Conjectures and Refutations

My notes from Conjectures and Refutations by Karl Popper. I found it very interesting and was prompted by David Deutsch to read it. Some of the chapters (read: lectures) were a bit too repetitive. I will extend the notes sometime soon.

our scientific knowledge, progresses by unjustified (and unjustifiable) anticipations, by guesses, by tentative solutions to our problems, in a word by conjectures

truth is not manifest, but extremely elusive, he believes that men need above all things, open-mindedness, imagination, and a constant willingness to be corrected

thesis that we can learn from our mistakesThey develop a theory of knowledge and of its growth. It is a theory of reason that assigns to rational arguments the modest and yet important role of criticizing our often mistaken attempts to solve our problems. And it is a theory of experience that assigns to our observations the equally modest and almost equally important role of tests which may help us in the discovery of our mistakes. Though it stresses our fallibility it does not resign itself to scepticism

way in which knowledge progresses, and especially our scientific knowledge, is by unjustified (and unjustifiable) anticipations, by guesses, by tentative solutions to our problems, by conjectures

conjectures are controlled by criticism; that is, by attempted refutations, which include severely critical tests

They may survive these tests; but they can never be positively justified: they can be established neither as certainly true nor even as ‘probablethe very refutation of a theory—that is, of any serious tentative solution to our problem—is always a step forward that takes us nearer to the truthAnd this is how we can learn from our mistakes

Since our knowledge can grow, there can be no reason here for despair of reason

Since none of them can be positively justified, it is essentially their critical and progressive character—the fact that we can argue about their claim to solve our problems better than their competitors— which constitutes the rationality of scienceliberal’, ‘liberalism’, etc. , always in a sense in which they are still generally used in England (though perhaps not in America): by a liberal I do not mean a sympathizer with any one political party but simply a man who values individual freedom and who is alive to the dangers inherent in all forms of power and authority

all our knowledge grows only through the correcting of our mistakes

we must already have some aim: we err if we stray from this aim. (A feedback thermostat depends on some aim—some definite temperature—which must be selected in advance.) Yet though in this way some aim must precede any particular instance of the trial and error method, this does not mean that our aims are not in their turn subject to this method. Any particular aim can be changed by trial and error, and many are

changed.(We can change the setting on our thermostat, selecting by trial and error one that better satisfies some aim—an aim of a different level. ) And our system of aims not only changes, but it can also grow in a way closely similar to the way in which our knowledge grows

O N T H E S O U R C E S O F K N O W L E D G E A N D O F I G N O R A N CIgnorance is something negative: it is the absence of knowledge

conspiracy theory of ignorance which interprets ignorance not as a mere lack of knowledge but as the work of some sinister power, the source of impure and evil influences which pervert and poison our minds and instil in us the habit of resistance to knowledge.

allow me to begin my story at the other end—with the sources of knowledge rather than with the sources of ignorance

old quarrel between the British and the Continental schools of philosophy—the quarrel between the classical empiricism of Bacon, Locke, Berkeley, Hume, and Mill, and the classical rationalism or intellectualism of Descartes, Spinoza, and Leibniz. In this quarrel the British school insisted that the ultimate source of all knowledge was

observation, while the Continental school insisted that it was the intellectual intuition of clear and distinct ideas

show of the two schools of empiricism and rationalism that their differences are much smaller than their similarities,

and that both are mistaken

show that neither observation nor reason can be described as a source of knowledge, in the sense in which they have been claimed to be sources of knowledge, down to the present day

The belief of a liberal—the belief in the possibility of a rule of law, of equal justice, of fundamental rights, and a free society—can easily survive the recognition that judges are not omniscient and may make mistakes about facts and that, in practice, absolute justice is never fully realized in any particular legal case. But the belief in the possibility of a rule of law, of justice, and of freedom, can hardly survive the acceptance of an epistemology which teaches that there are no objective facts; not merely in this particular case, but in any other case; and that the judge cannot have made a factual mistake because he can no more be wrong about the facts than he can be right.

the heart of this new optimistic view of the possibility of knowledge lies the doctrine that truth is manifest

Removing the veil may not be easy. But once the naked truth stands revealed before our eyes, we have the power to see it, to distinguish it from falsehood, and to know that it is truth

Man can know: thus he can be free. This is the formula which explains the link between epistemological optimism and the ideas of liberalism

Disbelief in the power of human reason, in man’s power to discern the truth, is almost invariably linked with distrust of man

As an epistemologist I have only one interest—to find out the truth about the problems of epistemology, whether or not this truth fits in with my political ideas.

in searching for the truth, it may be our best plan to start by criticizing our most cherished beliefsThis doctrine is at the heart of the teaching of both Descartes and Bacon. Descartes based his optimistic epistemology on the important theory of the veracitas dei. What we clearly and distinctly see to be true must indeed be true; for otherwise God would be deceiving us. Thus the truthfulness of God must make truth manifest. In Bacon we have a similar doctrine. It might be described as the doctrine of the veracitas naturae, the truthfulness of Nature. Nature is an open book. He who reads it with a pure mind cannot misread it. Only if his mind is poisoned by prejudice can he fall into error

The conspiracy theory of ignorance is fairly well known in its Marxian form as the conspiracy of a capitalist press that perverts and suppresses truth and fills the workers’ minds with false ideologies. Prominent among these, of course, are the doctrines of religion. It is surprising to find how unoriginal this Marxist theory

For the simple truth is that truth is often hard to come by, and that once found it may easily be lost again. Erroneous beliefs may have an astonishing power to survive, for thousands of years, in defiance of experience, with or without the aid of any conspiracy

Thus the optimistic epistemology of Bacon and of Descartes cannot be true

This false epistemology, however, has also led to disastrous consequences. The theory that truth is manifest—that it is there for everyone to see, if only he wants to see it—this theory is the basis of almost every kind of fanaticismYet the theory that truth is manifest not only breeds fanatics—men possessed by the conviction that all those who do not see the manifest truth must be possessed by the devil—but it may also lead, though perhaps less directly than does a pessimistic epistemology, to authoritarianism. This is so, simply, because truth is not manifest, as a rule. The allegedly manifest truth is therefore in constant need, not only of interpretation and affirmation, but also of re-interpretation and reaffirmation. An authority is required to pronounce upon, and lay down, almost from day to day, what is to be the manifest truth, and it may learn to do so arbitrarily and cynically. And many disappointed epistemologists will turn away from their own former optimism and erect a resplendent authoritarian theory on the basis of a pessimistic epistemology. It seems to me that the greatest epistemologist of all, Plato, exemplifies this tragic development

For as all natures are kindred and akin, our soul must be akin to all natures. Accordingly it knows them all: it knows all things.(On kinship and knowledge see also Phaedo, 79d; Republic, 611d; Laws, 899d. ) In being born we forget; but we may recover our memory and our knowledge, though only partially: only if we see the truth again shall we recognize it. All knowledge is therefore re-cognition—recalling or remembering the essence or true nature that we once knew

Plato’s famous theory of anamne

long as it dwells, and participates, in a divine world of ideas or essences or natures, prior to being born. The birth of a man is his fall from grace; it is his fall from a natural or divine state of knowledge; and it is thus the origin and cause of his ignorance.(Here may be the seed of the idea that ignorance is sin, or at least related to sin; cp.Phaedo, 76d. ) It is clear that there is a close link between this theory of anamne¯sis and the doctrine of the divine origin or source of our knowledge. At the same time, there is also a close link between the theory of anamne¯sis and the doctrine of manifest truth: if, even in our depraved state of forgetfulness, we see the truth, we cannot but recognize it as the truth.So, as the result of anamne¯sis, truth is restored to the status of that which is not forgotten and not concealed (ale¯the¯s): it is that which is manifest

Yet disappointment must have come to Plato; for in the Republic (and also in the Phaedrus) we find the beginnings of a pessimistic epistemology. In the famous story of the prisoners in the cave (514 ff. ) he shows that the world of our experience is only a shadow, a reflection, of the real world. And he shows that even if one of the prisoners should escape from the cave and face the real world, he would have almost insuperable difficulties in seeing and understanding it—to say nothing of his difficulties in trying to make those understand who stayed behind

Aristotle, and also Bacon, I wish to suggest, meant by ‘induction’ not so much the inferring of universal laws from particular observed instances as a method by which we are guided to the point whence we can intuit or perceive the essence or the true nature of a thing. 7 But this, as we have seen, is precisely the aim of Socrates’ maieutic: its aim is to help or lead us to anamne¯sis; and anamne¯sis is the power of seeing the true nature or essence of a thing, the nature or essence with which we were acquainted before birth, before our fall from grace. Thus the aims of the two, maieutic and induction, are the same

The framework of Bacon’s theory of induction is this. He distinguishes in the Novum Organum between a true method and a false method

the spelling out of, the book of Nature

true method, ‘

anticipatio’ means ‘prejudice’ or even ‘superstition

Thus the two methods are (1) ‘the spelling out of the open book of Nature’, leading to knowledge or episte¯me¯, and (2) ‘the prejudice of the mind that wrongly prejudges, and perhaps misjudges, Nature’, leading to doxa, or mere guesswork, and to the misreading of the book of Nature. This latter method, rejected by Bacon, is in fact a method of interpretation, in the modern sense of the word. It is the method of conjecture or hypothesis (a method of which, incidentally, I happen to be a convinced advocate).

Only after our souls have been cleansed in this way may we begin the work of spelling out diligently the open book of Nature, the manifest truth. In view of all this I suggest that Baconian (and also Aristotelian) induction is the same, fundamentally, as Socratic maieutic; that is to say, the preparation of the mind by cleansing it of prejudices, in order to enable it to recognize the manifest truth, or to read the open book of Nature.Descartes’ method of systematic doubt is also fundamentally the same: it is a method of destroying all false prejudices of the mind, in order to arrive at the unshakeable basis of self-evident truth

The sources of knowledge must be kept pure, because any impurity may become a source of ignorance

spite of the religious character of their epistemologies, Bacon’s and Descartes’ attacks upon prejudice, and upon traditional beliefs which we carelessly or recklessly harbour, are clearly anti-authoritarian and anti-traditionalist. For they require us to shed all beliefs except those whose truth we have perceived ourselves

But I do not think that Bacon and Descartes succeeded in freeing their epistemologies from authority; not so much because they appealed to religious authority—to Nature or to God—but for an even deeper reason

They could only replace one authority—that of Aristotle and the Bible—by another. Each of them appealed to a new authority; the one to the authority of the senses, and the other to the authority of the intellect

The solution lies in the realization that all of us may and often do err, singly and collectively, but that this very idea of error and human fallibility involves another one—the idea of objective truth: the standard which we may fall short of. Thus the doctrine of fallibility should not be regarded as part of a pessimistic epistemology. This doctrine implies that we may seek for truth, for objective truth, though more often than not we may miss it by a wide margin. And it implies that if we respect truth, we must search for it by persistently searching for our errors: by indefatigable rational criticism, and self-criticism.

Bacon and Descartes set up observation and reason as new authorities, and they set them up within each individual man. But in doing so they split man into two parts, into a higher part which had authority with respect to truth—Bacon’s observations, Descartes’ intellect—and a lower part. It is this lower part which constitutes our ordinary selves, the old Adam in us. For it is always ‘we ourselves’ who are alone responsible for error, if truth is manifest. It is we, with our prejudices, our negligence, our pigheadedness, who are to blame; it is we ourselves who are the sources of our ignorance

they believe that it is not our senses that err, but that it is always ‘we ourselves’ who err in our interpretation of what is ‘given’ to us by our senses. Our senses tell the truth, but we may err, for example, when we try to put into language—conventional, man-made, imperfect language—what they tell us. It is our linguistic description which is faulty because it may be tinged with prejudice

Thus there is indeed a familiar as well as a logically defensible sense in which the ‘true’ or ‘proper’ meaning of a term is its original meaning; so that if we understand it, we do so because we learned it correctly—from a true authority, from one who knew the language

This shows that the problem of the meaning of a word is indeed linked to the problem of the authoritative source, or the origin, of our usage. It is different with the problem of the truth of a statement of fact, a proposition

a statement of the inherent essence or nature of a thing. At the same time, it states the meaning of a word—of the name that designates the essence.(For

Moreover, Aristotle and all other essentialists held that definitions are ‘principles’; that is to say, they yield primitive propositions (example: ‘All bodies are extended’) which cannot be derived from other propositions, and which form the basis, or are part of the basis, of every demonstration. They thus form the basis of every science

disposal by which we can explain the logic of the view that questions of origin may decide questions of factual truth. For if origins can determine the true meaning of a term or word, then they can determine the true definition of an important idea, and therefore some at least of the basic ‘principles’ which are descriptions of the essences or natures of things and which underlie our demonstrations and consequently our scientific knowledge. So it will then appear that there are authoritative sources of our knowledge. Yet we must realize that essentialism is mistaken in suggesting that definitions can add to our knowledge of facts (although qua decisions about conventions they may be influenced by our knowledge of facts, and although they create instruments which may in their turn influence the formation of our theories and thereby the evolution of our knowledge of facts). Once we see that definitions never give any factual knowledge about ‘nature’, or about ‘the nature of things’, we also see the break in the logical link between the problem of origin and that of factual truth which some essentialist philosophers tried to forge

The problem of the validity of empiricism may be roughly put as follows: is observation the ultimate source of our knowledge of nature? And if not, what are the sources of our knowledge

The problem of the source of our knowledge has recently been restated as follows. If we make an assertion, we must justify it; but this means that we must be able to answer the following questions.‘How do you know? What are the sources of your assertion?’ This, the empiricist holds, amounts in its turn

shall try to show that this case is as little valid as Bacon’s; that the answer to the question of the sources of knowledge goes against the empiricist; and, finally, that this whole question of ultimate sources— sources to which one may appeal, as one might to a higher court or a higher authority—must be rejected as based upon a mistake

programme of tracing back all knowledge to its ultimate source in observation is logically impossible to carry through: it leads to an infinite regress

The doctrine that truth is manifest cuts off the regress. This is interesting because it may help to explain the attractiveness of that doctrine

The most striking thing about the observationalist programme of asking for sources—apart from its tediousness—is its stark violation of common sense. For if we are doubtful about an assertion, then the normal procedure is to test it, rather than to ask for its sources; and if we find independent corroboration, then we shall often accept the assertion without bothering at all about sources

what, then, are the sources of our knowledge? The answer, I think, is this: there are all kinds of sources of our knowledge; but none has authority

question of the validity of an historical assertion may be testable only, or mainly, in the light of the origin of certain sources. But in general the two questions are different; and in general we do not test the validity of an assertion or information by tracing its sources or its origin, but we test it, much more directly, by a critical examination of what has been asserted—of the asserted facts themselves.

They never challenge these questions, or dispute their legitimacy; the questions are taken as perfectly natural, and nobody seems to see any harm in them. This is quite interesting, for these questions are clearly authoritarian in spirit

propose to assume, instead, that no such ideal sources exist—no more than ideal rulers—and that all ‘sources’ are liable to lead us into error at times. And I propose to replace, therefore, the question of the sources of our knowledge by the entirely different question: ‘How can we hope to detect and eliminate error?

propose to assume, instead, that no such ideal sources exist—no more than ideal rulers—and that all ‘sources’ are liable to lead us into error at times. And I propose to replace, therefore, the question of the sources of our knowledge by the entirely different question: ‘How can we hope to detect and eliminate error?’

My modified question, ‘How can we hope to detect error?’ may be said to derive from the view that such pure, untainted and certain sources do not exist, and that questions of origin or of purity should not be confounded with questions of validity, or of truth. This

The proper answer to my question ‘How can we hope to detect and eliminate error?’ is, I believe, ‘By criticizing the theories or guesses of others and—if we can train ourselves to do so—by criticizing our own theories or guesses. ’ (The latter point is highly desirable, but not indispensable; for if we fail to criticize our own theories, there may be others to do it for us. ) This answer sums up a position which I propose to call ‘critical rationalism

Yet in the field of ethics, of moral knowledge, it was approached by Kant with his principle of autonomy

principle expresses his realization that we must not accept the command of an authority, however exalted, as the basis of ethics. For

So my answer to the questions ‘How do you know? What is the source or the basis of your assertion? What observations have led you to it?’ would be: ‘I do not know: my assertion was merely a guess. Never mind the source, or the sources, from which it may spring—there are many possible sources, and I may not be aware of half of them; and origins or pedigrees have in any case little bearing upon truth. But if you are interested in the problem which I tried to solve by my tentative assertion, you may help me by criticizing it as severely as you can; and if you can design some experimental test which you think might refute my assertion, I shall gladly, and to the best of my powers, help you to refute it. ’ This

answer 10 applies, strictly speaking, only if the question is asked about some scientific assertion as distinct from an historical

formulate the epistemological results of this discussion

ten theses.

There are no ultimate sources of knowledge. Every source, every suggestion, is welcome; and every source, every suggestion, is open to critical examination. Except in history, we usually examine the facts themselves rather than the sources of our information.2. The proper epistemological question is not one about sources; rather, we ask whether the assertion made is true—that is to say, whether it agrees with the facts.(That we may operate, without getting involved in antinomies, with the idea of objective truth in the sense of correspondence to the facts, has been shown by the work of Alfred Tarski. ) And we try to find this out, as well as we can, by examining or testing the assertion itself; either in a direct way, or by examining or testing its consequences.3. In connection with this examination, all kinds of arguments may be relevant. A typical procedure is to examine whether our theories are consistent with our observations. But we may also examine, for example, whether our historical sources are mutually and internally consistent.4. Quantitatively and qualitatively by far the most important source of our knowledge—apart from inborn knowledge—is tradition. Most things we know we have learnt by example, by being told, by reading books, by learning how to criticize, how to take and to accept criticism, how to respect truth.5. The fact that most of the sources of our knowledge are traditional condemns anti-traditionalism as futile. But this fact must not be held to support a traditionalist attitude: every bit of our traditional knowledge (and even our inborn knowledge) is open to critical examination and may be overthrown.Nevertheless, without tradition, knowledge would be impossible.6. Knowledge cannot start from nothing—from a tabula rasa—

yet from observation. The advance of knowledge consists, mainly, in the modification of earlier knowledge. Although we may sometimes, for example in archaeology, advance through a chance observation, the significance of the discovery will usually depend upon its power to modify our earlier theories.7. Pessimistic and optimistic epistemologies are about equally mistaken. The pessimistic cave story of Plato is the true one, and not his optimistic story of anamne¯sis (even though we should admit that all men, like all other animals, and even all plants, possess inborn knowledge). But although the world of appearances is indeed a world of mere shadows on the walls of our cave, we all constantly reach out beyond it; and although, as Democritus said, the truth is hidden in the deep, we can probe into the deep. There is no criterion of truth at our disposal, and this fact supports pessimism. But we do possess criteria which, if we are lucky, may allow us to recognize error and falsity. Clarity and distinctness are not criteria of truth, but such things as obscurity or confusion may indicate error. Similarly coherence cannot establish truth, but incoherence and inconsistency do establish falsehood.And, when they are recognized, our own errors provide the dim red lights which help us in groping our way out of the darkness of our cave.8. Neither observation nor reason is an authority. Intellectual intuition and imagination are most important, but they are not reliable: they may show us things very clearly, and yet they may mislead us. They are indispensable as the main sources of our theories; but most of our theories are false anyway. The most important function of observation and reasoning, and even of intuition and imagination, is to help us in the critical examination of those bold conjectures which are the means by which we probe into the unknown.9. Although clarity is valuable in itself, exactness or precision is not: there can be no point in trying to be more precise than our problem demands. Linguistic precision is a phantom, and problems connected with the meaning or definition of words are unimportant. Thus our table of Ideas (on p.25), in spite of its symmetry, has an important and an unimportant side: while the left-hand side (words and their meanings) is unimportant, the right-hand side (theories and the problems connected with their truth) is all-important. Words are significant only

instruments for the formulation of theories, and verbal problems are tiresome: they should be avoided at all cost.10. Every solution of a problem raises new unsolved problems; the more so the deeper the original problem and the bolder its solution. The more we learn about the world, and the deeper our learning, the more conscious, specific, and articulate will be our knowledge of what we do not know, our knowledge of our ignorance. For this, indeed, is the main source of our ignorance—the fact that our knowledge can be only finite, while our ignorance must necessarily be infinite

We may get a glimpse of the vastness of our ignorance when we contemplate the vastness of the heavens: though the mere size of the universe is not the deepest cause of our ignorance, it is one of its causes.‘Where I seem to differ from some of my friends’, F.P. Ramsey wrote in a charming passage of his Foundations of Mathematics (p.291), ‘is in attaching little importance to physical size, I don’t feel in the least humble before the vastness of the heavens. The stars may be large but they cannot think or love; and these are qualities which impress me far more than size does

might be well for all of us to remember that, while differing widely in the various little bits we know, in our infinite ignorance we are all equal.

If only we look for it we can often find a true idea, worthy of being preserved, in a philosophical theory which must be rejected as false. Can we find an idea like this in one of the theories of the ultimate sources of our knowledge

The first, the false idea, is that we must justify our knowledge, or our theories, by positive reasons, that is, by reasons capable of establishing them, or at least of making them highly probable; at any rate, by better reasons than that they have so far withstood criticism. This idea implies, I suggest, that we must appeal to some ultimate or authoritative source of true knowledge; which still leaves open the character of that authority—whether it is human, like observation or reason, or super-human (and therefore super-natural). The second idea—whose vital importance has been stressed by Russell—is that no man’s authority can establish truth by decree; that we should submit to truth; that truth is above human authority. Taken together these two ideas almost immediately yield the conclusion that the sources from which our knowledge derives must be super-human; a conclusion which tends to encourage selfrighteousness and the use of force against those who refuse to see the divine truth.

Some who rightly reject this conclusion do not, unhappily, reject the first idea—the belief in the existence of ultimate sources of knowledge. Instead they reject the second idea—the thesis that truth is above human authority. They thereby endanger the idea of the objectivity of knowledge, and of common standards of criticism or rationality. What we should do, I suggest, is to give up the idea of ultimate sources of knowledge, and admit that all knowledge is human; that it is mixed with our errors, our prejudices, our dreams, and our hopes; that all we can do is to grope for truth even though it be beyond our reach

We may admit that our groping is often inspired, but we must be on our guard against the belief, however deeply felt, that our inspiration carries any authority, divine or otherwise. If we thus admit that there is no authority beyond the reach of criticism to be found within the whole province of our knowledge, however far it may have penetrated into the unknown, then we can retain, without danger, the idea that truth is beyond human authority. And we must retain it. For without this idea there can be no objective standards of inquiry; no criticism of our conjectures; no groping for the unknown; no quest for knowledge.

Conjectures

1 S C I E N C E : C O N J E C T U R E S A N D R E F U TAT I O N S

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

The problem which troubled me at the time was neither, ‘When is a theory true?’ nor, ‘When is a theory acceptable?’ My problem was different. I wished to distinguish between science and pseudo-science; knowing very well that science often errs, and that pseudo-science may happen to stumble on the truth.

I knew, of course, the most widely accepted answer to my problem: that science is distinguished from pseudo-science—or from ‘metaphysics’—by its empirical method, which is essentially inductive, proceeding from observation or experiment

often formulated my problem as one of distinguishing between a genuinely empirical method and a non-empirical or even a pseudo-empirical method—that is to say, a method which, although it appeals to observation and experiment, nevertheless does not come up to scientific standards

The latter method may be exemplified by astrology, with its stupendous mass of empirical evidence based on observation—on horoscopes and on biographies

clinics. It was during the summer of 1919 that I began to feel more and more dissatisfied with these three theories—the Marxist theory of history, psycho-analysis, and individual psychology; and I began to feel dubious about their claims to scientific status.

Thus what worried me was neither the problem of truth, at that stage at least, nor the problem of exactness or measurability. It was rather that I felt that these other three theories, though posing as sciences, had in fact more in common with primitive myths than with science; that they resembled astrology rather than astronomy. I found that those of my friends who

were impressed by a number of points common to these theories, and especially by their apparent explanatory power.

the world was full of verifications of the theory

Marxist could not open a newspaper without finding on every page confirming evidence for his interpretation of history; not only in the news, but also in its presentation

that each in its turn had been interpreted in the light of ‘previous experience’, and at the same time counted as additional confirmation

Each of these two cases can be explained with equal ease in Freudian and in Adlerian terms

precisely this fact—that they always fitted, that

they were always confirmed—which in the eyes of their admirers constituted the strongest argument in favour of these theories. It began to dawn on me that this apparent strength was in fact their weakness.

impressive thing about this case is the risk involved in a prediction of this kind. If observation shows that the predicted effect is definitely absent, then the theory is simply refuted. The theory is incompatible with certain possible results of observation—in fact with results which everybody before Einstein would have expected. 1 This is quite different from the situation I have previously described, when it turned out that the theories in question were compatible with the most divergent human behaviour, so that it was practically impossible to describe any human behaviour that might not be claimed to be a verification of these theories.

It is easy to obtain confirmations, or verifications, for nearly every theory—if we look for confirmations.(2) Confirmations should count only if they are the result of risky predictions; that is to say, if, unenlightened by the theory in question, we

should have expected an event which was incompatible with the theory—an event which would have refuted the theory.(3) Every ‘good’ scientific theory is a prohibition: it forbids certain things to happen. The more a theory forbids, the better it is.(4) A theory which is not refutable by any conceivable event is nonscientific. Irrefutability is not a virtue of a theory (as people often think) but a vice.(5) Every genuine test of a theory is an attempt to falsify it, or to refute it. Testability is falsifiability; but there are degrees of testability: some theories are more testable, more exposed to refutation, than others; they take, as it were, greater risks.(6) Confirming evidence should not count except when it is the result of a genuine test of the theory; and this means that it can be presented as a serious but unsuccessful attempt to falsify the theory.(I now speak in such cases of ‘corroborating evidence’. ) (7) Some genuinely testable theories, when found to be false, are still upheld by their admirers—for example by introducing ad hoc some auxiliary assumption, or by re-interpreting the theory ad hoc in such a way that it escapes refutation. Such a procedure is always possible, but it rescues the theory from refutation only at the price of destroying, or at least lowering, its scientific status.(I later described such a rescuing operation as a ‘conventionalist twist’ or a ‘conventionalist stratagem’. ) One can sum up all this by saying that the criterion of the scientific status of a theory is its falsifiability, or refutability, or testability.

Moreover, by making their interpretations and prophecies sufficiently vague they were able to explain away anything that might

In order to escape falsification they destroyed the testability of their theory

Marxist theory of history, in spite of the serious efforts of some of its founders and followers, ultimately adopted this soothsaying practice

The two psycho-analytic theories were in a different class. They were simply non-testable, irrefutable

At the same time I realized that such myths may be developed, and become testable; that historically speaking all—or very nearly all— scientific theories originate from myths, and that a myth may contain important anticipations of scientific theories. Examples are Empedocles’ theory of evolution by trial and

I thus felt that if a theory is found to be non-scientific, or ‘metaphysical’ (as we might say), it is not thereby found to be unimportant, or insignificant, or ‘meaningless’, or ‘nonsensical’. 4 But

Years later—it must have been in 1928 or 1929—I called this first problem of mine the ‘problem of demarcation’. The criterion of falsifiability is a solution to this problem of demarcation, for it says that statements or systems of statements, in order to be ranked as scientific, must be capable of conflicting with possible, or conceivable, observations

The statements which may possibly fall within the province of science are those which may possibly be verified by observation statements; and these statements, again, coincide with the class of all genuine or meaningful statements. ’ For this approach, then, verifiability, meaningfulness, and scientific character all coincide

problem of induction

Hume, I felt, was perfectly right in pointing out that induction cannot be logically justified. He held that there can be no valid logical 9 arguments allowing us to establish ‘that those instances, of which we have had no experience, resemble those, of which we have had experience’. Consequently ‘even after the observation of the frequent or constant conjunction of objects, we have no reason to draw any inference concerning any object beyond those of which we have had experience’. For ‘shou’d it be said that we have experience’ 10 —experience teaching us that objects constantly conjoined with certain other objects continue to be so conjoined—then, Hume says, ‘I wou’d renew my question, why from this experience we form any conclusion beyond those past instances, of which we have had

experience’. This ‘renew’d question’ indicates that an attempt to justify the practice of induction by an appeal to experience must lead to an infinite regress. As a result we can say that theories can never be inferred from observation statements, or rationally justified by them

Hume’s psychology, which is the popular psychology, was mistaken, I felt, about at least three different things: (a) the typical result of repetition; (b) the genesis of habits; and especially (c) the character

those experiences or modes of behaviour which may be described as ‘believing in a law’ or ‘expecting a law-like succession of events

The typical result of repetition

far from creating a conscious expectation of law-like succession, or a belief in a law, may on the contrary begin with a conscious belief and destroy it by making it superfluous

Habits or customs do not, as a rule, originate in repetition. Even the habit of walking, or of speaking, or of feeding at certain hours, begins before repetition can play any part whatever

but we must not say that the practices in question originated as the result of many repetitions

Belief in a law is not quite the same thing as behaviour which betrays an expectation of a law-like succession of events; but these two are sufficiently closely connected to be treated together

As Hume admits, even a single striking observation may be sufficient to create a belief or an expectation—

But it is not only that certain empirical facts do not support Hume; there are decisive arguments of a purely logical nature against his psychological

The situation was a repetition-for-them because they responded to it by anticipating its similarity to the previous one

We must thus replace, for the purposes of a psychological theory of the origin of our beliefs, the naïve idea of events which are similar by the idea of events to which we react by interpreting them as being similar. But if this is so (and I can see no escape from it) then Hume’s psychological theory of induction leads to an infinite regress, precisely analogous to that other infinite regress which was discovered by Hume himself, and used by him to explode the logical theory of induction. For what do we wish to explain?

similarity-for-us is the product of a response involving interpretations (which may be inadequate) and anticipations or expectations (which may never be fulfilled

There are two possible answers: (1) We obtain our knowledge by a non-inductive procedure. This answer would have allowed Hume to retain a form of rationalism.(2) We obtain our knowledge by repetition and induction, and therefore by a logically invalid and rationally unjustifiable procedure, so that all apparent knowledge is merely a kind of belief—belief based on habit. This answer would imply that even scientific knowledge is irrational, so that rationalism is absurd, and must be given up.(I shall not discuss here the age-old attempts, now again fashionable, to get out of the difficulty by asserting that though induction is of course logically invalid if we mean by ‘logic’ the same as ‘deductive logic’, it is not irrational by its own standards, and as inductive logic admits; as may be seen from the fact that every reasonable man applies it as a matter of fact

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

This was a theory of trial and error—of conjectures and refutations. It made it possible to understand why our attempts to force interpretations upon the world were logically prior to the observation of similarities

belief that science proceeds from observation to theory is still so widely and so firmly held that my denial of it is often met with incredulity. I have even been suspected of being insincere—of denying what nobody in his senses can doubt

Observation is always selective. It needs a chosen object, a definite task, an interest, a point of view, a problem

for the scientist by his theoretical interests, the special problem under investigation, his conjectures and anticipations, and the theories which he accepts as a kind of background: his frame of reference, his ‘horizon of expectations

Which comes first, the hypothesis (H) or the observation (O)?’ is soluble

An earlier kind of hypothesis’. It is quite true that any particular hypothesis we choose will have been preceded by observations—the observations, for example, which it is designed to explain. But these observations, in their turn, presupposed the adoption of a frame of reference: a frame of expectations: a frame of theories. If they were significant, if they created a need for explanation and thus gave rise to the invention of a hypothesis, it was because they could not be explained within the old theoretical framework, the old horizon of expectations. There is no danger here of an infinite regress. Going back to more and more primitive theories and myths we shall in the end find unconscious, inborn expectations.

The theory of inborn ideas is absurd, I think; but every organism has inborn reactions or responses; and among them, responses adapted to impending events. These responses we may describe as ‘expectations’ without implying that these ‘expectations’ are conscious

Thus we are born with expectations; with ‘knowledge’ which, although not valid a priori, is psychologically or genetically a priori, i.e. prior to all observational experience. One of the most important of these expectations is the expectation of finding a regularity. It is connected with an inborn propensity to look out for regularities, or with

This ‘instinctive’ expectation of finding regularities, which is psychologically a priori, corresponds very closely to the ‘law of causality’ which Kant

For the expectation of finding regularities is not only psychologically a priori, but also logically a priori

Our propensity to look out for regularities, and to impose laws upon nature, leads to the psychological phenomenon of dogmatic thinking or, more generally, dogmatic behaviour: we expect regularities everywhere and attempt to find them even where there are none

events which do not yield to these attempts we are inclined to treat as a kind of ‘background noise’; and we stick to our expectations even when they are inadequate and we ought to accept defeat. This dogmatism is to some extent necessary. It is demanded by a situation which can only be dealt with by forcing our conjectures upon the world.Moreover, this dogmatism allows us to approach a good theory in stages, by way of approximations: if we accept defeat too easily, we may prevent ourselves from finding that we were very nearly right

For the dogmatic attitude is clearly related to the tendency to verify our laws and schemata by seeking to apply them and to confirm them, even to the point of neglecting refutations, whereas the critical attitude is one of readiness to change them—to test them; to refute them; to falsify them, if possible. This suggests that we may identify the critical attitude with the scientific attitude, and the dogmatic attitude with the one which we have described as pseudo-scientific

For the critical attitude is not so much opposed to the dogmatic attitude as super-imposed upon it: criticism must be directed against existing and influential beliefs in need of critical revision—in other words, dogmatic beliefs. A critical attitude needs for its raw material, as it were, theories or beliefs which are held more or less dogmatically

Thus science must begin with myths, and with the criticism of myths; neither with the collection of observations, nor with the invention of experiments, but with the critical discussion of myths, and of magical techniques and practices

it passes on its theories; but it also passes on a critical attitude towards them. The theories are passed on, not as dogmas, but rather with the challenge to discuss them and improve upon them

The critical attitude, the tradition of free discussion of theories with the aim of discovering their weak spots so that they may be improved upon, is the attitude of reasonableness, of rationality. It makes farreaching use of both verbal argument and observation—of observation in the interest of argument

From the point of view here developed all laws, all theories, remain essentially tentative, or conjectural, or hypothetical, even when we feel unable to doubt them any longer. Before a theory has been refuted we can never know in what way it may have to be modified

that the method of science is criticism, i.e. attempted falsifications

No rule can ever guarantee that a generalization inferred from true observations, however often repeated, is true

may summarize some of my conclusions as follows: (1) Induction, i.e. inference based on many observations, is a myth. It is neither a psychological fact, nor a fact of ordinary life, nor one of scientific procedure.(2) The actual procedure of science is to operate with conjectures

jump to conclusions—often after one single observation (as noticed for example by Hume and Born).(3) Repeated observations and experiments function in science as tests of our conjectures or hypotheses, i.e. as attempted refutations.(4) The mistaken belief in induction is fortified by the need for a criterion of demarcation which, it is traditionally but wrongly believed, only the inductive method can provide.(5) The conception of such an inductive method, like the criterion of verifiability, implies a faulty demarcation.(6) None of this is altered in the least if we say that induction makes theories only probable rather than certain

We can see this the moment we realize that the acceptance by science of a law or of a theory is tentative only; which is to say that all laws and theories are conjectures, or tentative hypotheses (a position which I have sometimes called ‘hypotheticism’); and that we may reject a law or theory on the basis of new evidence, without necessarily discarding the old evidence which originally led us to accept it

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

. One question which may be asked is this: how do we really jump from an observation statement to a theory?

can say first that the jump is not from an observation statement, but from a problem-situation, and that the theory must allow us to explain the observations which created the problem (that is, to deduce them from the theory strengthened by other accepted theories and by other observation statements, the so-called initial conditions

by jumping first to any theory and then testing it, to find whether it is good or not; i.e. by repeatedly applying the critical method, eliminating many bad theories, and inventing many new ones. Not everybody is able to do this; but there is no other way

the method of trial and error is a method of eliminating false theories by observation statements; and the justification for this is the purely logical relationship of deducibility which allows us to assert the falsity of universal statements if we accept the truth of singular ones

we are interested in theories with a high degree of corroboration. And I explained why it is a mistake to conclude from this that we are interested in highly probable theories

Accordingly every interesting and powerful statement must have a low probability; and vice versa: a statement with a high probability will be scientifically uninteresting, because it says little and has no explanatory power. Although we seek theories with a high degree of corroboration, as scientists we do not seek highly probable theories but explanations; that is to say, powerful and improbable theories. The

2 T H E N AT U R E O F P H I L O S O P H I C A L P R O B L E M S A N D T H E I R R O O T S I N S C I E N C

futility of the current controversy concerning the nature of philosophy: the naïve belief that there is an entity such as ‘philosophy’, or perhaps ‘philosophical activity’, and that it has a certain character or essence or ‘nature

Disciplines are distinguished partly for historical reasons and reasons of administrative convenience (

are not students of some subject matter but students of problems. And problems may cut right across the borders of any subject matter or discipline.

reaffirm my conviction that a philosopher should philosophize: he should try to solve philosophical problems, rather than talk about philosophy

Philosophers were accused—rightly, I believe—of ‘philosophizing without knowledge of fact

Hegelianism

downfall was brought about by a philosopher who like Leibniz, Berkeley, and Kant before him had a sound knowledge of science, and especially of mathematics. I am speaking of Bertrand Russell

Negations of pseudo-statements are again pseudo-statements, just as negations of proper statements (true or false) are proper statements (false or true, respectively

Wittgenstein went further. Led perhaps by the feeling that what philosophers, especially Hegelian philosophers, were saying was somewhat similar to the paradoxes of logic, he used Russell’s distinction in order to denounce all philosophy as strictly meaningless.

From the point of view of modern logic there no longer appears to be any justification for speaking of pseudo-statements or type mistakes or category-mistakes within ordinary, naturally grown languages

My first thesis is that every philosophy, and especially every philosophical ‘school’, is liable to degenerate in such a way that its problems become practically indistinguishable from pseudo-problems, and its cant, accordingly, practically indistinguishable from meaningless babble.This, I shall try to show, is a consequence of philosophical inbreeding

Genuine philosophical problems are always rooted in urgent problems outside philosophy, and they die if these roots decay

My second thesis is that what appears to be the prima facie method of teaching philosophy is liable to produce a philosophy which answers Wittgenstein’s description

Only if he understands the contemporary problem-situation in the sciences can the student of the great philosophers understand that they tried to solve urgent and concrete problems; problems which they found could not be dismissed. And only after understanding this can the student attain a different picture of the great philosophies—one which makes sense of the apparent nonsense

My view of Wittgenstein’s doctrine may be summed up as follows. It is perhaps true, by and large, that ‘pure’ philosophical problems do not exist; for indeed the purer a philosophical problem becomes the more is lost of its original significance, and the more liable is its discussion to degenerate into empty verbalism. On the other hand there exist not only genuine scientific problems, but genuine philosophical problems. Even if, upon analysis, these problems turn out to have factual components, they need not be classified as belonging to science. And even if they should be soluble by, say, purely logical means they need not be classified as purely logical or tautological

Wittgenstein’s doctrine turns out to be the result of the thesis that all genuine statements (and therefore all genuine problems) can be classi- fied into one of two exclusive classes: factual statements (synthetic a posteriori), which belong to the empirical sciences, and logical statements (analytic a priori), which belong to pure formal logic or pure mathematics. This simple dichotomy, although extremely valuable for a rough survey, turns out to be for many purposes too simple

Plato’s central philosophical doctrine, the socalled Theory of Forms or Ideas, cannot be properly understood except in an extra-philosophical context

The table is interesting also because it was taken over, with very little alteration, by Plato. The earliest version of Plato’s famous theory of ‘Forms’ or ‘Ideas’ may indeed be described, somewhat roughly, as the doctrine that the ‘Good’ side of the Table of Opposites constitutes an (invisible) Universe, a Universe of Higher Reality, of the Unchanging and Determinate ‘Forms’ of all things; and that True and Certain Knowledge (episte¯me¯ = scientia = science) can be of this Unchanging and Real Universe only, while the visible world of change and flux in which we live and die, the world of generation and destruction, the world of experience, is only a kind of reflection or copy of that Real World. It is only a world of appearance of which no True and Certain Knowledge can be obtained. All that can be obtained in the place of Knowledge (episte¯me¯) are the plausible but uncertain and prejudiced opinions (doxa) of fallible mortals. 18 In his interpretation of the Table of Opposites Plato was influenced by Parmenides, the man whose

Parmenides’ theory is simple. He finds it impossible to understand change or movement rationally, and concludes that there is really no change—or that change is only

For in a sense no change occurs in Einstein’s four-dimensional blockuniverse. Everything is there just as it is, in its four-dimensional locus; change becomes a kind of ‘apparent’ change; it is ‘only’ the observer who as it were glides along his world-line and becomes successively conscious of the different loci along this world-line; that is, of his spatio-temporal surroundings …

Democritus’ theory of change was of tremendous importance for the development of physical science. It was partly accepted by Plato, who retained much of atomism, explaining change, however, not only by unchanging yet moving atoms but also by other ‘Forms’ which were subject neither to change nor to motion. But it was condemned by Aristotle who taught in its stead 25 that all change was the unfolding of the inherent potentialities of essentially unchanging substances

But perhaps the most fascinating element in Democritus’ theory is his doctrine of the quantization of space and time. I have in mind the doctrine, now extensively discussed, 32 that there is a shortest distance and a smallest time interval; that is to say, that there are distances in space and time (elements of length and time, Democritus’ amere¯s 33 in contradistinction to his atoms) such that no smaller ones are possible

The English term ‘incommensurable’ is somewhat unfortunate. What is meant is, rather, the non-existence of a ratio of natural numbers; for example, what can be proved in the case of the diagonal of the unit square is that there do not exist two natural numbers, n and m, whose ratio, n/m, is equal to the diagonal of the unit square.‘Incommensurability’ thus does not mean incomparability by geometrical methods, or by measurement, but incomparability by arithmetical methods of counting, or by natural numbers, including the characteristic Pythagorean method of comparing ratios of natural numbers and including, of course, the counting of units of length (or of ‘measures

What we find in Plato and his predecessors is the conscious construction and invention of a new approach towards the world and towards knowledge of the world. This approach transforms an originally theological idea, the idea of explaining the visible world by a postulated invisible world, 48 into the fundamental instrument of theoretical science. The idea was explicitly formulated by Anaxagoras and Democritus 49 as the principle of investigation into the nature of matter or body; visible matter was to be explained by hypotheses about invisibles, about an invisible structure which is too small to be seen. With Plato this idea is consciously accepted and generalized; the visible world of change is ultimately to be explained by an invisible world of unchanging ‘Forms’ (or substances, or essences, or ‘natures’; that is, as I shall try to show in more detail, geometrical shapes or figures

To sum up, 56a it seems probable that Plato’s theory of Forms and also his theory of matter were both restatements of the theories of his predecessors, the Pythagoreans and Democritus respectively, in the light of his realization that the irrationals demanded that geometry should come before arithmetic. By encouraging this emancipation of geometry Plato contributed to the development of Euclid’s system, the most important and influential deductive theory ever constructed

As my second example, out of a great many interesting possibilities, I choose Kant. His Critique of Pure Reason is one of the most difficult books ever written

Kant wrote in great haste, 57 and about a problem which, I shall try to show, was not only insoluble but also misconceived. Nevertheless it was not a pseudoproblem, but an inescapable problem which arose out of the contemporary situation in science.

Mankind had obtained knowledge, real, certain, indubitable, and demonstrable knowledge—divine scientia or episte¯me¯, and not merely doxa, human opinion. This sense of conviction became—through Voltaire—the origin of the Enlightenment

Thus for Kant Newton’s theory was simply true, and the belief in its truth remained unshaken for a century after Kant’s death. Kant to the end accepted what he and everybody else took for a fact, the attainment of scientia or episte¯me¯. At first

Hume had taught that there could be no such thing as certain knowledge of universal laws, or episte¯me¯; that all we knew was obtained with the help of observation which could be only of singular (or particular) instances, so that all theoretical knowledge was uncertain. His arguments were convincing (and he was, of course, right). Yet there was a fact, or what appeared as a fact—Newton’s attainment of episte¯me

According to Kant’s theory, ‘pure natural science’ is not only possible; although he does not always realize this, it becomes, contrary to his intention, the necessary result of our mental outfit. For if the fact of our attainment of episte¯me¯ can be explained at all by the fact that our intellect legislates for nature, and imposes its own laws upon it, then the first of these two facts cannot be contingent any more than the second

His question, we now know, or believe we know, should have been: ‘How are successful conjectures possible?’ And our answer, in the spirit of his Copernican Revolution, might, I suggest, be something like this: Because, as you said, we are not passive receptors of sense data, but active organisms. Because we react to our environment not always merely instinctively, but sometimes consciously and freely. Because we can invent myths, stories, theories; because we have a thirst for explanation, an insatiable curiosity, a wish to know. Because we not only invent stories and theories, but try them out and see whether they work and how they work. Because by a great effort, by trying hard and making many mistakes, we may sometimes, if we are lucky, succeed in hitting upon a story, an explanation, which ‘saves the phenomena’; perhaps by making up a myth about ‘invisibles’, such as atoms or gravitational forces

3 T H R E E V I E W S C O N C E R N I N G H U M A N K N O W L E D G E 1. THE SCIENCE OF GALILEO AND ITS MOST RECENT BETRAYAL

There was no objection to Galileo’s teaching the mathematical theory, so long as he made it clear that its value was instrumental only; that it was nothing but a ‘supposition’, as Cardinal Bellarmino put it; 2 or a ‘mathematical hypothesis’—a

He saw that a decline of religious faith and religious authority would result from the new science unless its interpretation by the ‘free-thinkers’ could be refuted; for they saw in its success a proof of the power of the human intellect, unaided by divine revelation, to uncover the secrets of our world—the reality hidden behind its appearance

The instrumentalist view asserts that theories are nothing but instruments, while the Galilean view was that they are not only instruments but also—and mainly—descriptions of the world, or of certain aspects of the world. It is clear that in this disagreement even a proof showing that theories are instruments (assuming it possible to ‘prove’ such a thing) could not seriously be claimed to support either of the two parties to the debate, since both were agreed on this point

One of the most important ingredients of our western civilization is what I may call the ‘rationalist tradition’ which we have inherited from the Greeks. It is the tradition of critical discussion—not for its own sake, but in the interests of the search for truth. Greek science, like Greek philosophy, was one of the products of this tradition, 9 and of the urge to understand the world in which we live; and the tradition founded by Galileo was its renaissance

Within this rationalist tradition science is valued, admittedly, for its practical achievements; but it is even more highly valued for its informative content, and for its ability to free our minds from old beliefs, old prejudices, and old certainties, and to offer us in their stead

new conjectures and daring hypotheses. Science is valued for its liberalizing influence—as one of the greatest of the forces that make for human freedom. According to the

) The scientist aims at finding a true theory or description of the world (and especially of its regularities or ‘laws’), which shall also be an explanation of the observable facts.(This means that a description of these facts must be deducible from the theory in conjunction with certain statements, the so-called ‘initial conditions’. ) This is a doctrine I wish to uphold. It is to form part of our ‘third view’.(2) The scientist can succeed in finally establishing the truth of such theories beyond all reasonable doubt. This second doctrine, I think, needs correction. All the scientist can do, in my opinion, is to test his theories, and to eliminate all those that do not stand up to the most severe tests he can design. But he can never be quite sure whether new tests (or even a new theoretical discussion) may not lead him to modify, or to discard, his theory. In this sense all theories are, and remain hypotheses: they are conjecture (doxa) as opposed to indubitable knowledge (episte¯me¯).(3) The best, the truly scientific theories, describe the ‘essences’ or the ‘essential natures’ of things—the realities which lie behind the appearances. Such theories are neither in need nor susceptible of further explanation: they are ultimate explanations, and to find them is the ultimate aim of the scientist. This third doctrine (in connection with the second) is the one I have called ‘essentialism’. I believe that like the second doctrine it is mistaken. Now

And I do not even intend to criticize those who try to understand the ‘essence of the world’. The essentialist doctrine I am contesting is solely the doctrine that science aims at ultimate explanation; that is to say, an explanation which (essentially, or by its very nature) cannot be further explained, and which is in no need of any further explanation

Newton’s laws of motion simply describe in mathematical language the state of affairs due to the inherent properties of matter: they describe the essential nature of matter

it prevented fruitful questions from being raised, such as, ‘What is the cause of gravity?’ or more fully, ‘Can we perhaps explain gravity by deducing Newton’s theory, or a good approximation of it, from a more general theory (which should be independently testable)?’ Now it

have prevented this question from ever being raised. These examples, I think, make it clear that the belief in essences (whether true or false) is liable to create obstacles to thought—to the posing of new and fruitful problems.Moreover, it cannot be part of science (for even if we should, by a lucky chance, hit upon a theory describing essences, we could never be sure of it). But a creed which is likely to lead to obscurantism is certainly not one of those extrascientific beliefs (such as a faith in the power of critical discussion) which a scientist need accept.

My proposed criticism of the instrumentalist view of scientific theories can be summarized as follows. Instrumentalism can be formulated as the thesis that scientific theories—the theories of the so-called ‘pure’ sciences—are nothing but computation rules (or inference rules); of the same character, fundamentally, as the computation rules of the so-called ‘applied’ sciences.(One might even formulate it as the thesis that ‘pure’ science is a misnomer, and that all science is ‘applied’. ) Now my reply to instrumentalism consists in showing that there are profound differences between ‘pure’ theories and technological computation rules, and that instrumentalism can give a perfect description of these rules but is quite unable to account for the difference between them and the theories. Thus instrumentalism collapses.

This ‘third view’ is not very startling or even surprising, I think. It preserves the Galilean doctrine that the scientist aims at a true description of the world, or of some of its aspects, and at a true explanation of observable facts; and it combines this doctrine with the non-Galilean view that though this remains the aim of the scientist, he can never know for certain whether his findings are true, although he may sometimes establish with reasonable certainty that a theory is false. 32 One may formulate this ‘third view’ of scientific theories briefly by saying that they are genuine conjectures—highly informative guesses about the world which although not verifiable (i.e. capable of being shown to be true) can be submitted to severe critical tests. They are serious attempts to discover the truth. In this respect scientific hypotheses are exactly like Goldbach’s famous conjecture in the theory of numbers. Goldbach thought that it might possibly be true; and it may well be true in fact, even though we do not know, and may perhaps never know, whether it is true or not

The doctrine of an essential or ultimate reality collapses together with that of ultimate explanation

Although in one sense of the word ‘real’, all these various levels are equally real, there is another yet closely related sense in which we might say that the higher and more conjectural levels are the more real ones—in spite of the fact that they are more conjectural. They are, according to our theories, more real (more stable in intention, more permanent) in the sense in which a table, or a tree, or a star, is more real than any of its aspects

But if a theory is testable, then it implies that events of a certain kind cannot happen; and so it asserts something about reality.(This is why we demand that the more conjectural a theory is, the higher should be its degree of testability. ) Testable conjectures or guesses, at any rate, are thus conjectures or guesses about reality; from their uncertain or conjectural character it only follows that our knowledge concerning the reality they describe is uncertain or conjectural. And although only that is certainly real which can be known with certainty, it is a mistake to think that only that is real which is known to be certainly real. We are not omniscient and, no doubt, much is real that is unknown to us all. It is thus indeed the old Berkeleian mistake (in the form ‘to be is to be known’) which still underlies instrumentalism

Thus I agree with essentialism in its view that science is capable of real discoveries, and even in its view that in discovering new worlds our intellect triumphs over our sense experience. But I do not fall into the mistake of Parmenides—of denying reality to all that is colourful, varied, individual, indeterminate, and indescribable in our world.

Since I believe that science can make real discoveries I take my stand with Galileo against instrumentalism. I admit that our discoveries are conjectural. But this is even true of geographical explorations.Columbus’ conjectures as to what he had discovered were in fact mistaken; and Peary could only conjecture—on the basis of theories— that he had reached the Pole. But these elements of conjecture do not make their discoveries less real, or less significant

. I have in mind the distinction between the prediction of events of a kind which is known, such as eclipses or thunderstorms on the one

hand and, on the other hand, the prediction of new kinds of events (which the physicist calls ‘new effects’) such as the prediction which led to the discovery of wireless waves, or of zero-point energy, or to the artificial building up of new elements not previously found in nature. It seems to me clear that instrumentalism can account

our discoveries are guided by theory, in these as in most other cases, rather than that theories are the result of discoveries ‘due to observation’; for observation itself tends to be guided by theory.

The ‘third view’ of this matter is different. I hold that most observations are more or less indirect, and that it is doubtful whether the distinction between directly observable incidents and whatever is only indirectly observable leads us anywhere

do not think that a language without universals could ever work; and the use of universals commits us to asserting, and thus (at least) to conjecturing, the reality of dispositions—though not of ultimate and inexplicable ones, that is, of essences. We may express all this by saying that the customary distinction between ‘observational terms’ (or

160 c o n j e c t u r e s a n d r e f u t a t i o n s‘non-theoretical terms’) and theoretical terms is mistaken, since all terms are theoretical to some degree, though some are more theoretical than others; just as we said that all theories are conjectural, though some are more conjectural than others

Having studied for some time the methods of the natural sciences, I felt that it might be interesting to study also the methods of the social sciences. It was then that I first met with the problem of tradition

You have to take it; you cannot rationalize it; it plays an important role in society, and you can only understand its significance and accept it. The most important name associated with this anti-rationalist view is that of Edmund Burke

Certain types of tradition of great importance are local, and cannot easily be transplanted. These traditions are precious things, and it is very difficult to restore them once they are lost. I have in mind the scientific tradition, in which I am particularly interested. I have seen that it is very difficult to transplant it from the few places where it has really taken root. Two

One is to accept a tradition uncritically, often without even being aware of it. In many cases we cannot escape this; for we often just do not realize that we are faced with a tradition. If I wear my watch on my left wrist, I need not be conscious that I am accepting a tradition. Every day we do hundreds of things under the influence of traditions of which we are unaware. But if we do not know that we are acting under the influence of a tradition, then we cannot help accepting the tradition uncritically. The other possibility is a critical attitude, which may result either in acceptance or in rejection, or perhaps in a compromise. Yet we have to know of and to understand a tradition before we can criticize it, before we can say: ‘We reject this tradition on rational grounds. ’ Now I do not think that we could ever free ourselves entirely from the bonds of tradition. The so-called freeing is really only a change from one tradition to another. But we can free ourselves from the taboos of a tradition; and we can do that not only by rejecting it, but also by critically accepting it. We free ourselves from the taboo if we think about it, and if we ask ourselves whether we should accept it or reject it. In order to do that we have first to have the tradition clearly before us, and we have to understand in a general way what may be the function and significance of a tradition. That is why it is so important for rationalists to deal with this problem, for rationalists are those people who are ready to challenge and to criticize everything, including, I hope, their own tradition. They are ready to put question-marks to anything, at least in their minds. They will not submit blindly to any tradition

Another element in the rationalist tradition which we should question is the idea of observationalism—the idea that we know about the world because we look around, open our eyes and ears, and take down what we see, hear, and so on; and that this is what constitutes the material of our knowledge. This is an extremely deep-rooted prejudice and is, I think, an idea which impedes the understanding of scientific method. I shall return to this point later. So much by way of introduction

striking things about social life that nothing ever comes off exactly as intended. Things always turn out a little bit differently. We hardly ever produce in social life precisely the effect that we wish to produce, and we usually get things that we do not want into the bargain

we act with certain aims in mind; but apart from these aims (which we may or may not really achieve) there are always certain unwanted consequences of our actions; and usually these unwanted consequences cannot be eliminated. To explain why they cannot be eliminated is the major task of social theory

The characteristic problems of the social sciences arise only out of our wish to know the unintended consequences, and more especially the unwanted consequences which may arise if we do certain things. We wish to foresee not only the direct consequences but also these unwanted indirect consequences

I think that the people who approach the social sciences with a ready-made conspiracy theory thereby deny themselves the possibility of ever understanding what the task of the social sciences is, for they assume that we can explain practically everything in society by asking who wanted it, whereas the real task of the social sciences 3 is to explain those things which nobody wants—such

And it is, especially, the task of the social sciences to analyse in this way the existence and the functioning of institutions (such as police forces or insurance companies or schools or governments) and of social collectives (such as states or nations or classes or other social groups). The conspiracy theorist will believe that institutions can be understood completely as the result of conscious design; and as to collectives, he usually ascribes to them a kind of group-personality,

early Greek philosophers did indeed try to understand what happened in nature. But so did the more primitive myth-makers before them. How can we characterize that primitive type of explanation which was superseded by the standards of the early Greek philosophers—the founders of our scientific tradition

I think that the innovation which the early Greek philosophers introduced was roughly this: they began to discuss these matters. Instead of accepting the religious tradition uncritically, and as unalterable

instead of merely handing on a tradition, they challenged it, and sometimes even invented a new myth in place of the old one. We have, I think, to admit that the new stories which they put in the place of the old were, fundamentally, myths—just as the old stories were; but there are two things about them to be noticed

they were not just repetitions or re-arrangements of the old stories, but contained new elements

Greek philosophers invented a new tradition—the tradition of adopting a critical attitude towards the myths, the tradition of discussing them; the tradition of not only telling a myth, but also of being challenged by the man to whom it is told

My thesis is that what we call ‘science’ is differentiated from the older myths not by being something distinct from a myth, but by being accompanied by a second-order tradition—that of critically discussing the myth

shall understand that, in a certain sense, science is myth-making just as religion is. You will say: ‘But the scientific myths are so very different from the religious myths. ’ Certainly they are different. But why are they different? Because if one adopts this critical attitude then one’s myths do become different. They change; and they change in the direction of giving a better and better account of the world—of the various things which we can observe. And they also challenge us to observe things which we would never have observed without these theories or myths

In the critical discussions which now arose, there also arose, for the first time, something like systematic observation

From this point of view the growth of the theories of science should not be considered as the result of the collection, or accumulation, of observations; on the contrary, the observations and their accumulation should be considered as the result of the growth of the scientific theories.(This is what I have called the ‘searchlight theory of science’—the view that science itself throws new light on things; that it not only solves problems, but that, in doing so, it creates many more; and that it not only profits from observations, but leads to new ones. ) If in this way we look out for new observations with the intention of probing into the truth of our myths, we need not be astonished if we find that myths handled in this rough manner change their character, and that in time they become what one might call more realistic or that they agree better with observable facts. In other words, under the pressure of criticism the myths are forced to adapt themselves to the task of giving us an adequate and a more detailed picture of the world in which we live

Scientific theories are not just the results of observation. They are, in the main, the products of mythmaking and of tests. Tests proceed partly by way of observation, and observation is thus very important; but its function is not that of producing theories. It plays its role in rejecting, eliminating, and criticizing theories; and it challenges us to produce new myths, new theories which may stand up to these observational tests. Only if we understand this can we understand the importance of tradition for science

But you may get something of scientific interest if you say: ‘Here are the theories which some scientists hold today. These theories demand that such and such things should be observable under such and such conditions. Let us see whether they are observable. ’ In other words, if you select your observations with an eye on scientific problems and the general situation of science as it appears at the moment, then you may well be able to make a contribution to science

These are the questions which you should take up. ’ In other words, you should study the problem situation of the day

that we cannot start afresh; that we must make use of what people before us have done in science. If we start afresh, then, when we die, we shall be about as far as Adam and Eve were when they died (or, if you prefer, as far as Neanderthal man). In science we want to make progress, and this means that we must stand on the shoulders of our predecessors. We must carry on a certain tradition. From the point of view of what we want as scientists—understanding, prediction, analysis, and so on—the world in which we live is extremely complex

is necessary for us to see that of the two main ways in which we may explain the growth of science, one is rather unimportant and the other is important. The first explains science by the accumulation of knowledge: it is like a growing library (or a museum). As more and more books accumulate, so more and more knowledge accumulates. The other explains it by criticism: it grows by a method more revolutionary than accumulation—by a method which destroys, changes

It is interesting to see that the first method, the accumulation method, is much less important than people believe. There is much less accumulation of knowledge in science than there is revolutionary changing of scientific theories. It is a strange point, and a very interesting point, because one might at first sight believe that for the accumulative growth of knowledge tradition would be very important, and that for the revolutionary kind of development tradition would be less important. But it is exactly the other way round. If science could grow by mere accumulation, it would not matter so much if the scientific tradition were lost, because any day you could start accumulating afresh.

It is here that the part played by tradition in our lives becomes understandable. We should be anxious, terrified, and frustrated, and we could not live in the social world, did it not contain a considerable amount of order, a great number of regularities to which we can adjust ourselves. The mere existence of these regularities is perhaps more important than their peculiar merits or demerits. They are needed as regularities, and therefore handed on as traditions, whether or not they are in other respects rational or necessary or good or beautiful or what you will. There is a need for tradition in social life

Similarly traditions have the important double function of not only creating a certain order or something like a social structure, but also giving us something upon which we can operate; something that we can criticize and change. This point is decisive for us, as rationalists and as social reformers. We always have new ideas for a better social world, and these new ideas have a significant function. But too many social reformers have an idea that they would like to clean the canvas, as Plato called it, of the social world, wiping off everything and starting from scratch with a brand-new rational world. This idea is nonsense and impossible to realize

away. You may create a new theory, but the new theory is created in order to solve those problems which the old theory did not solve- Your Note on page 177 | Added on Saturday, 17 August 2019 18:25:20

bravs new world. seeing like a state

tradition in social life. What we found may now help us to answer the question

We can now understand why people (especially primitive peoples and children) are inclined to cling to anything that may be or become a uniformity in their lives. They cling to myths; and they tend to cling to uniformities in their own behaviour, first, because they are afraid of irregularity and change and therefore afraid to originate irregularity and change; and secondly, because they wish to reassure others of their rationality or predictability, perhaps in the hope of making them act in a similar way. Thus they tend both to create traditions and to reaffirm those they find, by carefully conforming to them and by anxiously insisting that others conform to them also. This is how traditional taboos arise and how they are handed on

all social criticism, and all social betterment, must refer to a framework of social traditions, of which some are criticized with the help of others, just as all progress in science must proceed within a framework of scientific theories, some of which are criticized in the light of others

Thus traditions are perhaps more closely bound up with persons and their likes and dislikes, their hopes and fears, than are institutions. They take, as it were, an intermediate place, in social theory, between persons and institutions.(We speak more naturally of a ‘living tradition’ than of a ‘living institution’

The ambivalence of social institutions is connected with their character—with the fact that they perform certain prima facie functions and with the fact that institutions can be controlled only by persons (who are fallible) or by other institutions (which are therefore fallible also). The ambivalence can undoubtedly be much reduced by carefully constructed institutional checks, but it is impossible to eliminate it completely. The working of institutions, as of fortresses, depends ultimately upon the persons who man them; and the best that can be done by way of institutional control is to give a superior chance to those persons (if there are any) who intend to use the institutions for their ‘proper’ social purpose

From the point of view of the most typical usages of the two terms, it may be said that one of the connotations of the term ‘tradition’ is an allusion to imitation, as being either the origin of the tradition in question, or the way it is handed on. This connotation is, I think, absent from the term ‘institution’: an institution may or may not have its origin in imitation, and it may, or may not, continue its existence through imitation

Even more precious perhaps is the tradition that works against the ambivalence connected with the argumentative function of language, the tradition that works against that misuse of language which consists in pseudo-arguments and propaganda. This is the tradition and discipline of clear speaking and clear thinking; it is the critical tradition—the tradition of reason. The modern enemies of reason want to destroy this tradition. They want to do this by destroying and perverting the argumentative and

perhaps even the descriptive functions of the human language; by a romantic reversion to its emotive functions—the expressive (there is too much talk about ‘self-expression’) and, perhaps, the signalling or stimulative function

rationality of the Presocratics. Wherein does this much discussed ‘rationality’ of the Presocratics lie? The simplicity and boldness of their questions is part of it, but my thesis is that the decisive point is the critical attitude which, as I shall try to show, was first developed in the Ionian School

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

Traditional empiricist epistemology and the traditional historiography of science are both deeply influenced by the Baconian myth that all science starts from observation and then slowly and cautiously proceeds to theories

We must not forget that the function of the Baconian myth is to explain why scientific statements are true, by pointing out that observation is the ‘true source’ of our scientific knowledge. Once we realize that all scientific statements are hypotheses, or guesses, or conjectures, and that the vast majority of these conjectures (including Bacon’s own) have turned out to be false, the Baconian myth becomes irrelevant. For it is pointless to argue that the conjectures of science—those which have proved to be false as well as those which are still accepted—all start from observation

In my opinion this idea of Anaximander’s is one of the boldest, most revolutionary, and most portentous ideas in the whole history of human thought. It made possible the theories of Aristarchus and of Copernicus. But the step taken by Anaximander was even more difficult and audacious than the one taken by Aristarchus and Copernicus. To envisage the earth as freely poised in mid-space, and to say ‘that it remains motionless because of its equidistance or equilibrium’ (as Aristotle paraphrases Anaximander), is to anticipate to some extent even Newton’s idea of immaterial and invisible gravitational forces

What prevented Anaximander from arriving at the theory that the earth was a globe rather than a drum? There can be little doubt: it was observational experience which taught him that the surface of the earth was, by and large, flat. Thus it was a speculative and critical argument, the abstract critical discussion of Thales’ theory, which almost led him to the true theory of the shape of the earth; and it was observational experience which led him astray

There can be no doubt whatever that Anaximander’s theories are critical and speculative rather than empirical: and considered as approaches to truth his critical and abstract speculations served him better than observational experience or analogy.But, a follower of Bacon may reply, this is precisely why Anaximander was not a scientist. This is precisely why we speak of early Greek philosophy rather than of early Greek science. Philosophy is speculative: everybody knows this. And as everybody knows, science begins only when the speculative method is replaced by the observational method, and when deduction is replaced by induction. This reply, of course, amounts to the thesis that, by definition, theories are (or are not) scientific according to their origin in observations, or in so-called ‘inductive procedures’. Yet I believe that few, if any, physical theories would fall under this definition. And I do not see why the question of origin should be important in this connection. What is important about a theory is its explanatory power, and whether it stands up to criticism and to tests. The question of its origin, of how it is arrived at—whether by an ‘inductive procedure’, as some say, or by an act of intuition—may be extremely interesting, especially for the biographer of the man who invented the theory, but it has little to do with its scientific status or character

false theory may be as great an achievement as a true one. And many false theories have been more helpful in our search for truth than some less interesting theories which are still accepted. For false theories can be helpful in many ways; they may for example suggest some more or less radical modifications, and they may stimulate criticism

We have here the first hint of what was soon to come: of the general problem of change, which became the central problem of Greek cosmology, and which ultimately led, with Leucippus and Democritus, to a general theory of change that was accepted by modern science almost up to the beginning of the twentieth century.(It was given up only with the breakdown of Maxwell’s models of the ether, an historic event that was little noticed before 1905. ) This general problem of change is a philosophical problem; indeed in the hands of Parmenides and Zeno it almost turns into a logical one. How is change possible—logically possible, that is? How can a thing change, without losing its identity? If it remains the same, it does not change; yet if it loses its identity, then it is no longer that thing which has changed.

For all change is the change of something: change presupposes something that changes. And it presupposes that, while changing

something must remain the same. We may say that a green leaf changes when it turns brown; but we do not say that the green leaf changes when we substitute for it a brown leaf. It is essential to the idea of change that the thing which changes retains its identity while changing. And yet it must become something else: it was green, and it becomes brown; it was moist, and it becomes dry; it was hot, and it becomes cold. Thus every

theory that dominated scientific thought until 1900. It is the theory that all change, and especially all qualitative change, has to be explained by the spatial movement of unchanging bits of matter—by atoms moving in the void. The next great step in our cosmology and the theory of change was made when Maxwell, developing certain ideas of Faraday’s, replaced this theory by a theory of changing intensities of fields

What was the secret of the ancients? I suggest that it was a tradition—the tradition of critical discussion

Now schools, especially primitive schools, all have, it appears, a characteristic structure and function. Far from being places of critical discussion they make it their task to impart a definite doctrine, and to preserve it, pure and unchanged

Thus not even the inventor admits that he has introduced an invention; he believes, rather, that he is returning to the true orthodoxy which has somehow been perverted. In this way all changes of doctrine—if any—are surreptitious changes. They are all presented as re-statements of the true sayings of the master, of his own words, his own meaning, his own intentions

There cannot, of course, be any rational discussion in a school of this kind. There may be arguments against dissenters and heretics, or against some competing schools. But in the main it is with assertion and dogma and condemnation rather than argument that the doctrine is defended. The great example of a school of this kind among the Greek philosophical schools is the Italian School founded by Pythagoras. Compared with the Ionian school, or with that of Elea, it had the character of a religious order, with a characteristic way of life and a secret doctrine

It is a tradition that allows or encourages critical discussions between various schools and, more surprisingly still, within one and the same school

How and where was this critical tradition founded? This is a problem deserving serious thought. This much is certain: Xenophanes who brought the Ionian tradition to Elea was fully conscious of the fact that his own teaching was purely conjectural, and that others might come who would know better. I shall come back to this point again in my next and last section. If we look for the first signs of this new critical attitude, this new freedom of thought, we are led back to Anaximander’s criticism of Thales. Here is a most striking fact: Anaximander criticizes his master and kinsman, one of the Seven Sages, the founder of the Ionian school

Yet I like to think that he did even more than this. I can hardly imagine a relationship between master and pupil in which the master merely tolerates criticism without actively encouraging

It was a momentous innovation. It meant a break with the dogmatic tradition which permits only one school doctrine, and the introduction in its place of a tradition that admits a plurality of doctrines which all try to approach the truth by means of critical discussion

thus leads, almost by necessity, to the realization that our attempts to see and to find the truth are not final, but open to improvement; that our knowledge, our doctrine, is conjectural; that it consists of guesses, of hypotheses, rather than of final and certain truths; and that criticism and critical discussion are our only means of getting nearer to the truth. It thus leads to the tradition of bold conjectures and of free criticism, the tradition which created the rational or scientific attitude, and with it our Western civilization, the only civilization which is based upon science (though of course not upon science alone

The rationalist tradition, the tradition of critical discussion, represents the only practicable way of expanding our knowledge—conjectural or hypothetical knowledge, of course. There is no other way. More especially, there is no way that starts from observation or experiment. In the development of science observations and experiments play only the role of critical arguments. And they play this role alongside other, nonobservational arguments. It is an important role; but the significance of observations and experiments depends entirely upon the question whether or not they may be used to criticize theories

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

the theory that knowledge proceeds by way of conjectures and refutations.

Two of the greatest men who clearly saw that there was no such thing as an inductive procedure, and who clearly understood what I regard as the true theory of knowledge, were Galileo and Einstein. Yet the ancients also knew it. Incredible as it sounds, we find a clear recognition and formulation of this theory of rational knowledge almost immediately after the practice of critical discussion had begun. Perhaps our oldest extant fragments in this field are those of Xenophanes. I will

My last quotation is a very famous one from Democritus ( ,  117): But in fact, nothing do we know from having seen it; for the truth is hidden in the deep. This is how the critical attitude of the Presocratics foreshadowed, and prepared for, the ethical rationalism of Socrates: his belief that the search for truth through critical discussion was a way of life—the best he knew

A N O T E O N B E R K E L E Y A S P R E C U R S O R O F M A C H A N D E I N S T E I N

A N T ’S C R I T I Q U E A N D C O S M O L O G Y

Kant believed in the Enlightenment. He was its last great defender. I

Enlightenment is the emancipation of man from a state of selfimposed tutelage … of incapacity to use his own intelligence without external guidance. Such a state of tutelage I call ‘self-imposed’ if it is due, not to lack of intelligence, but to lack of courage or determination to use one’s own intelligence without the help of a leader. Sapere aude! Dare to use your own intelligence! This is the battle-cry of the Enlightenment.

KANT’S NEWTONIAN COSMOLOGY

Kant tells us 11 that he came upon the central problem of his Critique when considering whether the universe had a beginning in time or not. He found to his dismay that he could produce seemingly valid proofs for both of these possibilities

But space and time themselves are neither things nor events: they cannot even be observed: they are more elusive. They are a kind of framework for things and events: something like a system of pigeon-holes, or a filing system, for observations. Space and time are not part of the real empirical world of things and events, but rather part of our mental outfit, our apparatus for grasping this world. Their proper use is as instruments of observation: in observing any event we locate it, as a rule, immediately and intuitively in an order of space and time

Kant always insisted 15 that the physical things in space and time are real

Euclid’s geometry is not based upon observation, he said, but upon our intuition of spatial relations. Newtonian science is in a similar position. Although confirmed by observations it is the result not of these observations but of our own ways of thinking, of our attempts to order our sense-data, to understand them, and to digest them intellectually

Euclid’s geometry is not based upon observation, he said, but upon our intuition of spatial relations. Newtonian science is in a similar position. Although confirmed by observations it is the result not of these observations but of our own ways of thinking, of our attempts to order our sense-data, to understand them, and to digest them intellectually. It is not these sense-data but our own intellect, the organization of the digestive system of our mind, which is responsible for our theories. Nature as we know it, with its order and with its laws, is thus largely a product of the assimilating and ordering activities of our mind. In Kant’s own striking formulation of this view, 18 ‘Our intellect does not draw its laws from nature, but imposes its laws upon nature

We must give up the view that we are passive observers, waiting for nature to impress its regularity upon us. Instead we must adopt the view that in digesting our sense-data we actively impress the order and the laws of our intellect upon them. Our cosmos bears the imprint of our minds

Kant all the way can accept his view that the experimenter must not wait till it pleases nature to reveal her secrets, but that he must question her. 20 He must cross-examine nature in the light of his doubts, his conjectures, his theories, his ideas, and his inspirations.Here, I believe, is a wonderful philosophical find. It makes it possible to look upon science, whether theoretical or experimental, as a human creation, and to look upon its history as part of the history of ideas, on a level with the history of art or of literature

Kant’s Copernican Revolution solves a human problem to which Copernicus’ own revolution gave rise. Copernicus deprived man of his central position in the physical universe. Kant’s Copernican Revolution takes the sting out of this

fundamental idea of Kant’s ethics amounts to another Copernican Revolution, analogous in every respect to the one I have described. For Kant makes man the lawgiver of morality just as he makes him the lawgiver of nature. And in doing so he gives back to man his central place both in his moral and in his physical universe. Kant humanized ethics, as he had humanized science. Kant’s

For whenever we are faced with a command by an authority, it is our responsibility to judge whether this command is moral or immoral. The authority may have power to enforce its commands, and we may be powerless to resist. But unless we are physically prevented from choosing the responsibility remains ours. It is our decision whether to obey a command, whether to accept authority

Always regard every man as an end in himself, and never use him merely as a means to your ends. ’ The spirit of Kant’s ethics may well be summed up in these words: dare to be free; and respect the freedom of others

Stepping back further to get a still more distant view of Kant’s historical role, we may compare him with Socrates. Both were accused of perverting the state religion, and of corrupting the minds of the young. Both denied the charge; and both stood up for freedom of thought. Freedom meant more to them than absence of constraint; it was for both a way of life

8 O N T H E S TAT U S O F S C I E N C E A N D O F M E TA P H Y S I C

experience’ in the sense in which we use it when we say that science is based on experience

One of the things a philosopher may do, and one of those that may rank among his highest achievements, is to see a riddle, a problem, or a paradox, not previously seen by anyone else. This is an even greater achievement than resolving the riddle

first sees and understands a new problem disturbs our laziness and complacency. He does to us what Hume did for Kant: he rouses us from our ‘dogmatic slumber’. He opens out a new horizon before us.

When Kant talked of ‘natural science’ he almost invariably had Isaac Newton’s celestial mechanics in mind

It was one of Kant’s greatest achievements that, roused by Hume, he recognized that this contention was paradoxical. Kant saw more clearly than anyone before or since how absurd it was to assume that Newton’s theory could be derived from observations. Since this important insight of Kant’s is falling into oblivion, partly because of his own contributions towards a solution of the problem he had discovered, I will now present and discuss it in detail.

The assertion that Newton’s theory was derived from observation will be criticized here on three counts: First, the assertion is intuitively not credible, especially when we compare the character of the theory with the character of observationstatements.Secondly, the assertion is historically false.Thirdly, the assertion is logically false: it is a logically impossible assertion

The theory, on the other hand, claims to apply in all possible circumstances—not only to the planets Mars or Jupiter, or even to the satellites in the solar system, but to all planetary motion and to all solar systems.Indeed, its claims go far beyond all this. For example the theory makes assertions about gravitational pressure inside the stars, assertions which even today have never been tested by observation.Moreover, observations are always concrete, while theory is abstract.

Kant realized much of this; and he also appreciated the fact that even physical experiments are not, genetically, prior to theories—no more than are astronomical observations. They too simply represent crucial questions which man poses to nature with the help of theories—just as Kepler asked nature whether his circle hypothesis was true

that we must compel Nature to answer our questions, rather than cling to Nature’s apron strings and allow her to guide us. For purely accidental observations, made without any plan having been thought out in advance, cannot be connected by a law—which is what reason

Kant saw with perfect clarity that the history of science had refuted the Baconian myth that we must begin with observations in order to derive our theories from them. And Kant also realized very clearly that behind this historical fact lay a logical fact; that there were logical reasons why this kind of thing did not occur in the history of science: that it was logically impossible to derive theories from observations

Let us now add to Hume’s simple finding a theorem of pure logic, namely: whenever a statement B can be conjoined without contradiction to a class of statements K, then it can also be conjoined without contradiction to any class of statements that consists of statements of K together with any statement that can be derived from K. And so we have proved our point: if Newton’s theory could be derived from a class K of true observation-statements, then no future observation B could possibly contradict Newton’s theory and the observations K. Yet it is known, on the other hand, that from Newton’s theory and past observations we can logically derive a statement that tells us whether or not there will be an eclipse of the sun tomorrow. Now if this derived statement tells us that tomorrow there will be no eclipse of the sun, then our B is clearly incompatible with Newton’s theory and the class K. From this and our previous results it follows logically that it is impossible to assume that Newton’s theory can be derived from observations

Newton’s dynamics goes essentially beyond all observations. It is universal, exact and abstract; it arose historically out of myths; and we can show by purely logical means that it is not derivable from observation-statements.

also showed that what holds for Newtonian theory must hold for everyday experience, though not, perhaps, to quite the same extent: that everyday experience, too, goes far beyond all observation. Everyday experience too must interpret observation; for without theoretical

interpretation, observation remains blind—uninformative. Everyday experience constantly operates with abstract ideas, such as that of cause and effect, and so it cannot be derived from observations.

grateful to him for having freed physics of the paralysing belief in the incontestable truth of Newton’s theory. Thanks to Einstein we now look upon this theory as a hypothesis (or a system of hypotheses)— perhaps the most magnificent and the most important hypothesis in the history of science, and certainly an astonishing approximation to the truth

While I regard this formulation of Kant’s as essentially correct, I feel that it is a little too radical, and I should therefore like to put it in the following modified form: ‘Our intellect does not draw its laws from nature, but tries—with varying degrees of success—to impose upon nature laws which it freely invents

we know since Einstein that very different theories and very different interpretations are also possible, and that they may even be superior to Newton’s. Thus reason is capable of more than one interpretation

Reason works by trial and error. We invent our myths and our theories and we try them out: we try to see how far they take us. And we improve our theories if we can. The better theory is the one that

has the greater explanatory power: that explains more; that explains with greater precision; and that allows us to make better predictions

But we no longer try to force our creations upon nature. On the contrary, we question nature, as Kant taught us to do; and we try to elicit from her negative answers concerning the truth of our theories: we do not try to prove or to verify them, but we test them by trying to disprove or to falsify them, to refute them. In this way the freedom and boldness of our theoretical creations can be controlled and tempered by self-criticism, and by the severest tests we can design. It is here, through our critical methods of testing, that scientific rigour and logic enter into empirical science

The possibility of refuting theories by observations is the basis of all empirical tests. For the test of a theory is, like every rigorous examination, always an attempt to show that the candidate is mistaken—that is, that the theory entails a false assertion. From a logical point of view, all empirical tests are therefore attempted refutations.

We may also compare, say, two theories in order to see which of them has stood up better to our severest tests—or in other words, which of them is better corroborated by the results of our tests. But it can be shown by purely mathematical means that degree of corroboration can never be equated with mathematical probability. It can even be shown that all theories, including the best, have the same probability, namely zero

THE PROBLEM OF THE IRREFUTABILITY OF PHILOSOPHICAL THEORIES

First, determinism: the future is contained in the present, inasmuch as it is fully determined by the present.Second, idealism: the world is my dream.Third, irrationalism: we have irrational or supra-rational experiences in which we experience ourselves as things-in-themselves; and so we have some kind of knowledge of things-in-themselves.Fourth, voluntarism: in our own volitions we know ourselves as wills. The thing-in-itself is the will.Fifth, nihilism: in our boredom we know ourselves as nothings. The thing-in-itself is Nothingness. So much for our list. I have chosen my examples in such a way that I can say of any one of these five theories, after careful consideration, that I am convinced that it is false. To put it more precisely; I am first of all an indeterminist, secondly a realist, thirdly a rationalist. As regards my fourth and fifth examples, I gladly admit—with Kant and other critical rationalists—that we cannot possess anything like full knowledge of the real world with its infinite richness and beauty. Neither physics nor any other science can help us to this end. Yet I am sure the voluntarist formula, ‘The world is will’, cannot help us either. And as to our nihilists and existentialists who bore themselves (and perhaps others), I can only pity them. They must be blind and deaf, poor things, for they speak of the world like a blind man of Perugino’s colours or a deaf man of Mozart’s music.

Although I consider each one of these five theories to be false, I am nevertheless convinced that each of them is irrefutable

considering that there may be two incompatible theories which are equally irrefutable—for example, determinism and its opposite, indeterminism. Now since two incompatible theories cannot both be true, we see from the fact that both theories are irrefutable that irrefutability cannot entail truth

9 W H Y A R E T H E C A L C U L I O F L O G I C A N D A R I T H M E T I C A P P L I C A B L E T O R E A L I T Y

that of the applicability of the rules of inference (in section ii), and that of the applicability of the logical calculi

a man knows how to argue without always being aware of the rules of procedure, then we usually say that he argues or reasons ‘intuitively

There is little doubt that most of us reason, as a rule, intuitively, in the sense indicated.

While every reasonably intelligent man knows how to argue— provided the arguments do not become too complicated—there are few who can formulate the rules which underlie these performances and which we may call ‘rules of inference’; there are few who know that (and fewer perhaps who know why) a certain rule of inference is valid

led to confusion between rules of inference and the corresponding conditional formulae. But there are important differences.(1) Rules of inference are always statements about statements, or about classes of statements (they are ‘meta-linguistic’); but the formulae of the calculi are not.(2) The rules of inference are unconditional statements about deducibility; but the corresponding formulae of the calculi are conditional or hypothetical ‘If … then … ’ statements, which do not mention deducibility or inference, or premises or conclusions.(3) A rule of inference, after substitution of constants for the variables, asserts something about a certain argument—an ‘observance’ of the rule—namely, that this argument is valid; but the corresponding formula, after substitution, yields a logical truism, i.e. a statement such as ‘All tables are tables’, although in hypothetical form, as for example, ‘If it is a table, then it is a table’ or ‘If all men are mortal, and all Greeks are men, then all Greeks are mortal’.(4) The rules of inference are never used as premises in those arguments which are formulated in accordance with them; but the corresponding formulae are used in this way. In fact, one of the main motives in constructing logical calculi is this: by using the ‘logician’s hypotheticals’ (i.e. those hypothetical truisms which correspond to a certain rule of inference) as a premise, we can dispense with the corresponding rule of inference. By this method we can eliminate all the different rules of inference—except one, the above-mentioned ‘principle of inference

Professor Ryle’s central thesis, if I understand him rightly, is this. The rules of logic, or more precisely, the rules of inference, are rules of procedure. This means that they apply to certain procedures, rather than to things or facts. They

Why are rules of inference applicable to reality?

Logical rules, rather, apply to the procedure of drawing inferences, comparable to the way in which the rules of the highway code apply to the procedure of riding a bicycle or driving a car

The man who finds observance of the rules of logic useful is, we have seen, a man who draws inferences. That is to say, he obtains from some statements or descriptions of facts, called ‘premises’, other statements or descriptions of facts, called ‘conclusions’. And he finds the procedure useful because he finds that, whenever he observes the rules of logic, whether consciously or intuitively, the conclusion will be true, provided the premises were true. In other words, he will be able to obtain reliable (and possibly valuable) indirect information, provided his original information was reliable and valuable

Accordingly we may lay it down that a logician’s rule of inference is, by definition, a good or ‘valid’ rule of inference if, and only if, its observance ensures that we obtain true conclusions, provided our premises are true. And if we succeed in finding an observance of a suggested rule which allows us to obtain a false conclusion from true premises—I call this a ‘counter example’—then we are satisfied that this rule was invalid. In other words, we call a rule of inference ‘valid’ if, and only if, no counter example to this rule exists; and we may be able to establish that none exists.Similarly, we call an observance of a rule of inference—that is to say an inference—‘valid’, if, and only if, no counter example exists to the observed

10 T R U T H , R AT I O N A L I T Y, A N D T H E G R O W T H O F S C I E N T I F I C K N O W L E D G E

THE GROWTH OF KNOWLEDGE: THEORIES AND PROBLEMS I My aim in this lecture is to stress the significance of one particular aspect of science—its need to grow, or, if you like, its need to progress

You will have noticed from this formulation that it is not the accumulation of observations which I have in mind when I speak of the growth of scientific knowledge, but the repeated overthrow of scientific theories and their replacement by better or more satisfactory ones.

The new problems I wish to discuss are mainly those connected with the notions of objective truth, and of getting nearer to the truth—notions that seem to me of great help in analysing the growth of knowledge

The new problems I wish to discuss are mainly those connected with the notions of objective truth, and of getting nearer to the truth—notions that seem to me of great help in analysing the growth of knowledge. Although I shall confine my discussion to the growth of knowledge in science, my remarks are applicable without much change, I believe, to the growth of pre-scientific knowledge also—that is to say, to the general way in which men, and even animals, acquire new factual knowledge about the world. The method of learning by trial and error—of learning from our mistakes—seems to be fundamentally the same whether it is practised by lower or by higher animals, by chimpanzees or by men of science

In particular, is there any danger that the advance of science will come to an end because science has completed its task? I hardly think so, thanks to the infinity of our ignorance. Among the real dangers to the progress of science is not the likelihood of its being completed, but such things as lack of imagination (sometimes a consequence of lack of real interest); or a misplaced faith in formalization and precision (which will be discussed below in section v); or authoritarianism in one or another of its many forms

I hold that even science is not subject to the operation of anything resembling such a law. The history of science, like the history of all human ideas, is a history of irresponsible dreams, of obstinacy, and of error. But science is one of the very few human activities—perhaps the only one—in which errors are systematically criticized and fairly often, in time, corrected

Within the field of science we have, however, a criterion of progress: even before a theory has ever undergone an empirical test we may be able to say whether, provided it passes certain specified tests, it would be an improvement on other theories with which we are acquainted. This is my first thesis. To put it a little differently, I assert that we know what a good

scientific theory should be like, and—even before it has been tested— what kind of theory would be better still, provided it passes certain crucial tests. And it is this (meta-scientific) knowledge which makes it possible to speak of progress in science, and of a rational choice between theories

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

characterizes as preferable the theory which tells us more; that is to say, the theory which contains the greater amount of empirical information or content; which is logically stronger; which has the greater explanatory and predictive power; and which can therefore be more severely tested by comparing predicted facts with observations. In short, we prefer an interesting, daring, and highly informative theory to a trivial one

we desire in a theory can be shown to amount to one and the same thing: to a higher degree of empirical content or of testability

My study of the content of a theory (or of any statement whatsoever) was based on the simple and obvious idea that the informative content of the conjunction, ab, of any two statements, a and b, will always be greater than, or at least equal to, that of any of its components

Writing Ct(a) for ‘the content of the statement a’, and Ct(ab) for ‘the content of the conjunction a and b’, we have (1) Ct(a)
Ct(ab)  Ct(b). This contrasts with the corresponding law of the calculus of probability, (2) p(a)  p(ab)
p(b), where the inequality signs of (1) are inverted. Together these two laws, (1) and (2), state that with increasing content, probability decreases, and vice versa; or in other words, that content increases with increasing improbability

Writing Ct(a) for ‘the content of the statement a’, and Ct(ab) for ‘the content of the conjunction a and b’, we have (1) Ct(a)
Ct(ab)  Ct(b). This contrasts with the corresponding law of the calculus of probability, (2) p(a)  p(ab)
p(b), where the inequality signs of (1) are inverted. Together these two laws, (1) and (2), state that with increasing content, probability decreases, and vice versa; or in other words, that content increases with increasing improbability.(This analysis is of course in full agreement with the general idea of the logical content of a statement as the class of all those statements which are logically entailed by it. We may also say that a statement a is logically stronger than a statement b if its content is greater than that of b—that is to say, if it entails more than b does. ) This trivial fact has the following inescapable consequences: if growth of knowledge means that we operate with theories of increasing content, it must also mean that we operate with theories of decreasing probability (in the sense of the calculus of probability). Thus if our aim is the advancement or growth of knowledge, then a high probability (in the sense of the calculus of probability) cannot possibly be our aim as well: these two aims are incompatible

Perhaps a head-on collision would be avoidable if people were not so generally inclined to assume uncritically that a high probability must be an aim of science, and that, therefore, the theory of induction must explain to us how we can attain a high degree of probability for our theories

Thus if we aim, in science, at a high informative content—if the growth of knowledge means that we know more, that we know a and b, rather than a alone, and that the content of our theories thus increases—then we have to admit that we also aim at a low probability, in the sense of the calculus of probability. And since a low probability means a high probability of being falsi- fied, it follows that a high degree of falsifiability, or refutability, or testability, is one of the aims of science—in fact, precisely the same aim as a high informative content

only a highly testable or improbable theory is worth testing, and is actually (and not merely potentially) satisfactory if it withstands severe tests—especially those tests to which we could point as crucial for the theory before they were ever undertaken

The theories of Kepler and Galileo were unified and superseded by Newton’s logically stronger and better testable theory, and similarly Fresnel’s and Faraday’s by Maxwell’s. Newton’s theory, and Maxwell’s, in their turn, were unified and superseded by Einstein’s. In each such case the progress was towards a more informative and therefore logically less probable theory: towards a theory which was more severely testable because it made predictions which, in a purely logical sense, were more easily refutable

But neither Oersted’s nor Röntgen’s nor Becquerel’s nor Fleming’s discoveries was really accidental, even though they had accidental components: every one of these men was searching for an effect of the kind he found. We can even say that some discoveries, such as Columbus’ discovery of America, corroborate one theory (of the spherical earth) while refuting at the same time another (the theory of the size of the earth, and with it, of the nearest way to India); and that they were chancediscoveries to the extent to which they contradicted all expectations, and were not consciously undertaken as tests of those theories which they refuted

most admirable deductive systems should be regarded as stepping stones rather than as ends: 5 as important stages on our way to richer, and better testable, scientific knowledge

perhaps even this picture of science—as a procedure whose rationality consists in the fact that we learn from our mistakes—is not quite good enough. It may still suggest that science progresses from theory to theory and that it consists of a sequence of better and better deductive systems. Yet what I really wish to suggest is that science should

progressing from problems to problems—to problems of ever increasing depth

Yet science starts only with problems. Problems crop up especially when we are disappointed in our expectations, or when our theories involve us in difficulties, in contradictions; and these may arise either within a theory, or between two different theories, or as the result of a clash between our theories and our observations.Moreover, it is only through a problem that we become conscious of holding a theory. It is the problem which challenges us to learn; to advance our knowledge; to experiment; and to observe

science starts from problems, and not from observations; though observations may give rise to a problem, especially if they are unexpected; that is to say, if they clash with our expectations or theories

THE THEORY OF OBJECTIVE TRUTH: CORRESPONDENCE TO THE FACTS

Tarski’s theory of truth and of the correspondence of a statement with the facts

simple elucidation of the idea of correspondence to the facts

The highly intuitive character of Tarski’s ideas seems to become more evident (as I have found in teaching) if we first decide explicitly to take ‘truth’ as a synonym for ‘correspondence to the facts’, and then (forgetting all about ‘truth’) proceed to explain the idea of ‘correspondence to the facts’.

we start from our subjective experience of believing, and thus look upon knowledge as a special kind of belief, then we may indeed have to look upon truth—that is, true knowledge—as some even more special kind of belief: as one that is well-founded or justified

can be shown that all subjective theories of truth aim at such a criterion: they try to define truth in terms of the sources or origins of our beliefs, 10 or in terms of our operations of verification, or of some set of rules of acceptance, or simply in terms of the quality of our subjective convictions. They all say, more or less, that truth is what we are justified in believing or in accepting, in accordance with certain rules or criteria, of origins or sources of our knowledge, or of reliability, or stability, or success, or strength of conviction, or inability to think otherwise

we search for truth, but may not know when we have found it; that we have no criterion of truth, but are nevertheless guided by the idea of truth as a regulative principle (as Kant or Peirce might have said); and that, though there are no general criteria by which we can recognize truth—except perhaps tautological truth—there are criteria of progress towards the truth (as I shall explain presently). The status of truth in the

A climber may not merely have difficulties in getting there—he may not know when he gets there, because he may be unable to distinguish, in the clouds, between the main summit and a subsidiary peak. Yet this does not affect the objective existence of the summit; and if the climber tells us ‘I doubt whether I reached the actual summit’, then he does, by implication

recognize the objective existence of the summit. The very idea of error or of doubt (in its normal straightforward sense) implies the idea of an objective truth which we may fail to reach

Thus while coherence, or consistency, is no criterion of truth, simply because even demonstrably consistent systems may be false in fact, incoherence or inconsistency do establish falsity; so, if we are lucky, we may discover the falsity of some of our theories. 13

subjectivism is still rampant in the philosophy of science, and especially in the field of probability theory. The subjectivist theory of probability, which interprets degrees of probability as degrees of rational belief, stems directly from the subjectivist approach to truth—especially from the coherence theory. Yet it is still embraced by philosophers who have accepted Tarski’s theory of truth. At least some of them, I suspect, have turned to probability theory in

table: objective or logical or subjective or psychological or ontological theories epistemological theories truth as correspondence truth as property of our state with the facts of mind—or knowledge or belief objective probability subjective probability (inherent in the situation, and (degree of rational belief based testable by statistical tests) upon our total knowledge) objective randomness lack of knowledge (statistically testable) equiprobability lack of knowledge ( physical or situational symmetry) In all these cases I am inclined to say not only that these two approaches should be distinguished, but also that the subjectivist approach should be discarded as a lapse, as based on a mistake—though perhaps a tempting mistake. There is, however, a similar table in which the epistemological (right hand) side is not based on a mistake.

truth conjecture testability empirical test explanatory or predictive power ‘verisimilitude’ degree of corroboration (that is, report of the results of tests) 3. TRUTH AND CONTENT: VERISIMILITUDE VERSUS PROBABILITY

classify philosophers as belonging to two main groups—those with whom I disagree, and those who agree with me. I might call them the veri- ficationists or the justificationist philosophers of knowledge or of belief, and the falsificationists or fallibilists or critical philosophers of conjectural knowledge.

verificationists or justificationists—hold, roughly speaking, that whatever cannot be supported by positive reasons is unworthy of being believed, or even of being taken into serious consideration

falsificationists or fallibilists—say, roughly speaking, that what cannot (at present) in principle be overthrown by criticism is (at present) unworthy of being seriously considered; while what can in principle be so overthrown and yet resists all our critical efforts to do so may quite possibly be false, but is at any rate not unworthy of being seriously considered and perhaps even of being believed—though only tentatively

falsificationists believe that we have also discovered a way to realize the old ideal of distinguishing rational science from various forms of superstition, in spite of the breakdown of the original inductivist or justificationist programme. We hold that this ideal can be realized, very simply, by recognizing that the rationality of science lies not in its habit of appealing to empirical evidence in support of its dogmas— astrologers do so too—but solely in the critical approach: in an attitude which, of course, involves the critical use, among other arguments, of empirical evidence (especially in refutations). For us, therefore, science has nothing to do with the quest for certainty or probability or reliability. We are not interested in establishing scientific theories as secure, or certain, or probable. Conscious of our fallibility we are only interested in criticizing them and testing them, hoping to find out where we are mistaken; of learning from our mistakes; and, if we are lucky, of proceeding to better theories

views about the positive or negative function of argument in science, the first group—the justificationists—may be also nicknamed the ‘positivists’ and the second—the group to which I belong—the critics or the ‘negativists

Yet we also stress that truth is not the only aim of science. We want more than mere truth: what we look for is interesting truth—truth which is hard to come by. And in the natural sciences (as distinct from mathematics) what we look for is truth which has a high degree of explanatory power, in a sense which implies that it is logically improbable truth

what we look for are answers to our problems

can therefore gladly admit that falsificationists like myself much prefer an attempt to solve an interesting problem by a bold conjecture, even (and especially) if it soon turns out to be false, to any recital of a sequence of irrelevant truisms. We prefer this because we believe that this is the way in which we can learn from our mistakes; and that in finding that our conjecture was false, we shall have learnt much about the truth, and shall have got nearer to the truth

shall give here a somewhat unsystematic list of six types of cases in which we should be inclined to say of a theory t1 that it is superseded by t2 in the sense that t2 seems—as far as we know—to correspond better to the facts than t1 , in some sense or other.(1) t2 makes more precise assertions than t1 , and these more precise assertions stand up to more precise tests.(2) t2 takes account of, and explains, more facts than t1 (which will include for example the above case that, other things being equal, t2 ’s assertions are more precise).(3) t2 describes, or explains, the facts in more detail than t1 .

has passed tests which t1 has failed to pass.(5) t2 has suggested new experimental tests, not considered before t2 was designed (and not suggested by t1 , and perhaps not even applicable to t1 ); and t2 has passed these tests.(6) t2 has unified or connected various hitherto unrelated problems. If we reflect upon this list, then we can see that the contents of the theories t1 and t2 play an important role in it.(

This suggests that we combine here the ideas of truth and of content into one—the idea of a degree of better (or worse) correspondence to truth or of greater (or less) likeness or similarity to truth; or to use a term already mentioned above (in contradistinction to probability) the idea of (degrees of) verisimilitude. It should be noted that the idea that every statement or theory is not only either true or false but has, independently of its truth value, some degree of verisimilitude, does not give rise to any multi-valued logic— that is, to a logical system with more than two truth values, true and false; though some of the things the defenders of multi-valued logic are hankering after seem to be realized by the theory of verisimilitude (and related theories alluded to in section 3 of the Addenda

Assuming that the truth-content and the falsity-content of two theories t1 and t2 are comparable, we can say that t2 is more closely similar to the truth, or corresponds better to the facts, than t1 , if and only if either

Assuming that the truth-content and the falsity-content of two theories t1 and t2 are comparable, we can say that t2 is more closely similar to the truth, or corresponds better to the facts, than t1 , if and only if either (a) the truth-content but not the falsity-content of t2 exceeds that of t1 , or (b) the falsity-content of t1 , but not its truth-content, exceeds that of t2 . If we now work with the (perhaps fictitious) assumption that the content and truth-content of a theory a are in principle measurable, then we can go slightly beyond this definition and can define Vs(a), that is to say, a measure of the verisimilitude or truthlikeness of a. The simplest definition will be

Ultimately, the idea of verisimilitude is most important in cases where we know that we have to work with theories which are at best approximations—that is to say, theories of which we actually know that they cannot be true.(This is often the case in the social sciences. ) In these cases we can still speak of better or worse approximations to the truth (and we therefore do not need to interpret these cases in an instrumentalist sense

always remains possible, of course, that we shall make mistakes in our relative appraisal of two theories, and the appraisal will often be a controversial matter

Verisimilitude, on the other hand, represents the idea of approaching comprehensive truth. It thus combines truth and content while probability combines truth with lack of content

BACKGROUND KNOWLEDGE AND SCIENTIFIC GROWTH

People involved in a fruitful critical discussion of a problem often rely, if only unconsciously, upon two things: the acceptance by all parties of the common aim of getting at the truth, or at least nearer to the truth, and a considerable amount of common background knowledge

we are at any given moment taking a vast amount of traditional knowledge for granted (for almost all our knowledge is traditional) creates no difficulty for the falsificationist or fallibilist. For he does not accept this background knowledge; neither as established nor as fairly certain, nor yet as probable. He knows that even its tentative acceptance is risky, and stresses that every bit of it is open to criticism, even though only in a piecemeal way

XVII One fact which is characteristic of the situation in which the scientist finds himself is that we constantly add to our background knowledge. If we discard some parts of it, others, closely related to them, will remain. For example, even though we may regard Newton’s theory as refuted—that is, his system of ideas, and the formal deductive system which derives from it—we may still assume, as part of our background knowledge, the approximate truth of its quantitative formulae

which means that we always look in the most probable kinds of places for the most probable kinds of counterexamples—most probable in the sense that we should expect to find them in the light of our background knowledge

Now if a theory stands up to many such tests, then, owing to the incorporation of the results of our tests into our background knowledge, there may be, after a time, no places left where (in the light of our new background knowledge) counterexamples can with a high probability be expected to occur. But this means that the degree of severity of our test declines. This is also the reason why an often repeated test will no longer be considered as significant or as severe: there is something like a law of diminishing returns from repeated tests (as opposed to tests which, in the light of our background knowledge, are of a new kind, and which therefore may still be felt to be significant). These are facts that are inherent in the knowledge-situation; and they have often been described—especially by John Maynard Keynes and by Ernest Nagel—as difficult to explain by an inductivist theory of science

THREE REQUIREMENTS FOR THE GROWTH OF KNOWLEDGE

new theory should proceed from some simple, new, and powerful, unifying idea about some connection or relation (such as gravitational attraction) between hitherto unconnected things (such as planets and apples) or facts (such as inertial and gravitational mass) or new ‘theoretical entities’ (such as fields and particles). This requirement of simplicity is a bit vague, and it seems difficult to formulate it very clearly

For, secondly, we require that the new theory should be independently testable. 25 That is to say, apart from explaining all the explicanda which the new theory was designed to explain, it must have new and testable consequences (preferably consequences of a new kind 25a ); it must lead to the prediction of phenomena which have not so far been observed

Yet I believe that there must be a third requirement for a good theory. It is this. We require that the theory should pass some new, and severe, tests

Clearly, this requirement is totally different in character from the previous two. These could be seen to be fulfilled, or not fulfilled, largely by analysing the old and the new theories logically.(They are ‘formal requirements’. ) The third requirement, on the other hand, can be found to be fulfilled, or not fulfilled, only by testing the new theory empirically.(It is a ‘material requirement’, a requirement of empirical success. ) Moreover

Even if a new theory (such as the theory of Bohr, Kramers, and Slater) should meet an early death, it should not be forgotten; rather its beauty should be remembered, and history should record our gratitude to it—for bequeathing to us new and perhaps still unexplained experimental facts and, with them, new problems; and for the services it has thus rendered to the progress of science during its successful but short life.

the first place, I contend that further progress in science would become impossible if we did not reasonably often manage to meet the third requirement; thus if the progress of science is to continue, and its rationality not to decline, we need not only successful refutations, but also positive successes. We must, that is, manage reasonably often to produce theories that entail new predictions, especially predictions of new effects, new testable consequences, suggested by the new theory and never thought of before.

first we require of a good theory that it should be successful in some of its new predictions; secondly we require that it is not refuted too soon—that is, before it has been strikingly successful

While the verificationists or inductivists in vain try to show that scientific beliefs can be justified or, at least, established as probable (and so encourage, by their failure, the retreat into irrationalism), we of the other group have found that we do not even want a highly probable theory. Equating rationality with the critical attitude, we look for theories which, however fallible, progress beyond their predecessors; which means that they can be more severely tested, and stand up to some of the new tests. And while the verificationists laboured in vain to discover valid positive arguments in support of their beliefs, we for our part are satisfied that the rationality of a theory lies in the fact that we choose it because it is better than its predecessors; because it can be put to more severe tests; because it may even have passed them, if we are fortunate; and because it may, therefore, approach nearer to the truthRefutations

11 T H E D E M A R C AT I O N B E T W E E N S C I E N C E A N D M E TA P H Y S I Cdrawing a line of demarcation between those statements and systems of statements which could be properly described as belonging to empirical science, and others which might, perhaps, be described as ‘pseudo-scientific’ or (in certain contexts) as ‘metaphysical’, or which belonged, perhaps, to pure logic or to pure mathematics

The most widely accepted view was that science was characterized by its observational basis, or by its inductive method, while pseudo-sciences and metaphysics were characterized by their speculative method or, as Bacon said, by the fact that they operated with ‘mental anticipations’— something very similar to hypotheses

This view I have never been able to accept. The modern theories of physics, especially Einstein’s theory (widely discussed in the year 1919), were highly speculative and abstract, and

On the other hand, many superstitious beliefs, and many rule-ofthumb procedures (for planting, etc. ) to be found in popular almanacs and dream books, have had much more to do with observations, and have no doubt often been based on something like induction.Astrologers

need for a different criterion of demarcation; and I proposed (though years elapsed before I published this proposal) that the refutability or falsifiability of a theoretical system should be taken as the criterion of demarcation

a system is to be considered as scientific only if it makes assertions which may clash with observations; and a system is, in fact, tested by attempts to produce such clashes; that is to say, by attempts to refute it. Thus testability is the same as refutability, and can therefore likewise be taken as a criterion of demarcation

view of science which takes its critical approach to be its most important characteristic

degrees of testability: some theories expose themselves to possible refutations more boldly than others. For example, a theory from which we can deduce precise numerical predictions about the splitting up of the spectral lines of light emitted by atoms in magnetic fields of varying strength will be more exposed to experimental refutation than one which merely predicts that a magnetic field influences the emission of light

A theory which is more precise and more easily refutable than another will also be the more interesting one. Since it is the more daring one, it will be the one which is less probable. But it is better testable, for we can make our tests more precise and more severe. And if it stands up to severe tests it will be better confirmed, or better attested, by these tests. Thus confirmability (or attestability or corroborability) must increase with testability.

This indicates that the criterion of demarcation cannot be an absolutely sharp one but will itself have degrees. There will be well-testable theories, hardly testable theories, and non-testable theories. Those which are non-testable are of no interest to empirical scientists. They may be described as metaphysical.

we must not try to draw the line too sharply. This becomes clear if we remember that most of our scientific theories originate in myths

1. FOUR MAJOR FUNCTIONS OF LANGUAGE 2. Karl Bühler appears to have been the first to propose, in 1918, 2 the doctrine of the three functions of language: (1) the expressive or symptomatic function; (2) the stimulative or signal function; (3) the descriptive function. To these I have added (4) the argumentative function

N O T E O N T H E B O D Y – M I N D P R O B L E M

My own contribution consisted, simply, in pointing out that, once the two languages (of physics and of psychology) are admitted not to be translatable into each other, they cannot any longer be said to talk about the same facts, and must be admitted to talk about different facts—where ‘facts’ means whatever the two-language theorists meant when they said that physics and psychology talked about the same facts

The method by which a solution is approached is usually the same; it is the method of trial and error. This, fundamentally, is also the method used by living organisms in the process of adaptation

The whole development of dialectic should be a warning against the dangers inherent in philosophical system-building. It should remind us that philosophy must not be made a basis for any sort of scientific system and that philosophers should be much more modest in their claims. One task which they can fulfil quite usefully is the study of the critical methods of science

My intention is to criticize the doctrine that it is the task of the social sciences to propound historical prophecies, and that historical prophecies are needed if we wish to conduct politics in a rational way. 1 I shall call this doctrine ‘historicism’. I consider historicism to be the relic of an ancient superstition, even though the people who believe in it are usually convinced that it is a very new, progressive, revolutionary, and scientific theory

tenets of historicism—that it is the task of the social sciences to propound historical prophecies, and that these historical prophecies are needed for any rational theory—are topical today because they form a very important part of that philosophy

by the name of ‘Scientific Socialism’ or ‘Marxism’. My analysis of the role of prediction and prophecy could therefore be described as a criticism of the historical method of Marxism

feel sympathy with Marxists is their insistence that the social problems of our time are urgent, and that philosophers ought to face the issues; that we should not be content to interpret the world but should help to change it. I am very much in sympathy with this attitude, and the choice by the present assembly of the theme ‘Man and Society’, shows that the need to discuss these problems is widely recognized. The mortal danger into which mankind has floundered—no doubt the gravest danger in its history—must not be ignored by philosophers

To be more specific, I believe that the best I can do as philosopher is to approach the problems armed with the weapons of a critic of methods

These simple ideas, especially the one claiming that it is the task of the social sciences to make historical predictions, such as predictions of social revolutions, I shall call the historicist doctrine of the social sciences. The idea that it is the task of politics to lessen the birthpangs of impending political developments I shall call the historicist doctrine of politics. Both these doctrines may be considered as parts of a wider philosophical scheme which may be called historicism—the view that the story of mankind has a plot, and that if we can succeed in unravelling this plot, we shall hold the key to the future

These ideas express one of the oldest dreams of mankind—the dream of prophecy, the idea that we can know what the future has in store for us, and that we can profit from such knowledge by adjusting our policy

The first is that the historicist does not, as a matter of fact, derive his

historical prophecies from conditional scientific predictions. The second (from which the first follows) is that he cannot possibly do so because long-term prophecies can be derived from scientific conditional predictions only if they apply to systems which can be described as well-isolated, stationary, and recurrent. These systems are very rare in nature; and modern society is surely not one of them

Society is changing, developing. This development is not, in the main, repetitive

There exists no law of evolution, only the historical fact that plants and animals change, or more precisely, that they have changed

conspiracy theory of society. It is the view that whatever happens in society—including things which people as a rule dislike, such as war, unemployment, poverty, shortages—are the results of direct design by some powerful individuals or groups. This view is very widespread, although it is, I have no doubt, a somewhat primitive kind of superstition

And this remark gives us an opportunity to formulate the main task of the theoretical social sciences. It is to trace the unintended social repercussions of intentional human actions

They do not allow us to make historical prophecies, but they may give us an idea of what can, and what cannot, be done in the political field

But I am convinced that these aims cannot be realized by revolutionary methods. On the contrary, I am convinced that revolutionary methods can only make things worse—that they will increase unnecessary suffering; that they will lead to more and more violence; and that they must destroy freedom. This becomes clear when we realize that a revolution always destroys the institutional and traditional framework of society. It must thereby endanger the very set of values for the realization of which it has been undertaken.Indeed, a set of values can have social significance only in so far as there exists a social tradition which upholds them. This is true of the aims of a revolution as much as of any other values

U T O P I A A N D V I O L E N C E

How can a decision be reached? There are, in the main, only two possible ways: argument (including arguments submitted to arbitration, for example to some international court of justice) and violence

A rationalist, as I use the word, is a man who attempts to reach decisions by argument and perhaps, in certain cases, by compromise, rather than by violence. He is a man who would rather be unsuccessful in convincing another man by argument than successful in crushing him by force, by intimidation and threats, or even by persuasive propaganda

Utopian rationalism is a self-defeating rationalism. However benevolent its ends, it does not bring happiness, but only the familiar misery of being condemned to live under a tyrannical government

If I were to give a simple formula or recipe for distinguishing between what I consider to be admissible plans for social reform and inadmissible Utopian blueprints, I might say: Work for the elimination of concrete evils rather than for the realization of abstract goods. Do not aim at establishing happiness by political means. Rather aim at the elimination of concrete miseries

fight for the elimination of poverty by direct means—for example, by making sure that everybody has a minimum income. Or fight against epidemics and disease by erecting hospitals and schools of medicine. Fight illiteracy as you fight criminality. But do all this by direct means. Choose what you consider the most urgent evil of the society in which you live, and try patiently to convince people that we can get rid of it

Do not allow your dreams of a beautiful world to lure you away from the claims of men who suffer here and now. Our fellow men have a claim to our help; no generation must be sacrificed for the sake of future generations, for the sake of an ideal of happiness that may never be realized. In brief, it is my thesis that human misery is the most urgent problem of a rational public policy and that happiness is not such a problem. The attainment of happiness should be left to our private endeavours.

The Utopianist attitude, therefore, is opposed to the attitude of reasonableness.Utopianism, even though it may often appear in a rationalist disguise, cannot be more than a pseudo-rationalism.

T H E H I S T O R Y O F O U R T I M E : A N O P T I M I S T ’S V I E W

Russell has more than once expressed the belief I wish to challenge. He has complained that our intellectual development has outrun our moral development. We have become very clever, according to Russell, indeed too clever. We can make lots of wonderful gadgets, including television, high-speed rockets, and an atom bomb, or a thermonuclear bomb, if you prefer. But we have not been able to achieve that moral and political growth and maturity which alone could safely direct and control the uses to which we put our tremendous intellectual powers. This is why we now find ourselves in mortal danger. Our evil national pride has prevented us from achieving the world-state in time.

As against this, I shall maintain precisely the opposite. My first thesis is this. We are good, perhaps a little too good, but we are also a little stupid; and it is this mixture of goodness and stupidity which lies at the root of our troubles. To avoid misunderstandings, I should stress that when I use the word ‘we’, in this thesis, I include myself. You may perhaps ask me why my first thesis should be part of an optimist’s view. There are various reasons. One is that wickedness is even more difficult to combat than a limited measure of stupidity, because good men who are not very clever are usually very anxious to learn.

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

They had a message; and they demanded sacrifices. It is sad to see how easily an appeal to morality can be misused. But it is simply a fact that the great dictators were always trying to convince their people that they knew the way to a higher morality

The absurdity of the communist faith is manifest. Appealing to the belief in human freedom, it has produced a system of oppression without parallel in history. But the nationalist faith is equally absurd. I am not alluding here to Hitler’s racial myth. What I have in mind is, rather, an alleged natural right of man—the alleged right of a nation to self-determination. That even a great humanitarian and liberal like Masaryk could uphold this absurdity as one of the natural rights of man is a sobering thought. It suffices to shake one’s faith in the wisdom of philosopher kings, and it should be contemplated by all who think that we are clever but wicked rather than good but stupid

The oppression of national groups is a great evil; but national self-determination is not a feasible remedy

Indeed, it seems to me possible that more people are killed out of righteous stupidity than out of wickedness

Few creeds have created more hatred, cruelty, and senseless suffering than the belief in the righteousness of the nationality principle; and yet it is still widely believed that this principle will help to alleviate the misery of national oppression

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

My third thesis is that since the time of the Boer War, none of the democratic governments of the free world has been in a position to wage a war of aggression. No democratic government would be united upon the issue, because they would not have the nation united behind them. Aggressive war has become almost a moral impossibility.

The war of ideas is a Greek invention. It is one of the most important inventions ever made.Indeed, the possibility of fighting with words instead of fighting with swords is the very basis of our civilization, and especially of all its legal and parliamentary institutions. And this habit of fighting with words and ideas is one of the few things which still unite the worlds on the two sides of the Iron Curtain (although on thethis may be formulated in my fourth thesis. It is as follows. The power of ideas, and especially of moral and religious ideas, is at least as important as that of physical resourcesThis important and influential idea—that truth is manifest—is one form of optimism which I cannot support. I am convinced that it is mistaken, and that, on the contrary, truth is hard, and often painful, to come by.This, then, is my fifth thesis. Truth is hard to come byThis thesis explains to some extent the wars of religion. And although it is a piece of epistemology, it can throw much light upon the history of Europe since the Renaissance, and even since classical antiquity. Let me now, in the time that remains, try to give a brief glimpse of this history—of the history of our time, especially since the Renaissance and the Reformation. The Renaissance, and the Reformation, may be considered as the conflict between the idea that truth is manifest—that it is an open book, there to be read by anybody of good will—and the idea that truth is hidden: that it is discernible only by the elect; that the book must be deciphered only by the ministry of the Church, and interpreted only by its authority. Although ‘the book’ meant, in the first instance, the Bible, it subsequently came to mean the book of nature. This book of nature, Bacon believed, was an open book. Those who misread it were misled by prejudice, impatience, and ‘anticipation’. If only you will read it without prejudice, patiently, and without anticipating the text, you will not err. Error is always your own fault. It is your own perverse and sinful refusal to see the truth which is manifest before you. This naïve and, I believe, mistaken view that truth is manifest became the inspiration for the advancement of learning in modern times. It became the basis of modern rationalism, as opposed to the more sceptical classical rationalism of the GreeksThe issue here can be described as one between individualistic rationalism and authoritarian traditionalism. The issue between rationalism and authoritarian traditionalism can also be described as that between, on the one hand, faith in man, in human goodness as well as in human reason, and, on the other hand, distrust of man, of his goodness and of his reason. I may confess that in the issue between faith in man and distrust of man, my feelings are all on the side of the naïve liberal optimists, even though my reason tells me that their epistemology was all wrong, and that truth is in fact hard to come by. I am repelled by the idea of keeping men under tutelage and authority. But I must admit, on the other hand, that the pessimists who feared the decline of authority and tradition were wise men. The terrible experience of the great religious wars, and of the French and Russian revolutions, prove their wisdom and foresightever existed. What was the mistake of the authoritarians? Why must their wisdom be rejected? I believe that there are three elements in our free world which have successfully replaced the dethroned authority. The first is our respect for the authority of truth: of an impersonal, interpersonal, objective truth which it is our task to find, and which it is not in our power to change, or to interpret to our liking. The second is a lesson learnt in the religious wars. For I think that in these wars we did learn our lesson: we did learn from our mistakes (though in the social and political field this seems a rare and difficult thing). We learnt that religious faith and other convictions can only be of value when they are freely and sincerely held, and that the attempt to force men to conform was pointless because those who resisted were the best, and indeed the only ones whose assent was worth having. Thus we learnt not only to tolerate beliefs that differ from ours, but to respect them and the men who sincerely held them. But this means that we slowly began to differentiate between sincerity and dogmatic stubbornness or laziness, and to recognize the great truth that truth is not manifest, not plainly visible to all who ardently want to see it, but hard to come by. And we learnt that we must not draw authoritarian conclusions from this great truth but, on the contrary, suspect all those who claim that they are authorized to teach the truth. The third is that we have also learnt that by listening to one another, and criticizing one another, we may get nearer to the truth

The critical rationalist can appreciate traditions, for although he believes in truth, he does not believe that he himself is in certain possession of it. He can appreciate every step, every approach towards it, as valuable, indeed as invaluable; and he can see that our traditions often help to encourage such steps, and also that without an intellectual tradition the individual could hardly take a single step towards the truth. It is thus the critical approach to rationalism, the compromise between rationalism and scepticism, which for a long time has been the basis of the British middle way: the respect for traditions, and at the same time the recognition of the need to reform them.

H U M A N I S M A N D R E A S O N

The Fabric of Reality

The Fabric of Reality by David Deutsch is his attempt at explaining the world a bit better. For this, he uses quantum theory to better understand what we experience. See below my notes/highlights throughout the book:

Preface

The whole goal of the book is to expand/explain some “deep theories about the structure of reality.” This in contrast to common sense, preconceptions, received opinion, authority. The answers may be very counterintuitive.

1. The Theory of Everything

There is a chance we might understand many more things than our ancestors. This doesn’t mean we can remember more facts or words (Greek poets were much better than us at this), but that our theories might explain (and let us understand) more about (the fabric of) reality.

This is done through having the right concepts, explanations, and theories.

“Scientific theories explain the objects and phenomena of our experience in terms of an underlying reality which we do not experience directly.”

• Others say it’s about prediction, this view is called instrumentalism
• But, prediction is no substitute for explanation
• We need theories (from bold conjectures) and then test them (experimentation)
• We can do this by testing them in the physical world (our ‘oracle’)

“To say that prediction is the purpose of a scientific theory is to confuse means with ends.” (passing the experimental test is only one of the aspects of a good theory)

“The deeper an explanation is, the more remote from immediate experience are the entities to which it must refer.” (we don’t see atoms, or stars far away, or evolution directly)

“… understanding comes through explanatory theories…” The generality of a these theories may make it possible for us to understand more.

“But at present we know of nothing that is capable of understanding an explanation – or of wanting one in the first place – other than a human mind.”

We can even understand (new) situations without knowing this beforehand. That is the reach of explanations. If you know maths, then you can also understand Roman numerals (but you will have to learn some facts about them first).

“We understand the fabric of reality only by understanding theories that explain it.”

There is both specialisation and a broadening going on (in scientific explanation). The reach of our explanations goes further than before, we understand areas we had no clue about before.

Deutsch’s thesis is that the depth of theories is winning (versus breath). We are moving towards a state in which a person can understand everything. In the book Deutsch argues for / lays the groundwork of a Theory of Everything.

Emergence is the high-level simplicity that emerges from low-level complexity (e.g. social systems from people, people from atoms). Some areas that can be studied are life, thought, and computation.

Holism is a mistaken way of thinking about emergence. This belief states that “the only legitimate explanations are in terms of higher-level systems.”… “There are explanations at every level of the hierarchy.”

Some components of the Theory of Everything are theories about electromagnetism, nuclear forces, and gravity. Two theories in physics stand out: 1) general theory of relativity (space, time, gravity), and 2) quantum theory. A quantum theory of gravity is something that could be very important/have great reach.

The four strands of Deutsch’s Theory of Everything are:

1. Quantum theory
2. Theory of evolution
3. Epistemology (theory of knowledge)
4. Theory of computation (what, in principle, computer can compute)

“Scientific knowledge, like all human knowledge, consists primarily of explanations. Mere facts can be looked up, and predictions are important only for conducting crucial experimental tests to discriminate between competing scientific theories that have already passed the test of being good explanations. As new theories supersede old ones, our knowledge is becoming both broader (as new subjects are created) and deeper (as our fundamental theories explain more, and become more general). Depth is winning. Thus we are not heading away from a state in which one person could understand everything that was understood, but towards it. Our deepest theories are becoming so integrated with one another that they can be understood only jointly, as a single theory of a unified fabric of reality. This Theory of Everything has a far wider scope than the ‘theory of everything’ that elementary particle physicists are seeking, because the fabric of reality does not consist only of reductionist ingredients such as space, time and subatomic particles, but also, for example, of life, thought and computation.”

2. Shadows

Using a torch (light beam), Deutsch shows how it demonstrates the multiverse.

He first talks about light being fuzzy (not having BRIGHT and DARK next to each other, but shades in between at the edges). If light moves very far away you can say it arrives in parts (yes/no), this is called quantization.

“There are no measurable continuous quantities in physics.”

So how is there a fuzzy area (penumbra)? That is because light does bend. And this is caused by interference (multiverse), so even one photon (light) is bent.

This inference is not a special case of light/photons, it occurs for every sort of particle. For every ‘tangible’ particle, there are infinite? (or at last a trillion) ‘shadow’ particles.

Collectively we may call the shadow particles a ‘parallel universe’. And all of those together, the ‘multiverse’.

“In other words, particles are grouped into parallel universes. They are ‘parallel’ in the sense that within each universe particles interact with each other just as they do in the tangible universe, but each universe affects the others only weakly, through interference phenomena.“

But why are these effects so small? “… every subatomic particle has counterparts in other universes, and is interfered only by those counterparts.” and “… the detection of interference between any two universes requires an interaction to take place between all the particles whose positions and other attributes are not identical in the two universes.”

“The quantum theory of parallel universes is not the problem, it’s the solution.”

“In interference experiments there can be places in a shadow-pattern that go dark when new openings are made in the barrier casting the shadow. This remains true even when the experiment is performed with individual particles. A chain of reasoning based on this fact rules out the possibility that the universe we see around us constitutes the whole of reality. In fact the whole of physical reality, the multiverse, contains vast numbers of parallel universes.”

3. Problem-solving

Deutsch talks about the ‘problem of induction’. Science was thought to move forward by observation, both in discovering of scientific theories and justification of them. It went like this, 1) observations, 2) are generalized to form a theory, 3) then more observations, 4) justify the theory. This is wrong.

He also argues that Solipsism (that only one mind can exist and the whole external world is an illusion outside of that mind) can’t be disproven.

A generalized prediction doesn’t equal a new theory. Bertrand Russell exemplified this with a chicken who was fed everyday, until the day it was slaughtered.

“… repeated observations cannot justify theories, but in doing so it entirely misses (or rather, accepts) a more basic misconception: namely, that the inductive extrapolation of observations to form new theories is even possible. In fact it’s impossible to extrapolate observations unless one has already placed them within an explanatory framework.”

Inductivism matches with our common-sense intuition that we can learn from experience.

Science progresses through an explanation-centered theory of knowledge. This is based on Karl Popper (Conjectures and Refutations). We start with our current/best theories (which are inadequate) and test these with observations (the ‘experience’). If these don’t confer, we make better/newer theories that can explain more/deeper parts of reality.

The process of scientific discovery or the problem-solving process is as follows, 1) problem, 2) conjectured solutions, 3) criticism (including experimental tests), 4) replacement of erroneous theories, 5) new problem.

“… theories that are capable of giving more detailed explanations are automatically preferred.”

“So all theories are being subjected to variation and selection, according to criteria which are themselves subject to variation and selection. The whole process resembles biological evolution.”

“One difference is that in biology variations (mutations) are random, blind and purposeless…” There is also no biological equivalent of an argument (although survival of something could maybe fill that role partly).

“In fundamental areas of science, observations of even smaller, more subtle effects are driving us to ever more momentous conclusions about the nature of reality. Yet these conclusions cannot be deduced by pure logic from the observations. So what makes them compelling? That is the ‘problem of induction’. According to inductivism, scientific theories are discovered by extrapolating the results of observations, and justified when corroborating observations are obtained. In fact, inductive reasoning is invalid, and it is impossible to extrapolate observations unless one already has an explanatory framework for them. But the refutation of inductivism, and also the real solution of the problem of induction, depends on recognizing that science is a process not of deriving predictions from observations, but of finding explanations. We seek explanations when we encounter a problem with existing ones. We then embark on a problem-solving process. New explanatory theories begin as unjustified conjectures, which are criticized and compared according to the criteria inherent in the problem. Those that fail to survive this criticism are abandoned. The survivors become the new prevailing theories, some of which are themselves problematic and so lead us to seek even better explanations. The whole process resembles biological evolution.”

4. Criteria for Reality

This chapter deals with the question of how we can draw conclusions about objective, external reality from (our mind’s) subjective experience and reason.

“Therefore [Galileo] insisted that scientific reasoning took precedence not only over intuition and common sense, but also over religious doctrine and revelation.”

Deutsch critiques Behaviourism and other forms of solipsisms (because they lack explanatory power.

“A prediction, or any assertion (bold conjecture), that cannot be defended might still be true, but an explanation that cannot be defended (tested/falsified) is not an explanation.”

A good metaphor for looking at reality is to see if something ‘kicks back’. This could be a rock that you kick, and it could be the light that reflects of faraway planets and ‘kicks’ your retina. This metaphor/thinking tool, originally by Dr. Johnson, is used throughout the book.

“If, according to the simplest explanation, an entity is complex and autonomous, then that entity is real.” or put into words related to complexity theory, “If a substantial amount of computation would be required to give us the illusion that a certain entity is real, then that entity is real.”

“Observational evidence is indeed evidence, not in the sense that any theory can be deduced, induced or in any other way inferred from it, but in the sense that it can constitute a genuine reason for preferring one theory to another.”

“[W]hat is genuinely out there is evidence, or, more precisely, a reality that will respond with evidence if we interact appropriately with it.”

“Thus reality contains not only evidence, but also the means (such as our minds, and our artefacts) of understanding it.”

The self-similarity of reality that we put/observe in theories, images, symbols can be called knowledge.

“Although solipsism and related doctrines are logically self-consistent, they can be comprehensively refuted simply by taking them seriously as explanations. Although they all claim to be simplified world-views, such an analysis shows them to be indefensible over-elaborations of realism. Real entities behave in a complex and autonomous way, which can be taken as the criterion for reality: if something ‘kicks back’, it exists. Scientific reasoning, which uses observation not as a basis for extrapolation but to distinguish between otherwise equally good explanations, can give us genuine knowledge about reality.”

5. Virtual Reality

“What computers can or cannot compute is determined by the laws of physics alone, and not by pure mathematics. One of the most important concepts of the theory of computation is universality. A universal computer is usually defined as an abstract machine that can mimic the computations of any other abstract machine in a certain well-defined class.”

Virtual reality is where this universality (or restrictions of some computations) can best be shown. In the book ‘virtual reality’ is used as a theoretical concept, but one day our computers might (within the laws of physics) do as described.

“We shall see that the existence of virtual reality does not indicate that the human capacity to understand the world is inherently limited, but, on the contrary, that it is inherently unlimited.” (that is quite the claim)

In the virtual reality experience you can see things that are not possible in real-life (e.g. flying through a mountain), but not logically impossible things (factorizing a prime number). It also doesn’t show/simulate internal experiences (e.g. your feelings, but they can of course be influenced by what you see/hear – the external experiences). (see table p105)

“Eventually it will become possible to bypass the sense organs altogether and directly stimulate the nerves that lead from them to the brain.” This machine that could render any sensation would be called the universal image generator.

Deutsch also argues that all our external experiences are, in effect, virtual reality (rendering on our brain’s own virtual reality generator). “All reasoning, all thinking and all external experiences are forms of virtual reality.”

“Virtual reality is not just a technology in which computers simulate the behaviour of physical environments. The fact that virtual reality is possible is an important fact about the fabric of reality. It is the basis not only of computation, but of human imagination and external experience, science and mathematics, art and fiction.”

6. Universality and the Limits of Computation

“[I]s there a single virtual-reality generator, buildable once and for all, that could be programmed to render any environment that the human mind is capable of experiencing?”

One trick to work towards this goal is to slow the processing of the human’s brain, vs speeding up the computer’s speed.

Deutsch defines a class of logically possible environments as Cantgotu environments.

He also re-defines the Turing principle as follows “It is possible to build a virtual-reality generator whose repertoire includes every physically possible environment” (see p133-135 for the steps)

“The diagonal argument shows that the overwhelming majority of logically possible environments cannot be rendered in virtual reality. I have called themCantgotu environments. There is nevertheless a comprehensive self-similarity in physical reality that is expressed in the Turing principle (see above). So a single, buildable physical object can mimic all the behaviours and responses of any other physically possible object or process. This is what makes reality comprehensible.”

7. A Conversation About Justification

This chapter tackles one objection, namely common sense.

“… inductivism rests upon a mistaken idea of science as seeking predictions on the basis of observations, rather than as seeking explanations in response to problems. … science does make progress, by conjecturing new explanations and then choosing between the best ones by experiment.”

This is justified (something Deutsch emphasizes) because it leaves fewer loose ends, it’s more generalizable, meshes better with other explanations, etc.

“For a theory to win an argument, all its rivals must be untenable, and that includes all the variants of the rivals which anyone has thought of.

Language also plays an important role in our theories and does quite a lot of the work. I think that somewhere else Deutsch also mentions that this is one of the reasons why many philosophers like to put things in mathematical equations (in a way also a language) that is less confusing/more universal.

The process of argument (making theories and testing them) starts in the middle. There is no ‘end’ that we can reach, nor a ‘beginning’ from which to base it all on.

8. The Significance of Life

“… life is a fundamental phenomenon of nature.” (as first coined by Aristotle) ” … life is theoretically fundamental and has large physical effect.”

Life on earth is based on replicators (genes/DNA/ACGT), the genetic code is the language of them.

“A gene can function as a replicator only in certain environments.”

“A replicator causes its environment to copy itself: that is, it contributes causally to its own copying.”

Deutsch mentions junk DNA. The views on this has changed and much of the ‘junk’ is now considered important/functional.

“An organism is not a replicator: it is part of the environment of replicators.”

“So an organism is the immediate environment which copies the real replicators: the organism’s genes.”

Also see The Selfish Gene. And The Extended Phenotype (not read yet)

“Genes embody knowledge about their niches.”

It’s the knowledge that is passed on. So a piece of knowledge, not the physical genes, is adapted to a specific niche.

On how we have influence and how life shapes the world/universe: “Thus one cannot predict the future of the Sun without taking a position on the future of life on Earth, and in particular on the future of knowledge.” or in other words “… the future history of the universe depends on the future history of knowledge.”

“Even non-intelligent life has grossly transformed many times its own mass of the surface and atmosphere of the Earth.” (think about oxygen from plants making up a part of the atmosphere)

Deutsch makes some remarks about the multiverse (re-read later).

“Where there is knowledge, there must have been life, at least in the past.”

“Scientific progress since Galileo has seemed to refute the ancient idea that life is a fundamental phenomenon of nature. It has revealed the vast scale of the universe, compared with the Earth’s biosphere. Modern biology seems to have confirmed this refutation, by explaining living processes in terms of molecular replicators, genes, whose behaviour is governed by the same laws of physics as apply to inanimate matter. Nevertheless, life is associated with a fundamental principle of physics – the Turing principle – since it is the means by which virtual reality was first realized in nature. Also, despite appearances, life is a significant process on the largest scales of both time and space. The future behaviour of life will determine the future behaviour of stars and galaxies. And the largest-scale regular structure across universes exists where knowledge-bearing matter, such as brains or DNA gene segments, has evolved.

9. Quantum Computers

“A quantum computer is a machine that uses uniquely quantum-mechanical effects, especially interferences, to perform wholly new types of computation that would be impossible, even in principle, on any Turing machine and hence on any classical computer.”

Universal virtual-reality generators are possible (as defined and explained earlier). Because of quantum computing, they are also tractable (i.e. possible to be made/calculated in a reasonable amount of time)

“Chaos theory is about limitations on predictability in classical physics, stemming from the fact that almost all classical systems are inherently unstable.” It’s very sensitive to initial conditions. See a YouTube video by Veritasium about this. Deutsch does however state that our world is built on quantum theory, not classical mechanics. “In quantum mechanical, small deviations from a specified initial state tend to cause only small deviations from the predicted final state.” If I understand it correctly, the fanning out (from the original state) is the ‘real’ reason why there is unpredictability (e.g. in the weather). “Even if we knew the initial conditions perfectly, the multiplicity, and therefore the unpredictability of the motion, would remain.” (i.e. if we could know exactly where a pendulum with 3 arms/parts starts, we still wouldn’t perfectly predict the state of it 10 seconds later.

Deutsch makes a distinction between unpredictability and intractability. Unpredictability as per above (so different behaviours in different universes for quantum theory). “Intractability, by contrast, is a computational-resource issue.”

Quantum theory/experiments don’t only make probabilistic predictions, there can also be “non-random interference phenomena” with one outcome.

Deutsch proved in 1985 that a universal quantum computer was possible.

There is much more detailed talk about why he came to this conclusion and how it works. One challenge put forward is Shor’s algorithm (he asks you to explain it without acknowledging the multiverse).

Quantum computing makes a new level of cryptography possible, one that can detect eavesdroppers.

“The laws of physics permit computers that can render every physically possible environment without using impractically large resources. So universal computation is not merely possible, as required by the Turing principle, it is also tractable. Quantum phenomena may involve vast numbers of parallel universes and therefore may not be capable of being efficiently simulated within one universe. However, this strong form of universality still holds because quantum computers can efficiently render every physically possible quantum environment, even when vast numbers of universes are interacting. Quantum computers can also efficiently solve certain mathematical problems, such as factorization, which are classically intractable, and can implement types of cryptography which are classically impossible. Quantum computation is a qualitatively new way of harnessing nature [or the fabric of reality].”

10. The Nature of Mathematics

This chapter is a bit far away from what I know or find interesting. Deutsch also remarks that it’s an attack/rebuttal of standard mathematical views, ones I do not share (or know about).

In mathematics, proof play the role of ‘kicking back’.

“For the idea that mathematics yields certainties is a myth too.”

“As mathematical reasoning became more sophisticated, it inevitably moved ever further away from everyday intuition.”

Deutsch argues that intuitionism (in mathematics, as conceived of by Brouwer – Dutch mathematician) is the solipsism of mathematics.

He also makes reference to Hilbert and then to Gödel (from Gödel’s incompleteness theorem). “Thanks to Gödel, we know that there will never be a fixed method of determining whether a mathematical proposition is true, any more than there is a fixed way of determining whether a scientific theory is true. Nor will there ever be a fixed way of generating new mathematical knowledge. Therefore progress in mathematics will always depend on the exercise of creativity. It will always be possible, and necessary, for mathematicians to invent new types of proof.”

(on the remaining pages I haven’t marked anything, so although it might be important – it didn’t register with me)

“Abstract entities that are complex and autonomous exist objectively and are part of the fabric of reality. There exist logically necessary truths about these entities, and these comprise the subject-matter of mathematics. However, such truths cannot be known with certainty. Proofs do not confer certainty upon their conclusions. The validity of a particular form of proof depends on the truth of our theories of the behaviour of the objects with which we perform the proof. Therefore mathematical knowledge is inherently derivative, depending entirely on our knowledge of physics. The comprehensible mathematical truths are precisely the infinitesimal minority which can be rendered in virtual reality. But the incomprehensible mathematical entities (e.g. Cantgotu environments) exist too, because they appear inextricably in our explanations of the comprehensible ones.”

11. Time: The First Quantum Concept

“We shall see that there is no such thing as the flow of time.” Wow, what a statement and one that seems very counter-intuitive.

“To put it bluntly, the reason why the common-sense theory of time is inherently mysterious is that it is inherently nonsensical. It is not just that it is factually inaccurate. We shall see that, even in its own terms, it does not make sense.”

(after making various illustrations – all which don’t really help) “So there is no single ‘present moment’, except subjectively. From the point of view of an observer at a particular moment, that moment is indeed singled out, and may uniquely be called ‘now’ by that observer, just as any position in space is singled out as ‘here’ from the point of view of an observer at that position.”

This does also make me think of a wider concept of ‘now’, that 1 millisecond is the now of say 1 mile around you, of 1 second around you is a part of the world, of 1 minute is part of space, etc. The ‘now’ of Alpha Centauri is much different (as is the place) as here. More discussion about time in The Order of Time.

“We do not experience time flowing, or passing. What we experience are differences between our present perceptions and our present memories of past perceptions. We interpret those differences, correctly, as evidence that the universe changes with time.” but, he continues, “We also interpret them, incorrectly, as evidence that our consciousness, or the present, or something, moves through time.”

“No accurate picture of the framework of time can be a moving or changing picture. It must be static.”

Our idea of time consists of two concepts that don’t work well together. We explain things as flowing/moving through time (things have causes). But we also describe things (and have static picture of that thing).

“None of Newton’s physical theories refers to the flow of time, nor has any subsequent physical theory referred to, or been compatible with, the flow of time.”

“Space and time, considered together like this as a four-dimensional entity, are called spacetime.” … “Spacetime is sometimes referred to as the ‘block universe’.”

This would (maybe) mean that the future is not open, there is no free will, everything is set in stone (or spacetime). But Deutsch goes on further, and will argue that the future is ‘open’.

“Subjectively, the future of a given observer may be said to be ‘open from that observer’s point of view’ because one cannot measure or observe one’s own future.” (but objectively it’s still fixed). The lottery will fall one way or the other, no matter if you don’t know this beforehand. “So according to spacetime physics, the openness of the future is an illusion … In reality we make no choices.”

“The property of snapshots being determined by other snapshots is called determinism.”

“So the snapshots have an intrinsic order, defined by their contents and by the real laws of physics. Any one of the snapshots, together with the real laws of physics, not only determines what all the others are, it determines their order, and it determines its own place in the sequence. In other words, each snapshot has a ‘time stamp’ encoded in its physical contents.”

“The predictability of one event from another does not imply that those events are cause and effect.”

So, all of this was according to pre-quantum physics. And that is what is messing us up, “because spacetime physics is false.”

“Physical reality is not a spacetime. It is a much bigger and more diverse entity, the multiverse.”

(earlier he also repeats how causation works: “For X to be a cause of Y, two conditions must hold: first, that X and Y both happen; and second, that Y would not have happened if X had been otherwise.”)

Multiverses then are infinite, but types of experiences/events are present in definitive proportions. Time would still be a sequence of events, but these events would happen in many universes. A moment here is referred to as a “super-snapshot”.

“[T]he super-snapshots beginning with a particular moment would be entirely and exactly determined by the previous super-snapshots. This complete determinism would not give rise to complete predictability, even in principle, because making a prediction would require a knowledge of what had happened in all the universes, and each copy of us can directly perceive only one universe.” But still, this picture also isn’t quite right, the ‘neat’ separation of universes next to each other (figure 11.6) isn’t correct.

“In the multiverse, snapshots do not have ‘time stamps’.” So that snapshot, that can’t be an accurate description. There is no overarching framework in which to put the multiverse.

“Therefore there is no fundamental demarcation between snapshots of other times and snapshots of other universes. This is the distinctive core of the quantum concept of time: Other times are just special cases of other universes.”

Only from our perspective do these other snapshots (our history/past) have special meaning. Our conditional logic (if … then) is based on this framework (us seeing a very similar snapshot in other times).

“… any snapshot that is present at all is present in an infinity of copies.” As stated above, it’s just about the proportion in which such a snapshot is present.

“Quantum theory does not in general determine what will happen in a particular snapshot, as spacetime physics does. Instead, it determines what proportion of all snapshots in the multiverse will have a given property.”

In the end, he does ‘defend’ the standard notion of time, “Alle experimental results currently available to us are compatible with the approximation that time is a sequence of moments.” but, “… theory tells us that it must break down in certain types of physical process.”

Time (or even the concept of it) comes to a halt at the Big Bang and black holes.

“… on a sub-microscopic scale quantum effects again warp and tear the fabric of spacetime, and that closed loops of time – in effect, tiny time machines – exist on that scale”

“… spacetime physics is never an exact description of reality.”

There is still cause-and-effect, and determinism.

Deutsch also remarks that heat and entropy (more randomness/variations) is one part of why we may see the flow of time going in one direction.

“Time is not a sequence of moments, nor does it flow. Yet our intuitions about the properties of time are broadly true. Certain events are indeed causes and effects of one another. Relative to an observer, the future is indeed open and the past fixed, and possibilities do indeed become actualities.”

(the end-of-chapter summary is very short) “Time does not flow. Other times are just special cases of other universes.”

12. Time Travel

If we slow down the body (or freeze it), we can have future-directed time travel. Ditto for if we accelerate or decelerate, we experience less time (time dilation).

If we want to travel back in time in virtual reality, it can only be a real/faithfull picture/time before we interact with it.

“… one can use a time machine only to travel to times and places at which it has existed. In particular, one cannot use it to travel back to a time before its construction was completed.”

See figure 12.3 (p306) for a rendering of the virtual time machine.

(about wanting to change the past) “Changing the past means choosing which past snapshot to be in, not changing any specific past snapshot into another one.”

Time travel is currently only possible (to the past) at the Planck time scale.

But if we (one day) would be able to go to the past, it would be that of another universe, so the info they would bring would not be about ‘our’ future (but could still be useful).

“Possession of a time machine would allow us access to knowledge from an entirely new source, namely the creativity of minds in other universes.” (and with quantum computers we’re already doing this in a way)

“Time travel may or may not be achieved one day, but it is not paradoxical. If one travels into the past one retains one’s normal freedom of action, but in general ends up in the past of a different universe. The study of time travel is an area of theoretical study in which all four of my main strands are significant, quantum mechanics, with its parallel universes and the quantum concept of time; the theory of computation, because of the connections between virtual reality and time travel, and because the distinctive features of time travel can be analysed as new modes of computation; and epistemology and the theory of evolution, because of the constraints they impose on how knowledge can come into existence.”

13. The Four Strands

Kuhn argues that scientific knowledge ‘revolutions’ happen only after they break through the old guard, their ways of thinking, their paradigm. But Deutsch (and Popper – The Myth of the Framework) think otherwise. Deutsch argues that the theory only explains how theories succeed each other, not how rival explanations compete. (Deutsch is also positive about the views of researchers when in that role (vs being ‘humans’))

The problem is outdated theories that Popper, Dawkins, and others have to defend their theories against.

Deutsch also argues that we do have free will, see page 339 (let’s call it quantum free will).

“The intellectual histories of the fundamental theories of the four strands contain remarkable parallels. All four have been simultaneously accepted (for in practical use) and ignored (as explanations of reality). One reason for this is that, taken individually, each of the four theories has explanatory gaps, and seems cold and pessimistic. To base a world-view on any of them individually is, in a generalized sense, reductionist. But when they are taken together as a unified explanation of the fabric of reality, this is no longer so.”

14. The Ends of the Universe

Our knowledge is what makes us special and what makes sure that we have influence over the universe.

Deutsch explains that in the end of the universe (The Big Crunch) we might expect to make infinitely many computations.

“… intelligence will survive, and knowledge will continue to be created, until the end of the universe.”

“reality is comprehensible.”

He also speaks about the omega-point theory (related to the computations we can do at the Big Crunch). The computer there will be omnipotent, but only with the available matter and energy, and within the laws of physics.

Our knowledge is becoming broader (more areas) and deeper (we can understand more with less theories).

“… the four strands: the quantum physics of the multiverse, Popperian epistemology, the Darwin-Dawkins theory of evolution and a strengthened version of Turing’s theory of universal computation.”

Cosmos

Cosmos by Carl Sagan is one of those books that both awe and inspire. It looks beyond our daily lives, our politics, and spans from the start of the universe to the depths of a black hole.

The fun thing is that the book was published in 1980, yet all basic facts still stand (of course there is some fierce discussion about quite many of them, that is science for you).

See more here (wiki).