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1: Empiricism, Theory and the Imagination

John Stuart Mill and his problems with Francis Bacon

Theory as you know it
Theories about science
Mill's spectacles or Bacon's blinkers?

Bacon's new directions
Deduction and Induction
Induction and statistics
Axioms and conceptions
Axioms and geometry
Conception, babies and universals
Hobbes: an example of a Baconian science
Imagination and memory
Make a list

Hypotheses: are they dangerous or essential?

Bacon, Hobbes and Newton


John Stuart Mill defends deductive theory
Induction and Ratiocination (Deduction)
Advanced science must be deductive

James Mill's Deductive Argument for Democracy
Women and children

Macaulay's empirical case against James Mill
Macaulay's Descriptive Empiricism
Macaulay's description of scientific method
Macaulay's actual practice

John Stuart Mill's Deductive Sociology
Custom and tradition and a science of character
The Direct Deductive Method
The Inverse Deductive Method

Mill's four stages of history writing
Comte's stages of historical development
How do we know this?

(¶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)   Technically, this essay, and chapter three, are about epistemology. Epistemology is the study of knowledge. (episteme being Greek for knowledge, and ology Greek for study)

So this essay is not about theories about society, but about theories about theories.

Theories about theories include many technical words, which can be off- putting. The advantage of learning these technical words is that they will give you a vocabulary to analyse 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.

Theory as you know it

(¶4)   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.

Theories about science

(¶5)   The theories I discuss in this essay are theories about what science is. 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 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 Mills 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.

Mill's spectacles or Bacon's blinkers?

(¶8)   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.


(¶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.

Bacon's new directions

(¶13)   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 1620 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.

Deduction and Induction

(¶14)   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 [axiom] 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?

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.

Induction and statistics

(¶16)   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.

Axioms and conceptions

(¶18)   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 1620 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 1620 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.

Axioms and geometry

(¶19)   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.

Conception, babies and universals
more about conception

(¶21)   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.

Hobbes: an example of a Baconian science

(¶23)   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)   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)

Imagination and memory

(¶28)   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 (discussed 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.

Make a list

(¶32)   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)   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.


Hypotheses: are they dangerous or essential?

(¶34)   At this point I want to compare Bacon's 17th century claims about a new method in science, with the way that the scientific achievements of the 17th century are described by a 20th century empiricist, Bertrand Russell. In his History of Western Philosophy, Russell has a chapter called The Rise of Science which begins

"Almost everything that distinguishes the modern world from earlier centuries is attributable to science, which achieved its most spectacular triumphs in the seventeenth century." (Russell, B. 1961 p. 512)
He says that the seventeenth century pioneers of science had two virtues: immense patience in observation, and great boldness in framing hypotheses. (Russell, B. 1961 Book 3, chapter 6, p. 514)

A hypothesis is an unproved theory. The Greek origin of the word (something placed under) suggests that hypotheses are the foundation of science. So the clearest difference between Bertrand Russell and Bacon's descriptions of science is that Russell thought science could use unproven theories (Russell, B. 1961 p.529) whilst Bacon thought that we can make our theories reliable by building them on the foundations of observation. I would equate "boldness in creating hypotheses" with having the imagination to create theories.


(¶35)   Theories can start in the imagination by learning them from our culture or by creating new ones. The new ones may be stimulated by direct observation, by a conflict between theory and observation, by a conflict between theories, by dreams, or whatever. In reality, I do not think one can learn from culture without recreating a theory in one's own mind. The theory that you recreate will be your understanding of the theory that you learnt and will contain features from your own imagination that will not be in the version of the same theory that someone else recreates. This is what we call interpretation. We cannot learn from our culture without adding to it something of ourselves. Nor can we learn theories without missing aspects of them that other people will recreate. On the other side, I do not think that we create our own theories without using elements of theories we have learnt. This is what I meant when I said that the individual mind works best in company. Even theories that emerge from dreams have this characteristic. For example, the central idea of Mary Shelley's novel, Frankenstein, emerged from a day dream, but when she wrote it down she became aware of numerous interconnections with the scientific culture of her time.

(¶36)   Russell's first quality of science, immense patience in observation, is the virtue that Bacon was calling for. One reason that Russell adds the importance of hypothesis is that John Stuart Mill had discovered problems in Bacon's philosophy that he could only resolve by suggesting that science often needs to make its theories before its observations, instead of building its theories on observations. Mill thought that theories would often have to engage with observations after the theory had been created.


Bacon, Hobbes and Newton

(¶37)   Bacon believed that we should make sure our axioms and conceptions are true by systematically deriving them from careful observation of the real world. If we build our theories on such sure foundations, he thought the theories would have the power to discover the hidden truth of the universe. Within fifty years of his death, two English theorists appeared to have followed his method through with astounding success.

  • The first of these (1651) was Hobbes, whose theories provided a very comprehensive account of the human world. Hobbes' theory, though very influential, was not accepted as the orthodox account of society.

  • The second (1686), Isaac Newton, presented a mathematical theory of the whole physical universe. Newton's theory received recognition throughout Europe as the true scientific explanation of nature. It, therefore, became the example that people looked at to demonstrate what Bacon had meant by a new method, science, that would enable modern humans to far outstrip the ancients in understanding and control of the world.

(¶38)   The problem is that, in some respects, Newton's theory of physics did not fit Bacon's theory of true knowledge.

I will list first the ways in which it did.

  • It had clear axioms and conceptions.

  • The theories developed with these axioms and conceptions were rigorously argued.

  • Anybody with the requisite skills could check the arguments through.

  • It also enabled people to predict the movements of the heavenly bodies with great accuracy, so its conclusions fitted in very well with the world as carefully observed.
The problem was that it was not immediately clear that its axioms and conceptions were based on systematic and careful observations. There is a lot of mathematics in the book, and once the argument gets going Newton brings in examples that look as if they could be turned into experiments. But his basic premises do not appear to be based on observation.

We will look at Newton's basic premise to see something of the problem.

(¶39)   Newton's basic premise is in his Preface to his first edition, where he says

"I offer this work as the mathematical principles of philosophy, for the whole burden of philosophy seems to consist in this - from the phenomena of motion to investigate the forces of nature, and from these forces to demonstrate the other phenomena".
After indicating how this applies to physics and astronomy (which his book deals with) he adds that he wishes
"we could derive the rest of the phenomena of nature by the same kind of reasoning from mechanical principles, for I am induced by many reasons to suspect that they may all depend on certain forces by which the particles of bodies, by some causes hitherto unknown, are either mutually impelled towards one another, and cohere in regular figures, or are repelled and recede from one another. These forces being unknown, philosophers have hitherto attempted the search of Nature in vain." (Newton 1686/1729 pp xvii-xviii)

(¶40)   Newton wants to explain everything in terms of the motion of particles of matter and the forces by which they interrelate. There may be some people in the world who, by carefully observing it, can induce that it all consists of particles of matter in motion that repel and attract one another. To me it sounds much more like a very imaginative hypothesis than a careful observation.

(¶41)   Let us move into the body of Newton's book to look at the formal conceptions and axioms with which it starts. I will take from list of definitions one that contains a very empirical observation. In his definition of centripetal force Newton draws on the empirical illustration of a stone swung round in a sling. The person holding the swing twirls it round and round and then, when one end of the sling is let go, the stone flies of with great force. I will come back to this sling when I have quoted the definition and the immediate illustrations that Newton gives.

(¶42)   The definition Newton gives is:

"A centripetal force is that by which bodies are drawn or impelled, or any way tend, towards a point as to a centre." (Newton 1686/1729 p.2 Definition 5).

He gives three illustrations, or examples:

  • gravity, by which bodies tend to the centre of the earth;

  • magnetism, by which iron tends to the loadstone;

  • that force; whatsoever it is, by which the planets are continually drawn aside from the rectilinear motions, which otherwise they would pursue, and made to revolve in curvilinear orbits

(¶43)   A centripetal force is the opposite of a centrifugal force. Centrifugal forces throw things away from a centre, centripetal forces draw them in towards the centre. To be clear about what Newton means by gravity it might be better to phrase these definitions a little differently: Centrifugal forces throw things away from each other, centripetal forces draw them in towards one another. For Newton, gravity is not just a pull of the earth that makes a stone fall if you drop it: it is also a pull that the stone has on the earth. Newton claims that all bodies exert on one another such a pull. Every object has a power, that he compares to that of a magnet, that draws other bodies towards it.

(¶44)   To see how much Newton's theory depends on his theoretical imagination, we will look at his third example of a centripetal force:

"that force; whatsoever it is, by which the planets are continually drawn aside from the rectilinear motions, which otherwise they would pursue, and made to revolve in curvilinear orbits."
Newton sought to show that this force was the same as the force of gravity "by which bodies tend to the centre of the earth".

When John Stuart Mill sought to explain what Newton did in terms of theorising from observations, he did it with reference to the empirical observations that Newton could (hypothetically) have made to measure the force of gravity at both ends of the argument: on earth and in the heavens, to show that planets and objects on earth obey the same laws.

Mill acknowledged that when Newton published his theory, he had not made the heavenly measurements. At that stage the heavenly end of the theory was a hypothesis. But the theory is a creation of imagination at a more fundamental level. Prior to the tests that Mill talks about, Newton had to form his conception of gravity and create the theory of how it operates with respect to bodies.

(¶45)   A tradition tells us that Newton's theory began when he saw an apple fall from a tree. If the apple hit him on the head, as it does in comedy sketches of the event, it would have been a very distinct observation on which to build his theory. But we have already seen that his conception of gravity is more than just the force that makes apples fall to the ground when they become detached from apple trees.

Newton argued that a basic force exists in the whole universe that draws all bodies towards one another. In terms of apples, he imagined the apple drawing the earth towards it, as well as the earth drawing the apple.

Even if we assume that the apple hitting him on the head made him see stars, and thus induce that the same forces operate in the heavens as on earth, Newton's conceptualisation of gravity requires a leap of creative imagination. The same applies to his theory.

(¶46)   Newton theorises (following Galileo) that

    any object that is moving will carry on moving at the same rate and in the same direction for ever unless it is slowed down or diverted by something else.
He theorises that
    planets have an impetus to travel through space in a straight line, but are diverted from that straight line by the pull of the sun's "gravity".
He theorises, that
    As a result of the balance of these forces, planets revolve round the sun.
Not one item that he has theorised here could he, or anyone living at his time, have observed. Since the invention of space craft, some people have seen the earth as a globe in space, but in Newton's day even that was speculation.

(¶47)   To return to that sling. You may have been confused by the image of a sling appearing in connection with centripetal force. The centre of the swirling sling is the slinger's hand, and the stone in the sling is impelled away from this centre. It is centrifugal (fleeing from the centre), not centripetal. Newton brings in the sling merely as a metaphor for the invisible force of gravity that he claims draws the sun and the planets towards one another. Any body whirling round another, he says, will have a tendency to fly away from the centre like the released stone. Planets have this impetus, but (just as the stone is held back by the sling) they are held back by a powerful counter force. The difference is that the sling is visible, but the counter force of gravity is invisible. You have to imagine it.

(¶48)   Newton's mathematical theory, all 500 or so pages of it, was based on foundations of speculative concepts and axioms like this. To Newton's second edition a Professor of Astronomy and Experimental Philosophy (Roger Cotes) provided a Preface that tried to show Newton as the example of inductive philosophy. Like earlier philosophers, he said, the experimental philosophers

"derive the causes of all things from the most simple principles possible",
but they do not use unproven hypotheses as their basic principles. Instead
"from some select phenomena they deduce by analysis the forces of Nature and the more simple laws of forces"
and on that basis they construct the theories that show how the world works (Newton 1686/1729 pp xx-xxi). Cotes recognised, as most people did, that the force of nature at the centre of Newton's theory is gravity. The best he could do in relating this to experimental observations, however, was to show that if we assume gravity to exist and to follow certain laws, the theory that Newton had based on that assumption was capable of explaining, in a very impressive way, recent experimental observations on earthly bodies, and astronomical observations. (Newton 1686/1729 p.xxi following).

(¶49)   Cotes argument has the same form as that of John Stuart Mill over a century later. As with Mill's argument it takes for granted the conceptualisation of gravity and the overall theory of universal interactions that is the basis of Newton's achievement. This aspect of Newton's work was not so much the achievement of careful observation, but one of theoretical imagination. Bertrand Russell was acknowledging this when he listed the virtues of scientists like Newton as being, not only, "immense patience in observation", but also "great boldness in framing hypotheses". In order to explain the world of observation, the scientist has to create theories.


(¶50)   James Mill and his son John Stuart Mill were amongst a group of people who created the sciences of society that were most widely accepted in nineteenth century England. There were two of these sciences: Political Economy and Utilitarianism. Utilitarianism was often called Benthamism.

Both utilitarianism and political economy depended on constructing deductive theories from axioms in the way that we have seen Newton do. Newton and Hobbes were the two examples of deductive theories in science that utilitarians were most likely to point to as early examples of their scientific methods. The main axiom that utilitarianism used was to the effect that all human actions are to be explained in terms of the pursuit of pleasure and the avoidance of pain. From axioms like this they constructed theories that explained human conduct in a way that they regarded as scientific. Further on I will give an example of James Mill's deductive reasoning in which he argues scientifically that representative democracy is the ideal system of government.

Induction and Ratiocination (Deduction)

(¶51)   John Stuart Mill's first book became the main British textbook on how to make a social science. Published in 1843, it was called A System of Logic Ratiocinative and Inductive - Being a connected view of the principles of evidence and the methods of scientific investigation.

With a title like that John Stuart Mill did not expect it to be a best seller in the new W.H. Smith railway bookshops. It was a book for (very) serious thinkers and scientists. Which is a pity, because once you break the language down it becomes quite interesting.

Loosely translated the title means:

In order to create a science you have to use two types of thinking or logic. One type, called inductive, is a way of working out generalisations from particular facts in the empirical world. The other type, called ratiocinative, just uses reasoning (ratiocination). [Ratiocination is also called deductive thinking or theory construction]. In order to make a science you need both types of thinking and you need to know how to fit them together. This book presents my system for doing this.

(¶52)   Inductive logic is the process that Bacon promoted, of developing theories that are grounded in observations. John Stuart Mill's book was mainly a defence of the importance of deductive (ratiocinative) logic to science. He was led to write it as a result of attacks made on his father, James Mill, by the historian Thomas Babington Macaulay (1800-1859). Macaulay said that James Mill based his science on deduction (ratiocination), a method promoted by the Greek philosopher, Aristotle, whose methods Bacon had discredited.

(¶53)   Neither of the Mills made any secret of their enthusiasm for deductive logic. As a twelve year old boy, John Stuart Mill was taught Aristotle's deductive logic by his father because, James said, when arguing a scientific point it is important to do more than just put your own point of view. You need to be able to analyse the theory behind your argument and the alternative theories that other people may present. As father and son walked on Bagshot Heath, James explained that a training in deductive logic would help John to do this. John Stuart never forgot the walk or the talk. As an old man he admitted that his father's careful explanations "did not make the matter at all clear to me". But his confusing experiences, as a twelve year old, made sense as he grew older.

"The first intellectual operation in which I arrived at any proficiency, was dissecting a bad argument, and finding in what part the fallacy lay." (Mill, J.S. 1874, chapter 1, p.12)

Advanced science must be deductive.

(¶54)   John Stuart Mill agreed with some of Macaulay's criticism of his father, but not with Macaulay's basic idea that science should be built on induction without deduction.

Elementary chemistry, Mill said, had made great use of induction, but for more complex sciences, including modern chemistry, deductive methods are essential. Most people who reason on political subjects, Mill said,

"know nothing whatever of the methods of physical investigation beyond a few precepts which they continue to parrot after Bacon, being entirely unaware that Bacon's conception of scientific inquiry has done its work, and that science has now advanced into a higher stage .... In an age in which chemistry itself, when attempting to deal with the more complex chemical sequences, those of the animal, or even the vegetable organism, has found it necessary to become, and has succeeded in becoming, a Deductive Science, it is not to be apprehended that any person of scientific habits, who has kept pace with the general progress of the knowledge of nature, can be in danger of applying the methods of elementary chemistry to explore the sequences of the most complex order of phenomena in existence" (Mill, J.S.1843 6.7.5).
Physics and astronomy, as developed by Newton, were deductive sciences and the social sciences also need deductive methods. Empirical observation could, as Macaulay had pointed out, show that James Mill's theories were wrong, but this meant there was something wrong with James Mill's theory, not that he should not have used theory in the first place.

(¶55)   I will now give, as an example of deductive (ratiocinative) science, the theory that James Mill constructed from utilitarian axioms in order to demonstrate the superiority of representative government over any other form of government. This is the example of deductive logic that Macaulay criticised as unscientific because it is not inductive. In the 1820s James Mill argued that the vote for all males is necessary to make sure that the government acts in the majority interest (Mill, J. 1820). His article on this, called Government, was published as an appendix to the Encyclopedia Britannica and widely circulated separately as well.

James Mill's argument was a formal one, based on axioms and reaching conclusions by a chain of reasoning from them. I have laid out his axioms and reasoning in the form that fits our discussion.

(¶56)   This is James Mill's argument to show that representative democracy is an essential of good government. It was an argument put at a time when very few people in Britain had a vote.


The only motive of human beings is the pursuit of one's own pleasure and the avoidance of one's own pain. No individual is motivated by the pursuit of another's pleasure or avoidance of another's pain.

Interim conclusion that becomes 1st premise of argument:

[any] "human being will desire to render the person and property of another subservient to his pleasures, notwithstanding the pain or loss of pleasure which it may occasion to that other individual" (Mill, J. 1820 par.40)


"The desire of the object implies the desire of the power necessary to accomplish the object". (Mill, J. 1820 par.40)

Interim conclusion respecting basic law of human nature:

"The desire, therefore, of that power which is necessary to render the persons and properties of human beings subservient to our pleasures, is a grand governing law of human nature". (Mill, J. 1820 par.40)


"The demand ... of power over the acts of other men is really boundless. It is boundless in two ways; boundless in the number of persons to whom we would extend it, and boundless in its degree over the actions of each". (Mill, J. 1820 par.42)

Axiom and three concepts of government:

At least three types of government are possible:

  • Government by one person (called monarchy);

  • government by a few (called oligarchy or aristocracy) and

  • government by the majority (called democracy)

    Interim conclusion:

    Governments by the one or the many will attempt to extract all the benefit they can from the many that they rule, in order to satisfy themselves. The levers at their disposal will be the manipulation of the human desire for pleasure and fear of pain. They will use these levers without restraint and so, if nothing checks the rulers, the ruled will be terrorised by them and robbed of everything except the bare means of subsistence.

    "It is proved therefore by the closest deduction from the acknowledged laws of human nature ... that the ruling one or the ruling few, would, if checks did not operate in the way of prevention, reduce the great mass of the people subject to their power, at least to the condition of negroes in the West Indies". [This was written before the abolition of slavery in the British West Indies, which took place in 1833]. (Mill, J. 1820 par.53)

    Interim conclusion put another way:

    There is no individual or combination of individuals, except the community itself, who would not have an interest in bad government if intrusted with its powers

    New axiom:

    The community itself is incapable of exercising those powers directly, but it can intrust them to individuals.

    Final conclusion: Representative democracy is a necessary check

    "In the grand discovery of modern times, the system of representation, the solution of all the difficulties, both speculative and practical, will perhaps be found. ... The conclusion is obvious: the community itself must check those individuals; else they will follow their interest and produce bad government". (Mill, J. 1820 par.72)

  • Women and children

    (¶57)   The argument as I have outlined it from James Mill appears self-contained. One can disagree with its premises and its conclusions, but as an argument it does not seem to need anything adding. However, James Mill did add a few points to make it more acceptable. In particular, he added that children and women would not need a vote.

    Macaulay's empirical case against James Mill

    (¶58)   Macaulay argued that James Mill should not have detached his reason from empirical reality. James Mill had said that empirical reality is ambiguous about the effect of absolute government on the well being of the people. Under Roman emperors like Nero and Caligula, for example, it had been the scourge of human nature, but on the other side, the people of Denmark, tired out with the oppression of an aristocracy, resolved that their king should be absolute, and under their absolute monarch, are as well governed as any people in Europe. From this uncertainty of empirical observation Mill concluded that we need to get behind the surface appearance by using deductive reason. As the surface of history affords, therefore, no certain principle of decision, we must go beyond the surface and penetrate to the springs within. (Mill, J. 1820 p.9)

    (¶59)   Macaulay used the term a priori, meaning prior to empirical data, to characterise James Mill's argument. Macaulay thought that all arguments should be a posteriori, or following on from empirical data. In the way Macaulay uses these terms, a priori corresponds to deductive reasoning and a posteriori to induction.

    (¶60)   Macaulay was astounded that James Mill should have used the uncertainty of empirical observation as a reason for pursuing the a priori method. The fact that experience of absolute monarchy showed it to be sometimes good and sometimes bad was, in Macaulay's opinion, irresistible proof that the a priori method is altogether unfit for investigations of this kind, and that the only way to arrive at the truth is by induction. If our observations lead us to contradictory conclusions, Macaulay argued, it just shows that there is something wrong with some hypothesis we are using. When we say that one fact is inconsistent with another fact, we mean only that it is inconsistent with the theory which we have founded on that other fact. But, if the fact be certain, the unavoidable conclusion is that our theory is false; and in order to correct it, we must reason back from an enlarged collection of facts to principles. (Macaulay 1829 p 364)

    (¶61)   Notice that Macaulay could have argued that when experience contradicted James Mill's theory, he should have altered his theory. Instead, he argues, that James Mill should have used a greater range of experiences, rather than a priori reasonings, as the base for his theories. If he had done this, Macaulay argued, he would have found that, in recent times in Europe, even the most undemocratic regimes tended to act in the people's interest. During the last two centuries, some hundreds of absolute princes have reigned in Europe. Is it true, that their cruelty has kept in existence the most intense degree of error; that their rapacity has left no more than the bare means of subsistence to any of their subjects, their ministers and soldiers excepted? Is this true of all of them? Of one half of them? Of one tenth part of them? Of a single one? (Macaulay 1829 pp 369- 370)

    (¶62)   Recent empirical history, Macaulay argued, showed absolute monarchs to be considerably better rulers than James Mill's theory suggested. Reasons for this could also be gathered by empirical observation, including observations on one's neighbours. No man of common sense can live among his fellow-creatures for a day without seeing innumerable facts which contradict James Mill's arguments (Macaulay 1829 p.370). James Mill had ignored the (benign) influence of civilisation or culture. His image of human nature was that of the Yahoos in Gulliver's Travels. These looked like human beings, but behaved in an entirely bestial manner. Human nature is not what Mr Mill conceives it to be, civilized men, pursuing their own happiness in a social state are not Yahoos fighting for carrion; because there is pleasure in being loved and esteemed, as well as in being feared and servilely obeyed (Macaulay 1829 p.386).

    (¶63)   James Mill, according to Macaulay, could not have ignored the influence of civilisation if he had been an empirical historian. If he had meticulously compared societies at different periods of history and in different parts of the world, he would have observed the civilising influence working on human character. As it was, Macaulay said, James Mill relied on this influence for the part of his argument respecting women, whilst ignoring it for the rest.

    (¶64)   James Mill had said that the interest of men would be the same as the interests of their wives and daughters, who would not, therefore, need a vote. Macaulay agreed that "the interest of a respectable Englishman may be said, without any impropriety, to be identical with that of his wife". But it was only so in a few civilised countries like England and the United States. Empirical observation would show that it was not the case elsewhere. "Is ... the interest of a Turk the same with that of the girls who compose his harem? Is the interest of a Chinese the same with that of the woman whom he harnesses to his plough? Is the interest of an Italian the same as that of the daughter he devotes to god?" (Macaulay 1829 p.386). "If there be a word of truth in history, women have always been, and still are, over the greater part of the globe, humble companions, playthings, captives, menials, beasts of burden. Except in a few happy and highly civilised communities, they are strictly in a state of personal slavery". (Macaulay 1829 p.385)

    "If there be in this country an identity of interest between the two sexes, it cannot possibly arise from any thing but the pleasure of being loved, and communicating happiness. For, that it does not spring from the mere instinct of sex, the treatment which women experience over the greater part of the world abundantly proves. And if it be said that our laws of marriage have produced it, this only removes the argument a step further; for those laws have been made by males. Now if the kind feelings of one half of the species" [men] "be a sufficient security for the happiness of the other why may not the kind feelings of a monarch or an aristocracy be sufficient at least to prevent them from grinding the people to the very utmost of their power?" Macaulay asked. "If Mr Mill will examine why it is that women are better treated in England than in Persia, he may perhaps find out, in the course of his inquiries, why it is that the Danes are better governed than the subjects of Caligula". (Macaulay 1829 pp 386-387)

    Macaulay's Descriptive Empiricism

    (¶65)   Macaulay did not just use empirical evidence to show that James Mill's theories were inadequate. Macaulay denied that a science of politics could be made on the basis of a theory of human nature. Human beings vary so much from society to society and time to time that a science of politics could only be established by carefully studying the facts of each period and each society. The need to rely on careful study of the facts, and to be cautious in theorising, was not, according to Macaulay, a feature of the social sciences alone. He thought it was the established method of all successful sciences.

    (¶66)   Macaulay was an enthusiastic reader of Bacon. He read and quoted him in Latin and English and wrote a famous article on him. Nevertheless, John Stuart Mill believed that Macaulay had misunderstood Bacon. If you look at the little I have quoted from Bacon, I think you will be able to see why. Bacon recognises the importance of theory in a way that Macaulay does not. I quoted, in connection with axioms and conceptions, Bacon's contention that science would develop methods that would look beneath the surface, rather than just describing the appearances. Bacon was specific that it was the axioms and conceptions of theories that he thought could be derived from experience. If he had lived in the nineteenth century he might have argued that James Mill's axioms about the selfishness of human nature were inadequately grounded in observation, but not that the whole method was wrong - which is what Macaulay argues in the following passages.

    Macaulay's description of scientific method

    (¶67)   Macaulay says that "the only way to arrive at the truth is by induction". We cannot "deduce a theory of government from the nature of man". We can only arrive at just conclusions in the "noble science of politics" by "that method which, in every experimental science to which it has been applied, has signally increased the power and knowledge of our species". That is "by the method of induction; - by observing the present state of the world, - by assiduously studying the history of past ages, - by sifting the evidence of facts, - by carefully combining and contrasting those which are authentic - by generalising with judgment and diffidence, - by perpetually bringing the theory which we have constructed to the test of new facts, - by correcting, or altogether abandoning it, according as those new facts prove it to be partially or fundamentally unsound".

    (¶68)   This is the method that I am calling descriptive empiricism. It is not entirely descriptive, Macaulay says that we do construct a theory, but we are very cautious in doing so to work from the historical evidence, and to correct or abandon it if it no longer fits. You can imagine a student following this method in an essay on the French Revolution. Let us say that the title is Examine the role of women in the French revolution. The student might carefully document the story of the French revolution mentioning every occasion when it appeared to involve women. At the end there might be a tentative conclusion It appears to me, from the evidence that women played an important part in the French revolution. We can also imagine the tutor's comments. "This is very well documented, but far too descriptive". The tutor was looking for an argument or theory - and that is what the Mill's wanted to create.

    Macaulay's actual practice

    (¶69)   Before moving on to look at John Stuart Mill's counter-argument, I should note that, whatever his theory of science, Macaulay did not just write descriptive histories, nor was he tentative in his conclusions. Macaulay's books sold in greater numbers than John Stuart Mill's because he turned history into a thumping good story. (Nobody has ever accused John Stuart Mill or his father of writing good stories). The method Macaulay used for this was to imagine himself writing history with the same attitude as a narrative poet or novelist. True he wallowed in data, but he was reluctant to let the data get the better of the story.

    (¶70)   We can compare Macaulay's description of scientific method directly with John Stuart Mill's conclusions about the methods that social science should follow. Mill wrote

    "The Social Science ... which ... has been termed Sociology ... is a deductive science; not, indeed, after the model of geometry, but after that of the more complex physical sciences. It infers the law of each effect from the laws of causation on which that effect depends; not, however, from the law merely of one cause, as in the geometrical method; but by considering all the causes which conjointly influence the effect, and compounding the laws with one another. Its method, in short, is the Concrete Deductive Method; that of which astronomy furnishes the most perfect ... example". (Mill, J.S. 1843 6.9.1)

    (¶71)   So, John Stuart Mill argues that Sociology is a deductive science, whereas Macaulay believed all science should be inductive.

    Mill argued that deductive sciences follow a common general form in that they have three stages:

    1. identifying causes in simple terms,

    2. reasoning from those causes to more complex conclusions,

    3. seeing how those conclusions correspond with empirical reality.

    In the example from James Mill that I gave the original cause identified was Axiom: The only motive of human beings is the pursuit of one's own pleasure and the avoidance of one's own pain. From this James Mill reasoned to an Interim conclusion: Governments by the one or the many will attempt to extract all the benefit they can from the many that they rule, in order to satisfy themselves.

    (¶72)   From an examination of this form you can see that there are two points at which one might try to relate it to empirical reality: the alleged original cause and the interim conclusion. We can only do this, however, because someone has constructed the theory in the first place. Or, to put it another way, the clarity with which the deductive theory has been laid out by James Mill allows us to test not only his reasoning, but also the relationship between his theory and empirical reality. John Stuart Mill argued that, ideally, both the axioms and conclusions of a deductive science should be subject to empirical testing, but that, in practice, scientists need to use hypotheses, or untested theories, as axioms. He thought, however, that the use of hypotheses as axioms should be a temporary measure. We should try to find ways of testing both ends of the argument against empirical reality.

    (¶73)   Notice that Macaulay tested James Mill's deductive theory in exactly the way that John Stuart Mill says we should attempt to test it. Against the axiom Macaulay argued that human beings have more complex motives than James Mill allows, and against the interim conclusion Macaulay argued that it was shown to be false by the empirical evidence of history. John Stuart Mill agreed with Macaulay on both these points. John Stuart Mill argued, however, that the fault was with the type of theory used.

    (¶74)   John Stuart Mill says that the model for sociology should not be geometry, but astronomy. He says that James Mill's mistake was to follow the geometrical model, like Hobbes; rather than the concrete deductive method, illustrated by Newton's physics and astronomy. The geometrical and physical or astronomical models are both deductive. They start with an idea of causes, which they take as their axioms, and from those they deduce by a chain of reasoning, the effects. The difference is that physics and astronomy study systems in which a large number of causes operate and interact, whereas geometry operates with a very small number of causes or axioms. In fact, John Stuart Mill says that a geometrical argument starts with just one cause. In the case of his father's theory the axiom is: The only motive of human beings is the pursuit of one's own pleasure and the avoidance of one's own pain. No individual is motivated by the pursuit of another's pleasure or avoidance of another's pain.

    (¶75)   Macaulay had argued that this was an over simplification of human nature, and John Stuart Mill agrees with him. Macaulay argued that scientists should ditch deductive arguments and just induce their theories cautiously from history, John Stuart Mill disagrees with this and says that scientists should use deductive methods that can cope with a multitude of causes operating within a system, rather that just one.

    Custom and tradition and a science of character

    (¶76)   It is not true, Mill said, that the actions even of average rulers are wholly, or anything approaching to wholly, determined by their personal interest. In particular, theories need to provide for the influence on their actions of the habitual sentiments and feelings, the general modes of thinking and acting, which prevail throughout the community and those of their class. And, he said, the maxims and traditions which have descended to them from other rulers, their predecessors. There was a need for a social science more complex than the utilitarianism of his father, and broader in its image of human motivation than political economy. It is easiest to demonstrate what Mill was thinking of if we consider economic motivation, rather then political. The issue is similar. Utilitarianism and political economy, as developed by James Mill, ascribed self seeking motives to humans with respect to politics and economics.

    (¶77)   John Stuart Mill outlined a contrary proposition that German economists were becoming particularly aware of, and which was later to be developed into a full-blown sociology by the German economist, Max Weber. The axioms of utilitarian science, at their vaguest, state that human beings follow their interests. However, what constitutes human interest seems to vary from society to society. English economics, therefore, turned out to be limited in its application to other countries because it presumed an English character. The English economist assumed that a shopkeeper would give his or her highest priority to the profits of the business. But, in another culture, the shopkeeper might place a higher value on leisure, and close shop when it had earned enough for the shopkeeper's immediate needs. Or the value placed on social respect might be higher than that placed on making profits. If business had a lower status in society than land-owning, the shopkeeper might work very hard until the shop had earned enough to buy land, and then give up shopkeeping and become a landowner. Variations like these could wreak havoc with the predictions of economists. John Stuart Mill thought economics needed to be complemented by a science of social, class, or national character. He also thought that the science would need an historic dimension, because social character changed over time.

    (¶78)   What was needed, he argued, was not just objective empirical description of the differences between societies, or of the changes in character over time, but theories that showed how these differences and changes could be related to causes. In this process one might start with the hypothetical causes (direct deduction), or reason backwards (inverse deduction) from the effects:

    The Direct Deductive Method would start, as James Mill had, from the hypothetical causes, but they would be more complicated ones. Mill thought this would be very difficult, but not impossible.

    Max Weber was later to develop a deductive theory on this basis which had models (ideal types) of people who could respond to a range of interests apart from egoism. They might, for example, respond to traditions, or to other worldly ends dictated by religion. Or they might be caught up by the fervour generated by a powerful leader. If you look at Weber's simplest book, The Protestant Ethic and the Spirit of Capitalism you will see the important part that the creation of theoretical models plays, and how Weber tries to relate this to the empirical data.

    The Inverse Deductive Method would start, as Macaulay wanted to, from empirical descriptions of national differences or historic changes. But would link these to hypothetical causes that would explain the differences or changes. We need objective empirical descriptions of changes and differences, Mill argued, but of themselves they are unsatisfactory as science.

    "But if the differences which we think we observe between French and English, or between men and women, can be connected with more general laws; if they be such as might be expected to be produced by the difference of government, former customs, and physical peculiarities in the two nations, and by the diversities of education, occupations, personal independence, and social privileges, and whatever original differences there may be in bodily strength and nervous sensibility between the two sexes; then, indeed, the coincidence of the two kinds of evidence justifies us in believing that we have reasoned rightly and observed rightly. Our observation though not sufficient as proof, is ample as verification. And having ascertained not only the empirical laws, but the causes of the peculiarities, we need be under no difficulty in judging how far they may be expected to be permanent, or by what circumstances they would be modified or destroyed." (Mill, J.S. 1843 6.5.3)

    (¶79)   In 1848 Mill published a book on economics, the title of which indicates his interest in broadening the base of the social sciences. It was called Principles of Political Economy - With Some of Their Applications to Social Philosophy. In 1869 he published The Subjection of Women, a book on the role of women in society that attempted to show their changing role in changing social structures, and to predict from that a more equal future for men and women.


    (¶80)   John Stuart Mill's ideas about a science of society developed as he was reading the works of two French writers: Saint-Simon and Auguste Comte. Comte began his work as a student of Saint-Simon, and it was Comte who created the word sociology for the science of society. Mill thought that Comte had shown how to develop the study of history into a science. Sociology, according to Comte, would have two parts, statics and dynamics. Statics is the study of the structure of society, dynamics is the study of its movement. Dynamics is history turned into a science.

    (¶81)   In this final part of the essay I want to illustrate the importance of imagination by setting out John Stuart Mill's ideas on writing history, and how history can be turned into a science. Mill said that history could be written in different ways, but that some of the ways needed the other ways first. Here are the ways in the order that they are necessary.

    If you look at these four ways you will see that the role of straightforward empirical observation gets less, and the role of imagination, theorising and deduction increases, as you move from stage to stage. The earliest stages are the most like Thomas Macaulay's histories, the last stage is the way that Comte and Mill considered scientific. So, according to Mill, science involves an increased role for the imagination and for theory.

    1. Copying or translating ancient histories.

      This is careful transcription "without ever bringing the writer's own mind in contact with the subject". (Mill, J.S. 1844 p.91)

      It is something that was very common before the invention of printing, when copying was necessary to maintain the society's knowledge of its past. Mill says that this is too accepting or uncritical to make good history. It is nevertheless necessary to have material to work on to make history, so we can say that history starts here, with the stories that we inherit. We can see why it is not scientific by considering an observation of the historian Niebuhr who pointed out that scribes would copy one source after another without attempting to weigh the evidence for the different accounts (Acton, J. 1895 p.34).

    2. Imagining history as the present.

      One can try to understand the people in history with the knowledge that one has of today and how people operate nowadays. Macaulay did this to a great extent by trying to identify the political characters in his history of England as either Tories, who wanted to defend the past, or Whigs, who were educated people in favour of progress. Mill says that this is an advance on simply copying or translating the old stories, because it tries to make the past alive. The historian who does this

      "does give a sort of reality to historical personages: he ascribes to them passions and personages, which, though not those of their age or position, are still human; and enables us to form a tolerably distinct, though, in general, an exceedingly false notion of their qualities and circumstances. This is the first step; and, that step made, the reader, once in motion, is not likely to stop there." (Mill, J.S. 1844 p.91)

    3. Imagining history as it was.

      Niebuhr, the German historian just mentioned, is Mill's example of an historian who successfully imagines the past as it was. Mill emphasises what an effort of imagination this requires. The historian here

      "attempts to regard former ages not with the eye of a modern, but as far as possible with that of a contemporary; to realize a true and living picture of the past time, clothed in its circumstances and peculiarities. This is not an easy task: the knowledge of any amount of dry generalities, or even of the practical life and business of his own time, go a very little way to qualify a writer for it. He needs some of the characteristics of the poet. He has to "body forth the form of things unknown". He must have the faculty to see, in the ends and fragments which are preserved of some element of the past the consistent whole to which they once belonged; to discern, in the individual fact which some monument hands down, or to which some chronicler testifies, the general, and for that reason unrecorded, facts which it presupposes." (Mill, J.S. 1844 pp 91-92)

      Mill does not envisage historians letting their imagination loose without control.

      "He must have the conscience and self-command to assert no more than can be vouched for, or reduced by legitimate inference from what is vouched for. With the genius for producing a great historical romance, he must have the virtue to add nothing to what can be proved to be true: What wonder if so rare a combination is not often realized? (Mill, J.S. 1844 p.92)"

    4. Finding the laws that govern history

      The "highest stage of historical investigation", according to Mill, was one where the aim is "to construct a science of history".

      "In this view, the whole of the events which have befallen the human race, and the states through which it has passed, are regarded as a series of phenomena, produced by causes, and susceptible of explanation. All history is conceived as a progressive chain of cause and effects." (Mill, J.S. 1844 pp 92-93)

      This was the kind of history that Mill thought Auguste Comte was engaged in. Comte was the man who was trying to create a science of society which he called sociology.

    Comte's stages of historical development

    (¶83)   Auguste Comte was a positivist. He invented this word as well as the word sociology. Some people use the word positivist to mean the same as empiricist, but this was not what Comte meant by it.

    Positivism, according to Comte, means trying to understand or describe the world as a sequence of cause and effect between objects that one can observe (See Mill, J.S. 1865).

    A positivist seeks to understand the world as it is, scientifically, rather than criticising it (Marcuse, H. 1941/1955 Part 2, chapter 2, pp 323-359). Comte was quite emphatic that theories are necessary to organise and perceive the world, so we should be reluctant to call him an empiricist.

    (¶84)   Comte divided the history of ideas into three stages: theological, philosophical (critical) and scientific (positive). He thought that humanity necessarily moves through each by a law of human progress which is that

    "each branch of our knowledge, passes successively through three different theoretical conditions: the Theological, or fictitious; the Metaphysical, or abstract; and the Scientific, or positive" (Comte, A. 1853 par. 1.1.3).

    Here are his descriptions of each (Comte, A. 1853 paragraphs 1.1.3 to 1.1.6):

    Theological thinking "is the necessary point of departure of the human understanding."

    "In the theological state, the human mind, seeking the essential nature of beings, the first and final causes (the origin and purpose) of all effects, - in short, Absolute knowledge, - supposes all phenomena to be produced by the immediate action of supernatural beings."

    "The Theological system arrived at the highest perfection of which it is capable when it substituted the providential action of a single Being for the varied operations of the numerous divinities which had been before imagined."

    Metaphysical thinking is "merely a state of transition".

    "In the metaphysical state, which is only a modification of the first, the mind supposes, instead of supernatural beings, abstract forces, veritable entities (that is personified abstractions) inherent in all beings, and capable of producing all phenomena. What is called the explanation of phenomena is, in this stage, a mere reference of each to its proper entity". "in the last stage of the Metaphysical system, men substitute one great entity (Nature) as the cause of all phenomena, instead of the multitude of entities at first supposed"

    Positivist thinking is the third and the "fixed and definite state" of human thought. In this stage

    "the mind has given over the vain search after Absolute notions, the origin and destination of the universe, and the causes of phenomena, and applies itself to the study of their laws, - that is, their invariable relations of succession and resemblance. Reasoning and observation, duly combined, are the means of knowledge. What is now understood when we speak of an explanation of facts is simply the establishment of a connection between single phenomena and some general facts, the number of which continually diminishes with the progress of science".

    "The ultimate perfection of the Positive system would be (if such perfection could be hoped for) to represent all phenomena as particular aspects of a single general fact; - such as Gravitation, for instance."

    (¶85)   How do we know this?   If the history of human thought moves, of necessity, in these three stages, how do we know that? John Stuart Mill suggests two ways. One is the empirical way, which he said is important, but very inadequate. This, he says, will establish an empirical law. The other way is by resolving the empirical law into more general, "ultimate", laws. (Mill, J.S. 1843 3.16.1)

    (¶86)   The empirical law could be tentatively established if we took many examples of thought in a certain science, arranged them in chronological order and found that theological theories came first, metaphysical theories next and positivist theories next. But this would only be tentative, and it would not tell us why the types of thought come in that order. It would be tentative because we would have no reason to believe that further examples of thought that we added to our collection would fall in the same order. If, on the other hand, we knew a reason for the order in terms of a more general law, we would understand the historic succession and have reason to rely on it. We would understand why thought comes in that order. In this case, the more general laws that Mill suggests are laws of mind. He suggest that Comte's succession of historic stages can be explained in terms of the necessary development of human thought; that we can establish it as a necessary process of thought in the individual mind as well as in culture. Comte's generalisation, Mill says, appears to me to have that high degree of scientific evidence which is derived from the concurrence of the indications of history with the probabilities derived from the constitution of the human mind (Mill, J.S. 1843 6.10.8). In other words, if psychological laws support historical laws, we can have more confidence in the historical laws.

    (¶87)   The following extracts from Comte's work illustrate what Mill means. First the empirical or actual evidence that he asserts for his laws: "Evidences of the law. Actual. ... There is no science which, having attained the positive stage, does not bear marks of having passed through the others. [Also] our most advanced sciences still bear very evident marks of the two earlier periods through which they have passed. [Also] The phases of the mind of a man correspond to the epochs of the mind of the race. ... each of us ... was a theologian in his childhood, a metaphysician in his youth, and a natural philosopher in his manhood." (Comte, A. 1853 p.126).

    (¶88)   Now the theoretical. These are reasons which correspond to John Stuart Mill's suggestion that, scientifically, we seek to resolve empirical laws into more fundamental ultimate laws. In this case Comte argues that imagination and theory have to be prior to observation in the development of human thought. "Theoretical ... Beside the observation of facts, we have theoretical reasons in support of this law. All good intellects have repeated, since Bacon's time, that there can be no real knowledge but that which is based on observed facts. This is incontestable, in our present advanced stage; but, if we look back to the primitive stage of human knowledge, we shall see that it must have been otherwise then. If it is true that every theory must be based upon observed facts, it is equally true that facts cannot be observed without the guidance of some theory. Without such guidance, our facts would be desultory and fruitless; we could not retain them: for the most part we could not even perceive them. Thus, between the necessity of observing facts in order to form a theory, and having a theory in order to observe facts, the human mind would have been entangled in a vicious circle, but for the natural opening afforded by theological conceptions." (Comte, A. 1853 pp 126-127).

    (¶89)   So, Comte argues, it is a law of the human mind, individually and collectively, that we develop from ideas about the total meaning of existence, conceived in terms that we can understand as infants (supernatural beings), then move on to abstract notions of the same (nature) before, finally, resigning ourselves to conceiving things scientifically as the cause and effect of known objects in the observed world. In other words, in the last phase of our development, we drop our attempts to claim knowledge of ultimate reality, and content ourselves with immediate reality. This general law of development is a theoretical explanation of the empirical laws of history and mind that Comte claims to have discovered.

    (¶90)   John Stuart Mill argues that by resolving observed sequences (empirical laws) into underlying causes, we move further towards the understanding the inner and more remote parts of nature that Bacon spoke of as the object of science. (See above under Axioms and conceptions). I am not asking you to accept that Comte's laws of successive stages are true, empirically or theoretically. But, if they are, would it not be true that we have a more profound understanding when we grasp the alleged underlying law, than when we just had a report that this is the order in which thought has always developed?

    (¶91)   Comte, in fact, goes on to resolve his general law of the development of the human mind into an even more general law about how we obtain knowledge. He comments on the paradox that, according to his theory, human thought starts with the most inaccessible questions, - those of the nature of beings, and the origin and purpose of phenomena. Why does it not start with the issues that are within our (collective) grasp? Why do humans start by speculating about supernatural beings, and only after thousands of years get on with making steam engines or (since Comte) sending men and women into space? Why do we try to solve the riddle of the universe before we try to resolve the riddle of the atom? The answer, according to Comte, is that we need meaningful theories in order to stimulate us to undertake the drudgery of intellectual inquiry. "The theological philosophy ... administered exactly the stimulus necessary to incite the human mind to the irksome labour without which it could make no progress. ... it is to the chimeras of astrology and alchemy that we owe the long series of observations and experiments on which our positive science is based." (Comte, A. 1853 p.127).

    (¶92)   We have ended with the conclusion that science must start in the imagination. Which is where I began, and where I wanted us to end. If you would have preferred a essay that began and ended with the necessity of starting with observation, you could either write it yourself, or read the book that John Locke has already written called An Essay Concerning Human Understanding. I discuss this book in essay three.

    chapter 1
Empiricism, Theory and Imagination chapter 2
Hobbes, Filmer, Locke chapter 3
What is Science? chapter 4
Can Theory Redesign Society? chapter 5
Social Science and the 1834 Poor Law chapter 6
Durkheim and Weber's Contrasting Imaginations

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    chapter 1
Empiricism, Theory and Imagination chapter 2
Hobbes, Filmer, Locke chapter 3
What is Science? chapter 4
Can Theory Redesign Society? chapter 5
Social Science and the 1834 Poor Law chapter 6
Durkheim and Weber's Contrasting Imaginations

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    chapter 1
Empiricism, Theory and Imagination chapter 2
Hobbes, Filmer, Locke chapter 3
What is Science? chapter 4
Can Theory Redesign Society? chapter 5
Social Science and the 1834 Poor Law chapter 6
Durkheim and Weber's Contrasting Imaginations

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    axioms: paragraphs:
    6-7: use of by empiricists
    14: premise
    18: and conceptions
    19-20: and geometry
    22-23 science and Hobbes (also 25-26 and 30-31
    31-34: make a list
    37-38, 41 and 48 Newton
    50: Mills and Macaulay
    55 James Mill example
    66: Macaulay
    71-74, 77 and 90 John Stuart Mill

    Francis Bacon

    Epistemology defined

    Thomas Hobbes

    Thomas Macaulay

    James Mill

    John Stuart Mill

    A System of Logic (1843): paragraphs 51 to 54   70 to 78   85 following

      Social science history weblinks