those phenomena. 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 or controlling most of 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 any one 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 understanding 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 (e.g. a computer program) 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 activated. 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.
I believe that the stress on predictive content derives from a misunderstanding of criteria 2 and 4, namely the requirement that the theory be definite and capable of explaining
Lack of predictive power, practical utility, or refutability need not rule out rational discussion of the scientific merits of an explanation of a range of possibilities. Neither should it rule out rational comparison with 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 or pseudo-science, 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: I am not arguing about the definition of 'science'. My point is that among the major merits of the generally agreed most profound scientific theories is the fact that they satisfy the 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 are among the objective criteria by which scientific and metaphysical theories are in fact often 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 limited theoretical interest. Moreover, it has bad effects on the training of scientists. Since Artificial Intelligence produces unfalsifiable, but rationally criticisable, theories, it should undermine this harmful trend.
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 these contexts all the normal stress on repeatability of scientific experiments is unnecessary and has misled some 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.
Beethoven's compositions are unique. Yet it is a fact that it was possible for a human being to create them. That possibility requires explanation.
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 it is the correct explanation. In practice, this becomes the question 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 can blind 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 often shirked because only laws and significant correlations are thought fit to be published. 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, or in courses for budding scientists. 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 (laws) 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.
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 suggest that anyone who tries this will discover, possibly to his surprise, that the scientific advances which he regards as most important include not only discoveries of new laws or regularities, or explanations thereof, but also discoveries of new types of phenomena, new explanations of ranges of possibilities, new concepts, new notations, and therein new means of asking questions about the world. For example, Boyle's discovery of his law relating pressure and volume of a gas, was not so profound as the prior invention of the concepts of pressure and volume. The search for laws presupposes the search for possibilities and their explanations, and this requires concepts and notations for representing possibilities.
For reasons which I do not fully understand, Popper is apparently strongly opposed to all this talk of concepts and possibilities. (See, for instance, pp. 123-4 of his (1972) where he describes it as an error to think that concepts and conceptual systems or problems about meaning are comparable in importance to theories and theoretical systems, or to problems of truth.) As far as I can tell, his argument rests on the curious assumption that concepts or meanings are purely subjective things, and that only complete statements containing them can be assessed or criticised according to objective criteria. I hope I have said enough to refute this.
Roughly, our disagreement seems to hinge on Popper's view that the only place for rationality in science is in the selection from among hypotheses expressible in a given language, whereas I have tried to show that there are rational ways of deciding how to extend a language, and therefore how to extend the set of expressible hypotheses. I admit that there are still serious gaps in my discussion: a theory of concept-formation is still lacking.
Note added 15 Nov 2008:
We can distinguish two kinds of ontology extension: "definitional" and "substantive".
In the first kind, a new concept, predicate, function, or logical operator is defined explicitly in terms of previously used concepts, etc. Thus nothing new can be thought or expressed as a result of the extension, though some things may be expressed or thought more concisely. Definitional ontology extension introduces only abbreviations for concepts and forms of expression that existed previously.
In substantive ontology extension, something new is introduced that is not definable in terms of what was previously understood. According to concept empiricism the only way to do the latter is to derive the new concept from experience of instances, e.g. experiencing a new colour, or taste, or smell. Approximately the same claim has been central to "Symbol Grounding" theory, introduced by S. HarnadThe Symbol Grounding Problem, Physica D, 42, 1990, pp. 335--346,However, the advance of science shows that it is possible to introduce new theoretical concepts that are neither abstracted from experience of instances (e.g. because instances cannot be experienced) nor defined in terms of previous concepts. E.g. this happened with concepts like proton, electron, charge, valence, chemical bond, magnetic field, gene, and others. The failure of logical empiricists to explain such conceptual innovations in terms compatible with concept empiricism led to new ideas about concepts that are implicitly defined by the theories that use them. For more on this see these presentations
Why symbol-grounding is both impossible and unnecessary, and why theory-tethering is more powerful anyway.
Evolution of minds and languages. What evolved first and develops first in children:
Languages for communicating, or languages for thinking (Generalised Languages: GLs)
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.
Similarly, rational processes of concept formation and theory construction will have to be built into an intelligent robot if it is to be capable of matching the learning ability of young children. The development of science, the learning of a child, and the mechanisms necessary for an intelligent robot all involve computational processes, which build up and deploy knowledge of the form and contents of the world. This is one of several points at which bridges can be built between philosophy of science, developmental psychology, and artificial intelligence.
The attempt to build these bridges will provide good tests for the philosophical theories outlined here. It is certain that my theories will prove inadequate. But I hope they may provide a useful basis for further research.
A review of this book was published by Steven P. Stich, in 1981
Review of: The Computer Revolution in Philosophy: Philosophy, Science and Models of Mind,
by Aaron Sloman.
Reviewed by Stephen P. Stich
The Philosophical Review,
Vol. 90, No. 2 (Apr., 1981), pp. 300-307
That review has now been made available, with the author's permission, here:
Part of the review criticised the notion of 'Explaining possibilities' as one of the aims of science and my use of Artificial Intelligence as an example. A partial response to the review is now available here:
(That is still work in progress.)
 This is because the definition of the set entails that it contains itself if and only if it does not contain itself. (Note added: 2001. See also A. Botterell 'Conceiving what is not there', Journal of Consciousness Studies vol 8, no 8, pp 21--42, 2001.)