¶0 SUMMARY OF TECHNICAL TERMS USED IN ESSAY ONE I do not use the terms in this essay in a very strict technical sense. To do so would have meant defining terms separately for each theorist, because they use the terms differently. This is a summary of the meanings I have given to the terms. I think my definitions are reasonably consistent with the ways the authors use them, and reasonably consistent with conventional English.
Argument: The case that someone makes. In a theory (for example) or in an essay (for another example).
Axioms: The starting points of an argument, deduction or theory that, by definition, are not proved by the theory. Premise.
Conception: Giving birth to an idea. Or another word for concept.
Deduction: Argument or theory starting with axioms or premises and leading to a conclusion.
Falsification: Testing a theory by using empirical data to try to disprove it. See verification.
Induction: Argument or theory starting with empirical observations and leading to a conclusion
Empirical: Based on experience
Empiricism: Theory that knowledge is based on experience
Hypothesis: A tentative or unproved theory
Imagination: Creative mental faculty. Ability to dream up ideas of one's own and ability to create in your own mind an interpretation of other people's ideas.
Positivism: Trying to understand or describe the world as a sequence of cause and effect between objects that one can observe. Seeking to understand the world as it is, scientifically, rather than criticising it.
Proof: Can mean testing a theory by showing that one point follows rationally from another (as in Geometry). Can mean testing a theory by showing that its premises and/or conclusions conform with empirical reality. John Stuart Mill argued that to strictly prove a theory we would have to show its rationality, show the conformity of its axioms and conclusions with empirical reality, and show that there is no other rational theory which also fits the empirical reality. To fully prove a theory to this extent is either very difficult (Mill thought Newton had done it); or impossible (Einstein demonstrated that Newton had not done it. There may always be a theory, waiting for someone to imagine it, which is better than the accepted one).
Theory: Set of ideas that we use to explain the world
Verification: Testing a theory by using empirical data to try to confirm it. See Falsification.
ESSAY ONE: EMPIRICISM, THEORY AND THE IMAGINATION
John Stuart Mill and his problems with Francis Bacon
¶1 I want this essay to explain why I think that theory and imagination are important to science. It will do so by introducing you to some of the theorists who have made theories about what science is. I have not chosen these writers because they are ones I agree with, but because they are theorists most often associated with the idea that science should be built on careful observation of data. I want to show, from their work, that imagination and theory construction are just as important. I will also mention Karl Popper, who is usually associated with the idea that imagination and theory construction are important, but who also stresses the importance of testing theories against the data. The other theorists I discuss are Francis Bacon, Thomas Hobbes and Isaac Newton from the 17th century; James Mill, John Stuart Mill (James Mill's son), Auguste Comte and Thomas Macaulay from the 19th century; and Bertrand Russell in the 20th century. In particular, I try to illustrate the importance of theory construction in the work of Francis Bacon, Sir Isaac Newton and John Stuart Mill.
¶2 Epistemology Technically, this essay is about epistemology. Epistemology is the study of knowledge. So this essay is not about theories about society, but about theories about theories. Books about epistemology frighten many people, including me. This is because theories about theories include a lot of technical words. The advantage of learning these technical words is that they will give you a vocabulary to analyze and talk about theories.
¶3 Many words used in this essay may be new to you. It should help you understand them if you realise, as I explain below, that they are words for describing things you already do. Science develops faculties that we already use all the time. So, if the essay confuses you, take it in smaller doses, and check that you understand the meaning of the words. To help you, I have put a summary of the most important technical terms used on the facing page.
¶4 Theory as you know it Theory should not frighten you. You have been making it for yourself ever since you started thinking.
Nowadays we use the word “theory” for sets of ideas that we use to explain the world. The word comes from a Greek word for observing, and this may suggest something that is not self-evident: which is that we use theory to look at the world. The world will appear different to you according to the theory you use. When you wake up in the morning do you lie in bed wondering who you are? Or do you feel your body to discover your identity? Or do you immediately bring into use a set of ideas you already have about yourself? If you are woken up by a baby crying your perception will be different if you think you are the baby's parent, than if you think you live next door to the baby. If you think you are a student and that you have a lecture in a few hours you will behave differently than if you think you are a Prime Minister who is facing a vote of no confidence in a few hours. Reality may come crashing in on you to suggest that your theory about yourself is wrong, but we do not wait for reality, we start with theories. It is the same whether we are dealing with the everyday concerns of nappy changing and parliamentary votes (according to who you are) as it is when we are trying to understand the world “scientifically”. To look at the world we use theories.
¶5 Theories about science The theories I discuss in this essay are theories about what science is. You may have looked for science already in my list of technical terms. But it is not there. People disagree about what science is and it is important that you learn different definitions and theories about it. Then you will be able to discuss, with yourself or other people, the different theories, and possibly reach conclusions for yourself.
¶6 Empiricism Empiricism is the name given to an idea about science that most people in Britain and America seem to believe. Empirical knowledge is knowledge based on experience. A strict empiricist is someone who believes that all knowledge comes from experience or observation. You might guess from this that empiricists would want us to build our theories on observed facts instead of theorising before we start. This is only true of some empiricists. Let me summarise what some of the empiricists we are discussing say on this point:
• Macaulay argues that we should observe history carefully before making theories. (But he did not do this himself).
• Bacon wants us to derive part of our theories, (called “axioms” and “conceptions”), from observation. This, he argues, will ensure that the rest of our theory has sound foundations. But he does not suggest, as Macaulay seems to, that theory as a whole could be (tentatively) derived from a mass of observations.
• John Stuart Mill thinks that we often have to theorise with axioms created in our imagination. For Mill, therefore, all of a theory might need to be created in the mind. John Stuart Mill also stresses that empirical testing is not the only testing that one applies to a theory, one also needs to examine it to see if it is logical, that is that the parts of the theory hang together in a rational way.
¶7 The majority of empiricists are like Mill in that they accept that all of (at least some) theories are created in the mind. They still claim to be empiricists because they believe that the empirical test of the theory lies in how it relates to the empirical world after it has been created in our imagination. Mill called this empirical testing “verification”, or finding out if the theory is true. Karl Popper, a 20th century theorist, calls it “falsification”, because his idea of science is that one creates theories that one tests by trying to show that they are false.
• Bacon, Hobbes, Newton, and both Mill's all think it vital that we have theories developed from axioms that reason deductively to conclusions. These theories are created in the mind. Bacon, however, believes that the axioms can be “induced” from empirical experiments. John Stuart Mill thinks that “hypotheses” would most often have to be the axioms.
• For John Stuart Mill the relationship between theory and empirical reality can be at either or both ends of the theory: at the axiomatic start or the conclusions. If the conclusions are found to be consistent with empirical reality, Mill calls this “verification”.
These issues will become clearer as you become more familiar with the terms empiricism, axiom, deduction and hypothesis through reading this essay.
¶8 Mill's spectacles or Bacon's blinkers? Theoretically you are a very rich person—you have inherited a civilisation worth of theory. A little of it you already know, but most of it is waiting for you to claim when you read books, surf the internet, listen to a lecture, talk to someone who thinks they know the truth, watch television, or whatever. But are these theories blinkers or spectacles? Do they stop you seeing things to the side of you, or allow you to see in front of you more clearly? Francis Bacon thought he had inherited a bundle of theories that were blinding him to the real world. John Stuart Mill thought he needed some of the same theories that Bacon discarded in order to discover the real world. Could they both be right? Can theories stop us seeing and help us to see? I am going to leave that question for you to think about.
FRANCIS BACON ¶9 Francis Bacon, who wrote in the early 17th century, is often thought of as the originator of modern empiricism. He was a very influential English writer on theory and science who lived in the early 17th century. All over Europe thinkers sought out his writings because he wrote of a radical new way for discovering truth.
¶10 Bacon's new way was by not doing what I suggest you do. He was opposed to theories that come before the facts. He thought we should start with observations and build our theories on them. However, he did think theories are important. The issue he would have disagreed with me on is where we should get our theories from. I am saying that the wealth of theories that you inherit from the past are an asset. He argued that they are a hinderance.
¶11 Bacon said that the theories that people had were leading them astray. He did not want people to use the theories they had inherited, he wanted them to build knowledge on experience. He also did not want it built on a little experience, or on unsystematic experience, but on a great deal of systematic experience. Finally he wanted the results of that systematically acquired experience to be rigorously converted into a true science.
¶12 In Bacon's time science just meant knowledge. Bacon's belief that there is a true way of gaining knowledge, different from the way that was taught in the universities of his time, gained a wide acceptance in the following centuries and this changed the meaning of science. People began to use the word science for knowledge that is rigorously built on the secure foundations of experience.
¶13 Bacon's new directions Bacon wrote a book called Novum Organum; Or, True Directions for the Interpretation of Nature. Book one of this was headed: Aphorisms on the Interpretation of Nature and the Kingdom of Man. An aphorism is a short saying, and just refers to the way he wrote. By the interpretation of nature he was referring to what we now call the natural sciences. By the interpretation of the kingdom of man he meant what we now call the social sciences. “We certainly understand”, he said, “that what we have said holds universally”. “Our method, which proceeds by induction, embraces all subjects” (Bacon 1627 aphorism 127). So Bacon prophesied that there would be a true natural science and a true social science if people followed the method that he called “induction”.
¶14 Deduction and Induction To understand what induction is we must bring in another term: deduction. A deduction is when you work out consequences from premises that you are told, or that you accept as true. The premise is the starting point. For example, let us start with the premise that “everything that Andrew Roberts writes is incomprehensible”. If this is true you could deduce that you are unable to understand what I am saying. The statement “everything that Andrew Roberts writes is incomprehensible” is a general statement because it applies generally to everything that I write. The statement that “you are unable to understand what I am saying” is a particular statement because it applies to this particular instant of your trying to understand this particular piece of writing. In deduction we work out a particular conclusion from a general premise.
¶15 Do you think you may have understood that? If you have then the particular conclusion that “you are unable to understand what I am saying” is false. Experience has shown you that it is false. But how did we get to a false conclusion? Was it because we reasoned falsely? Or was it because our general premise was false? I think you will find, if you look back at the example, that your reasoning was in order (we call that valid reasoning). The problem is that the general premise is false. If you can understand this piece of writing it can not be true that “everything that Andrew Roberts writes is incomprehensible”. This piece of writing, at least, is an exception as far as you are concerned.
¶16 Induction and statistics Now let us try it the other way round. Let us say that someone has tried to read this book and has failed to understand anything. They can certainly say from experience that this particular piece of writing by Andrew Roberts is incomprehensible to them. They might, in exasperation, say “everything that Andrew Roberts writes is incomprehensible”. If they did they would have reasoned from a particular experience to a general statement. In fairness, however, you would have to point out to them that you understood something that I wrote, so their general conclusion is false. In both cases we arrived at a false conclusion. But in the second case we started from a premise that we knew was true because it was a direct experience. The person who could not understand this knows that he or she cannot understand this, and we have no reason to doubt it. Bacon thought that the problem with culture in his day was that it was not built firmly on enough experiences. Let us see how we could get a true general conclusion from particular experiences about the comprehensibility of my writing.
¶17 We could send out a letter with everything I write, asking the reader if he or she can understand it. Obviously I should not write the letter, because we would have to be sure that the letter could be understood. Perhaps we would enclose a stamped addressed envelope and ask the reader to tick a box marked yes if they understood the book, a box marked no if they could not understand it and a box marked don't know if they were not sure. Then, when we got the replies, we could count how many people ticked each box. The general statement we could then make might have the form: 5% of people can understand what Andrew Roberts writes, 20% do not know if they can understand and 75% cannot understand him. (Or whatever the figures were).
To reason thus, from experience of particulars to a general conclusion, is what Bacon means by induction. As you can see, it seems a lot more secure and scientific than deduction.
¶18 Axioms and conceptions Bacon did not envisage science as something that just describes the external appearance of the world. He said he rejected “for the most part that operation of the mind which follows close upon the sense” ((Bacon 1627 Preface) and believed that science should penetrate below the surface. “The discoveries hitherto made in the Sciences are of a kind usually bordering upon common conceptions; but, in order that we might penetrate to the inner and more remote parts of nature, it is necessary that conceptions, as well as axioms, should be abstracted from things by a more certain and better constructed way, and that a method of applying the intellect, altogether better and more certain should be brought into use”. (Bacon 1627 aphorism 18). Our example of a statistical investigation of how many people can understand what I write has not got much hidden depth. It is just descriptive. For science to have power it needs to create theories that are built on axioms and conceptions that let us look behind appearances to the reality. Think of the movement of the sun. It appears to rise on one side of the flat plain of the earth and sink on the other. It appears to die on one horizon, to be born again on the other the next morning. Scientists did not conclude that the earth is a sphere circling the sun by carefully watching this process day after day. They built complex theories based on conceptions and axioms. It is these conceptions and axioms that Bacon thinks should be based on careful observation.
¶19 Axioms and geometry If we can understand what axioms and conceptions are we will have a better understanding of the importance of theory and imagination to science. Axioms are the parts of an argument that have to be accepted as true for the argument to work. Aristotle in his Metaphysics said that you cannot prove everything because you have to start somewhere. That somewhere is with the unproven axioms. “By the starting‑points of demonstration” Aristotle said “I mean the common beliefs, on which all men base their proofs; e.g. that everything must be either affirmed or denied, and that a thing cannot at the same time be and not be, and all other such premises”. (Aristotle/Metaphysics Book 3, section 2)
¶20 You may have come across axioms in geometry. Euclid defined a straight line as “that which lies evenly between its ends”, which is much the same as saying “the shortest distance between two points”. One of his axioms was that “it is possible to draw a straight line joining any two points” (Kline 1953/1972 p.62). For Euclid's proofs to work, you have to accept his definitions and his axioms. By creating new definitions and axioms, mathematicians have created different geometries.
¶21 Conception, babies and universals A conception is either the receiving of something into the womb and its formation there or, by analogy, receiving something into the mind and its formation there. The conception in the mind is different from the sensations that are received, just as the baby is different from the sperm and the ovum. What you receive into your mind is particular. It is this particular bundle of sensations. The concept that you have of those sensations is general or universal: it applies to all bundles of sensations of that kind. For example, I know a bundle of sensations that I call Randolph. To explain Randolph to you I tell you that he is a cat. Cat is a conception or universal. It does not just apply to Randolph but to all bundles of sensation that we categorise as cats.
¶22 Science deals with axioms and conceptions, and arguments developed from them. Bacon points out that you can reach different conclusions in science in two different ways. You can reason differently from the same conceptions and axioms (in which case you would check the reasoning to see if some of it was invalid) or you can reason from different conceptions and axioms. I am arguing that it is our imagination that creates these conceptions and axioms and that theory is the development of the argument from them. Bacon thought the axioms and conceptions could be induced from observation. By this he might have meant that they could be induced without imagination, or that the observations could exercise a tight control on the imagination.
¶23 Hobbes: an example of a Baconian science Thomas Hobbes helped Bacon by writing down his ideas when Bacon's infirmities prevented him doing it for himself. Sometime after Bacon's death, Hobbes presented a theory of social science which he claimed was based on axioms rooted in careful observation, rigorously argued through. If we look at how Hobbes starts his theory, we will see what is meant by saying that the Baconian method of science is to root one's concepts and axioms on empirical observation.
¶24 Hobbes starts by defining his terms. He says that we have some natural faculties, three of which he calls “sense”, “imagination”, and “memory”. By defining these terms he means being clear about the concepts and rooting these in the real world.
¶25 Sense Hobbes devotes the first chapter of his book to defining sense. His definition is to say that sense is the effect of objects on parts of our bodies. He then gives us one of his axioms. This is that there is nothing in our minds that has not, at some point, been started off by the effect of an object on our senses (Hobbes 1651 chapter 1: page 1).
¶26 This is a concept and an axiom that he thinks can be clearly understood and can be shown to be true because it corresponds with our perceptions. He says that he shown this “natural cause” of sense in another book. This refers to his writings on optics: or the study of the way objects create sensations in our mind via our eyes.
¶27 If we are clear about our definitions, in relating them to natural causes, Hobbes believes, we will achieve accuracy between our concepts and the real world. The force of what he is saying may be clearer if we look at his example of the alternative definition of visual sense used in the Universities and based, he said, on Aristotle. He calls this “insignificant speech” because it is not clearly defined, and so not rooted in careful observation: “the philosophy schools, through all the universities of Christendom, grounded upon certain texts of Aristotle,say, for the cause of vision, that the thing seen sendeth forth on every side a visible species, (in English) a visible show, apparition, or aspect, or a being seen; the receiving whereof into the eye is seeing.” (Hobbes 1651 chapter 1)
¶28 Imagination and memory Hobbes defines imagination and memory in terms of sense. Here the points to notice are two: 1) that he has rooted his definitions of imagination and memory in something (sense) he thinks we can clearly identify in the real world. 2) that he sticks to the definition he gives, without allowing all the other confusing meanings that can be attached to the terms imagination and memory.
¶29 Hobbes says that senses conjure images into our minds. These images are our ideas. They are not just there when we are receiving the sensations, but persist afterwards. They have what Hobbes calls a `motion' in our minds. This movement of images through our minds is what Hobbes calls imagination. “Imagination is nothing but decaying sense” (Hobbes 1651, chapter 2: paragraph 2). Images fade because they are obscured by stronger ones. The faded images are called memory. (Hobbes 1651 Chapter 2, margin: Memory). So images and memory are the same thing—the one fresh and virulent, the other faded.
¶30 From such clearly defined concepts and axioms, Hobbes reasons that a human being is a stream of images and desires seeking its own satisfaction, that this satisfaction runs into conflict with the desires of other human beings and becomes self defeating, that the power of a ruler imposed on the multitude of humans is necessary to produce order and to enable the mutual satisfaction of desires, etc. This, schematically, is the structure of Hobbes' science. It is Baconian in that:
• The empirical ground is at the beginning in the induction from experience of axioms and concepts
• There is a theory constructed on the basis of these concepts and axioms that allows us to find out something that would not be self-evident from observation. In this case, the conclusion that the power of a ruler imposed on the multitude of humans is necessary to produce order and to enable the mutual satisfaction of desires. Hobbes, in fact, concludes much more than that, but I am not going to attempt compressing the whole argument of his book into a few lines!
¶31 James Mill, who I discuss later, formed his theories on the same pattern as Hobbes. I give an example (under James Mill's Deductive Argument for Democracy) of how he reasoned from similar axioms and conception to Hobbes, to a different conclusion. Hobbes reasoned that government would have to be authoritarian, James Mill argued that it should be democratic. The fact that different conclusions can be argued from similar axioms and concepts does not mean that the Baconian method is wrong. It could mean that the axioms and concepts are not correctly defined, or it could mean that there is a fault in the theory: that the argument is not sufficiently rigorous.
¶32 Make a list Different theorists start from different axioms and conceptions. In reading the theorists in this book you should find it useful to keep your own checklist of the axioms and conceptions you think are peculiar to each. A list of basic principles will help you to recall the different theories and to compare them. The list could include items like: “Hobbes pictured people as streams of impressions and selfish desires, forever in motion”; “Locke considers that people are naturally aware of a law of nature guiding them”; “utilitarians claim that "good" is what avoids pain and maximizes pleasure”; “Durkheim thinks that society is real”. Such basic premises are very close to being axioms of their theories, and they contain conceptions like “impressions” (in Hobbes), “law of nature” (in Locke), “good” (in the utilitarians) and “society” (in Durkheim), which you need to understand in the way that the theorists use them.
¶33 Anticipate From the axioms and conceptions you should be able to anticipate what a theorist will think about a subject. For example, from “utilitarians claim that "good" is what avoids pain and maximizes pleasure” you might be able to work out what kind of laws they think are bad and what kind of laws they think are good. You may get it wrong, but the fact that you and they are both using reason will mean that you will often get it roughly right. It is thinking through the arguments of theorists, in this way, that will teach you what theory construction is and set you on the path for making your own theories.