Joan Hughes is a retired experimental chemist investigating the epistemological theories of physical and social science. Click here for poems by Joan Hughes

Summaries and Reviews by Joan Hughes

Science, Geometry, Imagination and Experiment
A summary and review of:
Science and Hypothesis by Henri Poincare

Experience and Inference
A summary and review of:
Human Knowledge By Bertrand Russell (1948)

Deductive Testing
A summary and review of:
The Logic of Scientific Discovery by Karl Popper (1934)

Science, Technology and Engineering

In medieval Europe, science might be theoretical understanding of truth as distinct from the moral understanding of one's conscience. Science could be any knowledge learnt by study.

The different branches of study were also known as sciences. Medieval universities taught seven sciences, in two groups:

grammar, logic, and rhetoric,

arithmetic, geometry, music, and astronomy

But now it means a special type of knowledge

How do we explain the type of knowledge that is modern science?

We know some of the things that science has done for us, but what is it? Science enables doctors to cure many diseases, it made it possible for human beings to walk on the moon, it genetically modifies plants and it turned two Japanese cities into radio active dust. We know that it is powerful and modern, but what is it?

conventionalism
inductivism
deductivism

When I worked as a research chemist, I always supported the inductivist view in practice, i.e. collecting facts based on observation, forming a hypothesis based on these facts and then making further experiments, which if they fitted in, would confirm a hypothesis so that it could be put forward as a theory. These are the ideas that are challenged by Poincare and Popper.

This is the complete text of Moore's article:

What is Science?

According to one view, called conventionalism, the human brains created or invented certain beautiful logical structures called laws of nature and then devised special ways, called experiments, of selecting sensory input data so that they would fit into the patterns ordained by the laws. In the conventionalist view, the scientist was like a creative artist, working not with paint or marble but with the unorganised sensations from a chaotic world. Scientific philosophers supporting this position included Poincare, Duhem and Eddington.

A second view of science, called inductivism, considered that the basic procedure of science was to collect and classify sensory input data into a form called observable facts. From these facts, by a method called inductive logic, the scientist then drew general conclusions which were the laws of nature. Francis Bacon, in his Novum Organum of 1620, argued that this was the only proper scientific method, and at that time his emphasis on observable facts was an important antidote to medieval reliance on a formal logic of limited capabilities. Bacon's definition accords most closely with the layman's idea of what scientists do, but many competent philosophers have also continued to support the essentials of inductivism, including Russell and Reichenbach.

A third view of science, called deductivism, emphasized the primary importance of theories. According to Popper, "Theories are nets cast to catch what we call 'the world': to rationalize, to explain, and to master it. We endeavour to make the mesh ever finer and finer." According to the deductivists, there is no valid inductive logic, since general statements can never be proved from particular instances. On the other hand, a general statement can be disproved by one contrary particular instance. Hence, a scientific theory can never be proved but it can be disproved. The role of an experiment is therefore to subject a scientific theory to a critical test. The three philosophies outlined by no means exhaust the variety of efforts made to capture science in the web of language. As we are studying the part of science called physical chemistry, we should pause sometimes (but not too often) to ask ourselves which philosophic school we are attending.

1. Only one straight line can pass through 2 points.
2. A straight line is the shortest distance between two points.
3. Through one point, only one parallel can be drawn to a given straight line.

Experience and Inference

Joan Hughes' Summary and Review of
Human Knowledge By Bertrand Russell (1948)

This book is divided into 6 parts:-
1. The World of Science
2. Language
3. Science and Perception
4. Scientific Concepts
5. Probability
6. Postulates of Scientific Inference.

According to Russell, human knowledge is gained from two sources; what we experience, and what we infer. Inferences are often made using induction. Russell has commonly been thought of as an uncritical advocate of scientific induction, but this is far from the case. Russell believes that induction leads as often to false conclusions as to true ones. (p.329-330). But we can make inductions about what is likely to be true, such as the generalization that "dogs bark." In order to do this we use postulates which we have formed in the gradual process of adapting to our environment (p.526).

In Part 1, Russell distinguishes individual knowledge from public knowledge, and briefly describes sciences which he believes have a strong theoretical basis, ie. astronomy, physics, biological evolution, physiology and psychology.

In the chapter on physiology, Russell accepts a mechanistic view of human behaviour, sometimes known as the Stimulus-Response (S-R) model. (p.67).

In Part 2, Russell discusses how we gain knowledge by means of language. He often refers to Hume, the philosopher, so that readers who have no previous knowledge of Hume may find that a preliminary reading of Andrew Robert's "What is Science?" essay helpful. Even then, there are difficulties. Russell uses a few words like intension and compresent which are not defined in the sense in which he uses them in a small dictionary.

A child first learns about things without the use of language. Ostensive learning is defined as any process by which we learn to understand a word without the use of other words. This is the way a child learns when shown a bottle or glass of milk and at the same time the word milk is uttered. The non-ostensive way of learning comes later when we learn a word like quadruped as a name for a class of other words.

Russell introduces the concept of minimum vocabulary (p.94). This is one which contains no word which can be defined in terms of the other words in it. Later in the book Russell explains how minimum vocabulary is applied to arithmetic by Peano (p.252). The minimum vocabulary of arithmetic is its axioms.

In Part 3, Russell distinguishes perceptual space from physical space. When we see something like a table which exists in physical space, we do not see the table exactly as it is in physical space. What we see depends on impulses to our brains along afferent nerves depending upon the effects of the reflected light from the table on our afferent nerves. All this takes time, which although very short means we are seeing the effect the table had on our afferent nerves, possibly a few (unmeasurable) nanoseconds ago. Two different people always see the table slightly differently even when standing close together.

What we know about the physical world comes to us from inference or interpretation of the visual data. We can infer what physical structures are like which exist in a physical space-time continuum. But what we infer depends on mental events taking place in our brains.

In Part 4, Russell explains the scientific concepts which make his conclusions understandable. These include Newton's concept of "Absolute Time" and Einstein's concept of the "Space-Time Continuum" which superseded it.

No total momentary experience reoccurs anywhere in space-time. This is an empiricist view, based on experience.(p.315). Empirical positions are only probable, not absolutely certain. Russell often alludes to the impossibility of complete knowledge. He says that it is impossible to know everything about a "complete complex of compresence." This means that it is impossible to know everything about an event which is happening to us now.

In Part 5, Russell distinguishes between mathematical probability and probability in everyday life. In mathematical probability, the odds for or against an event can be calculated exactly, because all the variables are known. An example of this would be the probability of drawing two red cards on the first and second draw from a pack of 52 playing cards. In everyday life , Bishop Butler advised "Let probability be the guide of life."

This is the second kind of probability, in which odds cannot be calculated. For example if we decide that Company X appears to give best value for our insurance contributions, we say "probably this is the best investment", but it would be impossible to calculate the mathematical probability as in the first case. There are many variables, some of which may be unknown.

In Part 6, Russell gives his conclusions.

In the chapter called "Summary of Postulates" Russell lists the postulates necessary to make scientific method possible.

1. Quasi-permanence.
2. Separable causal lines
3. Spatio-temporal continuity in causal lines.
4. Common causal origin of similar structures arranged about a centre.
5. Analogy.

In the last part of his book Russell explains in details the reasons why he considers these postulates necessary. It is easier to read after having read the first part of the book. Becoming used to Russell's style is useful, and also the way he gives many illustrations for difficult concepts, and explains them several times in different ways.

Quasi-permanence may be illustrated that we consider our kitten which after 14 years is an old cat, but is still the same "thing." Russell considers a drop of water in the sea, which though in motion remains the same drop. It is this drop rather than any other drop which is connected by a causal line.

Common causal origin can be illustrated as follows. If we consider the group cats, most cats will have whiskers, be carnivores, have four legs and a tail, have fur. Biologists will be able to add many more attributes. But cats who possess most of these attributes but not all of them, will still be considered cats. Manx cats are still cats. Cats are gathered about a centre in which Manx cats will be slightly off-centre.

Can these postulates be considered "Knowledge"? Russell believes they are habits of thought. These habits have been formed in order to ensure biological survival. They are not knowledge in the way that knowledge based on observation is knowledge. They enable both animal induction and sophisticated scientific inductions. And enable us not to make absurd inductions, such as those which can be invented by logicians.

Finally Russell concludes that there is a limit to knowledge which can be gained in an empirical way, based on experience. "Human knowledge is uncertain, inexact and partial."(p.527)

Though this book was written in 1948 and some of the language would not be used to-day, it is in no way out-of-date, and well worth reading.

Joan Hughes' Summary and Review of
The Logic of Scientific Discovery
by Karl Popper (1934)

Popper begins the book by saying that he intends to prove that scientific induction (proceeding from single observations to generalizations) is invalid in all cases. Popper uses the rules of classical logic. The theory which he intends to develop, he calls the deductive method of testing (p.30).

Popper agrees with the logical positivists (who he calls positivists) that a demarcation between science and metaphysics is necessary. This is not to say that Popper thinks metaphysics is useless, as they did; indeed he says that metaphysical thinking has often inspired science (p.38). Popper does not define metaphysics when he first talks about it on p.35. Instead he tells what positivists think about metaphysics - The nearest he gets to a definition is on p.38 as "faith in ideas of a purely speculative kind"

"The fact that value judgements influence my proposals does not mean that I am making the mistake of which I have accused the positivists - that of trying to kill metaphysics by calling it names. I do not even go as far as to assert that metaphysics has no value for empirical science. For it cannot be denied that along with metaphysical ideas which have obstructed the advance of science there have been others - such as speculative atomism - which have aided it. An looking at the matter from the psychological angle, I am inclined to think that scientific discovery is impossible without faith in ideas of a purely speculative kind, and sometimes even quite hazy; a faith which is completely unwarranted from the point of view of science, and which to that extent is metaphysical"

What he says is that metaphysics cannot be included in logical proofs of scientific theories. Logical proof is work that is done after the initial inspiration which pointed towards the theory and the practical work needed to test it, and is far more formal.

Induction is unsatisfactory because it may lead to an infinite regress. (An infinite regress means that we always have to appeal to a higher principle of induction to justify "the principle of induction" which we have used to deduce that the future observations on a set of objects will be the same as those we have made in the past.) Popper is concerned that systems of theories should be tested by means that do not lead to an infinite regress. He favours deductive testing which can only prove that theories are false; it cannot prove that they are true. Popper does not demand that every scientific statement should have been tested, but he does demand that every scientific statement should be capable of being tested.(p.48) The first few tests may corroborate a theory. But this not proof that eventually a scientist will not find a test which disproves a theory, once and for all.

Science is always advancing. There are no theories which cannot be overthrown or improved. We can feel quite comfortable with theories which may have a long "innings" even if they cannot be infallibly proved true.

Popper often defines rules which he is going to use in his future analysis. e.g. "I shall adopt a rule not to use undefined concepts as if they were implicitly defined." (p.75).

The book is quite difficult to understand in places, for most people who have not studied "classical logic". However Popper does explain those methods of classical logic which are necessary to understand his argument e.g "modus tollens" (P.76)

This book has extensive footnotes. I find it best on a first reading to omit the footnotes, unless there is a very difficult paragraph, which the footnote may throw light on.

Comparing the book with Russell's "Human Knowledge" I missed the flashes of humour with which Russell lightens his text. Though the book looks more difficult than Russell's, because there are fewer descriptive examples, and more symbols are used, nevertheless Popper does explain some terms much more clearly than Russell. For example Popper defines the term "intensional" very clearly (p.167) whereas Russell left this term undefined, and readers had to infer by his usage what the term meant. Popper tells us that an "intensionally" defined series is a series defined by an internal mathematical rule.

Towards the end of the book (p.215-250) there is a section on quantum theory which may prove difficult for readers unfamiliar with the subject. It can be omitted. Nevertheless in this section Popper relates his theories to experimental examples.

I feel most scientists even if they use induction because they are psychologically happy with it, would agree with Popper's conclusion that there is no formal proof of induction. One positive test can only corroborate or support a theory. It cannot prove it. But one negative test can disprove a theory.

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Index

conventionalism

deductivism

inductivism


Glossary

deduction

empirical

experiments

logic

induction