Popper at the Mont Pelerin Society - Public Opinion and Liberal Principles

Continuing the condensed version of Conjectures and Refutations, this is chapter 17.
The paper was first prepared to provide a starting point for debate at an international conference, the sixth meeting of the Mont Pelerin Society, held in Venice in 1954. It was published in Italian in 1955 and in German in 1956. It first appeared in English in the 1963 in this collection of papers.

As usual when Popper addressed a meeting, his aim was to challenge and provoke thought, rather than simply endorsing the assumptions that he shared with his audience.

The paper has seven sections:

The myth of public opinion.
The dangers of public opinion.
Liberal principles: group of theses.
The liberal principle of free discussion.
The forms of public opinion.
Some practical problems: censorship and monopolies of publicity.
A short list of political illustrations.

It may help to start with a summary of the liberal principles that Popper spelled out in section 3. This will be helpful for a general readership (unlike the Mont Pelerin meeting) where there are likely to be many people who do not hold non-socialist liberal principles and some who are not be clear about what these principles are.
(1) The state is a necessary evil and its powers should be kept to the minimum that is necessary.
(2) A democracy is a state where the government can be changed without bloodshed.
(3) Democracy cannot confer benefits on people. "Democracy provides no more than a framework within which the citizens may act in a more or less organised and coherent way".
(4) Democracy does not mean that the majority is right.
(5) Institutions need to be tempered and supported by traditions.
(6) There is no Liberal Utopia. There are always problems, conflicts of interests, choices to be made between the lesser of evils.
(7) Liberalism is evolutionary rather than revolutionary. It is about modifying or changing institutions and traditions rather than wholesale replacement of the existing order. The exception to this is when a tyranny is in place, that is a government that can only be changed by violence and bloodshed.
8) The importance of the moral framework.

Among the traditions that we must count as the most important is what we may call the 'moral framework' (corresponding to the institutional 'legal framework') of a society. This incorporates the society's traditional sense of justice or fairness, or the degree of moral sensitivity that it has reached... Nothing is more dangerous than the destruction of this traditional framework. (Its destruction was consciously aimed at by Nazism).

Returning to the beginning of the paper, on the myth of public opinion, Popper noted that we need to be wary of a number of ideas about public opinion which many people accept without thinking critically about them. He noted the following:
(a) The idea that the voice of the people is a kind of authority, based on the essential wisdom and "rightness" of the mythical "man in the street". Apart from his objections to any kind of authority, he noted that the people usually differ considerably on most issues. He also accepted a fragment of truth in the myth, because simple people can wiser than their governments, and also motivated by more honourable intentions.
(b) The "manifest truth" theory, which makes people impatient of differences of opinion.
(c) A dangerously irrational and romantic form of the "voice of the people" myth - that the popular will can represent the genius and Spirit of the People.

Moving on to the dangers of public opinion, he noted that it can be very powerful and hence liberals (wary of concentrations of power and their danger) should treat it with a degree of suspicion: "Owing to its anonymity, public opinion is an irresponsible form of power, and therefore particularly dangerous from the liberal point of view."

On the liberal theory of free discussion, he suggested that freedom of thought and discussion are ultimate liberal values that are not in need of further defence or justification. However he noted that they can be given additional support on account of the way they contribute to the search for truth and the elimination of error by critical public discussion.

In connection with some practical problems such as censorship and monopolies of publicity he had no theses to offer, just questions, for example what should be done about the influence and responsibility of the intelligentsia in connection with spreading ideas such as socialism, and their role in the acceptance of tyrannical fashions such as abstract art (and political correctness)?

He ended with some random thoughts on the use and abuse of public opinion.

It may sometimes assume the role of an enlightened arbiter of justice. Unfortunately it can be managed. These dangers can be counteracted only by strengthening the liberal tradition. Public opinion should be distinguished from the publicity of free and critical discussion which is (or should be) the rule in science, and which includes the discussion of moral and other issues. Public opinion is influenced by, but is not the result of, nor under the control of, discussions of this kind. Their beneficial influence will be the greater the more honestly, simply, and clearly, these discussions are conducted.

A note on the Mont Pelerin Society.

The Mont Pelerin Society formed in 1947 when Hayek invited a number of academics, writers and assorted others to consider that should be done to sustain the ideas of freedom at a time when socialist central planning in more or less coercive forms was under way in most countries. Popper was among the founding members, along with Hayek, Ludwig von Mises, Milton Friedman and Frank Knight.

Condensed Conjectures and Refutations, Chapter 19 The History of our time, an optimists view.

This was the Sixth Eleanor Rathbone Memorial Lecture, delivered at the University of Bristol in 1956. Eleanor Rathbone was a British MP and a stalwart campaigner on issues including female circumcision in Africa, child marriage in India and forced marriage in Palestine.

At the time of the lecture Popper considered that the optimist's view had considerable rarity value because "the wailings of the pessimists have become somewhat monotonous". This was the height of the Cold War and many people considered that it was only a matter of time before one side or the other precipitated a disastrous military confrontation.

As he usually did in his lectures, Popper laid down a challenge to received opinion. In this case he nominated the view that was something of a cliche of the times, expressed by Bertrand Russell among many others, that our intellectual development has outrun our moral development.

We have become very clever, according to Russell, indeed too clever. We can make lots of wonderful gadgets, including television, high speed rockets, and an atom bomb... But we have not been able to achieve that moral and political growth and maturity which alone could safely direct and control the uses to which we put our tremendous intellectual powers... To put this view in a nutshell: we are clever, perhaps too clever, but we are also wicked... As against this, I shall maintain precisely the opposite. My first thesis is this. We are good, perhaps a little too good, but we are also a little stupid; and it is this mixture of goodness and stupidity which lies at the root of our troubles.

The main troubles of our times are not due to our moral wickedness, but, on the contrary, to our often misguided moral enthusiasm: to our anxiety to better the world we live in. Our wars are fundamentally religious wars; they are wars between competing theories of how to establish a better world. And our moral enthusiasm is often misguided, because we fail to realise that our moral principles, which are sure to be over-simple, are often difficult to apply to the complex human and political situations to which we feel bound to apply them.

To demonstrate the way that an appeal to morality can be misused, he instanced the case of the then Bishop of Bradford who published a pamphlet in 1942 attacking a society which was so evil that it could be considered the work of the devil, so that a minister of the church was fully justified in working for its destruction. The social system under attack was that of the western democracies and the pamphlet was written to support Stalin's regime in the Soviet Union.
Popper considered that, by 1956, there was no need for further criticism of the communist system and he proceeded to criticise the nationalist faith which he regarded as equally absurd, when expressed as the doctrine of national self-determination.

The principle amounts to the demand that each state should be a nation-state: that it should be confined within a natural border, and that this border should coincide with the location of an ethnic group; so that it should be the ethnic group, the nation, which should determine and protect the natural limits of the state.

He noted that apart from the possible example of Iceland there are virtually no nation states of that kind and the attempt to realise that state of affairs has caused endless conflict and strife when ethnic minorities demanded that they be allowed to break away or join an adjacent state where they would be the majority. For example Czechoslovakia was formed under the principle of national self-determination but as soon as it was formed the Slovaks demanded (in the name of the same principle) to be free, and finally it was destroyed by the German minority, in the name of the same principle. The latest example of this principle is the demand for a Palestinian nation state which is used as a rationale for waging war on Israel.

There are ethnic minorities everywhere. The proper aim cannot be to "liberate" all of them, rather it must be to protect all of them. The oppression of national groups is a great evil; but national self-determination is not a feasible remedy... Few creeds have created more hatred, cruelty, and senseless suffering than the belief in the righteousness of the nationality principle; and yet it is still widely believed that this principle will help to alleviate the misery of national oppression. My optimism is a little shaken when I look at the near-unanimity with which this principle is still accepted -- even by those whose political interests are clearly opposed to it.

My second thesis is this: In spite of our great and serious troubles, and in spite of the fact that ours is surely not the best possible society, I assert that our free world is by far the best society which has come into existence during the course of human history.

That view was based on the claim that we have practically (not entirely) overcome a list of great social evils, ranging from poverty through penal cruelty and racial discrimination to war. His third thesis concerns war and it states that since the time of the Boer War, none of the democratic governments of the free world have been in a position to wage a war of aggression, or at least they could not wage an aggressive war with the public united behind them.
He instanced the unwillingness of Great Britain to confront the Kaiser prior to WW1 and Hitler prior to WW2. The Suez adventure tested the hypothesis and the dismal outcome (for Britain and France) confirmed it. The invasions of Afghanistan and Iraq also test the hypothesis, although it is apparent that extraordinary circumstances were required to prompt the military action and the significant body of internal resistance supports Popper's thesis that the nation would not be united behind an aggressive war.

His fourth thesis was related to the war of ideas, and it was prompted by some remarks made by the Russian premier, Mr Kruschev when he visited India and made a speech indicting British colonialism. Popper suggested that someone should have defended Britain, along the lines that there was nothing the matter with the world that Soviet colonialism was going to fix. But still absurd ideas about Britain were circulated, often enough originating from British sources. The fourth thesis is that the power of ideas, and especially religious and moral ideas, is at least as important as that of physical resources. He considered that this view of the power of ideas was shared by the early liberal and rationalist movements but they also believed that the truth was manifest, so that rival ideas did not need to join battle to sort out good from bad.

The fifth thesis of this talk is that truth is hard to come by. This contradicts the over-optimistic idea that the truth is manifest, an idea that he subjected to criticism in other essays in the collection, especially the Introduction.

The chapter ends with some comments on the need to take up the ideas of fallibilism and critical rationalism to avoid the extremes of relativism and fanaticism that result from defective theories of knowledge and rationality.

Postscript. With the benefit of five decades of hindsigh it is apparent that Popper was wildly over-optimistic. Who would have predicted that, with the disasters of Stalinism about to be admitted by the Soviet leadership, within a few years radical youth in the west would make brutal thugs like Che and Mao into cult figures?
That the "liberation" of the Third World from western colonisation, and the delivery of untold billions of aid would result in the worst famines and genocides that Africa has ever seen?
That left liberalism would become a religion with all the attendant intolerance and prejudice, and be widely promoted in the universities of the western world?
That a civilisation with leading figures like Shakespeare, Milton, Beethoven, Mozart, would produce generations that would assign cult status to the purveyors of narcissistic and irrational stuff like the Beats, and worse.
That Popper's ideas would be marginalised in the academic community by a series of fads and fashions - logical empiricism, language analysis, POMO? What next?

Condensed Conjectures and Refutations, Chapter 11 The Demarcation between Science and Metaphysics

The Demarcation between Science and Metaphysics

This paper stands as a rather sad legacy of one of the most useless debates that ever arose in one of the most unhelpful schools of supposedly rational thought, the logical positivists or logical empiricists. It was written for a volume called The Philosophy of Rudolph Carnap, in the Library of Living Philosophers series edited by P A Schilpp. (Some call this the 'library of almost dead philosophers' series). Each volume in the series has a standard format, first an autobiography by the philosopher, then a series of essays on his or her work from invited contributors, then a reply from the philosopher. The idea is to get a definitive statement of the authors views in response to a range of comments and criticisms in the hope that there will be a minimum of loose ends when the philosopher dies, so people are not left wondering -- what would he have said in reply to this or that criticism?

Albert Einstein was invited to contribute to the Carnap volume but he declined on the ground that discussing positivism had become a waste of space. I am inclinded to agree and it is hard to justify going to the trouble to write about this chapter in the book. Still, some good may come of it, if only a better understanding of the way that unhelpful research programs in philosophy have wasted so much time and effort.

Background

Some history of the Vienna Circle of Logical Positivists for background. The most immediate influence on the Circle was the philosopher-physicist Ernst Mach (1838-1916) an empiricist in the tradition of David Hume whose mission was to purge science of metaphysics and place it on the firm "positive" foundations of sensation. His major followers were Moritz Schlick (1882-1936), Rudolph Carnap (1891-1970) and Otto Neurath (1883-1945). Schlick took over Mach's chair at the university in Vienna and he became the front man for the Vienna Circle which pursued Mach's positivism, with Russell's Principia their inspiration and Wittgenstein's Tractatus providing the program. This was essentially a war on metaphysics by application of the strict "verificationist" definition of meaning. They proposed that statements should be regarded as literally meaningless if they could not be confirmed or verified by evidence. The propositions of logic and mathematics were exempt from the requirement for verification on the understanding that they are true by definition and they do not pretend to convey information about the world.

The most obvious casualties of the verification principle were religious and moral principles, though there were others that were less obvious, including the principle itself and, more surprisingly, the laws of science. When these laws are stated in their strong form, along the lines of "All swans are white", they cannot be verified by any number of observations of white swans, simply because you cannot be certain that you have sighted all the swans in the universe. This dilemma, with the unsolved problem of induction, represented twin "skeletons in the cupboard" of positivism, but still, by 1928 the Circle had an official program and a vehicle, the Ernst Mach Society, with a mission for scientific philosophy as a basis for popular education and social transformation. Nowadays they would have a web site and a blog as well.

In the words of Malachi Hacohen (Popper's biographer) "Neurath persuaded the militantly secularist Free Thinkers, now numbering most circle associates among them, to establish the Ernst Mach Society. Schlick was elected president, apparently without his prior knowledge, and other circle members chief officers". The circle gained worldwide influence, indeed they institutionalised the philosophy of science with a series of conferences in the 1930s with the sponsorship of luminaries such as Bertrand Russell. Then the predominantly Jewish and left wing members of the circle had to scatter for their lives, like Popper himself, and they were dispersed far and wide by 1939.

Popper addressed a different problem from that of meaning and metaphysics because he was concerned with the difference between science and pseudo-sciences such as astrology which appear to be based on observations but are actually "unsinkable". His exemplar of science was Einstein's theory which might have been refuted by a particular set of observations on the eclipse of the sun. Inspired by this example Popper advanced his criterion of falsification to demarcate between testable statements on the science side of the line ("All ravens are black" which is logically refuted by the observation of a white raven) and various categories of statements on the other side of the line (morals, metaphysics, methodological principles and, incidentally, nonsense). Moral principles, aesthetics, metaphysics and methodology are meaningful and they can be rationally discussed in terms of their adequacy for their purposes, their consistency and their consequences, though such discourse was in principle outlawed by the positivists.

Hacohen gives a lot of credit to the logical positivists of the Vienna Circle for putting up with Popper's Steppenwolf-like activity, prowling on the fringe of the circle where Schlick, Carnap, Neurath et al huddled around their campfire, seeking warmth and consolation from the dying embers of the verification principle They accepted Popper's book which most of them perceived to have merit even if none of them really agreed with Popper's turn from induction to a theory of conjectural knowledge that is tested but never confirmed.

Publication of the book aroused intense disagreement among the members of the Circle and no less than three reviews appeared in their house journal because Reichenbach and Neurath insisted on writing critical reviews after Carnap signaled assent to the turn from verification to testing. Support from Carnap was short-lived and the positivists generally managed to convince themselves, and many others, that Popper's falsification criterion was concerned with meaning which was their own ruling obsession. This misunderstanding persisted for some decades because the positivist diaspora carried it to Britain and North America where it became well entrenched while Popper was "down under" in New Zealand.

The Paper

Popper's paper has six sections: (1) Introduction, (2) My Own View of the Problem, (3) Carnap's First Theory of Meaninglessness, (4) Carnap and the Language of Science, (5) Testability and Meaning and (6) Probability and Induction.

1. Introduction

Writing about Carnap brings back to my mind the time when I first met him, at his Seminar, in 1928 or 1929. It brings back even more vividly a later occasion, in 1932, in the beautiful Tyrolese hills, when I had the opportunity of spending part of my holidays in prolonged discussions with Carnap and with Herbert Feigle, in the company of our wives. We had a happy time, with plenty of sunshine, and I think we all tremendously enjoyed those long and fascinating talks, interspersed with a little climbing but never interrupted by it. None of us will ever forget, I am sure, how Carnap once led us in a steep climb up a trackless hill, through a beautiful and almost impenetrable thicket of alpone rhododendrons, and how he led us at the same time, through a beautiful and almost impenetrable thicket of arguments whose topic induced Feigl to christen our hill 'Semantische Schnuppe', something like Semantical Shooting Star -- though several decades had to elapse before Carnap, simulated by Tarski's criticism, discovered the track that led him from Logical Syntax to Semantics.

Popper went on to say that Carnap was a captivating person, utterly absorbed in his problems, eager to listen to criticism, with the courage to change his mind even on fundamental aspects of his philosophy. It has to be said that Carnap cast a strange spell over his associates, friends and critics (like Popper) alike. Joe Agassi's comments on this topic are interesting and I will come back to that in some concluding comments.

Popper went to the mountains with a big manuscript in his kitbag, which in 1934/5 became Logik der Forschung (Logic of Scientific Investigation). The manuscript contained a lot of criticism of two books by Carnap; some of this criticism Carnap took on board and some he said exaggerated the differences between Popper's views and those of the Vienna Circle. That is a view that people like Richard Rorty have been pleased to accept as a justification for ignoring Popper's work, as though it is a dead end like logical empiricism. Amazingly, that rejoinder from Carnap resulted in Popper saying nothing about their differences for a decade after the publication of his own book. It seems that by the time he did speak up the damage had been done, Freddy Ayer's Language, Truth and Logic and the Continental diaspora had poisoned the wells of the western world.

2. Popper's view of the problem

In a nutshell:

The repeated attempts made by Rudolf Carnap to show that the demarcation between science and metaphysics coincides with that between sense and nonsense have failed... In all its variants demarcation by meaninglessness has tended to be at the same time too narrow and too wide: as against all intentions and all claims, it has tended to exclude scientific theories as meaningless, while failing to exclude even that part of metaphysics which is known as 'rational theology'.

Popper's perception of the need to specify the difference between science and (say) astrology was described above in the historical background. The key points are (a) his demarcation criterion had nothing to do with meaning (b) it was not designed to eliminate metaphyiscs in a stroke and (c) there are degrees of testability, so the line is not clear-cut and it shifts over time as theories develop and experimental technology improves.

3, 4 and 5. Carnap's various theories of meaninglessness

The Oxford Companion to Philosophy states that "Technical rigor was the hallmark of his important contributions to formal semantics, the philosophy of science and the foundations of inductive probability". Against that, it is my impression that his three major works stand like the masts of a sunken vessel, a warning to mariners to avoid the rocks that wrecked the good ship Carrnap. Popper spends a good deal of time on technical talk about Carnap's evolution from his early Tractatus-like view on meaning, through the language of science -- physicalistic, unified -- to "Testability and Meaning", a 1936 article where Carnap made some Popperian changes to his system but balked at the next decisive steps away from "justificationism" to a full-blooded fallibilism. That was probably the high tide of agreement between Carnap and Popper, later when Carnap moved on to the foundations of inductive logic there could be no raprochment.

6. Probability and induction

In this section Popper described how the full consequences of approaching confirmation as if it was just a weaker form of verification became apparent in Carnaps's two books on probability. This is all more of the same -- the appearance of rigor, new terms, tortured arguments, to what effect? What scientist in living memory has made any use of Carnap's logic of induction? It seems that some of the consequences of Carnap's wild goose chase are virtually paradigms of absurdity, presumably due to the structure of thinking that generated the paradox of the ravens discovered later by Carnap's younger colleague, Hempel. For example (and this is Popper's account, so be wary):

He [Carnap] proposes that we accept (as probable) a principle to the effect that the evidence 'Sandy is clever' increases the probability of 'A is clever' for any individual A -- whether A is the name of a cat, a dog, an apple, a tennis ball or a cathedral. This is a consequence of the definition of 'degree of confirmation' which he proposes. According to this definition, any two sentences with the same predicate ('clever' or 'sick') and different subjects are inter-dependent or positively correlated, whatever the subject may be... I am far from certain whether he has realised these consequences of his theory, for he nowhere mentions them explicitly.

A concluding comment from Joseph Agassi, from a review of a collection of papers dedicated to Carnap, reprinted in Agassi's book The Gentle Art of Philosophical Polemic.

I do not think that any of his doctrines are going to be cited for long: he said nothing original. I do not think any of the techniques he invented, his modal logic, his state-descriptions, his reduction sentences, his theoretical and observation languages, his inductive system, his c function, his lambda and the continuum of inductive methods -- all these are museum pieces and they never worked.

Condensed Conjectures and Refutations, Chapter 8 On the Status of Science and Metaphysics

On the Status of Science and of Metaphysics


This chapter contains the text of two radio talks for the Free Radio-University, Berlin, delivered in the late 1950s. These would have been prepared while Popper was working on The Postscript to The Logic of Scientific Discovery: After 25 Years, which was to appear shortly after The Logic of Scientific Discovery (1959). The 25 years referred to the period from 1934 (when the German version of the book was published) to 1959. When the postscript eventually appeared after fifty years it contained a fascinating epilogue on metaphysical research programs which would have been substantially written in the 1950s. This topic was briefly mentioned in his autobiography for the Schillp volume (published separately as Unended Quest) and it clearly signals his radical departure from the anti-metaphysical positivism of the Vienna Circle.

Part 1. Kant and the logic of experience.

This section contains a passage that Bryan Magee identified as the key to "locating" Popper in relation to the western tradition (that was in the chapter on Popper in Magee's Confessions of a Philosopher). Magee regards him as a reconstructed Kantian and this passage brings that out rather well, as Popper agreed although that was not the original purpose of the text.

In order to solve the riddle of experience, and to explain how natural science and experience are at all possible, Kant constructed his theory of experience and of natural science. I admire this theory as a truly heroic attempt to solve the paradox of experience, yet I believe that it answers a false question and hence that it is in part irrelevant. Kant, the great discoverer of the riddle of experience, was in error about one important point...

What was this error? As I have said, Kant, like almost all philosophers and epistemologists right into the twentieth century, was convinced that Newton's theory was true... before Einstein.

Even those who do not accept Einstein's theory of gravitation ought to accept that his was an achievement of truly epoch-making significance. For his theory established at least that Newton's theory, no matter whether true or false, was certainly not the only possible system of celestial mechanics that could explain the phenomena in a simple and convincing way...

Now if, unlike Kant, we consider Newton's theory as a hypothesis whose truth is problematic, then we must radically alter Kant's problem. No wonder that his solution no longer suits the new post-Einsteinean formulation of the problem, and that it must be amended accordingly.

Kant's solution to the problem is well known. He assumed, correctly I think, that the world as we know it is our interpretation of the observable facts in the light of theories that we ourselves invent. As Kant puts it: 'Our intellect does not draw its laws from nature... but imposes them upon nature.' While I regard this formulation of Kant's as essentially correct, I feel that it is a little too radical, and I should therefore like to put it in the following modified form: 'Our intellect does not draw its laws from nature, but tries -- with varying degrees of success -- to impose upon nature laws which it freely invents.'...

We invent our myths and our theories and we try them out: we try to see how far they take us. And we improve our theories if we can. The better theory is the one that has the greater explanatory power; that explains more; that explains with greater precision; and that allows us to make better predictions.

Since Kant believed that it was our task to explain the uniqueness and the truth of Newton's theory, he was led to the belief that this theory followed inescapably and with logical necessity from the laws of our understanding. The modification of Kant's solution which I propose, in accordance with the Einsteinian revolution, frees us from this compulsion. In this way, theories are seen to be the free creations of our own minds, the result of an almost poetic intuition, of an attempt to understand intuitively the laws of nature. But we no longer try to force our creations upon nature. On the contrary, we question nature, as Kant taught us to do, and we try to elicit from her negative answers concerning the truth of our theories: we do not try to prove or to verify them, but we test them by trying to disprove or falsify them, to refute them.

In this way the freedom and boldness of our theoretical creations can be controlled and tempered by self-criticism, and by the severest tests we can design. It is here, through our critical methods of testing, that scientific rigor and logic enter into empirical science.

Part 2. The problem of the irrefutability of philosophical theories.

Somewhere in Popper's writing prior to this time there is a passage where he stated that early in his career he considered that the domain of rational discussion was limited to "scientific" matters. Certainly he had given up that view by the time he wrote The Open Society and quite likely by the time he finished Logic der Forschung because that contains rational discussion of principles of method which cannot be empirically tested.

In this section of the paper he demonstrated how philosophical doctrines can be subjected to criticism even though they cannot be refuted by facts. He nominated a number of philosophical theories, all of which he considers to be false.

First, determinism: the future is contained in the present, inasmuch as it is fully determined by the present.
Second, idealism: the world is my dream.
Third, irrationalism: we have irrational or supra-rational experiences in which we experience ourselves as things-in-themselves; and so we have some kind of knowledge of things-in-themselves.
Fourth, voluntarism: in our own volitions we know ourselves as wills. The thing-in-itself is the will.
Fifth, nihilism: in our boredom we know ourselves as nothings. The thing-in-itsself is Nothingness.

After some discussion of the logic of testing and refutation, he approached his problem: If all philosophical theories are irrefutable, how can we distinguish between true and false philosophical theories? He then specified three types of theory.

1. Logical and mathematical theories.
2. Empirical (scientific) theories.
3. Philosophical or mataphysical theories.

Theories of type 1 are tested by attempted refutation, especally by finding internal contradictions. Decisions in these cases are usually final.

Scientific theories are similarly tested by the process of criticism and in this case observations can fit into the critical discussion.

For the third kind of problems, he proposed a solution that is based on a situational analysis to asses the adequacy of the theory as a solution to a problem. Actually he didn't use the term situational analysis but that is an important concept that will come in useful anytime we are contemplating the reasons for human actions or the rationality/adequacy of human decisons.

My solution is this: if a philosophical theory were no more than an isolated assertion about the world, flung at us with an implied 'take it or leave it' and without a hint of any connection with anything else, then indeed it would be beyond discussion. But the same might be said of an empirical theory... A theory is comprehensible and reasonable only in its relation to a given problem-situation, and it can be rationally discussed only by discussing this relation.

The critical approach in its widest ramifications can then be said to involve five kinds of criticsm:

1. The check on the problem.
2. The check of internal consistency.
3. The check of consistency with other well-tested theories.
4. The check of evidence -- observation and experiment.
5. The check on the metaphysics.

Condensed Conjectures and Refutations, Chapter 7 Kant

Kant's Critique and Cosmology


This was a radio broadcast in honour of the 150th anniversary of Kant's death. It was published in the BBC Listerner in 1954 and a number of very interesting footnotes have been added in this version.

After the introduction there are six sections. Popper started with an account of the large crowd that came to Kant's funeral, to the amazement of his friends who expected a quiet ceremony. Popper speculated that this had little to do with Kant's reputation as a great philosopher, instead he suggested that the people came to show their gratitude for a man who taught the rights of man, equality before the law, world citizenship, peace on earth and, "perhaps most important", of emancipation through learning.

The footnote to this reads:
"I say 'most important' because Kant's well-deserved rise from near poverty to fame and comparatively easy circumstances helped to create on the Continent the idea of emancipation through self-education (in this form hardly known in England where the 'self-made man' was the uncultured upstart). The significance of this idea is connected with the fact that on the Continent, the educated had been for a long time the middle classes, while in England they were the upper classes."

1. Kant and the Enlightenment

It seems that the good ideas that are associated with Kant's name reached the Continent from England, in a book by Voltaire (Letters About the English, 1732) which drew many comparisons between England and the mainland which favoured English representative government, tolerance and empirical science over the tyranny and bigotry that prevailed in the rest of Europe.

Voltaire's book was burnt, but its publication marks the beginning of a philosophical movement -- a movement whose peculiar mood of intellectual aggressiveness was little understood in England, where there was no occasion for it.

Kant is one of Popper's favorite philosophers and he associated him with all the positive ideas of the Englightenment, and especially with the struggle for intellectual and spiritual freedom. He quoted Kant: "Enlightenment is the emancipation of man from a state of self-imposed tutelage... of incapacity to use his own intelligence without external guidance... Dare to use your intelligence! This is the battle-cry of the Enlightenment."

However there is a different usage of the term 'Enlightenment' to mean shallow and pretentious intellectualism. This has given rise to considerable literature about the different aspects of the 'Enlightenment Project' which is no doubt complicated by the existence of two radically different meanings of the term. For some people the project derives from the radicalism of the French revolution and it is represented by all those utopian revolutionary movements that have causesd the death of millions. For others it is the simple goodness and gentle meliorism of Kant which is the line taken by Popper, although that is not pursued in this essay.

2. Kant's Newtonian Cosmology

Kant is best known (if not at first hand) as a philosopher but his major inspiration came from Newton's theory and he made a major contribution to cosmology and cosmogony with the Kant-Laplace hypothesis on the origin of the solar system. In the way that one problem leads to another, in the case of Kant his work on the structure of the universe led him to the problem of human knowledge.

3. The Critique and the Cosmological Problem

The central problem of the Critique of Pure Reason turned up when Kant was wrestling with the problem of the limit of the universe in time. Either it had a beginning in time or it did not. Kant found that he could produce apparently valid proofs for each option. That was the first of the "antimonies" of pure reason.

4. Space and Time

"What lesson did Kant draw from these bewildering antimonies? He concluded that our ideas of space and time are inapplicable to the universe as a whole. We can, of course, apply the ideas of space and time to ordinary physical things and physical events. But space and time themselves are neither things nor events... They are a kind of framework for things and events."

He gave his theory the unfortunate name 'Transcendental Idealism' which gave the impression that he denied the reality of physical objects. This opened the way for others to follow, using his difficult style of writing, to promulgate wildly speculative metaphysical views which he found repulsive. Popper quoted from the Critique:

There is no need for a critique of reason in its empirical use; for its principles are continuously submitted to tests, being tested by the touchstone of experience. Similarly there is no need for it within the field of mathematic... But in a field in which reason is constrained neither by sensation nor by pure intuition to follow a visible track -- namely, in the field of its transcendent use -- there is much need to discipline reason, so that its tendency to overstep the narrow limits of possible experience may be subdued.

5. Kant's Copernican Revolution

Kant's solution to the problem of the limits of sense experience, and his explanation for the truth of Newton's theory (which clearly exceeded the bounds of sensory experience) was to postulate that "our intellect does not draw its laws from nature, but imposes its laws upon nature". This later became known as the "lamp" theory of the mind, as opposed to the "mirror" theory. This is Copernican in the sense that it puts the observer in the centre of the process of generating knowledge, in the way that Copernicus turned the tables to break the deadlock of cosmology by shifting from a stationary observer and revolving heavens, to envisage that we, the observers, revolve while the heavens stand still.

6. The Doctrine of Autonomy

Kant makes man the lawgiver of morality just as he makes him the lawgiver of nature. And in so doing he gives back to man his central place both in his moral and in his physical universe. Kant humanised ethics, as he had humanised science... His doctrine of autonomy [states] that we cannot accept the command of an authority, however exalted, as the ultimate basis of ethics... it is our responsibility to judge whether this command is moral or immoral.

He also formulated the doctrine of people as ends in themselves, never to be used merely as the means to the ends of others. He argued that the just state will establish equality in those limitations of the freedom of the people which cannot be avoided "if the freedom of each is to coexist with the freedom of all". He envisaged a league of nations that would establish peace on earth [pity about that one].

I have tried to sketch in broad outline Kant's philosophy of man and his world, and its two main inspirations -- Newtonian cosmology, and the ethics of freedom; the two inspirations to which Kant referred when he spoke of the starry heavens above and the moral law within us.

Condensed Conjectures and Refutations, Chapter 5

Back to the Presocratics

This was the Presidential Address delivered to the Aristotelian Society in October 1958. Bryan Magee wrote an amusing account of this lecture in Confessions of a Philosopher.


"At that time there were only two books by him in the English language: The Open Society and its Enemies and The Poverty of Historicism. They caused me to think of him as a political philosopher, albeit a great one... I was curious to see him in the flesh."

I listened to his paper utterly engrossed -- and to the ensuing discussion with disbelief and dismay. The main contention [of the paper] is that the only practicable way of expanding human knowledge is by an unending feedback process of criticism. Put like that it may seem self-evident, but the real clout of the thesis lies in what it denies. It denies that we can get far if we attempt to base the extension of our knowledge on observation and experiment.

The other theme of the lecture concerned the pioneering role of the pre-Socratic philosophers in developing the speculative and critical approach to cosmology. Magee considered that this historical thesis was interesting and challenging but not earth-shattering. The real punch of the lecture was in the theory of knowledge and its growth.

If the method [of conjecture and refutation] is valid it overthrows an empirical tradition in philosophy of several hundred years standing, a tradition whose most important single tenet is that all our knowledge of the world must begin with experience. It is therefore, despite appearances, a theory that is radical -- revolutionary in a historic sense, and epic in its implications. It demolishes, almost incidentally, hundreds of years of philosophizing... I was intellectually thrilled by the argument... and agog to see it pounced on by this particular audience which contained some of the most distinguished philosophers in Britain most of whom were identified, and identified themselves, with empiricism.

I simply could not believe it when, in the question and answer period, not a single person raised this issue or referred to it. The entire discussion, which became impassioned, turned on whether or not this or that particular pre-Socratic philosopher had been correctly represented by Popper, which in turn meant arguing about whether an important fragment might be better understood in a different way...

When I got home I wrote letter to Popper. In it I said that although the intellectual frivolity of the audience was inexcusable, he himself was partly to blame for what had occurred. Instead of presenting his revolutionary idea head-on, he had presented it indirectly, in the form of a historical claim about the pre-Socratics... He had, I went on, made the same mistake in the way that he had written The Open Society, with similar consequences. Instead of presenting the most important arguments directly, he had put them forward in the course of discussing other people's ideas, with the result that most academics came away from the book thinking that it was about Plato and Marx... His ideas were immensely important, but he was presenting them in a way that almost ensured that they would be
misunderstood.

The original paper is fairly short and in the collection there is a lengthy appendix which is a reply to two classical scholars who challenged Popper's interpretation of the pre-Socratic fragments and also his views on the way that scientific knowledge advances.

The paper has 12 sections, some of them quite brief. In the first Popper makes a bid for a simple theory of knowledge and a return to cosmology, to attempts to understand the world we live in, including ourselves as a part of the world.

For me, both philosophy and science lose all their attraction when the give up that pursuit [of knowledge and understanding of the world] -- when they become specialisms and cease to see, and to wonder at, the riddles of our world. Specialization maybe a great temptation for the scientist. For the philosopher it is the mortal sin.

In the second section he introduced himself as an amateur student of the pre-Socratics "completely out of my depth when an expert begins to argue which words or phrases Heraclitus might, and which he could not possibly, have used". He also dissociated himself from the belief, which he attributed to Bacon, that science should start from observations of simple things like an orange. He prefers the notion that Western science started with bold theories about the world, not with collected observations of oranges.

In sections III to VIII he sketched the rapid, speculative evolution of theories about the relationship of the earth to its surrounds. First Thales suggested that the earth is floating in water like a ship. His student Anixamander suggested an alternative theory, that the earth is not held up by anything, but is a drum-shaped object that stays in place because it is equally distant from all other things.

As to the Presocratics, I assert that there is the most perfect possible continuity of thought between their theories and the later developments in physics. Whether they are called philosophers, or pre-scientists, or scientists, matters very little, I think. But I do assert that Anaximander's theory cleared the way for the theories of Aristarchus, Copernicus, Kepler and Galileo. It is not that he merely 'influenced' these later thinkers; 'influence' is a very superficial category. I would rather put it like this: Anaximander's achievement is valuable in itself, like a work of art. Besides, his achievement made other achievements possible, among them those of the great scientists mentioned.

The critical discussion of Anaximander's worldview led to the serious consideration of the general problem of change, a problem which became the central problem of Greek cosmology and resulted in the work of Democritus, Parmenides, Zeno and Heraclitus. Parmenides is a particular favorite of Popper, who credits him with the first hypothetico-deductive theory of the world. When Popper engaged in a debate with Einstein, he called Einstein 'Parmenides" to draw attention to some aspects of their theories which Popper considered they held in common.
In section IX he lamented that the significance of this exciting story was being "buried under the mounting heap of the minutiae of textual criticism". I wonder if he said that in the lecture or added it in later revisions for publication?

In section X he attempted to substantiate that view with some heavy criticism of two experts in the field (Kirk and Raven) who he claimed were not interpreting the ancient texts correctly.
In sections XI and XI he presented the central theses of the speech:

First, the great achievement of the ancient Greeks was their discovery or invention of the tradition of critical discussion.
Second, the tradition of critical discussion is the only way to expand our knowledge.

The first achievement was to transform the function of a school. The usual function of schools was (and is) to impart definite doctrines. "A school of this kind never admits a new idea. New ideas are heresies, and lead to schisms... There cannot, of course, be any rational discussion in a school of this kind".

An early example of a school of this kind was the religious order founded by Pythagoras, with a characteristic way of life and a secret doctrine. But something very different happened in the school started by Thales, where students challenged their teachers and set forth radical new doctrines without being expelled.

[As an aside, many people would like to see more written about the "Popper school" and the extent to which this deviated from the Popperian tenets of critical discussion of the ideas of the teacher. Joe Agassi wrote a book about his tormented relationship with Popper and he pointed out that Popper's personal behaviour was often and scandalously used as an excuse by philosophers of rival schools to refrain from coming to grips with Popper's ideas.]

This is the tradition which Popper claimed was rediscovered and consciously revived in the Renaissance, especially by Galileo. That led Popper to his final and most important thesis, that the critical method is the true method of science (and learning generally), in contrast to the empiricist and inductivist view that knowledge begins with observation, and ends up being verified or warranted by reference to sense impressions.

This, I believe, is the true theory of knowledge (which I wish to submit to 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.

Condensed Conjectures and Refutations, Chapter 3

Three Views Concerning Human Knowledge

One may formulate this 'third view' of scientific theories briefly by saying that they are genuine conjectures - highly informative guesses about the world which although not verifiable (capable of being shown to be true) can be submitted to severe critical tests. They are serious attempts to discover the truth.

The philosophy of physics was Popper's major concern until the 1960s when he began to write about biological themes. The three volumes of The Postscript to The Logic of Scientific Discovery (mostly written in the 1950s) are overwhelmingly concerned with physics, and this paper was first printed in 1956.

He was mainly concerned with instrumentalism in the philosophy of physics, especially in the Copenhagen interpretation of quantum theory but most of us struggle to understand the issues in this field. However the arguments are equally applicable in other contexts such as the debate in the methods of economics that was triggered by Milton Friedman's espousal of instrumentalism in his famous 1953 paper where he argued that prediction was all-important, regardless of the truth of assumptions used in the calculations.

The chapter has six sections and the first describes the dispute between Galileo and Cardinal Bellarmino before the Inquisition. In the second section he spelled out the issue at stake, whether the new science of celestial mechanics was true (or nearer to the truth than the pre-Copernican system) or whether it was merely a simpler and a more convenient instrument for astronomical calculations and predictions. The point was that the Church did not want science to become a competitor in the field of providing true statements about the cosmos. Bishop Berkeley took the same line in his criticism of Newton's theory because, like Bellarmino before him, he wanted scientific theories to be regarded as convenient instruments for calculation and not as true descriptions of anything real.

The third section of the paper is a critique of essentialism, the first of the three views. The fourth section is a more detailed exposition of instrumentalism and the fifth section is a critique of that view. The sixth section is "The Third View: Conjectures, Truth, and Reality".

Berkeley's criticism was hardly noticed by the physicists; but it was taken up by the philosophers, sceptical as well as religious. As a weapon it turned out to be a boomerang. In Hume's hands it became a threat to all belief - to all knowledge, whether human or revealed. In the hands of Kant, who firmly believed both in God and in the truth of Newtonian science, it developed into the doctrine that theoretical knowledge of God is impossible, and that Newtonian science must pay for the admission of its claim to truth by the renunciation of its claim to have discovered the real world behind the world of appearance...Physicists (with a few brilliant exceptions such as Mach, Kirchhoff, Hertz, Duhem, Poincare, Bridgeman and Eddington - all instrumentalists) kept aloof from these philosophical debates, which remained completely inconclusive. Faithful to the tradition created by Galileo they devoted themselves to the search for truth, as he had understood it. Or so they did until very recently... Without any further debate over the philosophical issues, without producing any new argument, the instrumantalist view has become an accepted dogma. It may well be called the official view of physical theory since it is accepted by most of our leading theorists of physics (although neither by Einstein nor by Schrodinger). And it has become part of the current teaching in physics.

Returning to the issues at stake in the modern debate: this is the way that instrumentalism has been adopted among physicists by default, without a good discussion, under the influence of developments in quantum physics and especially the Copenhagen interpretation.

Section 3. The First View: Ultimate Explanation by Essences

"(1) The scientist aims at finding a true theory or description of the world which shall also be an explanation of the observable facts...(2) The scientist can succeed in finally establishing the truth of such theories beyond all reasonable doubt...(3)The best, the truly scientific theories, describe the 'essences' or the 'essential natures of things' - the realities which lie behind the appearances."

The first proposition is part of the view that Popper defends. He contests 2 and 3.

Popper famously dissents from (2) in favour of the theory of conjectural knowledge, bearing in mind that the theories here concern deep explanations, not the existence of such things as the evolution of life on earth or the heliocentric structure of the solar system.

As to (3) Popper is not especially concerned to dispute the existence of "essences" that underly the visible appearance of nature. He argues that the essentialist doctrine has tended to stiffle criticism and the search for deeper explanations beyond the current orthodoxy.

Section 4: The Second View: Theories as Instruments

This section includes a comparison of the three views and some exploration of the instrumentalist view, including some considerations of language and meaning that indicate that Popper could have excelled in language analysis if he thought that this was a worthwhile occupation.

Section 5: Criticism of the Instrumentalist View

He summarise the criticism as follows:

Instrumentalism can be formulated as the thesis that scientific theories - the theories of the so-called 'pure' sciences - are nothing but computation rules (or inference rules); of the same character, fundamentally, as the computation rules of the so-called 'applied' sciences. One might even formulate it as the thesis that 'pure' science is a misnomer, and that all science is applied.

Now my reply to instrumentalism consists in showing that there are profound differences between pure theories and technological compputation rules, and that instrumentalism can give a perfect description of these rules but is quite unable to account for the difference between them and the theories.

That is the summary of Popper's argument and I don't have time to reproduce more detail from the three pages of compressed argument in this section.

Moving on to the final section on The Third View, Conjectures, Truth and Reality

He suggested that instrumentalism is an ad hoc response to some serious problems with the interpretation of quantum theory, and it has the effect of defecting criticism and limiting the field of seach (or even the perceived need) for improved theories that meet the computational requirements and provide a grip on the nature of reality as well.

There is an important distinction which we can make between two kinds of scientific prediction, and which instrumentalism cannot make; a distinction that is connected with the problem of scientific discovery. I have in mind the distinction between thet prediction of events of a kind which is known, such as eclipses and thunderstorms on the one hand and, on the other, the prediction of new kinds of events (which the physicist calls 'new effects') such as the prediction which led to the discovery of wireless waves, or of zero-point energy, or to the artificial building up of new elements not previously found in nature.

He ends the section with a further criticism of instrumentalism in connection with the alleged denial by instrumentalists of the descriptive function of abstract words and of disposition-words. This leads him to mention some of ideas that emerged in much more detail later, in connection with propensities, both the metaphysics of "a world of propensities", and the propensity theory of probabilities, designed to handle single events rather than frequency distributions, that he developed to contribute to quantum theory.

I do not think that a language without universals could ever work; and the use of universals commits us to asserting, and thus (at least) to conjecturing, the reality of dispositions - though not of ultimate and inexplicable ones, that is, of essences... But if we are committed, or at least prepared, to conjecture the reality of forces, and of fields of forces, then there is no reason why we should not conjecture that a die has a definite propensity (or a disposition) to fall on one or another of its sides... An interpretation of probability along these lines might allow us to give a new physical interpretation to quantum theory.

Condensed Conjectures and Refutations, Chapter 2

The nature of philosophical problems and their roots in science.

We must beware of mistaking the well-nigh senseless and pointless subtleties of the imitators for the pressing and genuine problems of the pioneer.

This chapter is based on a 1952 paper which Popper delivered to a meeting of the Philosophy of Science Group of the British Society for the History of Science.

He commenced by stating that he was not happy to talk about the present position of English philosophy because he thought it was more important to solve scientific or philosophical problems rather than talk about what he or other philosophers are doing or might do. He moved on to talk about the nature of philosophical problems, after some comments about the description and classification of subjects.

Disciplines are distinguished partly for historical reasons and reasons of administrative convenience (such as the organisation of teaching and appointments), and partly because the theories which we construct to solve our problems have a tendency to grow into unified systems. But all this classification and distinction is a comparatively unimportant and superficial affair. We are not students of some subject matter but students of problems. And problems may cut right across the borders of any subject matter or discipline.

His two main theses are:

1. Every philosophy and every philosophical school is likely to degenerate under the influence of philosophical inbreeding to the point where its problems become practically indistinguishable from pseudo-problems and its talk becomes almost meaningless babble.

2. This is likely to happen as a result of what Popper called the "prima facie" method of teaching philosophy, that is, starting off by reading the works of the great philosophers without reference to the problem situation in science or mathematics or politics which concerned them.

It is likely that the situation has improved since that time due to the rise of the history and philosophy of science which has stimulated a great deal of research on ancient problem situations and the social and political context of the times, but the benefits have been dissipated by some of the ideological and sociological postures that are adopted in the reseach.

What I mean by the prima facie method of teaching philosophy...is that of giving the beginner the works of the great philosophers to read; the works, say, of Plato and Aristotle, Descartes and Liebniz, Locke, Berkeley, Hume, Kant and Mill. What is the effect of such a course of reading? A world of astonishingly subtle and vast abstractions opens itself before the reader; abstractions of an extremely high and difficult level. Thoughts and arguments are put before his mind which sometimes are not only hard to understand, but which seem to him irrelevant because he cannot find out what they might be relevant to. Yet the student knows that these are the great philosophers, that this is the way of philosophy. Thus he will make an effort to adjust his mind to what he believes (mistekenly, as we shall see) to be their way of thinking. He will attempt to speak their queer language, to match the tortuous spiral of their argumentation, and perhaps even tie himself up in their curious knots.

He went on to argue that it is necessary to understand the real problems that concerned the great philosophers, not just the philosophical problems that they wrote about, and the real problems are actually problems in science and mathemtics, or in politics and law. The student needs to understand these problems, which means understanding the problem situation at the time, which means understanding some of the history of ideas.

He pursued his case with two examples, the first concerning Plato's theory of Forms and the crisis in Greek science following thte discovery of the irrationality of the square root of two. The second is Kant's Critique of Pure Reason.

Taking the second example first, the setting for Kant's work was twofold (1) the apparently overwhelming triumph of Newtonian mechanics in the Principia and (2) Hume's critique of the empirical base of knowledge which woke Kant from "dogmatic slumber". The problem was the conflict between the apparent success of Newton in gaining true and unassailable knowledge of the cosmos, and Hume's scepticism about the logic of induction and hence the observational basis of our knowledge of the cosmos.

Kant's proposed solution to this insoluble problem consisted of what he proudly called his 'Copernican Revolution' of the problem of knoweledge. Knowledge was possible because we are not passive receptors of sense data but their active digestors. By digesting and assimilating them we form and organise them into a Cosmos, the Universe of Nature...Thus our intellect does not discover laws in nature, but prescribes its own laws and imposes them upon nature. This theory is a strange mixure of absurdity and truth.

Popper's solution was of course to dissolve part (1) of Kant's dilemma, to insist that scientific knowledge, even that which appears to be as unassailable as Newton's theory at the time, is inevitably conjectural, so there is no need to speculate how it is that we can obtain certain and unassailable truths. Then if the best that we can manage is conjectural knowledge, Hume's scepticism about induction ceases to be a serious problem, thus taking the sting out of part (2) of Kant's problem situation.

Turning to Popper's first example, I will draw on a previous account of the problem which Popper write up in some of the notes to The Open Society and its Enemies and in an Addendum to the 1962 edition. The reason for this is entirely pragmatic, I happen to have some passages of OSE in electronic form.

My thesis here is that Plato's central philosophical doctrine, the so-called Theory ofForms or Ideas, cannot be properly understood except in an extra-philosophical context; more especially in the context of the critical problem situation in Greek science which developed as a result of the discovery of the irrationality of the square root of two.

It seems likely that Plato's Theory of Forms is both in its origin and in its content closely connected with the Pythagorean theory that all things are in essence numbers. The detail of this connection and the connection between Atomism and Pythagoreanism are perhaps not so well known.

From Addendum 1 to volume 2 of The Open Society and its Enemies.

In the second edition of this book, I made a lengthy addition to note 9 to chapter 6 (pp. 248 to 253). The historical hypothesis propounded in this note was later amplified in my paper 'The Nature of Philosophical Problems and Their Roots in Science' (British Journal for the Philosophy of Science, 3, 1952, pp. 1241 ff.; now also in my Conjectures and Refutations). It may be restated as follows: (1) the discovery of the irrationality of the square root of two which led to the breakdown of the Pythagorean programme of reducing geometry and cosmology (and presumably all knowledge) to arithmetic, produced a crisis in Greek mathematics; (2) Euclid's Elements are not a textbook of geometry, but rather the final attempt of the Platonic School to resolve this crisis by reconstructing the whole of mathematics and cosmology on a geometrical basis, in order to deal with the problem of irrationality systematically rather than ad hoc, thus inverting the Pythagorean programme of arithmetization; (3) it was Plato who first conceived the programme later carried out by Euclid: it was Plato who first recognized the need for a reconstruction; who chose geometry as the new basis, and the geometrical method of proportion as the new method; who drew up the programme for a geometrization of mathematics, including arithmetic, astronomy, and cosmology; and who became the founder of the geometrical picture of the world, and thereby also the founder of modern science-of the science of Copernicus, Galileo, Kepler, and Newton.

From the notes to chapter 6 of The Open Society and its Enemies.
(2) According to tradition an inscription over the door of Plato's academy said: 'Nobody untrained in geometry may enter my house.' I suspect that the meaning of this is not merely an emphasis upon the importance of mathematical studies, but that it means: 'Arithmetic (i.e. more precisely, Pythagorean number theory) is not enough; you must know geometry!' And I shall attempt to sketch the reasons which make me believe that the latter phrase adequately sums up one of Plato's most important contributions to science. See also Addendum, p. 319.

As is now generally believed, the earlier Pythagorean treatment of geometry adopted a method somewhat similar to the one nowadays called 'arithmetization'. Geometry was treated as part of the theory of integers (or 'natural' numbers, i.e. of numbers composed of monads or 'indivisible units'; cp. Republic, 525e) and of their logoi', i.e. their 'rational' proportions. For example, the Pythagorean rectangular triangles were those with sides in such rational proportions. (Examples are 3:4 15; or 5: 12: 13.) A general formula ascribed to Pythagoras is this: 2n + 1: 2n(n + 1): 2n(n + 1) + 1. But this formula, derived from the 'gnomon', is not general enough, as the example 8: 15: 17 shows. A general formula, from which the Pythagorean can be obtained by putting m = n + 1, is this: m2-n2: 2mn: m2 + n2 (where m > n). Since this formula is a close consequence of the so-called 'Theorem of Pythagoras' (if taken together with that kind of Algebra which seems to have been known to the early Pythagoreans), and since this formula was, apparently, not only unknown to Pythagoras but even to Plato (who proposed, according to Proclus, another non-general formula), it seems that the 'Theorem of Pythagoras' was not known, in its general form, to either Pythagoras or even to Plato. (See for a less radical view on this matter T. Heath, A History of Greek Mathematics, 1921, vol. I, pp. 80-2. The formula described by me as 'general' is essentially that of Euclid; it can be obtained from Heath's unnecessarily complicated formula on p. 82 by first obtaining the three sides of the triangle and by multiplying them by 2/mn, and then by substituting in the result m and n and p and q.)

The discovery of the irrationality of the square root of two (alluded to by Plato in the Greater Hippias and in the Meno; cp. note 10 to chapter 8; see also Aristotle, Anal.
Priora, 413a6 f.) destroyed the Pythagorean programme of 'arithmetizing' geometry, and with it, it appears, the vitality of the Pythagorean Order itself. The tradition that this discovery was at first kept secret is, it seems, supported by the fact that Plato still calls the irrational at first 'arrhetos', i.e. the secret, the unmentionable mystery; cp. the Greater Hippias, 303b/c; Republic, 546c. (A later term is 'the non-commensurable'; cp. Theaetetus, 147c, and Laws, 820c. The term 'alogos' seems to occur first in Democritus, who wrote two books On Illogical Lines and Atoms (or and Full Bodies) which are lost; Plato knew the term, as proved by his somewhat disrespectful allusion to Democritus' title in the Republic, 534d, but never used it himself as a synonym for 'arrhetos'. The first extant and indubitable use in this sense is in Aristotle's Anal. Post., 76b9. See also T. Heath, op. cit., vol. I, pp. 84 f., 156 f. and my first Addendum on p. 319, below.)

It appears that the breakdown of the Pythagorean programme, i.e. of the arithmetical method of geometry, led to the development of the axiomatic method of Euclid, that is to say, of a new method which was on the one side designed to rescue, from the breakdown, what could be rescued (including the method of rational proof), and on the other side to accept the irreducibility of geometry to arithmetic. Assuming all this, it would seem highly probable that Plato's role in the transition from the older Pythagorean method to that of Euclid was an exceedingly important one-in fact, that Plato was one of the first to develop a specifically geometrical method aiming at rescuing what could be rescued from, and at cutting the losses of, the breakdown of Pythagoreanism. Much of this must be considered as a highly uncertain historical hypothesis, but some confirmation may be found in Aristotle, Anal. Post., 76b9 (mentioned above), especially if this passage is compared with the Laws, 818c, 895e (even and odd), and 819e/820a, 820c (incommensurable). The passage reads: 'Arithmetic assumes the meaning of "odd" and "even", geometry that of 'irrational"..' (Or 'incommensurable'; cp. Anal. Priora, 41a26 f., 503a7. See also Metaphysics, 983a20, 1061b1-3, where the problem of irrationality is treated as if it were the proprium of geometry, and 1089a, where, as in Anal. Post., 76b40, there is an allusion to the 'square foot' method of the Theaetetus, 147d.) Plato's great interest in the problem of irrationality is shown especially in two of the passages mentioned above, the Theaetetus, 147c-148a, and Laws, 819d-822d, where Plato declares that he is ashamed of the Greeks for not being alive to the great problem of
incommensurable Magnitudes.

Now I suggest that the 'Theory of the Primary Bodies' (in the Timaeus, 53c to 62c, and perhaps even down to 64a; see also Republic, 528b-d) was part of Plato's answer to the challenge. It preserves, on the one hand, the atomistic character of Pythagoreanism-the indivisible units ('monads') which also play a role in the school of the Atomists-and it introduces, on the other hand, the irrationalities (of the square roots of two and three) whose admission into the world had become unavoidable. It does so by taking two of the offending rectangular triangles-the one which is half of a
square and incorporates the square root of two, and the one which is half of an equilateral triangle and incorporates the square root of three-as the units of which everything else is composed. Indeed, the doctrine that these two irrational triangles are the limits (peras; cp. Meno, 75d-76a) or Forms of all elementary physical bodies may be said to be one of the central physical doctrines of the Timaeus.

All this would suggest that the warning against those untrained in geometry (an allusion to it may perhaps be found in the Timaeus, 54a) might have had the more pointed significance mentioned above, and that it may have been connected with the belief that geometry is something of higher importance than is arithmetic. (Cp. Timaeus, 31c.) And this, in turn, would explain why Plato's 'proportionate equality', said by him to be something more aristocratic than the democratic arithmetical or numerical equality, was later identified with the 'geometrical equality', mentioned by Plato in the Gorgias, 508a (cp. note 48 to this chapter), and why (for example by Plutarch, loc. cit.) arithmetic and geometry were associated with democracy and Spartan aristocracy respectively-in spite of the fact, then apparently forgotten, that
the Pythagoreans had been as aristocratically minded as Plato himself; that their programme had stressed arithmetic; and that 'geometrical', in their language, is the name of a certain kind of numerical (i.e. arithmetical) proportion.

It may be suggested that all this exegesis of Plato and cognate texts is a long way from the issues in epistemology that concern us at the present time. That may be true, and Popper's theory needs to be tested by more examples, by exploring whether contemporary debates in epistemology can be understood in isolation from problems in science or elsewhere. In defence of Popper's interest in the Platonic Theory of Forms, that is a central part of his exegesis of Plato's political thought in the first volume of The Open Society. It is my contention that the ideas in that book have huge contemporary relevance as we try to control the destructive force of defective ideas about the proper function of government.

APPENDIX: AN INTRODUCTION TO PHILOSOPHY

Philosophy could be introduced as a study of critical thinking and Bartley has proposed four types of criticism or tests that may be applied to arguments. These are the test of experience; the test of comparison with other theories; the check on the problem; and the test of logical consistency. None of these tests or checks are unproblematical and Bartley refers to them as 'non-justificationist criticism'.

The study of critical thinking that is proposed here could be taught at school, it could be used for an introduction to university courses in philosophy, it could be a core subject for all tertiary students. Its content could be adjusted for the interests and capacities of the class and it offers an alternative to the debacle of general studies where students of marketing and organic chemistry have to shuffle and fidget for a certain number of hours in lectures on Introductory Psychology or Medieval Drama. The course would consist of exploration and applications of the four methods of criticism to any theories or beliefs which interest the class.
The test of evidence and experience could lead to the philosophy of science, to a study of rules of evidence in law, to the use of diagnostic tests by doctors, motor mechanics or plumbers, and to the use of clues by detectives and archeologists.

The test of comparison with other theories would raise questions about the weight and authority to be assigned to assumptions imported into arguments, more or less uncritically, from other domains. For example the psychological theories assumed by literary critics, the physical theories assumed by geologists, the sociological theories assumed by engineers, the economic theories assumed by politicians. This part of the course should open student's eyes to the inter-dependence of the so-called disciplines and with any luck the artificial nature of boundaries between subjects would become apparent. At the same time students may learn how to use readily available resources, including other students and staff, to pursue problems from one discipline to another (for example by walking from the Philosophy Department to Physics or Life Sciences).

The check on the problem is in some ways the most fundamental criticism of all. This part of the course would indicate how a revised formulation of a problem may be decisive, how background theories can unconsciously direct how problems are identified and formulated, how fashions and fads (and funding) can dictate the directions of intellectual effort. It would lead to a study of the history of ideas, showing that problems have histories, that philosophical problems usually have their roots elsewhere, in science, or religion or in social and moral dilemmas, that powerful themes can leak from one discipline to another and preoccupations often run in parallel in more than one field.

The section on logic would call for study of both the formal and informal methods of argument. Formal logic concerns rules of inference and the way that logical steps can be used to draw out the consequences of an argument or of a scientific theory, perhaps for testing or for technological application. Informal logic encompasses the tricks of debate that may be used to cover up logical and factual defects in a position. Discourse by politicians, theologians, creation scientists and advertisers would furnish material for critical study.

All of this could lead to exploratory reading of the Great Philosophers, though preferably not until the students have a firm sense of their own interests and problems. In this mood they might be less deferential to the greats, more critical and at the same time more willing to learn. This would contrast with the traditional situation where the young student is confronted with soaring abstractions and profound arguments utterly unconnected with the historical background or the problem situations which agitated the titans of the past. The novice is completely overwhelmed (who am I to criticise the great?) or else clings to a critique provided by the teacher. The usual result is either a student who is indoctrinated into a system of thought, or else a person who is skilled in certain methods and techniques without any sense of purpose or perspective. No course can be rendered failsafe against authoritarian teachers, or against complete lack of interest on the part of students but the approach sketched above would provide interested people with a chance to avoid the more obvious dead ends of contemporary philosophy, and to apply imaginative criticism to their own professional and personal concerns.

Condensed Conjectures and Refutations: Introduction

The traditional systems of epistemology may be said to result from yes-answers and no-answers to questions about the sources of our knowledge. They never challenge these questions, or dispute their legitimacy; the questions are taken as perfectly natural, and nobody seems to see any harm in them. This is quite interesting, for these questions are clearly authoritarian in spirit.

Conjectures and Refutations is a collection of Popper’s papers that appeared in 1963, shortly after The Logic of Scientific Discovery (1959) and a long time after The Open Society and its Enemies (1945). OSE achieved the status of a banned book in some leftwing circles, and possibly in some conservative circles as well on account of the criticism of Plato.

The Introduction is a pivotal piece because it pinpointed the authoritarian structure of Western thought. It exerted a great deal of influence on William W Bartley who became one of Popper's best expositors, partly on account of the message that he picked up from this paper. He actually heard it live when it was delivered as the Annual Philosophical Lecture read before the British Academy in 1960.

The paper 'On the sources of knowledge and of ignorance' provides some important insights into the structure of thinking that is embedded in traditional philosophy, especially the authoritarian element that has really important consequences in politics.

The paper contains seventeen sections after a short introduction.

Empiricism and Rationalism

The problem which I wish to examine afresh in this lecture...may perhaps be described as an aspect of the old quarrel between the British and the Continental schools of philosophy - the quarrel between the classical empiricism of Bacon, Locke, Berkeley, Hume and Mill, and the classical rationalism or intellectualism of Descartes, Spinoza and Leibniz. In this quarrel the British school insisted that the ultimate source of all knowledge was observation, while the Continental school insisted that it was the intellectual intuition of clear and distinct ideas.

Most of these issues are still very much alive. Not only has empiricism, still the ruling doctrine in England, conquered the United States, but it is now widely accepted, on the European Continent, as the true theory of scientific knowledge. Cartesian intellectualism, alas, has been only too often distorted into one or other of the various forms of modern irrationalism. In this lecture I shall try to show of the two schools of empiricism and rationalism that their differences are much smaller than their similarities, and that both are mistaken. I hold that they are mistaken although I am myself an empiricist and a rationalist of sorts. But I believe that, though observation and reason each have an important role to play, these roles hardly resemble those which their classical defenders attributed to them. More especially, I shall try to show that neither observation nor reason can be described as a source of knowledge, in the sense that they have been claimed to be sources of knowledge, down to the present day.

III

In this section Popper noted the important and helpful function of the doctrine that "truth is manifest", while he also warned of the downside of such an optimistic but false idea.
The great movement of liberation that started in the Renaissance and led through the many vicissitudes of the reformation and the religious and revolutionary wars to the free societies in which the English-speaking people are privileged to live, this movement was inspired throughout by an unparalleled epistemologial optimism: by a most optimistic view of man's power to discern truth and to acquire knowledge.

At the heart of this new optimistic view of the possibility of knowledge lies the doctrine that truth is manifest.Chief among the standard bearers of this idea were Bacon and Descartes, and it inspired the birth of modern science and technology which has done so much to emancipate people from ignorance, from political despotisms and also from want and poverty.

IV

In this short section Popper noted that even an abstract study like epistemology can be motivated, even unconsciously, by political hopes and dreams. He suggested that this should be a warning to us. But what can we do about it?

He confessed to being a liberal, in the English, non-collectivist sense. And he wrote "I feel that few things are more important for a liberal than to submit the various theories of liberalism to a searching critical examination". He found that many of the ideas and doctrines which had inspired political liberals are not tenable, including the doctrine of the manifest truth and the inevitability of progress.

V and VI

In the course of Popper's examination of the ideas that underpinned liberalism, alongside the "manifest truth" theory he encountered what he called "the conspiracy theory of ignorance". The two are connected because if the truth is manifest to honest and clear-eyed seekers, then if they fall into error, or promulgate it, then either their motivation is suspect or they have been taken in and deluded or led astray by some other evil person or group.

This false epistemology was the major inspiration of an intellectual and moral revolution without parallel in history. It encouraged men to think for themselves. It gave them hope that through knowledge they might free themselves and others from servitude and misery. It made modern science possible. It became the basis of the fight against censorship and the suppression of free thought... It made men feel responsible for themselves and for others, and eager to improve not only their own condition but also that of their fellow men.

It is a case of a bad idea inspiring many good ones. This false epistemology, however, has also led to disastrous consequences. The theory that truth is manifest - that it is there for everyone to see, if only he wants to see it - this theory is the basis of almost every kind of fanaticism. For only the most depraved wickedness can refuse to see the manifest truth; only those who have reason to fear truth conspire to suppress it.

VI to XII

In these sections Popper examined the historical roots of optimistic and pessimistic epistemologies, from Plato to Bacon and Descartes, with some space devoted to the quest for the truth of statements in their origin and also the pursuit of the true meaning of terms (essentialism). I will not dwell on the material in these sections but will return to the main topic of the paper.

XIII

"I will now leave all these largely historical reflections aside, and turn to the problems themselves, and to their solution".

The whole of this section is on line http://www.geocities.com/criticalrationalist/popperempiricalbase.htm.

This section of the lecture is an attack on empiricism, that is, the doctrine that knowledge has to rest on the firm foundations of observation, that is, facts that have been presented to the senses or have lodged in the memory after entering by way of the senses.

According to this doctrine, "if we make an assertion, we must justify it," but this means that we must be able to answer the following questions: 'How do you know? What are the sources of your assertion?'

The counter-argument is that we usually do not make assertions based on immediate obervations of the events in question, the more usual sources are things like newspaper or Encyclopedia Britannica, a lecture, a textbook or a journal article.

The empiricist replies that nevertheless the basis of the reports in the secondary sources are observations, otherwise the reports might be classified as poetry, fiction or even lies.

The gist of Popper's argument at this point is that the usual method of checking reports is not to investigate into the source which could result in an infinite regress to check each stage of the transmission of the information, but rather to seek corroborating information from another source or in science to repeat a critical experiment to ensure that the same result can be obtained in different laboratories.

The most striking thing about the observationalist program of asking for sources - apart from its tediousness - is its stark violation of commonsense. For if we are in doubt about an observation, then the normal procedure is to test it, rather than to ask for its sources; and if we find independent corroboration, then we shall often accept the assertion without bothering at all about the source.

However that is not always the case and there are occasions when it is important to ascertain the source, where some sources are known to be better than others (though none can be regarded as infallible). Another situation where sources do have to be checked is historical research.

"Testing an historical assertion always means going back to sources; but not, as a rule, to the reports of eyewitnesses".

XIV

In this short section Popper sums up his view that there are many sources of knowledge but none have authority.

XV

The authoritarian structure of traditional philosophy

The traditional systems of epistemology may be said to result from yes-answers and no-answers to questions about the sources of our knowledge. They never challenge these questions, or dispute their legitimacy; the questions are taken as perfectly natural, and nobody seems to see any harm in them. This is quite interesting, for these questions are clearly authoritarian in spirit. They can be compared with the traditional questions of political theory, 'Who should rule?' which begs for an authoritarian answer such as 'the best', or 'the wisest' or 'the people', or 'the majority'. (It suggests, incidentally, such silly alternatives as 'Who should be our rulers: the capitalists or the workers?', analogous to 'What is the ultimate source of knowledge, the intellect or the senses?').

This political question is wrongly put and the answers which is illicits are paradoxical (Chapter 7 of OSE). It should be replaced by a completely different question such as 'How can we organise our political institutions so that bad or incompetent rulers cannot do too much damage?' The question about the sources of our knowledge can be replaced in a similar way.

The alternative that Popper suggested is the question of detecting and eliminating error, by means of critical appraisal by all the methods of criticism that we can muster - logical analysis, experimental testing, consistency with other theories etc.

XVI

This section is on line. Popper spells ten theses to summarise the results of the discussion in the lecture.

1. There are no ultimate sources of knowledge. Every source, every suggestion, is welcome; and every source, every suggestion, is open to critical examination. Except in history, we usually examine the facts themselves rather than the sources of our information.

10. Every solution to a problem raises new unsolved problems; the more so the deeper the original problem and the bolder its solution.

XVII

The final section makes a case to give up the quest for the conclusive justification of our knowledge, but not to abandon the idea of truth as the goal of investigation. Some who accept that knowledge is essentially fallible abandon the quest for truth or opt for arbitrary authorities. Popper followed Russell in the belief that no person can establish the truth by decree, instead we should accept that truth is above human authority.

Bill Bartley on the structure of Popper's epistemology

The importance of Bartley's take on Popper was exemplified by my own experience in a series of lectures to an elderly group of people who convened to discuss the Philosophy of Humanism. They met for an afternoon every two weeks over a period of ten years and they covered a huge amount of ground although they never produced anything that aroused much interest from the committee of the local Humanist Society or the membership at large. I led the discussion fairly regularly for about a year, late in the 10-year period and a very interesting pattern emerged.
After about four sessions the group seemed to be getting the idea of Popper's theory of conjectural knowledge, then they decided to invite some other discussion leader (a professional philosopher) just for variety. When I returned I had to start all over again to get across the idea of conjectural knowledge and the criticism of induction. Then the same process occurred, they made good progress with Popper's views on knowledge and some other issues like essentialism, then they had a session or two with other discussion leaders and when I came back, the process had to start from the beginning again.

This was reminiscent of the mythical figure of Sisyphus who pushed a stone up hill all day and it rolled back down to the bottom during the night. Then I decided to move backwards or sideways and so I fed them some papers by Bill Bartley. Most of the group members were keen enough to undertake quite serious reading, even though they often struggled with the interpretation. They certainly struggled with Bartley but two of them stuck to the task and as a result they never rolled back down the hill again. Some of the Bartley articles are now on line.

The point of that story is that Bartley explained something about the structure of Popper's ideas that is rendered invisible by the more common approaches to the theory of knowledge and belief, especially the aim of justification or confirmation of beliefs. When the difference in structure is grasped, it is much harder (though by no means impossible) for people to lose the plot and revert back to the conventional ways. For academic philosophers of course the situation is complicated by the need to maintain credibility in the profession in order to achieve tenure and promotion.