In this talk I do not propose to speak of ordinary everyday experience. I intend, rather, to use the word ‘experience’ in the sense in which we use it when we say that science is based on experience. Since, however, experience in science is after all no more than an extension of ordinary everyday experience what I shall have to say will apply, by and large, to everyday experience also.
In order not to get lost in abstractions I intend to discuss the logical status of a specific empirical science—Newtonian dynamics. I do not, however, presuppose any knowledge of physics on the part of my audience.
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. The philosopher who 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.
The first philosopher clearly to apprehend the riddle of natural science was Kant. I do not know of any philosopher, either before or since, who has been so profoundly stirred by it.
When Kant talked of ‘natural science’ he almost invariably had Isaac Newton’s celestial mechanics in mind. Kant himself made important contributions to Newtonian physics and he was one of the greatest cosmologists of all time. His two principal cosmological works are the Natural History and Theory of the Heavens (1755) and the Metaphysical Foundations of Natural Science (1786). Both themes were (in Kant’s own words) ‘treated according to Newtonian Principles’.1
Like almost all of his contemporaries who were knowledgeable in this field, Kant believed in the truth of Newton’s celestial mechanics. The almost universal belief that Newton’s theory must be true was not only understandable but seemed to be well-founded. Never had there been a better theory, nor one more severely tested. Newton’s theory not only accurately predicted the orbits of all the planets, including their deviations from Kepler’s ellipses, but also the orbits of all their satellites. Moreover, its few simple principles supplied at the same time a celestial mechanics and a terrestrial mechanics.
Here was a universally valid system of the world that described the laws of cosmic motion in the simplest and clearest way possible—and with absolute accuracy. Its principles were as simple and precise as geometry itself—as Euclid’s supreme achievement, that unsurpassed model of all science. Newton had indeed propounded a kind of cosmic geometry consisting of Euclid supplemented by a theory (which too could be represented geometrically) of the motion of mass-points under the influence of forces. It added, apart from the concept of time, only two essentially new concepts to Euclidean geometry: the concept of mass or of a material mass-point, and the even more important concept of a directed force (vis in Latin and dynamis in Greek from which the name ‘dynamics’ for Newton’s theory is derived).
Here then was a science of the cosmos, of nature; and, it was claimed, a science based upon experience. It was a deductive science, exactly like geometry. Yet Newton himself asserted that he had wrested its functional principles from experience by induction. In other words, Newton asserted that the truth of his theory could be logically derived from the truth of certain observation-statements. Although he did not describe these observation-statements precisely it is nevertheless clear that he must have been referring to Kepler’s laws, the laws of the elliptic motions of the planets. And we can still find prominent physicists who maintain that Kepler’s laws can be derived inductively from observation-statements, and that Newton’s principles can in turn be derived, entirely or almost entirely, from Kepler’s laws.
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 observation-statements.
Secondly, the assertion is historically false.
Thirdly, the assertion is logically false: it is a logically impossible assertion.
Let us examine the first point—that it is intuitively not credible that observations can show Newton’s mechanics to be true.
To see this we merely have to remember how utterly Newtonian theory differs from any observation-statement. In the first place observations are always inexact, while the theory makes absolutely exact assertions. Moreover, it was one of the triumphs of Newtonian theory that it stood up to subsequent observations which as regards precision went far beyond what could be attained in Newton’s own time. Now it is incredible that more precise statements, let alone the absolutely precise statements of the theory itself, could be logically derived from less exact or inexact ones.2 But even if we forget all about the question of precision we should realize that an observation is always made under very special conditions, and that each observed situation is always a highly specific situation. 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. For example we never observe mass points but rather extended planets. This may perhaps not be so very important; but what is of the utmost importance is that we can never—I repeat, never—observe anything like Newtonian forces. Admittedly, since forces are so defined that they may be measured by measuring accelerations, we can indeed measure forces; and we may at times measure a force not by measuring an acceleration, but for instance with the help of a spring balance. Yet in all these measurements, without exception, we always presuppose the truth of Newtonian dynamics. Without the prior assumption of a dynamical theory it is simply impossible to measure forces. But forces, and changes of forces, are among the most important things of which the theory treats. Thus we may assert that at least some of the objects of which the theory treats are abstract and unobservable objects. For all these reasons it is intuitively not credible that the theory should be logically derivable from observations.
This result would not be affected even if it were possible so to reformulate Newton’s theory that any reference to forces was avoided. Nor would it be affected by a dismissal of force as a mere fiction, or perhaps as a purely theoretical construction which serves only as a tool or instrument for prediction. Because the thesis which we are questioning says that Newton’s theory can be shown to be true by observation. And our objection was that we can only observe concrete things, while theory, and particularly Newtonian forces, are abstract. These difficulties are in no way mitigated if we make the theory even more abstract by eliminating the notion of force or by unmasking it as a mere auxiliary construction.
So much for my first point.
My second point was that it is historically false to believe that Newton’s dynamics was derived from observation. Though this belief is widespread, it is nevertheless a belief in a historical myth—or, if you like, a bold distortion of history. To show this I shall briefly refer to the part played by the three most important precursors of Newton in this field: Nicolaus Copernicus, Tycho Brahe, and Johannes Kepler.
Copernicus studied in Bologna under the Platonist Novara; and Copernicus’ idea of placing the sun rather than the earth in the centre of the universe was not the result of new observations but of a new interpretation of old and well-known facts in the light of semi-religious Platonic and Neo-Platonic ideas. The crucial idea can be traced back to the sixth book of Plato’s Republic, where we can read that the sun plays the same role in the realm of visible things as does the idea of the good in the realm of ideas. Now the idea of the good is the highest in the hierarchy of Platonic ideas. Accordingly the sun, which endows visible things with their visibility, vitality, growth and progress, is the highest in the hierarchy of the visible things in nature.
This passage in the Republic is of outstanding importance among the passages upon which Neo-Platonic philosophy—particularly Christian Neo-Platonic philosophy—was based.
Now if the sun was to be given pride of place, if the sun merited a divine status in the hierarchy of visible things, then it was hardly possible for it to revolve about the earth. The only fitting place for so exalted a star was the centre of the universe.3 So the earth was bound to revolve about the sun.
This Platonic idea, then, forms the historical background of the Copernican revolution. It does not start with observations, but with a religious or mythological idea. Such beautiful but wild ideas have often been put forward by great thinkers, and just as often by cranks. But Copernicus, for one, was not a crank. He was highly critical of his own mystical intuitions, which he rigorously examined in the light of astronomical observations reinterpreted with the aid of the new idea. He rightly considered these observations to be extremely important. Yet looked at from a historical or genetical point of view observations were not the source of his idea. The idea came first, and it was indispensable for the interpretation of the observations: they had to be interpreted in its light.
Johannes Kepler—the pupil and assistant of Tycho Brahe, to whom that great teacher left his unpublished observations—was a Copernican. Like Plato himself, Kepler, though always a critical thinker, was steeped in astrological lore; and he also was like Plato deeply influenced by the number-mysticism of the Pythagoreans. What he hoped to discover, what he searched for throughout his life, was the arithmetical law underlying the structure of the world, the law upon which rested the construction of the circles of Copernicus’ solar system, and upon which, in particular, their relative distances from the sun were based. He never found what he sought. He did not find in Tycho’s observations the hoped-for confirmation of his belief that Mars revolved about the sun in a perfectly circular orbit with uniform velocity. On the contrary, he discovered in Tycho’s observations a refutation of the circle hypothesis. Thus he discarded the circle hypothesis; and having tried in vain various other solutions, he hit upon the next best thing: the hypothesis of the ellipse. And he found that the observations could be made to agree with the new hypothesis—although only under the assumption, at first far from welcome, that Mars did not travel with uniform velocity.
Historically, therefore, Kepler’s laws were not the result of observations. What happened was that Kepler tried in vain to interpret Tycho’s observations by means of his original circle hypothesis. The observations refuted this hypothesis, and so he tried the next best solutions—the oval, and the ellipse. The observations still did not prove that the hypothesis of an ellipse was correct, but they could now be explained by means of this hypothesis: they could be reconciled with it.
Moreover, Kepler’s laws partly support, and are partly inspired by, his belief in a cause, a power, emanating like light rays from the sun and influencing, steering, or causing the movement of the planets, including the earth. But the view that there is an influx or ‘Influence’ from the stars reaching the earth was at the time considered as the fundamental tenet of astrology as opposed to Aristotelian rationalism. Here we have an important dividing line which separated two schools of thought: for example, Galileo (himself a great critic of Aristotle), or Descartes or Boyle or Newton, belonged to the (Aristotelian) rationalist tradition. This is why Galileo remained sceptical of Kepler’s views and also why he was unable to accept any theory of the tides which explained them by the ‘influence’ of the moon, so that he felt compelled to develop a non-lunar theory which explained the tides merely by the motion of the earth. This is also why Newton was so reluctant to accept his own theory of attraction (or Robert Hooke’s) and why he was never quite reconciled to it. And this is why the French Cartesians were so long unwilling to accept Newton’s theory. But in the end the originally astrological view proved so successful that it was accepted by all rationalists and its disreputable origin was forgotten.4
Such, from an historical and genetical point of view, were the main antecedents of Newton’s theory. Our story shows that as a matter of historical fact the theory was not derived from observations.
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. Thus Kant wrote in the preface to the 2nd edition of the Critique of Pure Reason:
When Galileo let his globes run down an inclined plane with a gravity which he had chosen himself; when Torricelli caused the air to sustain a weight which he had calculated beforehand to be equal to that of a column of water of known height; … then a light dawned upon all natural philosophers. They learnt that our reason can understand only what it creates according to its own design: 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 is searching for.5
This quotation from Kant shows how well he understood that we ourselves must confront nature with hypotheses and demand a reply to our questions; and that, lacking such hypotheses, we can only make haphazard observations which follow no plan and which can therefore never lead us to a natural law. In other words, 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.
My third point—the contention that it is logically impossible to derive Newton’s theory from observations—follows immediately from Hume’s critique of the validity of inductive inferences, as pointed out by Kant. Hume’s decisive point may be put as follows:
Take a class consisting of any number of true observation-statements and designate it by the letter K. The statements in the class K will describe actual observations, i.e. past observations: thus K will be any class whatsoever of true statements about observations actually made in the past. Since we have assumed that K consists only of true statements, all statements in the class K must also be self-consistent statements, and, furthermore, all statements belonging to the class K must be compatible with one another. Now take a further observation-statement which we shall designate by the letter B. We assume B describes some future, logically possible observation; for example, B may say that an eclipse of the sun will be observed tomorrow. Since eclipses of the sun have already been observed, we can be certain that a statement B, asserting that there will be an eclipse of the sun tomorrow, is a statement which, on purely logical grounds, is possible; that is to say, our B is self-consistent. Now Hume shows the following: if B is a self-consistent statement about some possible future observation, and K any class of true statements about some past observations, then B can always be conjoined with K without contradiction; or, in other words, if we add a statement B about a possible future observation to statements in K we can never arrive at a logical contradiction. Hume’s finding can also be formulated as follows: no logically possible future observation can ever contradict the class of past 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.
Thus we have proved our third point. And we can now see the whole riddle of experience—the paradox of the empirical sciences, as discovered by Kant:
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.
Kant 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.
In order to solve the riddle of experience, and to explain how natural science and experience are at all possible, Kant constructed his theory of experience and of natural science. I admire this theory as a truly heroic attempt to solve the paradox of experience, yet I believe that it answers a false question, and hence that it is in part irrelevant. Kant, the great discoverer of the riddle of experience, was in error about one important point. But his error, I hasten to add, was quite unavoidable, and it detracts in no way from his magnificent achievement.
What was this error? As I have said, Kant, like almost all philosophers and epistemologists right into the twentieth century, was convinced that Newton’s theory was true. This conviction was inescapable. Newton’s theory had made the most astonishing and exact predictions, all of which had proved strikingly correct. Only ignorant men could doubt its truth. How little we may reproach Kant for his belief is best shown by the fact that even Henri Poincaré, the greatest mathematician, physicist and philosopher of his generation, who died shortly before the First World War, believed like Kant that Newton’s theory was true and irrefutable. Poincaré was one of the few scientists who felt about Kant’s paradox almost as strongly as Kant himself; and though he proposed a solution which differed somewhat from Kant’s, it was only a variant of it. The important point, however, is that he fully shared Kant’s error, as I have called it. It was an unavoidable error— unavoidable, that is, before Einstein.
Even those who do not accept Einstein’s theory of gravitation ought to admit that his was an achievement of truly epoch-making significance. For his theory established at least that Newton’s theory, no matter whether true or false, was certainly not the only possible system of celestial mechanics that could explain the phenomena in a simple and convincing way. For the first time in more than 200 years Newton’s theory became problematical. It had become, during these two centuries, a dangerous dogma—a dogma of almost stupefying power. I have no objection to those who oppose Einstein’s theory on scientific grounds. But even Einstein’s opponents, like his greatest admirers, ought to be 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.6
Now if, unlike Kant, we consider Newton’s theory as a hypothesis whose truth is problematic, then we must radically alter Kant’s problem. No wonder then that his solution no longer suits the new post-Einsteinian formulation of the problem, and that it must be amended accordingly.
Kant’s solution of the problem is well known. He assumed, correctly I think, that the world as we know it is our interpretation of the observable facts in the light of theories that we ourselves invent. As Kant puts it: ‘Our intellect does not draw its laws from nature … but imposes them upon nature.’ While I regard this formulation of Kant’s as essentially correct, I feel that it is a little too radical, and I should therefore like to put it in the following modified form: ‘Our intellect does not draw its laws from nature, but tries—with varying degrees of success—to impose upon nature laws which it freely invents.’ The difference is this. Kant’s formulation not only implies that our reason attempts to impose laws upon nature, but also that it is invariably successful in this. For Kant believed that Newton’s laws were successfully imposed upon nature by us: that we were bound to interpret nature by means of these laws; from which he concluded that they must be true a priori. This is how Kant saw these matters; and Poincaré saw them in a similar way.
Yet 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. Nor can it impose its interpretation upon nature once and for all time. 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.
Since Kant believed that it was his task to explain the uniqueness and the truth of Newton’s theory, he was led to the belief that this theory followed inescapably and with logical necessity from the laws of our understanding. The modification of Kant’s solution which I propose, in accordance with the Einsteinian revolution, frees us from this compulsion. In this way, theories are seen to be the free creations of our own minds, the result of an almost poetic intuition, of an attempt to understand intuitively the laws of nature. But we no longer try to force our creations upon nature. On the contrary, we question nature, as Kant taught us to do; and we try to elicit from her negative answers concerning the truth of our theories: we do not try to prove or to verify them, but we test them by trying to disprove or 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.
We have seen that theories cannot be logically derived from observations. They can, however, clash with observations: they can contradict observations. This fact makes it possible to infer from observations that a theory is false. 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.
In conclusion I should like to say that ever since Laplace attempts have been made to attribute to our theories instead of truth at least a high degree of probability. I regard these attempts as misconceived. All we can ever hope to say of a theory is that it explains this or that; that it has been tested severely, and that it has stood up to all our tests. 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. But the degree to which they are corroborated (which, in theory at least, can be found out with the help of the calculus of probability) may approach very closely to unity, i.e. its maximum, though the probability of the theory is zero. That an appeal to probability is incapable of solving the riddle of experience is a conclusion first reached long ago by David Hume.
Thus logical analysis shows that experience does not consist in the mechanical accumulation of observations. Experience is creative. It is the result of free, bold and creative interpretations, controlled by severe criticism and severe tests.
In order to avoid right from the start the danger of getting lost in generalities, it might be best to explain at once, with the help of five examples, what I mean by a philosophical theory.
A typical example of a philosophical theory is Kant’s doctrine of determinism, with respect to the world of experience. Though Kant was an indeterminist at heart, he said in the Critique of Practical Reason7 that full knowledge of our psychological and physiological conditions and of our environment would make it possible to predict our future behaviour with the same certainty with which we can predict an eclipse of the sun or of the moon.
In more general terms, one could formulate the determinist doctrine as follows.
The future of the empirical world (or of the phenomenal world) is completely predetermined by its present state, down to its smallest detail.
Another philosophic theory is idealism, for example, Berkeley’s or Schopenhauer’s; we may perhaps express it here by the following thesis: ‘The empirical world is my idea’, or ‘The world is my dream’.
A third philosophic theory—and one that is very important today— is epistemological irrationalism, which might be explained as follows.
Since we know from Kant that human reason is incapable of grasping, or knowing, the world of things in themselves, we must either give up hope of ever knowing it, or else try to know it otherwise than by means of our reason; and since we cannot and will not give up this hope, we can only use irrational or supra-rational means, such as instinct, poetic inspiration, moods, or emotions.
This, irrationalists claim, is possible because in the last analysis we are ourselves such things-in-themselves; thus if we can manage somehow to obtain an intimate and immediate knowledge of ourselves, we can thereby find out what things-in-themselves are like.
This simple argument of irrationalism is highly characteristic of most nineteenth-century post-Kantian philosophers; for example of the ingenious Schopenhauer, who in this way discovered that since we, as things-in-themselves, are will, will must be the thing-in-itself. The world, as a thing-in-itself, is will, while the world as phenomenon is an idea. Strangely enough this obsolescent philosophy, dressed up in new clothes, has once again become the latest fashion, although, or perhaps just because, its striking similarity to old post-Kantian ideas has remained hidden (so far as anything may remain hidden under the emperor’s new clothes). Schopenhauer’s philosophy is nowadays propounded in obscure and impressive language, and his self-revealing intuition that man, as a thing-in-itself, is ultimately will, has now given place to the self-revealing intuition that man may so utterly bore himself that his very boredom proves that the thing-in-itself is Nothing— that it is Nothingness, Emptiness-in-itself. I do not wish to deny a certain measure of originality to this existentialist variant of Schopenhauer’s philosophy: its originality is proved by the fact that Schopenhauer could never have thought so poorly of his powers of self-entertainment. What he discovered in himself was will, activity, tension, excitement—roughly the opposite of what some existentialists discovered: the utter boredom of the bore-in-himself bored by himself. Yet Schopenhauer is no longer the fashion: the great fashion of our post-Kantian and post-rationalist era is what Nietzsche (‘haunted by premonitions, and suspicious of his own progeny’) rightly called ‘European nihilism’.8
Yet all this is only by the way. We now have before us a list of five 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.
Why then have I made a point of selecting for my examples a number of philosophical theories that I believe to be false? Because I hope in this way to put more clearly the problem contained in the following important statement.
Although I consider each one of these five theories to be false, I am nevertheless convinced that each of them is irrefutable.
Listening to this statement you may well wonder how I can possibly hold a theory to be false and irrefutable at one and the same time—I who claim to be a rationalist. For how can a rationalist say of a theory that it is false and irrefutable? Is he not bound, as a rationalist, to refute a theory before he asserts that it is false? And conversely, is he not bound to admit that if a theory is irrefutable, it is true?
With these questions I have at last arrived at our problem.
The last question can be answered fairly simply. There have been thinkers who believed that the truth of a theory may be inferred from its irrefutability. Yet this is an obvious mistake, 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.
To infer the truth of a theory from its irrefutability is therefore inadmissible, no matter how we interpret irrefutability. For normally ‘irrefutability’ would be used in the following two senses:
The first is a purely logical sense: we may use ‘irrefutable’ to mean the same as ‘irrefutable by purely logical means’. But this would mean the same as ‘consistent’. Now it is quite obvious that the truth of a theory cannot possibly be inferred from its consistency.
The second sense of ‘irrefutable’ refers to refutations that make use not only of logical (or analytic) but also of empirical (or synthetic) assumptions; in other words, it admits empirical refutations. In this second sense, ‘irrefutable’ means the same as ‘not empirically refutable’, or more precisely ‘compatible with any possible empirical statement’ or ‘compatible with every possible experience’.
Now both the logical and the empirical irrefutability of a statement or a theory can easily be reconciled with its falsehood. In the case of logical irrefutability this is clear from the fact that every empirical statement and its negation must both be logically irrefutable. For example, the two statements, ‘Today is Monday’, and, ‘Today is not Monday’, are both logically irrefutable; but from this it follows immediately that there exist false statements which are logically irrefutable.
With empirical irrefutability the situation is a little different. The simplest examples of empirically irrefutable statements are so-called strict or pure existential statements. Here is an example of a strict or pure existential statement. ‘There exists a pearl which is ten times larger than the next largest pearl.’ If in this statement we restrict the words ‘There exists’ to some finite region in space and time, then it may of course become a refutable statement. For example, the following statement is obviously empirically refutable: ‘At this moment and in this box here there exist at least two pearls one of which is ten times larger than the next largest pearl in this box.’ But then this statement is no longer a strict or pure existential statement; rather it is a restricted existential statement. A strict or pure existential statement applies to the whole universe, and it is irrefutable simply because there can be no method by which it could be refuted. For even if we were able to search our entire universe, the strict or pure existential statement would not be refuted by our failure to discover the required pearl, seeing that it might always be hiding in a place where we are not looking.
Examples of empirically irrefutable existential statements which are of greater interest are the following.
‘There exists a completely effective cure for cancer, or, more precisely, there is a chemical compound which can be taken without ill effect, and which cures cancer.’ Needless to say, this statement must not be interpreted as meaning that such a chemical compound is actually known or that it will be discovered within a given time.
Similar examples are: ‘There exists a cure for any infectious disease’, and, ‘There exists a Latin formula which, if pronounced in proper ritual manner, cures all diseases.’
Here we have an empirically irrefutable statement that few of us would hold to be true. The statement is irrefutable because it is obviously impossible to try out every conceivable Latin formula in combination with every conceivable manner of pronouncing it. Thus there always remains the logical possibility that there might be, after all, a magical Latin formula with the power of curing all diseases.
Even so, we are justified in believing that this irrefutable existential statement is false. We certainly cannot prove its falsehood; but everything we know about diseases tells against its being true. In other words, though we cannot establish its falsity, the conjecture that there is no such magical Latin formula is much more reasonable than the irrefutable conjecture that such a formula does exist.
I need hardly add that through almost 2,000 years learned men have believed in the truth of an existential statement very much like this one; this is why they persisted in their search for the philosopher’s stone. Their failure to find it does not prove anything—precisely because existential propositions are irrefutable.
Thus the logical or empirical irrefutability of a theory is certainly not a sufficient reason for holding the theory to be true, and hence I have vindicated my right to believe, at the same time, that these five philosophical theories are irrefutable, and that they are false.
Some twenty-five years ago I proposed to distinguish empirical or scientific theories from non-empirical or non-scientific ones precisely by defining the empirical theories as the refutable ones and the non-empirical theories as the irrefutable ones. My reasons for this proposal were as follows. Every serious test of a theory is an attempt to refute it. Testability is therefore the same as refutability, or falsifiability. And since we should call ‘empirical’ or ‘scientific’ only such theories as can be empirically tested, we may conclude that it is the possibility of an empirical refutation which distinguishes empirical or scientific theories.
If this ‘criterion of refutability’ is accepted, then we see at once that philosophical theories, or metaphysical theories, will be irrefutable by definition.
My assertion that our five philosophical theories are irrefutable may now sound almost trivial. At the same time it will have become obvious that though I am a rationalist I am in no way obliged to refute these theories before being entitled to call them ‘false’. And this brings us to the crux of our problem:
If philosophical theories are all irrefutable, how can we ever distinguish between true and false philosophical theories?
This is the serious problem which arises from the irrefutability of philosophical theories.
In order to state the problem more clearly, I should like to reformulate it as follows.
We may distinguish here between three types of theory.
First, logical and mathematical theories.
Second, empirical and scientific theories.
Third, philosophical or metaphysical theories.
How can we, in each of these groups, distinguish between true and false theories?
Regarding the first group the answer is obvious. Whenever we find a mathematical theory of which we do not know whether it is true or false we test it, first superficially and then more severely, by trying to refute it. If we are unsuccessful we then try to prove it or to refute its negation. If we fail again, doubts as to the truth of the theory may have cropped up again, and we shall again try to refute it, and so on, until we either reach a decision or else shelve the problem as too difficult for us.
The situation could also be described as follows. Our task is the testing, the critical examination, of two (or more) rival theories. We solve it by trying to refute them—either the one or the other—until we come to a decision. In mathematics (but only in mathematics) such decisions are generally final: invalid proofs that escape detection are rare.
If we now look at the empirical sciences, we find that we follow, as a rule, fundamentally the same procedure. Once again we test our theories: we examine them critically, we try to refute them. The only important difference is that now we can also make use of empirical arguments in our critical examinations. But these empirical arguments occur only together with other critical considerations. Critical thought as such remains our main instrument. Observations are used only if they fit into our critical discussion.
Now if we apply these considerations to philosophical theories, our problem can be reformulated as follows:
Is it possible to examine irrefutable philosophical theories critically? If so, what can a critical discussion of a theory consist of, if not of attempts to refute the theory?
In other words, is it possible to assess an irrefutable theory rationally—which is to say, critically? And what reasonable argument can we adduce for and against a theory which we know to be neither demonstrable nor refutable?
In order to illustrate these various formulations of our problem by examples, we may first refer again to the problem of determinism. Kant knew perfectly well that we are unable to predict the future actions of a human being as accurately as we can predict an eclipse. But he explained the difference by assuming that we know far less about the present conditions of a man—about his wishes and fears, his feelings and his motives—than about the present state of the solar system. Now this assumption contains, implicitly, the following hypothesis:
‘There exists a true description of the present state of this man which would suffice (in conjunction with true natural laws) for the prediction of his future actions.’
This is of course again a purely existential statement, and it is thus irrefutable. Can we, in spite of this fact, discuss Kant’s argument rationally and critically?
As a second example we may consider the thesis: ‘The world is my dream.’ Though this thesis is clearly irrefutable, few will believe in its truth. But can we discuss it rationally and critically? Is not its irrefutability an insurmountable obstacle to any critical discussion?
As to Kant’s doctrine of determinism, it might perhaps be thought that the critical discussion of it might begin by saying to him: ‘My dear Kant, it simply is not enough to assert that there exists a true description that is sufficiently detailed to enable us to predict the future. What you must do is tell us exactly what this description would consist of, so that we may test your theory empirically.’ This speech, however, would be tantamount to the assumption that philosophical—that is, irrefutable—theories can never be discussed and that a responsible thinker is bound to replace them by empirically testable theories, in order to make a rational discussion possible.
I hope that our problem has by now become sufficiently clear; so I will now proceed to propose a solution of it.
My solution is this: if a philosophical theory were no more than an isolated assertion about the world, flung at us with an implied ‘take it or leave it’ and without a hint of any connection with anything else, then it would indeed be beyond discussion. But the same might be said of an empirical theory also. Should anybody present us with Newton’s equations, or even with his arguments, without explaining to us first what the problems were which his theory was meant to solve, then we should not be able to discuss its truth rationally—no more than the truth of the Book of Revelation. Without any knowledge of the results of Galileo and Kepler, of the problems that were resolved by these results, and of Newton’s problem of explaining Galileo’s and Kepler’s solutions by a unified theory, we should find Newton’s theory just as much beyond discussion as any metaphysical theory. In other words every rational theory, no matter whether scientific or philosophical, is rational in so far as it tries to solve certain problems. A theory is comprehensible and reasonable only in its relation to a given problem-situation, and it can be rationally discussed only by discussing this relation.
Now if we look upon a theory as a proposed solution to a set of problems, then the theory immediately lends itself to critical discussion—even if it is non-empirical and irrefutable. For we can now ask questions such as, Does it solve the problem? Does it solve it better than other theories? Has it perhaps merely shifted the problem? Is the solution simple? Is it fruitful? Does it perhaps contradict other philosophical theories needed for solving other problems?
Questions of this kind show that a critical discussion even of irrefutable theories may well be possible.
Once again let me refer to a specific example: the idealism of Berkeley or Hume (which I have replaced by the simplified formula ‘The world is my dream’). It is notable that these authors were far from wishing to offer us an extravagant, an incredible theory. This may be seen from Berkeley’s repeated insistence that his theories were really in agreement with sound common sense.9 Now if we try to understand the problem situation which induced them to propound this theory, then we find that Berkeley and Hume believed that all our knowledge was reducible to sense-impressions and to associations between memory-images. This assumption led these two philosophers to adopt idealism; and in the case of Hume, in particular, very unwillingly. Hume was an idealist only because he failed in his attempt to reduce realism to sense-impressions.
It is therefore perfectly reasonable to criticize Hume’s idealism by pointing out that his sensualistic theory of knowledge and of learning was in any case inadequate, and that there are less inadequate theories of learning which have no unwanted idealistic consequences.
In a similar way we could now proceed to discuss Kant’s determinism rationally and critically. Kant was in his fundamental intention an indeterminist: even though he believed in determinism with respect to the phenomenal world as an unavoidable consequence of Newton’s theory, he never doubted that man, as a moral being, was not determined. Kant never succeeded in solving the resulting conflict between his theoretical and practical philosophy in a way that satisfied himself completely, and he despaired of ever finding a real solution.
In the setting of this problem-situation it becomes possible to criticize Kant’s determinism. We may ask, for example, whether it really follows from Newton’s theory. Let us conjecture for a moment that it does not. I do not doubt that a clear proof of the truth of this conjecture would have persuaded Kant to renounce his doctrine of determinism—even though this doctrine happens to be irrefutable and even though he would not, for this very reason, have been logically compelled to renounce it.
Similarly with irrationalism. It first entered rational philosophy with Hume—and those who have read Hume, that calm analyst, cannot doubt that this was not what he intended. Irrationalism was the unintended consequence of Hume’s conviction that we do in fact learn by Baconian induction coupled with Hume’s logical proof that it is impossible to justify induction rationally. ‘So much the worse for rational justification’ was a conclusion which Hume, of necessity, was compelled to draw from this situation. He accepted this irrational conclusion with the integrity characteristic of the real rationalist who does not shrink from an unpleasant conclusion if it seems to him unavoidable.
Yet in this case it was not unavoidable, though it seemed to be so to Hume. We are not in fact the Baconian induction machines that Hume believed us to be. Habit or custom does not play the role in the process of learning which Hume assigned to it. And so Hume’s problem dissolves and with it his irrationalist conclusions.
The situation of post-Kantian irrationalism is somewhat similar. Schopenhauer in particular was genuinely opposed to irrationalism. He wrote with only one desire: to be understood; and he wrote more lucidly than any other German philosopher. His striving to be understood made him one of the few great masters of the German language.
Yet Schopenhauer’s problems were those of Kant’s metaphysics— the problem of determinism in the phenomenal world, the problem of the thing-in-itself, and the problem of our own membership of a world of things-in-themselves. He solved these problems—problems transcending all possible experience—in his typically rational manner. But the solution was bound to be irrational. For Schopenhauer was a Kantian and as such he believed in the Kantian limits of reason: he believed that the limits of human reason coincided with the limits of possible experience.
But here again there are other possible solutions. Kant’s problems can and must be revised; and the direction that this revision should take is indicated by his fundamental idea of critical, or self-critical, rationalism. The discovery of a philosophical problem can be something final; it is made once, and for all time. But the solution of a philosophical problem is never final. It cannot be based upon a final proof or upon a final refutation: this is a consequence of the irrefutability of philosophical theories. Nor can the solution be based upon the magical formulae of inspired (or bored) philosophical prophets. Yet it may be based upon the conscientious and critical examination of a problem-situation and its underlying assumptions, and of the various possible ways of resolving it.
Two Radio Talks written for the Free Radio-University, Berlin; first published in Ratio, 1, 1958, pp. 97–115.
1 Also of great importance is the Latin Physical Monadology of 1756 in which Kant anticipated the main idea of BOSCOVIč; but in his work of 1786 Kant repudiated the theory of matter propounded in his Monadology.
2 A similar consideration may be found in Bertrand Russell’s The Analysis of Mind, 1922, pp. 95 f.
3 Cp. Aristotle, De Caelo, 293b1–5, where the doctrine that the centre of the universe is ‘precious’ and therefore to be occupied by a central fire is criticized and ascribed to the ‘Pythagoreans’ (which perhaps means his rivals, the successors of Plato who stayed in the Academy).
4 I think that Arthur Koestler’s criticism of Galileo, in his remarkable book The Sleep-walkers, suffers from the fact that he does not take into account the schism described here. Galileo was as justified in trying to see whether he could not solve the problems within the rationalist framework as was Kepler in his attempts to solve them within the astrological framework. For the influence of astrological ideas see also note 4 to ch. 1 of the present volume.
5 The original has no italics.
6 See Einstein’s own formulation in his Herbert Spencer lecture ‘On the Method of Theoretical Physics’, 1933, p. 11, where he writes: ‘It was the general Theory of Relativity which showed … that it was possible for us, using basic principles, very far removed from those of Newton, to do justice to the entire range of the data of experience …’
7 Kritik der praktischen Vernunft, 4th to 6th edn., p. 172; Works, ed. Cassirer, vol. v, p. 108.
8 Cf. Julius Kraft, Von Husserl zu Heidegger, 2nd edn., 1957, e.g. pp. 103 f., 136 f. and particularly p. 130, where Kraft writes: ‘Thus it is hard to understand how existentialism could ever have been considered to be something new in philosophy, from an epistemological point of view.’ Cf. also the stimulating paper by H. Tint, in the Proc. Aristot. Society 1956–7, pp. 253 ff.
9 It may also be seen from Hume’s frank admission that ‘whatever may be the reader’s opinion at this present moment, … an hour hence he will be persuaded there is both an external and internal world’ (Treatise, I, IV, end of section ii; Selby-Bigge, p. 218).