Karl Popper and Religious Knowledge

Applying Critical Rationalism to Theology

Academic Paper, 2017

73 Pages




Chapter 1. Signs and speculations

Listeners interpret prophetic teachings, consciously or unconsciously, in terms of their metaphysical assumptions. For western Gentile converts to Christianity, this meant in terms of Platonic and Aristotelean philosophies. The advent of the empiricism with the Enlightenment led to less emphasis placed on intuitive thought and more on sensory experience, not unlike the older Hebrew approach. While empiricism was not wholly consistent in its rejection of inferred entities, it became the dominant methodology of science. Mental experience, being beyond the reach of sensory observation, was rejected in favour of observable behaviour and was assumed to be completely explained by bodily processes. The success of empiricism led it to become, in the form of reductive materialism, the received metaphysic, first among scientists and later among people in general. No place was left for transcendental experience

Chapter 2. Life in Vienna

Karl Popper’s early life was spent in the remarkably fertile culture of early twentieth-century Vienna, a major component of which was the logical positivism of the Vienna Circle. Positivists reject unverifiable metaphysical statements as meaningless, but universal scientific statements of the kind regarded by the positivists as meaningful are also unverifiable. They are, however, falsifiable, and it is this that makes them scientific. Scientific statements are those which have not yet been falsified, but in the absence of verification they always remain conjectural. Metaphysical statements which are, in any case, unavoidable are both unverifiable and unfalsifiable, but this does not make them meaningless

Chapter 3. Searching for knowledge

A great deal of our knowledge is said to come from passive observation, based upon the assumption that the future will be like the past. This theory and the conclusions drawn by this method are unacceptable, even when the conclusions are qualified in probabilistic terms. Sensory observation depends on the prior existence of a conjecture, and is active in nature. We acquire knowledge by making conjectures, testing them by observation, and rejecting those which are false. In this way, we move towards truth without actually reaching it or, at least, knowing for certain that we have done so

Chapter 4. The heart of the matter

Knowledge is acquired by the three-fold process of conjecture-formation, observational-testing, leading to either refutation or provisional acceptance of the conjecture. As knowledge grows conjectures of increasing complexity are sought and tested. Critical testing is the necessary component. It cannot be replaced by appeals to authority of any kind. Equally, it cannot be terminated by appeal to essences of the kind basic to Platonic and Aristotelean epistemologies. Along with essentialism, we must reject definitions as a source of knowledge. Definitions are no more than labels for what is already known

Chapter 5. To be or not to be

Universal statements explain, or account for, existential statements of a given kind. While scientific universal statements can only be falsified, not verified, unbounded existential statements can only be verified not falsified. Historical statements are existential in character and may be true, but if they are true then, because they are not universal, they cannot be used to predict future events. Historicism is untenable

Chapter 6. Clockwork dream or cloudy reality

Certain long-standing metaphysical questions are existential in nature but are neither verifiable nor falsifiable. Nevertheless, there may be good reasons why one position or another should be taken with respect to them. On such grounds, determinism can be rejected as leading to impossible situations and idealism rejected as being contrary to common-sense. Indeterminism, by contrast, allows for free-will and for the validity of moral precepts which, however, cannot be characterised other than figuratively as true or false. Metaphysical statements are needed because no system can be completely validated from within itself

Chapter 7. Discovering a New World

Scientific knowledge exists as an entity in its own right, irrespective of its bodily manifestation as scientific literature or its mental manifestation as a thought in the knower’s mind. This is equally true of other kinds of knowledge and of similar products of human mental activity, like works of art and social entities. Having been produced, they assume an autonomy which allows them to act in a reciprocal manner, thus influencing human thought

Chapter 8. Three worlds or two worlds or, one world

Materialism – the claim that only bodily entities really exist – cannot account for mental and transcendental entities and nor for the effects that they have on bodily entities. Despite this reductive materialism has assumed a dominant influence in Western society. Full understanding, on the other hand, calls for a pluralistic metaphysics which accounts for the reality of bodily, mental, and the products of mental activity entities and the interactions between them

Chapter 9. Getting it together

In summary, Popper’s metaphysics postulates a three-world system of bodily, mental and transcendental entities which are real and interactive. Popper’s epistemology is based upon a distinction between existential (including metaphysical) statements and universal statements and an active theory of knowledge acquisition which involves conjecture-formation, prediction-testing, error-elimination, and conjecture-revision all aimed at solving problems. Conjectures are not evaluated according to their sources but by their success in avoiding falsification. The process of evaluation has no final conclusion, and provided it can be subjected to critical appraisal, no existential or universal statement is deemed invalid on principle. The process does not seek to find essences

Chapter 10. Searching for certainty

Just as certainty in scientific knowledge is unattainable, so also is certainty in religious knowledge. This is recognised in the distinction between knowing and believing where belief implies some degree of uncertainty. Belief is an expression of confidence in the face of uncertainty. In this respect, nothing is gained by virtue of careful definition. Attempts to define theological doctrines more carefully lead only to irresolvable enigmas like the problem of evil. They should be abandoned along with historicist attempts to predict the future. In all of these respects Popper’s epistemology echoes what can already be found in theological discourse

Chapter 11. Stairway to heaven

In dualistic (that is, body-mind) systems attempts to accommodate transcendental ideas lead to supernaturalism which postulates a state of disembodied minds. Supernaturalism falls an easy prey to reductive materialism. Pluralistic (that is three-world) systems provide a way out from this dilemma. Spiritual entities exist in their own right by virtue of having been thought of, which means that we can examine the God-conjecture without first having to prove that that conjecture exists. Whether or not the God-conjecture survives examination, it is justified in the first place by the human search for meaning in the Universe and by human experiences of transcendence

Chapter 12. Talking about God

An evaluation of the God-conjecture relies initially upon the evidence presented by those prophets who claim to have access to knowledge of that kind. This demands an act of faith on the part of the evaluator, but that is no more than is most often found is evaluating conjectures of other kinds. Much of the evidence takes the form of tautologies which, however, may be useful in the way that mathematical theorems – also tautologies – are useful. Beyond that, universal statements may be derived from prophetic knowledge as recorded in Scriptures and tested accordingly. In all of this, account must be taken of individual differences between persons in how they respond to spiritual experiences

Chapter 13. Describing how and explaining why

Scriptures contain statements of all kinds and their validity must be evaluated accordingly. Existential, including historical, statements may be checked against alternative sources but they remain unfalsifiable. Many statements are tautologies but may be valuable nevertheless. Falsifiable universal statements relating to natural events may be tested by scientific experiment and rejected if falsified, although even if falsified they may serve to edify. Falsifiable universal statements relating to mental experiences may be tested in a similar manner but with more difficulty. Metaphysical statements cannot be finally resolved but may be accepted or rejected on rational grounds

Chapter 14. Defending the Faith

Many theological doctrines are universal statements intended, as scientific universal statements are intended, to explain or account for singular existential statements of a given kind. If a theological doctrine, or conjecture, of this kind is found, on testing, to imply outcomes which are, for other reasons, unacceptable then the conjecture must be amended or rejected. Rejecting the conjecture does not imply that the original existential statements are false. Nor does it invalidate spiritual entities formed as a result of human experience of the original existential events

Chapter 15. Summing up

Theology is open to the application of Popper’s epistemology and metaphysics. Popper’s active theory of knowledge acquisition in particular is a valid and helpful aid in arriving at religious knowledge. It requires a constant re-evaluation of explanatory statements in the light of both the original existential events and contemporary events of a similar kind. Unlike the positivistic approach of popular contemporary reductive materialism, Popper’s methodology is tolerant and open to knowledge of all kinds. Nothing is rejected in principle provided it can be subjected to rational criticism




During the 1950s and 1960s I was a member of the staff of a Medical Research Council unit based in the Department of Psychology at University College London. At that time a colleague introduced me to the writings of Karl Popper. My colleague, Peter Wason, was carrying out experiments on how human subjects tested the truth of a proposition, evaluating their behaviour against Popper's assertion that propositions could only be logically and conclusively falsified, not verified. Wason found that most of his subjects showed what he labelled confirmation bias, seeking evidence aimed only at verifying a proposition. The same bias is seen in academic journals whose editors seem to prefer positive results to negative ones.

Some years later, when I was a member of the staff of the National Research Council in Ottawa, I read Popper’s The Logic of Scientific Discovery. I was impressed by Popper's views on demarcation. Scientific propositions, he asserted, are propositions that may conceivably be falsified. Propositions that cannot be falsified are not scientific even though they may, in fact, be true. Metaphysical propositions can be neither verified nor falsified but they are not for that reason meaningless. Popper’s epistemology left religious and theological propositions open for serious, rational consideration, unlike the epistemology of his positivistic contemporaries or the narrow, dogmatic epistemology adopted by many popular anti-religious writers.

Having moved to Vancouver, I read Popper’s writings more extensively. It left me regretting that I had not taken his views more seriously while I was making my modest contributions in the field of experimental psychology. I believe that they would have been marginally more useful if I had. All the same, I was still able to pursue the idea of applying Popper's ideas to the evaluation of religious statements. The result of that pursuit is this monograph.

The monograph falls into three parts. In Chapter 1, I attempt to state the problem. The problem as I see it is that the Enlightenment has led people in Western society to adopt reductive materialism as a prevailing philosophy. Natural scientists were the first to do this, and they were followed by others as a consequence of the success of their scientific endeavours. In these circumstances, religious statements could no longer be expressed adequately by reference to Platonic and Aristotelean philosophy. My thesis is that the epistemology and metaphysics of Karl Popper meet the need for a new approach.

In Chapters 2 - 9, I present a synopsis of the epistemology and metaphysics of Popper in so far as they are relevant – or so it seems to me – to the stated need. I do not argue for the truth of Popper’s thought but take that for granted. My synopsis takes Popper’s ideas beyond the place that he intended. His interest was in scientific, not religious or theological, knowledge but I like to think that he would not have been averse to my project.

In Chapters 10 - 14, I endeavour to apply the epistemological and metaphysical principles thus adduced to theological statements. This inevitably leads me into fields for which I have no academic qualification. My theological knowledge has been gained by listening to countless sermons and by reading books of popular theology. If, then, in discussing these issues I have reached unacceptable theological conclusions, I apologise. However, it need not detract from my main purpose which is to show how Popper’s thought may be applied to the issues in question. My position should stand or fall, I believe, on how adequately I have understood Popper, and how adequately I have applied his ideas, and not on the validity of my theological opinions.

I believe that my thesis applies to theology in general and not to the theology of one Faith alone, but my own religious practice relates to the Christian Faith. That unavoidably colours my discourse.

My principal sources are listed in the Bibliography. Specific references are indicated in the endnotes. Citations of the works of Popper are not exhaustive. Many of his publications are compilations of lectures in which he repeated previously published ideas, discussions and conclusions. Any particular citation, therefore, can be most often be replaced by another citation of equivalent significance.

Vancouver, Canada, 2017.

Chapter 1: Signs and speculations

Prophets are not usually interested in providing a logical foundation for the truth of their teachings. They simply tell it the way they think it is. Equally, they accept and conform to the metaphysical assumptions and the common knowledge of their culture. The Scriptural texts suggest that Jesus regarded the Universe as being of three parts – Heaven, Earth and Hell – and we may suppose that he believed the Earth to be flat. It would be stretching belief to the utmost to imagine that Jesus had any particular epistemological or metaphysical system consciously in mind when he taught, healed, and accepted death, any more than did the Galilean men and women – peasants, fisher folk and tax collectors - who heard and followed him and continued after the experience of the Resurrection to propagate his teachings.

The prophet’s listeners, on the other hand, may find themselves reflecting on whether that which they are being asked to believe is consistent with what they already know and, more generally, whether it fits their metaphysical assumptions – assumptions of which, of course, they are probably quite unaware. “Does it all hang together?”, they may ask themselves. In this respect, St Paul observed that whereas “Jews demand signs … Greeks desire wisdom”,[1] suggesting that as soon as the first Gentiles were converted to the new Faith, they were asking questions of this kind. They asked themselves whether it was true and how it related to what they already knew. For this, they needed both an epistemology - a means of addressing the question - and a metaphysics - a framework within which to set the answers, and into the gap the Greeks brought Plato, to be supplanted in due time in the Western Church by Aristotle.

The Gospel of St John, in its very first sentence, uses a term, ‘Word’, which was well-established in Greek thought but absent from Hebrew thought, indicating that at least by the beginning of the second century new converts were resorting to Greek philosophy to help understand the Faith. In fact, Clement of Alexandria stated it quite explicitly: “For philosophy was a schoolmaster to bring the Greek mind to Christ, as the Law brought the Hebrews.”[2] With this background, the early Gentile theologians set about making valiant attempts to bring Hebrew ideas of a God with personality and attitude into line with the more austere Unmoved Mover of Greek philosophy.

In some respects, we might regard Gnosticism as the epitome of this approach. Salvation came, the Gnostics (or some of them) said through having the correct knowledge, knowledge that had been given by Jesus directly to the Apostles. Those who knew would be saved. Even though that view was rejected by the institutional church (especially to the extent that it required possessing secret knowledge), the history of the Trinitarian and Christological disputes shows that getting it right was still considered critical. As the Athanasian Creed puts it: “Whosoever will be saved: before all things it is necessary that he hold [that is, know] the Catholick Faith.”[3] How, then, were they to be sure that they had the right knowledge?

For Plato, knowledge was acquired by careful thought. “[K]nowledge is not to be derived from the senses, but is only to be achieved by the intellect.”[4] Intellectual knowledge is concerned, for example, with beauty as such, not with any particular thing of beauty since that thing is necessary contaminated in some degree, however slight, by ugliness. To contemplated a particular thing of beauty is, therefore, mere opinion, not knowledge. Truth is found by employing verbal argument and intuitive reasoning. Aristotle, compared to Plato, took more note of observable phenomena, but he, too, relied on his intellect to reach his conclusions, leading his successors, even if not Aristotle himself, to highly imaginative outcomes.

We can label this as the top-down, or analytic, approach. We rely on careful reasoning to produce a rational conceptual system which then allows us to understand and account for that which is immediately to hand. This was the approach which informed the human search for knowledge for centuries, with what at times were stultifying consequences. For example, Plato was intellectually persuaded by careful reasoning that heavenly bodies, being of divine creation, necessarily moved in perfect circles at uniform speed. This was all very well as far as the multitude of fixed stars (fixed, that is, in relation to each other) was concerned but for the seven wandering stars – Sun, Moon and the five planets – appearances did not coincide with dictum. The task of making them do so saw its culmination in the Ptolemaic system of epicycles – circles within circles – which showed how doctrine could trump appearance. Thus it remained until the sixteenth century when Johannes Kepler succeeded in disregarding the dogma, at least to the extent of substituting elliptical motion for circular motion, and the stranglehold on cosmology was broken.

With the advent of the Enlightenment the top-down approach was challenged by the bottom-up, or synthetic, approach of the empiricists. Philosophers now looked not to intuition as the means to increase knowledge, but to empirical sense experience. As John Locke wrote: “Whence has [the mind] all the materials of reason and knowledge? To this I answer in one word, from experience.”[5] Here, then, were Gentiles who, like the Jews, demanded a sign, a sign from Nature if not from God, but certainly not intuitive speculation. They wanted signs that everyone could agree were there to see, hear, touch, taste or smell. From those signs, they set about building an explanatory structure from the bottom up to replace the one imposed from the top down.

Of course, the scientific revolution, based upon sensory experience rather than intuitive speculation, inevitably came with difficulties of its own. It was one thing to find agreement about physical, or bodily, signs derived from the senses but when it came to mental signs derived from experiences of knowing, feeling and striving, a problem arose. Such signs were intensely personal – subjective, in fact. It was difficult enough to describe them verbally and quite impossible to share them experientially. When it came to transcendental experiences (assuming that such were distinct from mental experiences) the problem was compounded. Scientific endeavour was focussed on bodily sensory data that could be mutually experienced. It depended upon a group of observers agreeing consensually that certain events had been mutually observed and had, therefore, occurred. In these circumstances, it was hardly surprising that in due time psychology, as an enterprise in scientific research, ceased to be concerned with mental experiences. Instead, with the advent of behaviourism, it addressed only behavioural events, both bodily and verbal. Unlike mental experiences, behaviour, being part of as the physical world, can be seen and heard just as the other parts of the physical world can be seen and heard. Scientific endeavour had even more difficulty in addressing religious and spiritual experiences, how ever they may have been defined, and pretty well gave up the attempt to do so.

As the outcome of this situation, scientific methodology became centred upon a positivist, reductionist, materialist metaphysics that rejected mental (and, even more so, transcendental) experiences. Such experiences, the reductionists now came to claim, are at best mere epiphenomena, and at worst delusional. Explanations about events in the natural world (the world that science recognises) are to be expressed in terms of the interactions between bodily entities, with no room for intangible, or occult, entities and forces like human intention and divine intervention.

Here again, though, a problem arises. The occult cannot be dismissed quite as completely as might have been hoped. To account for the interactions between bodily entities it is necessary to postulate the existence of unseen forces like those of gravity and magnetism. These forces can be precisely defined and measured, and their effects can be observed. An apple can be seen to fall from a tree and its weight in the hand can be felt, and a pivoted iron-needle can be seen to rotate towards north, but in both cases only the sensory outcomes – visual and tactile – can be perceived. In neither case, can the force itself – gravity or magnetism – be perceived but only inferred. Isaac Newton expressed his misgivings about gravity this way:

That gravity should be innate, inherent, and essential to matter, so that one body may act upon another at a distance through which their action and force may be conveyed from one to another, is to me so great an absurdity that I believe no man who has in philosophical matters a competent faculty of thinking can ever fall into it.[6]

In this respect, gravity and magnetism resemble the modern-day phenomenon of telekinesis, whereby a mental force is said to displace a bodily entity at a distance. We may claim that telekinesis is ephemeral in the sense that it is less readily controlled and demonstrated, but neither telekinesis nor gravity and magnetism can be seen, heard, touched, tasted or smelled. We can observe only their effects. The dilemma over gravity was, in due course, resolved by Albert Einstein, but, for two or three centuries meanwhile, few scientists doubted the reality of gravity.

As a methodology, reductive materialism has had remarkable success in generating scientific knowledge. Following the pragmatic maxim that what works must be true, many scientists have concluded, without much logical support, that the underlying metaphysics is not only a useful assumption but also the true state of affairs. The point has been made clearly and quite explicitly by Michael Shermer:

Materialism became the predominant worldview of science by the end of the 19th century because it works – it enables scientists to search for and find mechanistic explanations for a wide spread of phenomena, from atoms and molecules to ecologies and economies. This is not an act of faith … but of confidence built over centuries of data-gathering, hypothesis-testing, and theory-building, all contested through the competitive enterprise of science in which skeptics have … tried to find out what might be wrong with their own and especially others ideas.[7]

Nor are scientists the only persons to think in this way. Willard Quine the philosopher has said:

I hold that physical objects are real and exist externally and independently of us. … But I don’t recognize the existence of minds, of mental entities in any sense other than as attributes or activities on the part of physical objects, mainly persons. … It is a basic principle of physical science that there is no change without a change in the distribution of microphysical properties over space. Rejection of this principle I would find uncongenial, because the successes in natural science have been such that we must take its presuppositions very seriously.[8]

With the new epistemology, common knowledge expanded far beyond that which the early Christians had known. The collateral development of technologies, in the form of agronomy, medicine and engineering, has produced remarkable consequences for human longevity, wellbeing and way of living. As a consequence, the materialist understanding of the Universe has been passed on from the scientific world and has become the dominant metaphysics in Western culture. Because of this, materialism has entered extensively into popular discourse, even among those who in other contexts count themselves as believers in religious creeds and, supposedly, in a world beyond the natural world. A cursory examination of popular media, for example, shows how ‘brain’ is used as a synonym for ’mind’. Brains, not persons, are said to see, hear, think, solve problems and even sleep. The tacit acceptance, in this way, of a materialist approach is an impediment to making the case for meaningful transcendental, or even mental, experiences.

While the stranglehold of intuitive metaphysics on scientific endeavour was broken at the Enlightenment, we cannot say the same of theological endeavour. Christian theological speculation, it seems, has kept to the top-down approach even though popular metaphysics, following scientific fashion, is represented more closely by the bottom-up approach. This leaves us effectively with two parties who are unable to talk to each other. To overcome the impasse, Christian apologists have the choice of either persuading their target audience to return to Plato and Aristotle, or themselves adopting the empirical approach. There is no fundamental reason for choosing the first course; Platonic and Aristotelean epistemologies are not sacrosanct. The Hebrews, like the empiricists, demanded signs and from them formed their ideas of God without the assistance of prior dictums. Modern Judaism has maintained the same approach, as has Islam. The Christian Faith grew from empirical Hebrew thought and at the very least we should consider re-establishing theological empiricism. In doing this, we may ask whether the epistemology and metaphysics of Karl Popper will aid our endeavour.

In all of this, we must maintain the distinction between, on the one hand, a prophet’s teaching and, on the other, the question of how we know what the prophet teaches and what we believe is true. A person can believe in, and follow, the teachings of Jesus or another prophet without necessarily addressing or even being interested in either the question at hand or its answer, just as one can appreciate and enjoy music without being a musicologist. To believe in someone or something implies a commitment to the person or confidence in the teaching, the kind of confidence that Shermer has expressed in reductive materialism. This is the implication of St Paul’s further statement “[W]e proclaim Christ crucified.”[9]

Belief in the teaching depends upon confidence in an existential event. Belief of that kind – what we may call belief in as against belief that – stands over and against belief arising from signs or speculations. From this perspective, to the question “Why do we believe in the teaching?” the answer “Because the prophet says so” is perfectly adequate (as are the answers “Because the Bible tells me so” and “Because the Church tells me so”). On the other hand, to believe that something is the case requires a justification of a different kind. At that point, persons other than the believer become parties to the issue and to its outcomes. For this situation, personal commitment and reflection is not sufficient; a conversation is needed, one that involves signs and speculations. For this we need a mutually-accepted epistemology and metaphysics. The thesis of this monograph is that Popper’s epistemology and metaphysics provide what is necessary.

Chapter 2: Life in Vienna

Karl Popper was born in Vienna in 1902 and died in London in 1994. Vienna at the beginning of the twentieth century was the capital of Austria-Hungary, a multilingual, multi-faith state at a time when nationalist sentiments were dominant and, unlike today, multiculturalism was not in fashion. The people were of six languages, if not more, and of four religions, if not more, but their heterogeneity was about to be lost by the homogenising post-war settlements of the First World War. In the pre-war diverse city of Vienna, however, persons of all kinds contributed to its life, including Jewish families like the Poppers. The family had converted to Lutheranism. To us this may be seen negatively as a betrayal of heritage but in the light of the then-current circumstances it is better seen positively as a wish to participate and to assimilate, at least in part, to the prevailing Catholic culture. Other families of Jewish origin did much the same, the family of Ludwig Wittgenstein, for example, converting to Catholicism.

In the first three or four decades of the twentieth century Vienna passed, despite the intervention of the First World War, through a remarkable period of artistic, scientific, philosophical and political activity led by persons such as Gustav Mahler, Oscar Kokoschka and Sigmund Freud, and, more disturbingly, Adolf Hitler. In 1919 Popper worked in the child-guidance clinic of another such luminary, Freud’s one-time collaborator, Alfred Adler. On one occasion Popper presented Adler with a case which, to Popper, did not seem particularly Adlerian in flavour, but which Alder had no difficulty resolving in terms of his theory of inferiority feelings. Alder attributed his success in this regard to his “thousandfold experience”.[10] Popper was not impressed. If all behavioural problems could be explained by a unitary theory, the theory, it seemed to Popper, was not really very useful. A useful theory is one which distinguishes between positive and negative cases, predicting when an outcome could be expected and when not. To many the universality of the theory was its strength, but to Popper it was its weakness. It is rather like attributing all events to the intervention of God. In both cases, the attribution may be true, and in certain circumstances emotionally comforting, but in intellectual terms it is trivial.

At this time Popper, like many others, became familiar with the theories of Karl Marx. Marxists claimed that scientific research had revealed the course of history, and that history determined that contemporary western economic systems were certain to develop from capitalism into communism. The task of Marxists was to facilitate this development, if necessary by inciting enough violence to foment strife, thus accelerating the inevitable historical outcome. Popper sympathized with the humanitarian and egalitarian objectives of the Marxists, but he was shocked by the experience of street fighting and he rejected the justification of violence on the basis of theories about historical progress that were of questionable validity.[11] It was one thing to detect a trend in the history of economic systems, but another to infer that the trend would continue unchanged into the future and then to use this inference to justify violence. Popper observed the lethal clashes between police and socialist demonstrators and rejected both their violence and their justification. Adler’s theory was at least benign, and according to many actually beneficial, whereas Marx’s theory was merely destructive. In all events, Popper believed that neither could claim scientific validity.

In contrast to Adler and Marx, Popper was struck by the work of Einstein whose theory of general relativity had appeared in 1916. Until then, Newton’s law of universal gravitation had proved immensely successful in understanding physics and astronomy, despite Newton’s unease about what gravity really was. Einstein’s new theory dealt with that unease. More to the point, it disagreed with Newton’s theory by claiming, among other things, that light rays bend towards any massive body placed near their trajectory. This disagreement provided an empirical means of choosing between the two theories.

As a distant star moves across the sky we can record its transit time between two chosen points. If a massive body like the Sun is placed in that transit arc the transit time remains the same; the star takes the same time to complete its trajectory, part of which now lies in the shadow of the Sun. However, if the light rays coming from the star are deflected from a straight course when passing close to the Sun, then the star will still be visible to an observer on Earth even when, on a straight-line course, it lies behind the Sun. The star will also come into view earlier as it moves towards the edge of the shadow of the Sun. Put another way, the time during which the star is out of sight behind the Sun will be shorter than the time otherwise taken to move across that portion of the trajectory. If the rays are not bent it will be the same. Under normal circumstances the time spent by the star behind the Sun cannot be observed because the Sun is too bright, but the Sun’s brightness is diminished during an eclipse. In the solar eclipse of 1919 Arthur Eddington was able to measure the relevant times, and his observation confirmed Einstein’s prediction.

For Popper, this showed a genuinely scientific approach: Einstein had proposed a theory and he used it to predict an event that could conceivably be fulfilled or not fulfilled. The prediction could be either confirmed or disconfirmed. If not confirmed the theory would be falsified. It is the possibility of falsification, Popper asserted, that allows us to label Einstein’s theory (like Newton’s theory) as scientific.[12] By contrast, neither Adler nor Freud proposed behaviour that, if observed, would falsify his theory. Whatever happened, the theory stood; it could account for all behaviour. While neither theory was necessarily wrong, each was, on Popper’s criterion, unscientific.

As for Marx’s theory, it was scientific in so far as Marx used it to make a prediction that could conceivably have been falsified. He predicted that communism would be first established in a country of relatively advanced economic status. In fact, communism was established (or, at least, a successful communist-led revolution occurred) first in a country of relatively poor economic status. This event, Popper asserted, falsified the theory. Upholding the theory, as it stood, despite this refutation made Marxism no longer scientific.[13] From this starting point, Popper developed an epistemological theory about how scientific knowledge grew which differed from the positivist theory held by many of his contemporaries.

The aim of scientists is to produce universal statements (or hypotheses or theories or laws or assertions or claims - the choice of term is not important) which provide knowledge about the nature of ourselves and the world in which we live. Popper did not attempt to define science. He believed that definitions of themselves contributed nothing to knowledge. Rather, he demarcated two kinds of universal statement, those which, conceivably, could be falsified and those which could not be falsified. To the former he assigned the label scientific.

Universal statements are designed to account for, or explain, singular existential statements of a given kind. A simple universal statement is All swans are white. From this we can account for the observation that for all singular existential statements of the kind We observe a swan we may also state The swan is white. However, Popper asserted that “. . . the verification of a natural law could only be carried out by empirically ascertaining every single event to which the law might apply, and by finding that every such event actually conforms to the law – clearly an impossible task.”[14] We can never observe all swans at all times and in all places or, for that matter, know that we have done so even if that were the case. No matter how many white swans we observe, it is always possible that at a future date or another place a non-white swan may be observed, and if that were to happen the universal statement would be falsified. Universal statements cannot be verified, but some can conceivably be falsified and it is those that we can label as scientific.

Scientific experiments are (or should be) designed to falsify the hypothesis under test. For example, from the universal statement Water boils when its temperature reaches 100OC we can deduce the singular statement that this container here at hand contains cold water which, when heated to 100OC, will boil, but not before then. This prediction can be tested by setting up the specified initial conditions and observing what happens. If the prediction is not confirmed then the universal statement is falsified. It is shown to be not true or, at least, not true at it stands. (In this instance, we might modify the original hypothesis thus: Water at sea level boils when its temperature reaches 100OC.) However, if the prediction is confirmed, such confirmation does not make the universal statement true. Apart from the impossibility of observing all containers of water at all times and in all places, the observation may be the result of some other, unrecognised cause.

The presence of some other possible causal factor (like altitude) is explicitly acknowledged by the practice of including a control condition: in this case that of heating cans of water to a range of temperatures at a range of altitudes to test at what temperature in each case the water boils. This example is, of course, somewhat trivial, but the principle holds. In Eddington’s case, he measured the transit time of his chosen star across the given arc of sky when the Sun did not obscure its path. In like manner, a pharmacologist compares the effect of a therapeutic drug with that of a placebo drug. From the subject’s point of view (and, in a properly conducted double-blind experiment, the experimenter’s point of view also) the placebo drug and the way it is delivered to the subject are indistinguishable from the therapeutic drug and the way it is delivered. In other words, all factors other than the drug (including unintended bias on the part of the experimenter), are held constant. If an effect is found it can be attributed to the known difference between the experimental and control conditions - the presence of the therapeutic drug - not attributed for certain, of course, but at least while that result remains unfalsified.

The scientist’s aim should be to refute the statement in question. As Popper put it, “The method of science is the method of bold conjectures and ingenious and severe attempts to refute them”.[15] Scientists should try to show that their theories are wrong. This is, at least, the logic of scientific research, as is made quite clear in the title of his 1934 publication, Logik der Forschung, published in English as The logic of scientific discovery. But as anyone involved in the business knows, it is not necessarily how scientists actually go about their research. An account of what we might call the psychology of scientific research, based upon an analysis of how scientists have behaved historically, has been provided by Thomas Kuhn.[16]

Scientific research proceeds, Kuhn wrote, in stages, each marked by a common acceptance of a certain established paradigm. From time to time the paradigm is overturned and another takes its place in what Kuhn labelled a paradigm shift. As an example of paradigm shift Kuhn described how Newton’s concept of light as consisting of material corpuscles was replaced by the theories of Young and Fresnel that conjectured light as being a transverse wave motion, to be replaced in turn by photons (part corpuscle, part wave) based upon quantum-mechanic theory.[17] At any given stage, scientists spend a lot of time and energy investigating the ramifications and implications of the paradigm, in effect confirming it by collecting positive instances, just as taxonomists collect cases of a current object of interest or as biologists collect genes. They are like explorers investigating a territory newly-discovered (newly-discovered, that is, from the explorers’ perspective). We can equate a Kuhn-paradigm with a Popper-conjecture, and to that extent their views are compatible. But in any case, how scientists may or may not do their work does not alter the logic by which scientific knowledge is established. Popper’s stated the logic of scientific discovery, which stands irrespective of what scientists actually do.

Popper wrote The logic of scientific discovery at the time when the members of the Vienna Circle were attempting to eliminate metaphysics from science on the grounds that metaphysical statements were meaningless. Scientific statements, they claimed, were those derived from statements that could be established by observation. True observations served to verify scientific statements, and on that account such statements could be said to be meaningful. The meaning of a statement corresponded to tis proposed means of verification. The task of the scientist was to test scientific statements by seeking confirmatory evidence from sensory observations. Because metaphysical statements could not be verified in this way they were meaningless; they were non-statements.

This approach, known as logical positivism, appears to be very straightforward. As A.J.Ayer put it: “It brought about a great emphasis on clarity, and a great opposition to … wooliness.”[18] However, the statement All metaphysical statements are unverifiable is itself unverifiable by means of sensory observation. If it is unverifiable the statement is meaningless, making the position that is dependent on it – logical positivism - invalid. Alternatively, we must accept that at least one metaphysical statement is meaningful. For reasons like this Ayer could go on to say: “… very little survives. What survives is the general rightness of the approach.”

Popper was in close touch with members of the Circle, although not a member himself. He was never invited to join; whether or not he would have accepted an invitation is a moot question, but either way, he would, we may surmise, have agreed with Ayer’s assessment. He asserted, however, that the important question was not which statements were meaningless but which statements were scientific. For him, the distinction should be made not between verifiable and non-verifiable statements but between falsifiable and non-falsifiable statements. Even so, despite the demise of logical positivism, its influence continues - in the form of reductive materialism - to be the metaphysical position of choice taken by many scientists as well as by many non-scientists for whom science is a contemporary idol.

Popper’s falsifiability criterion does not define truth nor suggest that if a statement is not scientific it is for that reason not true. Popper’s epistemology does not carry the reproach of irrationality for metaphysics that logical positivism carries. Not everyone may wish to examine metaphysical statements, just as not everyone wants to talk about art, but that is a matter of interest, a psychological question rather than a logical one. There is a sense, then, in which we can characterise Popper’s system as tolerant: any universal statement can be examined, no matter what its source, whether that be oral tradition, written tradition, current paradigms, intuitive reasoning, speculative thinking, or even supposed hallucination, provided that it can then be criticised and, if necessary, rejected as false.

Behind Popper’s claims lies the disturbing suggestion that scientific endeavour can never provide us with certain knowledge. We can falsify a theory and show that it needs at best re-casting and at worst abandoning, but we can never know that we have reached final truth. Perhaps scientific knowledge, or certain parts of it, have reached that position, but perhaps a new Einstein will show that our supposed certainties are ill-founded. We may, like Shermer, have confidence, that is, faith, in our scientific knowledge, but faith is not certainty. Popper wrote:

Science does not rest on solid bedrock. The bold structure of its theories rises, as it were, above a swamp. It is like a building erected on piles. The piles are driven down from above into the swamp, but not down to any natural or ‘given’ base; and if we stop driving the piles deeper, it is not because we have reached firm ground. We simply stop when we are satisfied that the piles are firm enough to carry a structure, at least for the time being.[19]

The swamp metaphor brings to mind the Gospel of St Matthew:

Everyone then who hears these words of mine and acts on them will be like a wise man who built his house on rock. The rain fell, the floods came, and the winds blew and beat on that house, but it did not fall, because it had been founded on rock. And everyone who hears these words of mine and does not act on them will be like a foolish man who built his house on sand. The rain fell, and the floods came, and the winds blew and beat against that house, and it fell—and great was its fall![20]

We may believe in a prophet and believe in the prophet’s teaching, but this differs from believing that any particular statement about the natural world is indisputably true. Believing in and believing that denote different mental dispositions.

Chapter 3: Searching for knowledge

When we observe that events repeat themselves in a regular manner we infer that they will continue to occur in the same manner. The Sun has risen every day for all of the past days of our lives and we believe without doubt that it will rise tomorrow. However, there always remains the possibility that tomorrow the Sun will not rise. As much as it may seem the reasonable thing to do, there is no logical reason for believing that the future will be the same as the past. No number of observations, however large, permits us logically to do so. In spite of this, we continue to rely on inductive logic, opening ourselves, as David Hume pointed out, to the charge of irrationality. The charge disturbed Bertrand Russell to the point where he stated that Hume’s conclusion represented “the bankruptcy of eighteenth-century reasonableness.” To avoid its implications Russell insisted that induction must be regarded as “an independent logical principle, incapable of being inferred either from experience or from other logical principles.”[21]

Hume formulated the problem in psychological terms, asking why all reasonable people expect, and believe, that instances of which they have had no experience at all (because they have not yet occurred) will conform to those of which they have experience (because they have already occurred). He posed his question in subjective terms, that is, he asked why the specified mental process (reasoning) should produce the result (belief in the truth of an event not yet experienced). Hume answered the question by attributing the result to custom and habit. Popper addressed the problem by translating Hume’s question into objective terms. He asked whether the claim that an explanatory universal theory (one used to predict the nature of instances of which we have not yet had experience) is true can be justified by observation statements (that is, instances of which we have had experience).

For example, can we justify the truth of the universal statement It always rains on Sunday by our observation that on every Sunday in the past it has rained? This re-formulation moves the question from the realm of psychology to that of logic.[22] Popper then expanded the question, changing is true to is true or is false. For example, is the universal statement It always rains on Sunday true or false? Popper’s answer to this question was that we can know if it is false. We can know if it is false by taking our theory, selecting some suitable initial conditions, and from them deducing a consequence. For example, on a specified Saturday we can predict that it will rain tomorrow. This prediction can then be checked against empirical observation. The process involves deductive logic, not inductive logic, thus avoiding Hume’s problem. If our test shows that the prediction is not confirmed, then the theory is false; if it is confirmed the theory may be true (but not necessarily true).

In practice, we often recognise the uncertainty inherent in a theory produced by induction and we attempt to deal with it by assigning a probability to our expectation that the future will be like the past. In doing this we must distinguish between subjective and objective forms of probability. Subjective probability is found in the statement I believe that it is likely to rain tomorrow, or to be a little more precise, I believe there is a 60 percent chance that it will rain tomorrow. The statement implies that there is a 40 percent chance that it will not rain tomorrow so that whether it rains or not the prediction is met. Not surprisingly, Popper rejected this tactic on the grounds that such modification rendered the theory “impervious to strict falsification”.[23] The statement is, in effect, an expression of confidence in the prediction that it will rain; that is, it is a bet. The reason for betting that way may be interesting and the argument, if not logical, at least rational, but the statement is not scientific.

However, we may express the statement in objective terms and thus render it scientific, that is, susceptible to falsification. We do this by specifying objective initial conditions thus: Given that certain meteorological conditions will occur on 100 days (or instances), on 60 of those instances it will rain and on 40 instances it will not rain. This is a prediction of frequency and it makes the statement scientific because by observing the days and counting the number on which it rains the statement can, conceivably, be shown to be false.

Hume, along with other empiricists who gave primacy to sensory experience, held to what Popper labelled the bucket theory of knowledge acquisition, and it is this misconceived theory that Popper saw as the source of Hume’s problem.[24] On this theory the mind is a blank slate, a tabala rasa, onto which fall sensory impressions derived from sight, hearing, touch, taste, smell and the bodily senses (proprioception, kinesthesis, and the vestibular, temperature and pain senses). By virtue of repetition and association through features like similarity, contrast and contiguity these impressions are systematised into perceptions, memories and expectations. Errors and misunderstandings occur when prejudices and other irritants are allowed to interfere with the pure and simple process of accumulating sensory impressions. In this somewhat passive manner we arrive at our knowledge of the Universe. But if, as Hume asserted, logic forbids our using these past experiences to predict the future, we have not got very further forward. We have reasons for forming conjectures but not for claiming the conjectures to be true.

Emmanuel Kant agreed with the empiricists that sensory experience provided the raw material of knowledge but asserted that mental processes digest, as it were, the incoming material so as to produce a view of the external world that is coherent and systematic. In other words, we actively generate our perception of the world and do not passively accept it. Popper took Kant’s proposal further. He agreed that, as Kant proposed, the laws of nature are our invention, but he then went on to assert: “We try to impose them upon nature … and very often we fail.”[25] We impose order on our sensory impressions and we then test the imposed order by examining whether it is confirmed, or falsified, by further sensory impressions. This turns the situation completely around. We begin not with sensory impressions but with expectations (or theories or hypotheses or conjectures, the label is immaterial). We expect or anticipate that the world takes a certain shape or behaves in a certain way. We then test this expectation by looking for sensory evidence that confirms, or falsifies, the expectation. Sensory experiences are actively sought out in order to test the antecedent expectation; they are not passively accepted.

Popper labelled his theory as the searchlight theory of knowledge acquisition. Everyday experience shows that it is not possible to make pure, uncontaminated, observations. We cannot observe all that is at any moment available so our observations must necessarily be selective. If we stay quiet and listen, we listen for the sound of traffic, for the birds in the trees, for the cry of a child, or for whatever relates to the situation in which we find ourselves, a situation of which we are already aware. If we stay still and look, we look for a movement, for an unusual aspect, for an object in the sky, or, again, for whatever relates to the situation in which we stand, a situation of which we are already aware. If we ask someone to observe, the immediate response is “Observe what?”[26] All observations presuppose an existing question or expectation, conscious or unconscious. When our observations take the form of measurements, the measurements have meaning only in relation to a pre-existing theory. The weight of a small body may be directly sensed by kinesthesis by holding the object in the hand. The weight can be inferred, but not directly sensed, from visual observation by placing it in a spring balance. The visual experience of observing the rotation of the needle on a spring balance allows us to make this inference only because we already believe (or conjecture) that a force associated with the action of the mass of the Earth upon the object in the scales causes the needle to rotate. We always begin with a conjecture (or hypothesis or expectation) that has been formulated irrespective of any observations that may or may not have been already made. Therefore, “We must give up the view that we are passive observers, waiting for nature to impress its regularity upon us.”[27]

From these considerations Popper produced a theory of how we learn by experience. The theory postulates, first, the presence of a problem with a tentative solution (the conjecture), then a search for sensory evidence to confirm or falsify the tentative solution, followed by the rejection of false solutions on the basis of the observed sensory evidence, and finally the resolution of the problem. As an illustration, we may consider the problem of finding our bus stop at an unfamiliar location. We begin by conjecturing that on the basis of our experience at other locations the bus stop will be situated at, say, close to a cross-street, so we look in that direction. If we fail to see it in the direction first chosen we look elsewhere. Eventually, when we see it our search is ended and our problem solved, provided, that is, we have not mistakenly accepted another bus stop for the one we are searching for. (In other words, although we can falsify a choice and look elsewhere, we cannot be fully certain that our final choice is in fact the correct one.) In all events, our initial problem has now been resolved into a new problem: how do we get from here to there. From this experience, we cannot inductively conclude that all bus stops stand at cross-streets and that the next time we look it will be there. In the mean-time it may have been moved.

On this account, we follow a continuous process of problem solving consisting of conjecture, testing by observation, correction of error, and a new or modified conjecture to be applied to the next problem. We do not passively perceive but actively observe in order to answer a question that encapsulates a problem. Since this is a continuous process it can be traced backwards, one set of observations, based on a certain expectation, going back to a previous set based on an earlier expectation. The process is regressive, reaching back eventually to the innate (but, of course, unconscious and unarticulated) expectations of the new-born child who expects to be fed. In all cases (including the primitive one formulated here) the observer tests the expectation and then goes on to formulate new expectations on the basis of the test results. Every organism is born with a “horizon of expectations.”[28] These take the form of, for example, the expectation to find a nipple and the expectation to be cared for. They remain, however, expectations or conjectures. There may be no nipple and there may be no caregiver.

Popper used his searchlight theory as the model for the growth of scientific knowledge. To the question “Which comes first, the hypothesis or the observation?” he replied, “An earlier kind of hypothesis.”[29] We begin with a problem (or conjecture) and check it out in the light of experience in the form of sensory observation. Our observations then lead us to modify the earlier conjecture in the light of experience, forming a new or modified conjecture that represents a new problem. Science does not proceed from theory to theory but from problem to problem, with every fruitful theory leading to new problems. “[T]he most lasting contribution to the growth of knowledge that a theory can make are the new problems which it raises.”[30]

As far as scientific research is concerned, the process is continuous and no ultimate truth is reached. This does not mean that there is no truth, or that we cannot approach it, but it does mean that we can never be certain that we have grasped it. It may be, in fact, that we have actually formulated a true statement, but we cannot be certain that this is so. We may be certain that we are in error and so exclude what is false, and in doing so we believe that we move closer to the truth. Thus, we may suppose, statements that have been more rigorously tested, and have withstood attempts to falsify them, are closer to the truth than those less rigorously tested, an idea that Popper labelled as verisimilitude. Popper did not thereby suggest that we give up the search for truth, but only the search for justification. “[I am] very far from suggesting that we give up the search for truth. … [T]ruth plays the role of a regulative idea. We test for truth by eliminating falsehood.”[31]

Chapter 4: The heart of the matter

“[A]ll thinking [people] are interested [in] the problem of understanding the world in which we live, and thus ourselves who are part of that world …”[32] In so far as we address this problem in terms of scientific knowledge we proceed, Popper asserted, by way of conjecture, prediction, observation, and revised conjecture. One mode of entry into the process is by means of existential observations, observations of things or events as they are or as they appear to be. For example, an observation of the weather may lead to the singular statement It is raining and then to the conjectural universal statement When the ambient temperature falls below the dew point it rains. If further observation fails to falsify the conjecture, that is, we do not observe it to rain when the ambient temperature is not below the dew point, then the second, universal, statement can be said to explain the first, singular, statement. The term ‘universal’ implies that it is true for all singular statements of the same kind.

However, our solution of the first problem “Why is it raining?” leads to another problem: “Why does it rain when the ambient temperature falls below the dew point?” This may then produce a second conjectural universal statement The amount of water vapour present in a body of air varies with temperature such that a body of air of lower temperature holds a lesser amount water vapour. This second statement, if not falsified by observation, can be said to explain the first universal statement, and lead to another problem: “Why does the amount of water vapour present in a body of air vary with its temperature?” In this way, our knowledge is increased step by step by formulating increasingly all-encompassing universal statements which, if not falsified, bring us closer to the truth. Each statement at one level poses the need for an explanation at a higher level. This process can conceivably go on forever in an infinite regression.

Popper identified two ways in which we can avoid an infinite regression of explanation: by appealing to authority and by seeking the essential nature of things. By appealing to authority, we may assert that the amount of water vapour present in a body of air varies with its temperature because God made it that way, or because the Philosopher (or Scientist) said that it was so. (This is the Platonic, or top-down, approach.) Much can be, and is, explained in this manner of appealing to authority. Popper asserted that such an appeal is not in itself to be deplored. All enquiries must have a point of departure, and that point might be provided by tradition, sacred writings, canonized philosophers, our senses or intellect or feelings of conviction. Traditions are not to be rejected just because they are traditions. Even those rationalists who claim to reject tradition do themselves appeal to the tradition of approaching every statement critically, an approach Popper ascribed to the pre-Socratic philosophers whose secret, he claimed, was “a tradition – the tradition of critical discussion.”[33]

More explicitly, Popper asserted “[W]e cannot start afresh … we must make use of what people before us have done in science.”[34] Science, in fact, establishes its own traditions, being “myth-making, just as religion is.”[35] Scientific research starts with a myth, a conjecture which even after being tested remains a conjecture. The difference lies in that scientific myths change, and they change in the direction of giving a better and better account of the world or, at the very least, one that has not been falsified. Religious myths, by contrast, tend not change, or if they do, they change much less rapidly.

Beginning in the seventeenth century, Francis Bacon and the British Empiricists turned away from the appeals to authority offered by older systems and towards sensory observation as the source of knowledge. René Descartes and the Continental Rationalists adopted a similar attitude to the older systems but they still looked to thought and intellect as the source of knowledge. Descartes relied on the truthfulness of God which must make truth manifest, while Bacon might be said to have relied on the truthfulness of Nature which was an open book to be read with a pure mind. Popper, on the other hand, asserted that the Baconian empiricists and Cartesian rationalists were simply offering new authorities: the senses or the intellect. But no source, he asserted, offers certain truth; we must acknowledge that, whatever our source, we can be mistaken.

We have to think beyond what is immediately observable. Truth cannot be decided by pedigree, asking how we know, any more than by decree. The question to be asked is not “How do we know?” because we don’t know, we can only guess. We need to ask “Where are we wrong?” Objective truth exists, but we must search for it by identifying our errors, not by expecting to find it by virtue of our sources. Our failure to discern truth is due to human error; if we can see the error, we can approach closer to the truth. In short, we must ask if an assertion is true, not where it comes from.

Observation is only one source from which to form conjectures, and it can be misleading if unconsciously-held expectations bias our observations. The universal statement The Sun sets and rises once every twenty-four hours is, for many persons, demonstrably and incontrovertibly true. For this reason, the Greeks derided Pythias of Marseilles who claimed otherwise - but he had sailed across the Arctic Circle and knew better. Observations may also be inconclusive. Scientific researchers are always left with the questions of whether the observation predicted by the theory under scrutiny has actually occurred and whether it has occurred for the conjectured reason. Did I really feel a spot of rain and was it really because the temperature had dropped? In all events, the observation may have occurred quite fortuitously, a possibility recognised by introducing the so-called null hypothesis which postulates that the observation has, in fact, occurred by chance. The null hypothesis is rejected, and the observation taken as being significant, only if the probability, p, of a fortuitous occurrence is such that p < 0.01 (or, in some cases, p < 0.05), as calculated by statistical tests. Even so, the possibility that it occurred by chance remains for p can never reach zero. The customary criterion of p < 0.01 (or of p < 0.05) is, after all, only a tradition.

Popper contrasted rationalism, in the sense of an appeal to reason and experience, with irrationalism, which appeals to emotion and passion. Reasoning means listening to criticism and criticising in return, addressing the argument rather than rejecting it by virtue of the person doing the arguing or the source cited in evidence. Popper wrote: “I may be wrong and you may be right, and by an effort, we may get nearer to the truth.”[36] He asserted that the choice between rationalism and irrationalism is, in part, a moral choice. We treat our interlocutors with respect by taking seriously what they have to say and we consider the consequences of our assertions. Irrationalism can lead us to impose conditions on unwilling recipients on the grounds that we know better than they what is good for them, torturing them, if necessary, in order to save their souls or purify their intellects. When they object we can discount their objections as ill-considered, explaining it away in the way that psychoanalysts examine motives rather than reasons.

Popper was not hostile to traditions provided they are regarded as valuable, not sacrosanct. The conflict is not between faith and knowledge but between two kinds of faith.

“[T]he choice with which we are confronted is between a faith in reason and in human individuals and a faith in the mystical faculties of man by which he is united to a collective. … [T]his choice is at the same time between an attitude that recognizes the unity of mankind and an attitude that divides men into friends and foes, into masters and slaves.”[37]

The adepts are distinguished from the non-adepts, and those possessing grace from those not. Rationalism is consistent with a belief in the equality of all. This is true, of course, no matter from which side the tradition is approached.

Popper’s second way of avoiding the infinite regression implied in seeking explanation is by supposing that scientific research seeks to describe essences, or the essential nature of things. It always rains on Sunday because it is of the essential nature of Sunday that it should rain. Popper set out three propositions regarding the aim of scientific research: that it seeks to produce an explanation of the observable facts, or an explanation which is true beyond any reasonable doubt, or an explanation which describes the essential nature of things.[38] According to Popper, the third proposition was that espoused, for example, by Galileo. By contrast, modern theoretical physicists are, Popper claimed, instrumentalists, holding to the first proposition and rejecting the third. They reject the third proposition on the grounds that essences are either not there to be discovered or, if they are, are not discoverable. More to the point, instrumentalists regard scientific theories as devices for manipulating the world (much as engineers use such theories) without necessarily claiming that the devices provide a true description of the world.

Popper agreed with the instrumentalists in rejecting essentialism but for a different reason, claiming that essentialism is obscurantist. If it is thought that a final explanation has been reached, further investigation is thereby discouraged or even forbidden. This was the case for those scientists who regarded gravity – meaning the attraction that one body has towards another - as being an inherent property of matter, the view rejected by Newton. In such circumstances the question, “What causes bodies to attract each other?” is meaningless: they attract each other because they have the inherent property of doing so. Einstein showed that this position could be surpassed.[39]

Essentialism has a long and distinguished history, reaching back to Plato who said that the world as we experience it is to be ultimately explained in terms of a pre-existing world of eternal, absolute and immutable Forms or Ideas. A singular event in the present world is as it is by virtue of its share in the ultimate character of the Form that gives rise to it. True knowledge refers to knowledge of the world of Forms: “[O]pinion is of the world presented to the senses, whereas knowledge is of a super-sensible eternal world.”[40]

Popper speculated about why Plato thought that way. He suggested that Plato was seeking to find stability and order in an imperishable world of eternal truth. Such a world contrasted with the degeneration and chaos that he observed around him in the Greece of his day.[41] Plato had observed that the world of sensible things was continually changing and was changing for the worse. Perfect knowledge, therefore, could not be found in the present and even less in the future. Knowledge was to be found in the past. His world of Forms constituted the point of departure for subsequent change. Knowledge of the Forms constituted real knowledge and this provided the basic premises from which universal statements, and ultimately singular events, could be deduced.

In his epistemology Aristotle took a similar position, distinguishing, like Plato, between opinion and knowledge and, also like Plato, asserting that knowledge of essences is grasped intuitively. Thus, he intuitively determined that “Some men are by nature [that is, essentially] free and others slaves.”[42] However, Aristotle’s optimism in contrast to Plato’s pessimism led him to see change as progress not deterioration so that the Final Cause, the end to which each thing moves, is good. The Form stands at the end not the beginning and the essence is in the thing itself, not prior to it. Popper agreed with both Plato and Aristotle in asserting that intuition exists as a mental experience, but intuition does not establish truth; it only gives a reason to search for arguments for establishing truth – or, rather, for identifying falsity.

From the perspective of essentialism, what we need to do is to define our words and concepts with care and clarity. In Popper’s view, the essentialist approach amounts to a matter of defining words: the meaning of a word, its essence, tells us something about that which it denotes and thus of the Universe. Against this, Popper set the approach of methodological nominalism. The meaning of a word tells us nothing about the Universe: words just offer a convenient reference for what we already know. Looking for more just leads us into a preoccupation with “purging our language and eliminating linguistic puzzles.”[43] It does not advance knowledge.

In the definition of a word, the word to be defined stands on the left side and the defining formula on the right. The essentialist view reads the definition from left to right but the scientific view reads from right to left. Instead of defining gravity as the force that causes apples to fall from trees we agree to label the force that causes apples to fall from trees as gravity, and then go on to ask more questions about the force. Words offer us brevity of expression, not meaning. They are merely useful devices for formulating propositions. They have no inherent value of themselves. Essences are “hypostasized words.”[44]

The physical sciences and biological sciences, unlike the social sciences, are largely free of essentialism. They address questions like “Why does the apple fall from the tree?” not “What is gravity?”, and “How do organisms live?” not “What is life?”, and do so with notable success. Social scientists, according to Popper, are too interested in definitions, asking “What is the State?” rather than “What does the State do?”[45], to which we might add “What is the Church” rather than “What does the Church do?” Such preoccupation with meaning can lead to barren scholasticism and mysticism. Popper eschewed writings that were “full of definitions which seemed to me arbitrary, pointless, and question-begging, so far as there was any question at all. It gave me a lifetime’s dislike of theorizing about God”.[46]

In short, we cannot avoid an infinite regression by recourse to essentialism any more than by appealing to authority. Scientific knowledge remains a structure built upon a swamp.

Chapter 5: To be or not to be

The task of research scientists is to produce conjectures in the form of universal statements and to attempt to falsify them. Those conjectures which are not falsified represent, for the moment, steps closer to a true description of the Universe. Such universal statements can be said to explain certain singular statements. The term ‘universal’ implies that it is true for all singular statements of the same kind. Universal statements refer to all times and all places. The term ‘singular statement’ refers to an existential event, that is, to an entity that exists or to an event that has occurred. Examples are Here is a swan, There are fairies at the bottom of my garden, The Sun rises and It is raining. That a statement of this kind is true is determined by reference to consensual sensory observation: the entity or event, by common consent, has been seen, heard, touched, or in some other way experienced.

Clearly, consensus is not guaranteed. Even in the case of a scientific experiment where stringent statistical tests may be applied in order to settle the question, there may not be agreement whether the predicted entity has or has not been observed or the event has or has not occurred. In this connection, we may note, for example, the celebrated case of Neville Maskelyne, the Astronomer Royal whose colleagues observed transits of Venus across the Sun of lengths that differed from his own. Maskelyne attributed the differences to the incompetence of his colleagues. More reasonably, the discrepancies were attributed to ‘personal equations’, now known as naturally-occurring variations in individual reaction time.

Popper stated the relation between universal and existential statements thus: The negation of a universal statement is an affirmative existential statement.[47] The negation of the universal statement All swans are white is the statement Not all swans are white which is logically equivalent to the existential statement There is a non-white swan. If a non-white swan is, by agreement of the observers, observed then the existential statement is true, and so, too, is the negation of the universal statement. Hence the universal statement is false by the law of non-contradiction: a statement and its negation cannot both be true.

The statement There is a non-white swan can conceivably be verified but not falsified, because it is not possible to visit all places at all times where a non-white swan might be observed. This is true of all existential statements that are unbounded in time and space. (An unbounded existential statement is: There is a non-white swan immediately here at hand. That statement may be, by consensual observation, falsified.) Because they are not falsifiable, they are not scientific statements. They are not for that reason meaningless but their being meaningful does not make them true. Thus, there is a symmetry between universal and existential statements: universal statements can be falsified by a singular observation but not verified, while existential statements can be verified by a singular observation but not falsified.

Historical statements and statements about historical trends, all of which can conceivably be verified but not falsified, were regarded for that reason, by Popper, as existential statements. With respect to the truth of historical statements, Popper noted that, unlike the truth of universal statements, the status of the source of the evidence is pertinent. “Testing an historical assertion always means going back to sources; but not, as a rule, to the reports of eyewitnesses.”[48] This is because direct empirical evidence, including the reports of reliable eyewitnesses, may be hard to come by. But one ancient historian may, for various reasons, be considered more reliable than another, and thus be a preferred source for verification of an event.

Being existential statements, historical statements cannot be used to make predictions, at least not logically so used. Historical statements about trends can be used to make inductive predictions on the basis that the trend will continue, that is, that the future will be like the past, but Popper, like Hume, rejected inductive logic. They cannot be used to make deductive predictions. For that, a universal statement is needed, one that applies to multiple instances and which can be tested by a different instance. “The most careful observation of one developing caterpillar will not help us predict its transformation into a butterfly.”[49] To make a prediction, we require a system that is “well-isolated, stationary, and recurrent”[50] like the solar system, or the life cycle of an organism, but human society is not such a system. We can predict seasons and eclipses but we cannot predict revolutions or the Second Coming.

Despite this logical difficulty, historians endeavour not only to describe past singular events but also to explain them. This is often done by identifying a concatenation of antecedent singular events. Thus, they may, perhaps, account for the outbreak of the First World War by the singular statement Archduke Franz Ferdinand was assassinated taken together with other singular statements such as Once put into motion general mobilisation could not be stopped. But some social scientists believe that this is not sufficient, claiming that the effects of the fortuitous interplay of singular events upon the unfolding of events is trivial compared to that of long-term causes. They believe that these causes that can be expressed as universal statements.

According to this point of view, history develops inexorably and necessarily along a pre-determined course. The task of the historian and social scientist is, then, to detect trends in historical narratives, to elucidate the laws (or universal statements) governing these trends, and to foresee, and perhaps prepare for, the inevitable end. But it is logically not feasible to predict future states of society. Apart from any other consideration, as Popper pointed out, any future state of affairs will be determined in part by knowledge that will be available at that time but which, as it is being gathered at the present time, is not already known.

Popper claimed that it is not possible adequately to describe a totality like ‘The history of mankind’. An entity or a sequence of events has multi-faceted aspects, any set of which may be chosen for investigation. But when that set has been chosen, others remain unchosen. The choice is inevitably influenced by the known and unknown prejudices of the investigator, “For undoubtedly there can be no history without a point of view.”[51] Social science is itself a social institution and those involved in applying predictions and testing outcomes are unavoidably caught up in the situation they are manipulating, just as nuclear physicists influence the effects they are observing. Recent growing interest in the stories of common people draws attention to the fact that previous interest was focussed upon uncommon people like monarchs and other warmongers, indicating a very selective point of view and choice of aspects.

It may be that historical trends can be identified, but trends are not universal statements and from them we can make only prophecies, not predictions. Popper coined the term ‘historicism’ to denote the attempt to make predictions from trends, and he saw the systems of Plato and Marx as epitomizing historicism. “[T]he kind of prophecies which Marxism offers”, he wrote, “are in their logical character more akin to those of the Old Testament than to those of modern physics.”[52] Popper regarded Plato and Marx as not only fundamentally wrong in their historicism but also as dangerously totalitarian in its application. Those who have available to them the knowledge of historical laws feel justified in imposing their prophecies upon others regardless of actual outcomes. Popper called this approach ‘Utopian social engineering’. In its place, he advocated what he called ‘piecemeal social engineering.’[53] We should make experimental interventions in the structure of society that are limited in scope in order to reduce what may be the ill effects of unintentional misjudgements. If all works out well, an advance will have been made; if not, not too much damage will have been done. Popper was here assuming that politicians and systems-managers would be willing to recognise their errors.

Popper asserted that Darwin’s theory of evolution was, in similar manner, a statement about a historical trend and as such was an existential statement. Darwin developed his theory to address among other problems that of why very similar, but non-identical, species of living organisms were to be found in close but separate geographical locations. From his observations, he produced several conjectures starting with the hypothesis that species adapted, over generations, to variations in the habitat in which they lived and going on to hypotheses concerning common descent and the evolution of less complex organisms into more complex organisms. Compelling evidence in support of the last hypothesis comes from palaeontology. If the lower layers of the crust of the Earth were laid down before the upper layers then the pattern of fossils found in the layers of different age clearly indicates a temporal progression from less complexity to more complexity in the organisms of which the fossils are the remnants. Other evidence supporting the hypothesis comes from embryology, biogeography and the study of vestigial organs.

Darwin’s theory, as it stands, offers no conjecture as to how evolution came about. It is a theory of its coming about, that is, it is the statement of an existential trend. The conjecture of common descent, for example, is a singular historical statement that disparate organisms have a common ancestor. The statement does not offer an explanation why that should be so. To fill the gap, Herbert Spencer proposed the theory of natural selection. Spencer’s theory conjectured that spontaneously-generated variations within a species survived, and propagated themselves, depending on the extent to which each was fitted to its habitat. However, Spencer proposed no independent criterion of fitness so that his theory is tautological: species survive because they are fitter and they are judged fitter because they survive.

It may be that recent developments in the field of molecular biology will allow biologists to produce more rigorous conjectures. In the meantime, despite the lack of universal statements that could conceivably be falsified, evolutionary theory is used widely to explain current human behaviour in terms of evolved adaptations, often with reference to the conditions supposedly found on the African savannah some two hundred thousand years ago. The evolutionary scientist Stephen Jay Gould labelled these conjectures as Just-So stories.

The theory of evolution is commonly said to be scientific because, as is clearly the case, its investigation involves the use of procedures based on scientific technologies and techniques. For this reason, evolutionary research may be compared to archaeological research where procedures using scientific techniques and technologies are also used, but here, too, the outcome is the description of a trend. In neither case are we left with a universal statement which, given certain initial conditions, allows us on the basis of deductive logic to predict a future event. We can describe how people lived in past cultures but we cannot predict the shape of future civilisations.

Along with his rejection of laws of historical trends, Popper asserted “There are no Darwinian laws of evolution”[54], to which we might add, nor laws of cultural development, and nor laws of divine revelation. Given this perspective, it may be said that evolutionary and archaeological research on the one hand and historical research on the other are not as different as is sometimes suggested. C.P.Snow deplored the gulf between the ‘two cultures’, science and the humanities, but both, in fact, have similarities. They produce statements of trends, based upon data from ancient records (fossils, artefacts and documents, respectively) and use sophisticated techniques to identify and evaluate the data. Such statements, whether biological, cultural or historical, are insightful, useful, interesting and valuable and may be true, but on Popper’s criterion they are not scientific.

Chapter 6: Clockwork dream or cloudy reality

Popper’s distinction between universal and existential statements lies at the heart of his epistemology, clarifying what we can know and cannot know and elucidating the means of determining what we know and do not know. Popper made important assertions about other kinds of statements (or theories, or hypotheses, or conjectures – he used these terms interchangeably), distinguishing empirical and scientific theories from philosophical or metaphysical theories, and from logical and mathematical theories.[55] (He did not assert that this list was exhaustive.)

An example of a metaphysical statement is: The present contains the future or, to put it more fully, The present contains the future in that the future is fully determined by the present. This means that if, at a particular time in the present we were to possess the relevant knowledge, we could fully predict the characteristics that will be present at a particular future time. Another example of a metaphysical statement is: The world exists only in my mental experience. This means that the reality that appears to me to be present in the exterior world is not really there - only I really exist - a view labelled as solipsism.

Metaphysical statements are existential statements. A metaphysical statement points to a particular situation, to a singular state of affairs, to things as they are. It is not a universal statement pointing to all such states of a given kind. As such, it cannot be used to formulate a scientific prediction. For that purpose, we need a universal statement and a statement of initial conditions. In so far as it describes a state of affairs, a metaphysical statement is a statement of initial conditions. Like all existential statements, metaphysical statements can conceivably be verified but they cannot be falsified. To verify a metaphysical statement we must point, by consensual agreement, to a sensory observation which provides a positive instance. But for statements like the two cited, observers find it difficult to agree. Consequently, metaphysical statements like these are irresolvable and are, at the same time, irrefutable. Whether they are, despite this, accepted as true or as false must depend upon intuition, not sensory observation. Popper labelled the philosophical position expressed by the first of these two statements as determinism, and the second as idealism.[56]

That determinism is true, at least in relation to physical entities, appeared to be a consequence of Newtonian theory.[57] That some events appeared to be indeterminate, it was claimed, was due only to ignorance of the complete state of affairs. But Newtonian theory can be only accepted as a best case given that our measurements of the physical world and its characteristics are inevitably imprecise. Every measurement, however detailed, inevitably involves rounding up or rounding down. The pointer on an instrument is seldom precisely on the mark and even if it appears to be so, the mark necessarily has width. The advent of quantum theory and its associated indeterminism made this argument even more pertinent. In these circumstances, Popper concluded, “Physical determinism … was a daydream of omniscience.”[58]

The more significant point, however, is that determinism poses the question of whether persons are really free agents, as they to themselves appear to be. Are the human experiences of choosing and deciding mere epiphenomena without real effect upon bodily events? Determinists assert that that is the case, but it can lead to outlandish conclusions. A fully determined system, of both bodily and mental events, implies that a deaf physicist who had heard no music could, with a full knowledge of the purely physical conditions, write Beethoven’s symphonies and even symphonies that Beethoven did not compose but might have composed if Beethoven’s situation had been slightly different. Popper considered this idea to be absurd. But in any case, the real problem at hand is whether we can have moral responsibility for our decisions and actions which, Popper asserted, is the case. Since we do have moral responsibility, determinism is irrefutable but false, while indeterminism is irrefutable and true.

The position known as idealism arose from the British empiricists’ emphasis on the role of sensory experience as the foundational basis for knowledge. We are aware of our sensory impressions in a very real and immediate manner, and from them we conjecture that entities exist in a world that is external to our impressions. But we have no immediate knowledge of those entities; our knowledge of them is mediated only through our sensory impressions. This can lead to the conclusion that we do not know that those entities really exist; only our impressions really exist. The world, then, is our impressions, or to put it more romantically, our dreams.

The empiricists’ argument in favour of idealism followed from their passive bucket-theory of acquiring sensory experience. Popper rejected that theory, postulating in its place the active searchlight-theory. He asserted that the world presents the observer with problems to be solved, not mere experiences. If these problems, and the language in which they are posed, are unreal, then so also is scientific endeavour as a whole. So, too, is the argument being advanced in favour of idealism. He further noted that, from his perspective, idealism implied that he had himself created his world, including the works of art that he found within it, and that he denied. Common sense readily distinguishes between reality and appearance, even though appearance has a reality of its own, as the object and its reflection in a mirror – the reality and the appearance - are both real. Thus, although common sense is not infallible, it witnesses against idealism. Popper conceded that none of this logically refutes idealism but claimed, even so, that the world is real. In short, despite its being irrefutable, Popper asserted that idealism, like determinism, is false.

Popper asserted that metaphysical statements are not meaningless in themselves, contrary to the official position of the Vienna Circle whose members rejected metaphysical statements as meaningless. In the circumstances, it is hardly surprising that while Popper waited for an invitation to join the Circle the invitation was never made. However, there was no need for him to have bothered because, as Popper recognised,[59] a far more devastating critique of the aim of the Circle was offered by a paid-up member, Kurt Gödel. Gödel, using strictly logical techniques, proved several important theorems which may be summarised by the statement The consistency of a formal system cannot be proved within the system.[60] This means that a closed system like that of arithmetic includes statements that are true but which cannot be shown to be true within the constraints of the system itself. To show that they are true, we have to view the system from outside, as it were. These outside proofs are, from the perspective of the system, metaphysical statements.

A very simple example of such a statement is If x = y, then y = x, where x and y are natural numbers. This is one of the axioms of arithmetic and is so obviously true that we might wonder why it should ever be questioned. The point, however, is that it cannot be shown to be true using arithmetical techniques. The proof lies outside mathematics and, with respect to mathematics, the statement is metaphysical (or metamathematical). A more general example of such a statement was provided by Roger Penrose. The statement Propositions deducible from [true] axioms are themselves true follows from “an obviously true property that the axiom system itself has.”[61]

Pursing this point, Penrose also noted with respect to the halting problem of Alan Turing, that whether a universal computer (a closed system) will stop is not something that can be decided algorithmically, that is, by the method used by a computer.[62] We may consider the case of a computer that has been constructed to execute a specific program or application. Examples of special applications (apps) are to compute logarithms, to translate from one language into another, and to complete an income tax return. In each case, we can identify the input (a natural number, a piece of text, statements of income), the computer program, and the output (a logarithm, a translation, a completed tax return). A human operator can examine the input and output in each case and evaluate whether the program has performed correctly.

We now construct a higher-level computer to take the place of the human operator. The input of this higher-level computer is the input, program and output of each of the apps and the output of the higher-level computer is the statement C orrect or the statement Not correct. A human operator can examine the input and output of the higher-level computer and evaluate whether the program has performed correctly. We can then construct an even-higher-level computer, and repeat the procedure. Clearly, at any particular level we must go to a higher level, one external to the computers, in order to evaluate the situation at the lower level. No matter which level we reach, the final evaluation is made at a higher level and by a human operator, not a computer. While computers function by means of algorithms, human thinking, or intuition, cannot be represented by an algorithm, a point which argues against the possibility of artificial intelligence based upon computer operation.

To return to Popper, with regard to mathematical statements he pointed out that if they are true then they are tautological. Perhaps for that reason (and provided one can understand them) they produce strong feelings of conviction. The truth or falsity of mathematical statements depends on initial axiomatic statements, not on any empirical observation. Given that the axioms of mathematics are true, the statements or theorems which are logically inferred from them are true irrespective of observations in the natural world. The statement The internal angles of a triangle on a plane surface sum to half a complete turn or two right angles is true by logical inference and if empirical measurement of the angles of a particular triangle demonstrated otherwise the observation, not the statement, would be deemed inaccurate. Whether the axioms are true is a different question. They are not true by virtue of logical inference and nor by sensory observation. The proof of the size of the interior angles of a triangle depends upon the axiom The distance between parallel lines is constant to infinity, but if we believe that statement to be true it is by virtue of something other than logical inference or sensory observation, that is, by intuition.

Mathematical statements are useful devices for providing precise and coherent statements about the natural world. Logical positivists wished to do without intuition but without intuition there are no mathematical theorems. Mathematical statements are often seen as the epitome of science, but they are not themselves part of the natural world. We use logical criticism to investigate mathematical conjectures, not sensory observation. We use sensory observation to investigate scientific theories. Mathematical statements are not scientific statements.

Metaphysical and tautological statements are of the kind to which it is appropriate to assign the adjectives ‘true’ and ‘false’ - but not, of course, both at the same time. They are often labelled as natural laws in that they express an unvarying regularity about nature. They cannot be broken; rather than being broken they can be refuted. If it appears that a natural law has been broken, it means that the law has been incorrectly expressed; it must be either abandoned or re-formulated.

Natural laws contrast with norms such as prohibitions, commandments and maxims of the kind to which it is appropriate to assign to any one of them the adjectives ‘right’ and ‘wrong’, or ‘good’ and ‘bad’ - but again not both at the same time.[63] These also are often labelled as laws, but the sense is quite different.


Chapter 1

[1] “Jews demand signs” 1 Corinthians 1:22. NRSV

[2] “For philosophy was a schoolmaster” Bettenson, Documents of the Christian Church. OUP, 1967, p6.

[3] “Whosoever will be saved” At Morning Prayer, Book of Common Prayer.

[4] “[K]nowledge is not to be” Russell, History of Western Philosophy. Allen and Unwin, 1946, p126.

[5] “Whence has [the mind]” Locke, An Essay Concerning Human Understanding. Dent, Everyman Edition, 1947, p26.

[6] “That gravity should be innate” Cohen, Isaac Newton’s Papers. Harvard University Press, 1978, pp302-303.

[7] “Materialism became the predominant worldview” Sheldrake and Shermer, Arguing Science. Monkfish, 2016, p55.

[8] “I hold that physical objects are real” Magee, Men of Ideas. BBC, 1978, pp171-172.

[9] “[W]e proclaim Christ crucified” 1 Corinthians 1:23. NRSV.

[10] “thousandfold experience” Popper, Conjectures and Refutations. Routledge, 2002, p46.

[11] Popper’s reaction to street violence. Popper, Unended Quest. Fontana, 1976, pp33-34.

[12] Popper and Einstein’s theory. Popper, Conjectures and Refutations. Routledge, 2002, p47.

[13] Popper and Marxism. Popper, Replies to my Critics. Open Court, 1974, pp984-985.

[14] “the verification of a natural law” Popper, Logic of Scientific Discovery. Hutchinson, 1986, p63.

[15] “The method of science” Popper, Objective Knowledge. OUP, 1979, p81.

[16] Kuhn, The Structure of Scientific Revolutions. University of Chicago Press, 1996.

[17] Paradigm shift. Kuhn, The Structure of Scientific Revolutions. University of Chicago Press, 1996, pp11-12.

[18] “It brought about a great emphasis” Magee, Men of Ideas. BBC, 1978, p131.

[19] “Science does not rest on solid bedrock” Popper. Logic of Scientific Discovery. Hutchinson, 1986, p111.

[20] “Everyone then who hears” Matthew 7:24-27. NRSV.

[21] “the bankruptcy of eighteenth-century reasonableness.”” Russell, History of Western Philosophy. Allen and Unwin, 1946, pp698-700.

[22] Popper’s re-formulation of Hume. Popper, Objective Knowledge. OUP, 1979, p7.

[23] “impervious to strict falsification” Popper, Logic of Scientific Discovery. Hutchinson, 1986, p146.

[24] Source of Hume’s problem. Popper, Objective Knowledge. OUP, 1979, Appendix 1.

[25] “We try to impose upon nature” Popper, Objective Knowledge. OUP, 1979, p92.

[26] “Observe what?” Popper, Conjectures and Refutations. Routledge, 2002, p61.

[27] “We must give up the view. Popper, Conjectures and Refutations. Routledge, 2002, p245.

[28] “horizon of expectations” Popper, Objective Knowledge. OUP, 1979, p347.

[29] “An earlier kind of hypothesis” Popper, Conjectures and Refutations. Routledge, 2002, p62.

[30] “[T]he most lasting contribution” Popper, Conjectures and Refutations. Routledge, 2002, p301.

[31] “[I am] very far from suggesting” Popper. Objective Knowledge. OUP, 1979, p29.

[32] “[A]ll thinking [people] are interested” Popper, Conjectures and Refutations. Routledge, 2002, p183.

[33] “a tradition … of critical discussion” Popper, Conjectures and Refutations. Routledge, 2002, p200.

[34] “[W]e cannot start afresh” Popper, Conjectures and Refutations. Routledge, 2002, p173.

[35] “myth-making, just as religion is” Popper, Conjectures and Refutations. Routledge, 2002, p171.

[36] “I may be wrong and you may be right” Popper, Open Society. Princeton University Press, 1966, Volume 2, p225.

[37] “[T]he choice with which we are confronted” Popper, Open Society. Princeton University Press, 1966, Volume 2, p246.

[38] The aim of scientific research. Popper, Conjectures and Refutations. Routledge, 2002, pp139-140.

[39] Einstein surpassing Newton. Popper, Conjectures and Refutations. Routledge, 2002, p141-144.

[40] “[O]pinion is of the world” Russell, History of Western Philosophy. Allen and Unwin, 1946, p142.

[41] Plato’s observation of the world. Popper, Open Society. Princeton University Press, 1966, Volume 1, pp18-19, pp31-32.

[42] “Some men are by nature … free” Popper, Open Society. Princeton University Press, 1966, Volume 2, p2.

[43] “purging our language” Popper, Open Society. Princeton University Press, 1966, Volume 2, p20.

[44] “hypostasized words” Popper, Objective Knowledge. OUP, 1979, p123.

[45] “What is the State?” Popper, Open Society. Princeton University Press, 1966, Volume 2, p119.

[46] “full of definitions” Popper, Unended Quest. Fontana, 1976, p18.

[47] Negation of a universal statement. Popper, Logic of Scientific Discovery. Hutchinson, 1986, p68.

[48] “Testing an historical assertion” Popper, Conjectures and Refutations. Routledge, 2002, p30.

[49] “The most careful observation” Popper, The Poverty of Historicism. Ark Paperbacks, 1986, p109.

[50] “well-isolated, stationary, and recurrent” Popper, Conjectures and Refutations. Routledge, 2002, p457.

[51] “For undoubtedly there can be no history” Popper, The Poverty of Historicism. Ark Paperbacks, p150.

[52] “[T]he kind of prophecies which Marxism offers” Popper, Conjectures and Refutations. Routledge, 2002, p454.

[53] Utopian social engineering. Popper, The Poverty of Historicism. Ark Paperbacks, 1986, p64.

[54] “There are no Darwinian laws of evolution” Popper. Objective Knowledge. OUP, 1979, p267.

[55] Kinds of statement. Popper, Conjectures and Refutations. Routledge, 2002, p266.

[56] Determinism and idealism. Popper, Conjectures and Refutations. Routledge, 2002, p263.

[57] Newtonian theory and determinism. Popper, Objective Knowledge. OUP, 1979, p210.

[58] “Physical determinism … was a daydream” Popper, Objective Knowledge. OUP, 1979, p222.

[59] Popper’s recognition of Gödel. Popper, Conjectures and Refutations. Routledge, 2002, p362.

[60] Consistency of a formal system. Goldstein, Incompleteness. Norton, 2005, p23.

[61] “an obviously true property” Penrose, The Emperor’s New Mind. OUP, 1989, p146, n3.

[62] Turing’s halting problem. Penrose, The Emperor’s New Mind. OUP, 1989, pp414-415.

[63] Natural laws contrasted with norms. Popper, Open Society. Princeton University Press, 1966, Volume 1, p57.

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Karl Popper and Religious Knowledge
Applying Critical Rationalism to Theology
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