Notes on Popper’s Conjectures & Refutations

ie the chapter of the same name (ch.1) of the book, pp33-65

I

"When should a theory be ranked as scientific?"

or "Is there a criterion for the scientific character or status of a theory?"

[The ‘problem of demarcation’] (This is not the same as asking when a theory is true/acceptable.)

It is widely accepted that science is distinguished from pseudo-science/metaphysics by its empirical method, essentially inductive [eg making rules from observations] – proceeding from observation to experiment.

But Popper saw the problem as distinguishing between a genuinely empirical and a pseudo-empirical method such as astrology, which may appeal to observation and experiment but does not come up to scientific standards.

He felt, of theories widely discussed in his Vienna of post WWI: Einstein’s relativity, Marx’s theory of history, Freud’s psycho-analysis and Adler’s "individual psychology", only relativity had a genuine claim to scientific status.

It was neither a problem of truth (since he wasn’t sure he believed in relativity then) nor of exactness or measurability. Adherents to Freud and Adler were impressed by their explanatory power: the world was full of verifications of their theories – whatever happened confirmed them.

[NB: later he explains that explanatory power is vital for the worth of a theory but is not sufficient.]

Once he reported a case to Adler which did not seem particularly Adlerian to Popper. Adler readily analysed the case in terms of his own theory even though he had never seen the child in question. Popper asked how he had been so sure of his analysis, and when Adler replied: "Because of my thousandfold experience," Popper couldn’t help saying: "And with this new case, I suppose, your experience has become thousand-and-one-fold."

"I could not think of any human behaviour that could not be interpreted in terms of either [Freud or Adler’s] theory. It was precisely this fact – that they always fitted, that they were always confirmed – which in the eyes of their admirers constituted the strongest argument in favour of these theories. It began to dawn on me that this apparent strength was in fact their weakness."

With Einstein’s theory of gravitation though, a single observation could refute it if it violated one of the theory’s predictions. The impressive thing is the risk involved in such predictive theories. The theory is incompatible with certain possible results of observation. [NB – note the absolute sense in which he uses the term ‘refute’ here and throughout!!!.]

"These conclusions led me in the winter of 1919-1920 [:-)] to conclusions which I now reformulate as follows:

(1) It is easy to obtain confirmations, or verifications, for nearly every theory – if we look for confirmations.

(2) Confirmations should count only if they are the result of risky predictions; [ie] if unenlightened by the theory in question, we should have expected an event which was incompatible with the theory – an event which would have refuted the theory.

(3) Every ‘good’ scientific theory is a prohibition: it forbids certain things to happen. The more a theory forbids, the better it is.

(4) A theory which is not refutable by any conceivable event is non-scientific. Irrefutability is not a virtue of a theory (as people often think) but a vice.

(5) Every genuine test of a theory is an attempt to falsify it, or to refute it. Testability is falsifiability; but there are degrees of testability: some theories are more testable, more exposed to refutation, than others; they take greater risks.

(6) Confirming evidence should not count except when it is the result of a genuine test of the theory; and this means that it can be presented as a serious but unsuccessful attempt to falsify the theory. (I now speak in such cases of ‘corroborating evidence’.)

(7) Some genuinely testable theories, when found to be false, are still upheld by their admirers – for example by introducing ad hoc some auxiliary assumption, or by re-interpreting the theory ad hoc in such a way that it escapes refutation. Such a procedure is always possible, but it rescues the theory from refutation only at the price of destroying, or at least lowering, its scientific status. (I later described such a rescuing operation as a ‘conventionalist twist’ or a ‘conventionalist strategem.)

One can sum up all this by saying that the criterion of the scientific status of a theory is its falsifiability, or refutability, or testability."

II

With astrology, believers were too impressed by confirming evidence to be impressed by unfavourable evidence; and of course vagueness helped them escape testability [and thus all worth as a theory].

Marxism did make testable predictions, but these were falsified. However the followers reinterpreted both the theory and the evidence in order to make them agree.

Unlike Marxism, although Freud and Adler’s theories describe some facts, they do so in the manner of myths and so are not testable. They contain most interesting psychological suggestions, but not in testable form.

He avers that such myths may however contain considerable truth, and in fact historically speaking very nearly all scientific theories originate from myths. Such myths are not necessarily unimportant, insignificant, meaningless or nonsensical. However these characteristics were not the ones he attempted to solve by posing his criterion of falsifiability. This criterion determined the scientific status of a hypothesis, and the problem it addressed he termed the ‘problem of demarcation’ (in 1928/29).

III

"…this ‘problem of demarcation’ – the criterion of testability [etc] – is far from obvious…"

However at the time he thought it so trivial he assumed others must have reached a similar solution.

"That this was not the case I learnt from Wittgenstein’s work and from its reception; and so I published my results thirteen years later in the form of a criticism of Wittgenstein’s criterion of meaningfulness.

[We follow him in a brief peregrination around Wittgenstein…]

"Wittgenstein, as you all know [;-)] tried to show in the Tractacus (see for example his propositions 6.53, 6.54 and 5) that all so-called philosophical or metaphysical propositions were actually non-propositions or pseudo-propositions: that they were senseless or meaningless." All genuine or meaningful propositions depend on facts which can in principle be ascertained by observation, according to W. "This idea was used by Wittgenstein for a characterisation of science, as opposed to philosophy. We read (eg in 4.11 were natural science is taken to stand in opposition to philosophy) ‘The totality of true propositions is the total natural science (or the totality of the natural sciences.)’ This means that the propositions that belong to science are those deducible from true observation statements; they are those propositions which can be verified by true observation statements.

"This amounts to a crude verifiability criterion of demarcation."

But this is a definition of both meaning and science, and Popper "…was never interested in the so-called problem of meaning." [He stressed this in his earlier famous book ‘The Logic of Scientific Discovery’.] But anyway, Wittgenstein’s criterion of demarcation as verifiability or deducibility from observation statements [ie proving true as opposed to surviving proofs against] "…excludes from science practically everything that is in fact characteristic of it (while failing in effect to exclude astrology). No scientific theory can ever be deduced from observation statements, or be described as a truth function of observation statements."

Popper tried to explain to the Vienna Circle that he was talking about a definition of science whereas they were talking about meaning, but oh dear…

"But my contribution was classified by members of the circle as a proposal to replace the verifiability criterion of meaning by a falsifiability of meaning – which effectively made nonsense of my views. My protests that I was trying to solve, not their pseudo-problem of meaning, but the problem of demarcation, were of no avail.

"My attacks upon verification had some effect, however. They soon led to complete confusion in the camp of the verification philosophers of sense and nonsense. The original proposal of verifiability as the criterion of meaning was at last clear, simple and forceful. The modifications and shifts which were now introduced were the very opposite. This I should say is now seen even by the participants. But since I am usually quoted as one of them I wish to repeat that although I created this confusion I never participated in it. Neither falsifiability nor testability were proposed by me as criteria of meaning; and although I may plead guilty to having introduced both terms into the discussion, it was not I who introduced them into the theory of meaning.

"Criticism of my alleged views was widespread and highly successful. I have yet to meet a criticism of my views. Meanwhile, testability is being widely accpeted as a criterion of demarcation."

:)

So that’s what they get up to in those coffee shops!

IV

"I have discussed the problem of demarcation in some detail because I believe that its solution is the key to most of the fundamental problems of the philosophy of science." One of the most significant is the problem of induction.

[I think of induction as being the process of learning or creating rules ab initio, much along the lines of behaviouristic learning. Deduction on the other hand is the production of rules by combining others using logical operations: for example if we have already discovered that all A’s are B, and also that all B’s are C, then we can deduce that any examples of A we might have are also C. Deduction allows things to be proven for certain, (eg ‘all A’s are C’ so long as the propositions they are based on (eg all A’s are B etc) are reliable. Induction is often a natural psychological phenomenon, which can be simulated using statistics, but doesn’t enjoy the certainty that deduction, based on the rules of logic, does under theoretically ideal conditions.]

He approached the problem of induction through Hume, who argued that induction could not be logically justified. Just because day had followed night on the last trillion occasions, there is no justification depending entirely on logic for saying it will on the trillion and first.

After a lot of wrestling over the issue of whether we are justified in basing our beliefs on induction, Popper decided the practice of induction was psychologically intrinsic:

"Without waiting passively for repetitions to impress or impose regularities upon us, we actively try to impose regularities upon the world. We try to discover similarities in it, and to interpret it in terms of laws invented by us. Without waiting for premises we jump to conclusions. These may have to be discarded later, should observations show they are wrong."

…a process basic to both common sense, and scientific practice:

"This was a theory of trial and error – of conjectures and refutations. It made it possible to understand why our attempts to force interpretations upon the world were logically prior to the observation of similarities. [It was an important part of his argument that before noting regularities, you had to recognise similarities.] Since there were logical reasons behind this procedure, I thought that it would apply in the field of science also; that scientific theories were not the digest of observations, but that they were inventions – conjectures boldly put forward for trial, to be eliminated if they clashed with observations; with observations which were rarely accidental, but as a rule undertaken with the definite intention of testing a theory by obtaining, if possible, a decisive refutation. [Before you can observe, you have to know what to observe – and this depends on what you already believe.]"

[Survival in the natural world requires decisions for action made prior to or in the absence of complete, or even adequate information. "I survive, therefore I guess (and perhaps learn from my mistakes)." In the field of machine cognition the dual strategy of ‘generate and test’ has long been taken as a powerful and essential tenet. Not the least of its advantages is that it allows us to exploit sometimes that which we do not necessarily understand very well, and this is not a weakness but a strength.

On the subject of logic, guessing or whatever as the basis of thought, Marvin Minsky of AI fame, said on p186 of ‘The Society of Mind’:

"When do we actually use logic in real life? We use it to simplify and summarize our thoughts. We use it to explain arguments to other people and to explain to them that those arguments are right. We use it to reformulate our own ideas. But I doubt that we often use logic actually to solve problems or to "get" new ideas. Instead, we formulate our arguments and conclusions in logical terms after we have constructed or discovered them in other ways; only then do we use verbal and other kinds of formal reasoning to "clean things up," to separate the essential parts from the spaghettilike tangles of thoughts and ideas in which they first occurred.

"To see why logic must come afterward, recall the idea of solving problems by using the generate and test method. In any such process, logic can be only a fraction of the reasoning; it can serve as a test to keep us from coming to invalid conclusions, but it cannot tell us which ideas to generate, or which processes and memories to use. Logic no more explains how we think than grammar explains how we speak…"]

V

"The belief that science proceeds from observation to theory is still so widely and so firmly held that my denial of it is often met with incredulity."

"But in fact the belief that we can start with pure observations alone, without anything in the nature of a theory, is absurd; as may be illustrated by the story of the man who dedicated his life to natural science, wrote down everything he could observe, and bequeathed his priceless collection to the Royal Society to be used as inductive evidence. This story should show us that beetles may be collected, observations may not."

"It is quite true that any particular hypothesis we choose will have been preceeded by observations – the observations, for example, which it is designed to explain. But these observations, in their turn, presupposed the adoption of a frame of reference: a frame of expectations: a frame of theories." [Earlier he had quoted Katz: "A hungry animal divides the environment into edible and inedible things. An animal in flight sees roads to escape and hiding places…" and Popper added that objects can be classified, and can become similar or dissimilar only in this way – by being related to needs and interests. This rule applies not only to animals but also to scientists. Sober (writing much later in 'Reconstructing the Past' ) also stresses that hypotheses cannot realisitically be considered independent of an environment of background assumptions.]

"The theory of inborn ideas is absurd, I think; but every organism has inborn reactions or responses; and among them, responses adapted to impending events. These responses we may describe as ‘expectations’ without implying [they] are conscious. […] In view of the close relation between expectation and knowledge we may even speak in quite a reasonable sense of ‘inborn knowledge’. This knowledge is not however valid a priori; an inborn expectation, no matter how strong and specific, may be mistaken."

"One of the most important of these expectations is the expectation of finding a regularity."

Interestingly, Popper now anticipates the core activity of Vorpal Enterprises:

"To sum up this logical criticism of Hume’s psychology of induction we may consider the idea of building an induction machine. Placed in a simplified ‘world’ (for example, one of sequences of coloured counters) such a machine may through repetition ‘learn’, or even ‘formuate’, laws of succession which hold in its ‘world’. If such a machine can be constructed (and I have no doubt that it can) then, it might be argued, my theory must be wrong; for if a machine is capable of performing inductions on the basis of repetition, there can be no logical reasons preventing us from doing the same."

Popper had claimed repetition was not the basis of induction, our propensity to see and seek rules was; so a machine that created rules simply out of repetition would he thought violate his understanding of induction. But it is possible to build a rule generating mechanism with a variety of influences – repetition plays its role, as well as various aspects of motivation and mind set. Such a machine would still be proactively rule-seeking, and I see no reason why this should violate Popper’s claim that animals and scientists must be too. He continues:

"The argument sounds convincing, but it is mistaken. In constructing an induction machine we, the architects of the machine, must decide a priori what constitutes its ‘world’; what things are to be taken as similar or equal; and what kinds of ‘laws’ we wish the machine to be able to ‘discover’ in its ‘world’. In other words we must build into the machine a framework determining what is revelant or interesting in its world: the machine will have its ‘inborn’ selection principles. The problems of similarity will have been solved for it by its makers who thus have interpreted the ‘world’ for the machine."

He is saying that such a machine would not have to rely on repetition, it would also have a capacity to detect similarity (and relevance) built in by its creators. [However, it is surely impossible to detect regularity without being able to detect similarity. If such a machine’s similarity detectors were based on low-level sensory similarity, but could build more complex criteria, it would surely resemble us in this. And a capacity for assigning relevance, which would in effect be an attention director, need not mean the machine didn’t use a mechanism for detecting regularities where repetition might play a part.]

VI

"Our propensity to look out for regularities, and to impose laws upon nature, leads to the psychological phenomenon of dogmatic thinking or, more generally to dogmatic behaviour: we expect regularities everywhere, and expect to find them where there are none; events which do not yield to these atempts we are inclined to treat as a kind of ‘background noise’; and we stick to our expectations even when they are inadequate and we ought to accept defeat. This dogmatism is to some extent necessary. It is demanded by a situatoin which can only be dealt with by forcing our conjectures on the world."

A dogmatic attitude, which makes us stick to our first impressions is indicative of a strong belief; a critical attitude, which is ready to modify its tenets, which admits doubt, and demands tests, is indicative of a weaker belief. He suggests that because Hume’s theory (and popular belief) claim strength of belief should depend on repetition, more experienced people should be more dogmatic.

"But dogmatic thinking, an uncontrolled wish to impose regularities, a manifest pleasure in rites and in repetition as such, are characteristics of primitives and children; and increasing experience and maturity sometimes create an attitude of caution and criticism rather than of dogmatism."

[I’m not too sure about any of that. I know so many old people who ought to know better who are terribly dogmatic that I’m not convinced we get more open minded as we age. Many ‘rites’ amongst sophisiticated folk (always ourselves) are not recognised. However, this all starts to remind me of Terrence Deacon’s claim (in 'The Symbolic Species' eg p403) that symbolic thought characteristic of humans and their language often involves very strong links between elements that never occur together once let alone repetetively; also certain social symbolic relationships seem Deacon says to need considerable ritual to become established.]

He proceeds to discuss neuroticism and other psychopathologies in terms of reluctance to discard hypotheses, and finishes the section with:

"…my ideas about induction originated with a conjecture about the evolution of Western polyphony. But you will be spared this story."

VII

He relates the dogmatic attitude to the tendency to verify laws and schemata, which he identifies as pseudo-scientific, and he relates the critical attitude to the tendency to change, test and refute laws, and this he identifies as scientific.

The critical attitude is not opposed to the dogmatic attitude but superimposed on it. A critical attitude needs dogmas for its raw material.

"…science must begins with myths, and with the criticism of myths; neither with the collection of observations, nor with the invention of experiments, but with the critical discussion of myths, and of magical techniques and practices."

The scientific tradition passes on its theories but also its critical attitude to them.

"This tradition is Hellenic [ie Greek]: it may be traced back to Thales, founder of the first school [not philosophic school, just the first school] which was not mainly concerned with the preservation of dogma."

"Criticism is an attempt to find the weak spots in a theory, and these, as a rule, can be found only in the more remote logical consequences which can be derived from it. [These remote logical consequences may take considerable teasing out; deciding something is testable may be decidedly non-trivial.] It is here that purely logical reasoning pays an important part in science."

"There is [nothing] irrational in relying for practical purposes upon well-tested theories, for no more rational course of action is open to us."

VIII

"Let us now turn from our logical criticism of the psychology of experience to our real problem – the problem of the logic of science." [Yup – all that was just a preamble ! :-( ]

"It was easy to see that the method of science is criticism, i.e. attempted falsifications. Yet it took me a few years to notice that the two problems – of demarcation [ie deciding what is science] and of induction – were in a sense one.

"Why, I asked, do so many scientists believe in induction? I found they did so because they believed natural sciences to be characterised by the inductive method – by a method starting from, and relying on, long sequences of observations and experiments. They believed that the difference between genuine science and metaphysical or pseudo-scientific speculation depended soley upon whether or not the inductive method was employed. They believed (to put it in my own terminology) that only the inductive method could provide a satisfactory criterion of demarcation.

"I recently came across an interesting formulation of this belief in a remarkable philosophical book by a great physicist – Max Born’s Natural Philosophy of Cause and Chance. He writes: ‘Induction allows us to generalise a number of observations into a general rule: that night follows day and day follows night . . . But while everyday life has no definite criterion for the validity of an induction , . . . science has worked out a code, or rule of craft, for its application.’ Born nowhere reveals the contents of this inductive code (which, as his wording shows, contains a ‘definite criterion for the validity of an induction’); but he stresses that ‘there is no logical argument’ for its acceptance: ‘it is a question of faith’; and he is therefore ‘willing to call induction a metaphysical principle’. But why does he believe that such a code of valid inductive rules must exist? This becomes clear when he speaks of the ‘vast communities of people ignorant of, or rejecting, the rule of science, among them the members of anti-vaccination societies and believers in astrology. It is useless to argue with them; I cannot compel them to accept the same criteria of valid induction in which I believe: the code of scientific rules.’ This makes it quite clear that ’valid induction’ was here meant to serve as a criterion of demarcation between science and pseudo-science.

"but it is obvious that this rule or craft of ‘valid induction’ is not even metaphysical: it simply does not exist. No rule can ever guarantee that a generalisation inferred from true observations, however often repeated, is true. […] And the success of science is not based upon rules of induction, but depends upon luck, ingenuity, and the purely deductive rules of critical argument.

"I may summarise some of my conclusions as follows:

(1) Induction, i.e. inference based on many observations, is a myth. It is neither a psychological fact, nor a fact of ordinary life, or one of scientific procedure.

(2) The actual procedure of science is to operate with conjectures: to jump to conclusions – often after one single observation (as noticed for example by Hume and Born).

(3) Repeated observations and experiments function in science as tests of our conjectures or hypotheses, i.e. as attempted refutations.

(4) The mistaken belief in induction is fortified by the need for a criterion of demarcation which, it is traditionally but wrongly believed, only the inductive method can provide.

(5) The conception of such an inductive method, like the criterion of verifiability, implies a faulty demarcation.

(6) None of this is altered in the least if we say that induction makes theories only probable rather than certain."

IX

"If, as I have suggested, the problem of induction is only an instant or facet of the problem of demarcation, then the solution to the problem of demarcation must provide us with a solution to the problem of induction. This is indeed the case, I believe, although it is perhaps not immediately obvious.

"For a brief formulation of the problem of induction we can turn again to Born, who writes: '…no observation or experiemnt, however extended, can give more than a finite number of repetitions'; therefore, 'the statement of a law - B depends on A- always transcends experience. Yet this kind of statement is made everywhere and all the time, and sometimes from scanty material.'

"In other words, the logical problem of induction aises from

(a) Hume's discovery (so well expressed by Born) that it is impossible to justify a law by observation or experiment, since it 'transcends experience';

(b) the fact that science proposes and uses laws 'everywhere and all the time'. (Like Hume, Born is struck by the 'scanty material', i.e. the few observed instances upon which the law may be based.)

To this we have to add

(c) the principle of empiricism which asserts that in science, only observation and experiment may decide upon the acceptance or rejection of scientific statements, including laws and theories.

"These three principles, (a), (b), and (c), appear at first sight to clash; and this apparent clash constitutes the logical problem of induction.

"Faced with this clash, Born gives up (c), the principle of empiricism (as Kant and many others, including Bertrand Russell, have done before him), in favour of what he calls a 'metaphysical principle'; a metaphysical principle which he does not even attempt to formulate; which he vaguely describes as a 'code or rule of craft' ; and of which I have never seen any formulation which even looked promising and was not clearly untenable.

"But in fact the principles (a) to (c) do not clash. We can see this the moment we realise that the acceptance by science of a law or of a theory is tentative only, which is to say that all laws and theories are conjectures, or tentative hypotheses (a position which I have sometimes called 'hypotheticism'); and that we may reject a law or theory on the basis of new evidence, without necessarily discarding the old evidence which originally led us to accept it.

"The principle of empiricism (c) can be fully preserved, since the fat of a theory, its accpetance or rejection, is decided by obervation and experiment - by the result of tests. So long as a theory stands up to the severest tests we can design, it is accepted; if it does not, it is rejected. But it is naver inferred, inany sense, from the empirical evidence. There is neither a psychological nor a logical induction. Only the falsity of the theory can be inferred from empirical evidence, and this inference is a purely deductive one.

"Hume showed that it is not possible to infer a theory from observation statements; but this does not affect the possibility of refuting a theory by observation statements. The full appreciation of this possibility makes the relation between theories and observations perfectly clear.

"This solves the problem of the alleged clash between principles (a), (b), and (c), and with it Hume's problem of induction."

X

"Thus the problem of induction is solved. But nothing seems less wanted than a simple solution to an age-old philosophical problem." [! And not just philosophical ones!]

He acknowledes there are other possible problems of induction.

"[H]ow do we really jump from an observation statement to a theory?"

"One can say first that the jump is not from an observation statement, but from a problem-situation, and that the theory must allow us to explain the observations which created the problem […inevitably a description of objects, characteristics and sequences of actions; hence all knowledge, science included, is based on some form of narrative - not that any sensible person ever doubted this…] (that is, to deduce them from the theory strengthened by other accepted theories, and by other observation statements, the so-called initial conditions). This leaves, of course an immense number of theories, good and bad; and it thus appears that our question has not been answered.

"But this makes it fairly clear that when we asked our question we had more in mind than , 'How do we jump from an observation statement to a theory?' The question we had in mind was, it now appears, 'How do we jump from an observation statement to a good theory?' But to this the answer is: by jumpingfirst to any theory and then testing it, to find whether is is good or not; i.e. by repeatedly applying the critical method, eliminating many bad theories, and inventing many new ones. Not everybody is able to do this; but there is no other way." [That definition doesn't help us towards a better way of perfecting this skill unfortunately.]

"Another question sometimes asked is this: why is it reasonable to prefer non-falsified statements to falsified ones? To this question some involved answers have been produced, for example pragmatic answers. But from a pragmatic point of view the question does not arise, since false theories often serve well enough. Most formulae used in engineering or navigation are known to be false, although they may be excellent approximations and easy to handle; and they are used with confidence by people who know them to be false.

"The only correct answer is the straightforward one: because we search for truth (even though we can never be sure we have found it), and because the falsified theories are known or believed to be false, while the non-falsified theories may still be true..."

"Yet another way of putting the problem of induction is in terms of probability. Let t be the theory and e the evidence: we can ask for P(t,e), [i.e.] the probability of t given e. The problem of induction, it is often believed, can then be put thus: construct a calculus of probability which allows us to work out for any theory t what its probability is, relative to any given empiral evidence e; and show that P(t,e) increases with the accumulation of supporting evidence, and reaches high values - at any rate values greater than 1/2.

"In The Logic of Scientific Discovery I explained why I think that this approach to the problem is fundamentally mistaken. To make this clear, I introduced there the distinction between probability and degree of corroboration or confirmation."

"I explained in my book why we are interested in theories with a high degree of corroboration. And I explained why it is a mistake to conclude from this that we are interested in highly probable theories. [Presumably the high probabilities depend on aspects of the pre-existing theories, so a new theory with a high probability will need to agree with the old, discriminating against extremely novel though valid insights…?] I pointed out that the probability of a statement (or set of statements) is always the greater the less the statement says: it is inverse to the content or the deductive power of the statement, and thus to its explanatory power. Accordingly every interesting and powerful statement must have a low probability; and vice versa: a statement with a high probability will be scientifically uninteresting, because it says little and has no explanatory power. Although we seek theories with a high degree of corroboration, as scientists we do not seek highly probable theories but explanations; that is to say powerful and improbable theories. [It can't be stressed too often that explanation is central to science!] The opposite view - that science aims at high probability - is a characteristic development of verificationism: if you find that you cannot verify a theory, or make it certain by induction, you may turn to probability as a kind of 'Ersatz' for certainty, in the hope that induction may yield at least that much."

He completes the chapter with a list of some other aspects of the broader topic apart from demarcation and induction, which we will allow the reader to investigate for themself. [And you won't believe the struggle I had with the big sister that lives in 'Word' about how that last sentence should be terminated!]

The remainder of this survey will cover a sparse selection from some of the rest of the book which seem to me noteworthy.

Straight away, at the start of chapter 2, he deals with something that specialists in other fields might have considered when offered advice of a philosophical nature: 'What is this thing 'philosophy' that has been thrown at us, supposedly for our benefit?' Not for Mr. Popper the characterisation of the contribution of philosophy as a remote commentary on what scientists do:

"…I believe that the function of a scientist or of a philosopher is to solve scientific or philosophical problems, rather than to talk about what he or other philosophers are doing or might do."

"We are not are not students of some subject matter but students of problems."

Halfway through Ch.4 we return to that dutiful cove we met earlier:

"…But even if you go to the end of your lives, notebook in hand, writing down everything you observe, and if you finally bequeath this important notebook to the Royal Society, asking them to make science out of it, then the Royal Society might preserve it as a curiosity, but decidedly not as a source of knowledge. It might be lost perhaps in some cellar of the British Museum (which as you know cannot afford to catalogue most of its treasures) but more likely it will end up on a rubbish heap." [Dr. Popper appears to be unaware of the Mass Observation project which had begun in the ten years preceding the writing (in 1948/49) of ch.4, and which is has been considered a valuable resource to this day!]

Ch.5, section 6:

"…What is important about a theory is its explanatory power, [again: no explanation - no science] and whether it stands up to criticism and to tests. The question of its origin, of how it is arrived at - whether by an 'inductive procedure', as some say, or by an act of intuition - may be extremely interesting, especially for the biographer of the man who invented the theory, but it has little to do with its scientific status or character."

Ch.5, section 7:

"…But are not Anaximander's theories false, and therefore non-scientific? They are false, I admit; but so are many theories, based upon countless experiements, which modern science accepted until recently, and whose scientific character nobody would dream of denying, even though they are now believed to be false. (An example is the theory that the typical chemical properties of hydrogen belong to only one kind of atom - the lightest of all atoms.) There were historians of science who tended to regard as unscientific (or even as superstitious) any view no longer accepted at the time they were writing; but this is an untenable attitiude. A false theory may be as great an achievement as a true one. And many false theories have been more helpful in our search for truth than some less interesting theories which are still accepted. For false theories can be helpful in many ways; they may for example suggest some more or less radical modifications, and they may stimulate criticism. Thus Thales' theory that the earth floats on water reappeared in a modified form in Anaximenes, and in more recent times in the form of Wegener's theory of continental drift. How Thales' theory stimulated Anaximander's criticism has been shown already." […though I am not convinced either of them were involved in the formulation of Wegener's theory. The latter didn't become 'accepted' until the 60's or 70's, and this chapter was written at the end of the '50's, though Popper doesn't actually refer to it as 'accepted'.]

Ch.5, section 11:

Popper repeatedly refers to the importance of the critical tradition in the development of science:

"…To my knowledge the critical or rationalist tradition was invented only once [see Thales (above)]. It was lost after two or three centuries, perhaps owing to the rise of the Aristotelian doctrine of episteme, of certain and demonstrable knowldege (a development of the Eleatic and Heraclitean distinction between certain truth and mere guesswork). It was rediscovered and consciously revived by the renaissance, especially by Galileo Galilei.

Running straight on to Ch.12, we have another excellent summary of his definition of the operation of good science:

"I now come to my last and most central contention. It is this. The rationalist tradition, the tradition of critical discussion, represents the only practicable way of expanding our knowledge - conjectural or hypothetical knowledge, of course. There is no other way. More especially, there is no way that starts from observation or experiment. In the development of science, observations and experiments play only the role of critical arguments. And they play this role alongside other, non-observational arguments. It is an important role; but the significance of observations and experiements depends entirely upon the question whether or not they may be used to criticise theories.

"According to the theory of knowledge here outlined there are in the main only two ways in which theories may be superior to others: they may explain more [perhaps their value, if 'true']; and they may be better tested [perhaps our best estimate of their 'truth'] - that is, they may be more fully and more critically discussed, in the light of all we know, of all the objections we can think of, and especially also in the light of observational or experiemental tests which were designed with the aim of criticising the theory.

"There is only one element of rationality in our attempts to know the world: it is the critical examination of our theories. These theories themselves are guesswork. We do not know, we only guess. If you ask me, 'How do you know?' my reply would be, 'I don't; I only propose a guess. If you are interested in my problem, I shall be most happy if you criticise my guess, and if you offer counter proposals, I in turn will try to criticise them.'

"This, I believe, is the true theory of knowledge (which I wish to submit for your criticism): the true description of a practice which arose in Ionia and which is incorporated in modern science (though there are many scientists who still believe in the Baconian myth of induction): the theory that knowledge proceeds by way of conjectures and refutations.

"Two of the greatest men who clearly saw that there was no such thing as an inductive procedure, and who clearly understood what I regard as the true theory of knowledge, were Galileo and Einstein. Yet the ancients also knew it." [He quotes Xenophanes.]

Ch. 8 is fascinating on irrefutability, but I could discover no lessons in it for paleontology.

Ch. 10, I:

"…The history of science, like the history of all human ideas, is a history of irresponsible dreams, of obstinacy, and of error."

Ch. 10, II:

"… we can know of a theory, even before it has been tested, that if it passes certain tests it will be better than some other theory." […by dint of its explanatory power.]

"… we have a criterion of relative potential satisfactoriness, or of potential progressiveness, which can be applied to a theory even before we know whether or not it will turn out, by the passing of some crucial tests, to be satisfactory in fact.

"This criterion of relative potential satisfactoriness (which I formulated some time ago, [as I did in the 'Site Philosophy' page of my website; he did it earlier and in somewhat more detail in his L. of Sci. D.] and which, incidentally, allows us to grade theories according to their degree of relative potential satisfactoriness) is extremely simple and intuitive [Oh, thanks mate! ;-)]. It characterizes as preferable the theory which tells us more; that is to say, the theory which contains the greater amount of empirical information or content; which is logically stronger; which has the greater explanatory and predictive power; and which can therefore be more severely tested by comparing predicted facts with observations. In short, we prefer an interesting, daring, and highly informative theory to a trivial one. [Compare this with the typical derogatory jeers by classical dinosaurologists at 'speculative theories'!]

"All these properties which, it thus appears, we desire in a theory can be shown to amount to one and the same thing: to a higher degree of empirical content or of testability."

Ch. 10, V:

Although he earlier considered theories whose intrinsic irrefutability he considered fairly immediately apparent (eg determinism), he says, presumably about more run of the mill theories:

"…as a rule, a theory cannot be tested except by testing one by one some of its more remote consequences; consequencess which cannot immediately be seen upon inspecting it intuitively."

[Last, but not least, it should be mentioned that not only does the index of his attempt to define science not include the term "peer review", but nowhere in it, as far as I recall, does he suggest it is any part of the scientific process to restrict commentary and contribution to a limited circle of individuals, whatever claims they may make to special excellence. The peer review system is not part of science, but merely a cosy arrangement between editors who find it saves them effort and responsibility, and established figures for whom it minimises the risk of embarrassment and loss of position.]