Chapter V

Further Evidence for this Identification

[ Preface | Part One | Part Two | Notes | Bibliography | Cover ]


Recapitulating the conclusions of the preceding chapter, but omitting now the details of the sub-arguments for empiricism and for the fallibility of induction, Hume's argument was the following:

    Fallibility of }
      Induction    }
                   } -> Inductive Scepticism }
    Deductivism    }                         } -> Scepticism about
                        Empiricism           }      the Unobserved

That is, the immediate grounds of his scepticism about the unobserved were the thesis that only propositions about the observed can be a reason to believe anything about the unobserved, plus the thesis that even they are not such a reason. And for this latter sceptical thesis, his ultimate grounds were premises which entail that the invalidity of inductive arguments is incurable by any additional premises which are either observational or necessarily true; plus the assumption that the premise of an argument is no reason to believe its conclusion, unless the argument is valid, or can be made so by additional premises which are either observation-statements or necessary truths. But from empiricism, or from inductive fallibilism, or from their conjunction, no sceptical or irrationalist consequence follows. When they are combined with deductivism, however, first scepticism about induction follows, and then scepticism concerning any contingent proposition about the unobserved. The key premise of Hume's argument, therefore, in the sense of being that premise without which the argument would have no sceptical or irrationalist consequences, is deductivism.

All of this is exactly true of Popper as well. His irrationalism about scientific theories is no other than Hume's scepticism concerning contingent propositions about the unobserved; nor are his grounds for it other than Hume's. Popper is no less an empiricist than Hume: he does not believe, any more than Hume did, that any propositions except observation-statements can be a reason to believe a scientific theory. And at the same time he is, as he is always telling us, a Humean sceptic about arguments from the observed to the unobserved. For this inductive scepticism in its turn, Popper's argument is just, as he tells us, that `flawless gem' of an argument which was Hume's: from the fact that inductive arguments are invalid, and that this condition cannot be cured by additional premises either observational or necessarily true; plus the deductivist assumption that if an argument is of this kind, then its premises is no reason to believe its conclusion. In Popper's philosophy of science, therefore, as in Hume's, the premises on which all the irrationalist consequences depend is deductivism. And since our other authors' philosophy of science is derived almost entirely from Popper's, deductivism is the key to their irrationalism too.

Recent irrationalist philosophy of science is therefore to be ascribed (insofar as it can be ascribed to intellectual causes at all) to acceptance of the thesis of deductivism. What has been decisive in leading these authors to conclude that there can be no reasonable belief in a scientific theory, and a fortiriori that there has been no accumulation of knowledge in the last few centuries, is a certain extreme belief, by which their minds are dominated, about what is required for one proposition to be a reason to believe another.

The truth of the key premise of our authors' philosophy is not (as was said at the beginning of this Part) a question with which this book is concerned. But we have now at least identified the proposition to which criticism of their philosophy, if it is not to be entirely indecisive, needs to be directed. To criticize our authors on the basis of the history of science, for example, is sure to be in practice indecisive at best, but is futile even in principle. For the assumption on which everything distinctive of their philosophy rests is in fact one which has nothing at all to do with science, and least of all with the history of science. It is a simple thesis in the philosophy of logic or of reasonable inference, and it is nothing more. It has not even, it should be emphasized, any necessary connection with the subject of inductive inference; for, as was pointed out near the end of the preceding chapter, deductivism is a thesis logically independent of inductive scepticism.

Deductivism, is not, of course, explicit in Popper's writings; though it is more nearly so there than it is with Hume. At the same time I know of no reason to doubt that Popper would accept the attribution of that thesis to him. Of course virtually no philosopher nowadays, if he were to embrace deductivism explicitly, would bother to retain that part of it which refers to necessary truths as possible validators of arguments. On the contrary, philosophers now assume that the addition of a necessary truth of the premises of an invalid argument will never turn it into a valid one. The reason is, that the conjunction of any necessarily true R to any P is logically equivalent to P itself; and that two arguments cannot differ in logical value, and hence one of them cannot be valid and the other not, if they have logically equivalent premises and the same conclusion. Accordingly I too will henceforth omit the phrase "[...] or necessary truths" from the thesis of deductivism; and when I sometimes in the following pages call an argument incurably invalid, I will here mean just that no additional premise which is observational would turn it into a valid argument.

I have now given my answer to the question to which Part Two of this book is addressed: how did our authors come to embrace irrationalist philosophy of science? My answer is, through embracing deductivism. My main grounds for thinking this answer correct are those which have now been given: that our authors' irrationalism about science is derived from Hume, and that the key premise of Hume's irrationalist philosophy of science is deductivism.

But there are other grounds as well for thinking this answer correct. These are, in sum, that it explains extremely well a number of prominent and distinctive features of our authors' writings, including some features which seem at first quite unconnected with deductivism, or even opposed to it. This is what I now intend to show.


First, the deductivism of our authors is what ultimately necessitated those two devices which were the subject of Part One above, and which are those authors' literary hall-mark.

If you are a deductivist, then you cannot allow yourself to use, in earnest, the word "confirms", or any of the weak or non-deductive-logical expressions. To say of an observation-statement O that is confirms a scientific theory T, entails that those two propositions stand in some logical relation such that O is a reason to believe T. But this cannot be so if deductivism is true, in view of the truth of the fallibilist thesis, that neither O, nor O conjoined with any other observation-statements, entails T. So instead of saying that O confirms T, a deductivist, at least if he is resolved, as our authors are, not to be openly and constantly irrationalist about science, must often write that O `confirms' T; or write that scientists regard T as confirmed by O; or write something, anyway, which, while it purports to be a statement of logic, is in fact nothing of the kind. In other words, he must often sabotage the logical expression `confirms'.

In this way, all logical pipes, along which reasonable belief might travel from observation to scientific theories, are cut by deductivism. But our authors are also empiricists, and do not for a moment suppose that there are any sources, other than observation, from which reasonable belief in scientific theories might come. And neither they nor anyone else, of course, suppose that scientific theories are directly accessible to knowledge or reasonable belief. According to these authors, therefore, reasonable belief cannot accrue to scientific theories in any way at all. And that is why success-words, like "knowledge" and "discovery", which imply that reasonable belief has accrued to the propositions which are their objects, must be neutralized by our authors when they are employed in connection with science; or, if not neutralized, then simply avoided altogether.

We thus see that, of our authors' two devices for making irrationalism plausible, the primary one is the sabotage of logical expressions: the need to neutralize success-words is consequential upon that. But the sabotage of logical expressions is in its turn necessitated by a substantive philosophical thesis; and that is deductivism.

It has been widely recognized, and was admitted at the beginning of this book, that the answer in general terms to the question, "How have these authors made irrationalism plausible to their readers?", is: by fostering the confusion of questions of logical value with questions of historical fact, or of the philosophy with the history of science. I undertook to show in detail how this trick is turned. This has now been done. For, of our authors' devices for making irrationalism plausible, the basic one, we have now found, is the sabotage of logical expressions; their favorite way of doing this, we saw in Chapter II, is by embedding a statement of logic in an epistemic context about scientists; and now, the effect of that is, precisely, to disguise historical statements as logical ones. Thus for example, the schematic logical statement, "Observation-statement O confirms theory T", attributes a certain logical value to the argument from O to T; but its ghost-logical surrogate, "Scientists regard T as confirmed by O", for all its artful suggestions of logic, is nothing but a historical proposition after all.

A deductivist philosopher of science, if he is an empiricist and an inductive fallibilist, must sabotage logical expressions which are weak. But even the strong or deductive-logical expression will almost inevitably undergo misuse at his hands. Recall the `primal scene' of the sabotage of a deductive-logical expression: that is, Popper contemplating the logical relation between E, "The relative frequency of males among births in human history so far is 0.51", and H, "The probability of a human birth being male is 0.9". A deductivist cannot say, what anyone else can and would say, that E is a reason to believe that H is false. For this cannot be true if deductivism is true; since neither E nor the conjunction of E with any other observation-statement entails not-H. What, then, is the deductivist to say about the relation between E and H? Since "falsifies" entails "is inconsistent with", he cannot, for the fallibilist reason just mentioned, say without falsity that E falsifies H. Being cut off from using weak logical expressions, he cannot say, what is of course true, that E disconfirms H, or confirms not-H. Rather, then, than write down nothing at all, or something which is obviously false, the deductivist, very understandably, writes instead that E `falsifies' H; or that any scientists would regard E as falsifying H; or else he himself `proposes' that E be regarded as falsifying H.

In this way, the cast of mind which will acknowledge only deductive-logical relations between propositions back-fires, so to speak, on its own possessors. It obliges them, on pain of suffering the fate which to them is even worse, of acknowledging non-deductive logical relations, to misuse those very logical expressions which they themselves regard as being the only admissible ones. This is the phenomenon referred to in Chapter II above, of deductivists being obliged in the end to strangle their own children.


There are, of course, very few people who believe that deductivism is true. The human race at large is decidedly of the opposite opinion, and holds that there are extremely numerous values of P, Q, and R, such that P is a reason to believe Q, without Q being entailed either by P or by P-and-R for some observational R. Confirmation-theory, or non-deductive logic, or `inductive' logic as Carnap called it, is the attempt to put into systematic form the very many intuitive beliefs which everyone has about when P is a reason to believe Q. Our authors entertain a boundless hostility and contempt for non-deductive logic; and the explanation of this fact lies, of course, in their deductivism.

Carnap speaks of `inductive' logic, because he chose to use the word "inductive", as his Glossary indicates [1], simply as a synonym for "non-deductive". This is a neologism which was apparently unconscious, and which has nothing at all to recommend it. There is nothing to be said for calling the argument, for example, to "Socrates is a man", from "All men are mortal and Socrates is mortal", "inductive"; nor for calling so the argument to "Socrates is mortal" from "99% of men are mortal and Socrates is a man". But there is a great deal to be said against it. It suggests, what is false, that non-deductive logic is concerned exclusively with arguments from the observed to the unobserved; whereas this class of arguments, for all its special importance for empiricist philosophers of science, is only one among many classes of non-deductive arguments. It suggests, what is false, that the thesis of the incurable invalidity of inductive arguments is an analytic triviality; which it is so far from being that Mill and many others, as we saw in Chapter IV, have by implication denied it. And it therefore further suggests, what is also false, that deductivism, and scepticism about induction, are logically equivalent theses; whereas they are, as we have seen, actually independent. These consequences suffice to show that Carnap's neologism was tragically inept. But it has acquired too much currency to be soon reversed, and accordingly I adopt it here; though never without a protest in the form of quotation-marks around "inductive", whenever I use it as an adjective to "logic" or "logicians".

The chief land-marks of `inductive' logic are Carnap's Logical Foundations of Probability (1950), and the articles of Hempel which are collected in Aspects of Scientific Explanation [2]. Now these writings, despite both their self-imposed limitations and their consequent essentially fragmentary nature, and despite some positive errors which they undoubtedly contain, represent far more progress, in an area of the first intellectual importance, than the entire history of the human race can show before. Their only serious fore-runners, indeed, are some of the writings which belong to the `classical' period of the theory of probability, between 1650 and 1850. And what immense strides Carnap, in particular, made, in clarifying, in improving, and in extending, that priceless but profoundly confused historical deposit, many students of probability know; even if others do not. Not contempt, then, but rather all honor, is due to these writers, for the mighty fragments of non-deductive logic which they have left us.

But even if Carnap, Hempel, and their followers, had achieved, as their deductivist critics allege that they have achieved, nothing constructive at all in the way of systematic non-deductive logic, they would still merit the respect which is due to their having been in earnest with empiricist philosophy of science. There can be no serious philosophy, of science or of anything else, without seriousness about the logical relations between propositions. And there can be no serious empiricist philosophy of science, in particular, without seriousness about the non-deductive logical relations between propositions. Arguments from the observed to the unobserved really are incurably invalid: this much of Hume's philosophy of science is true, and in this much all empiricists are now agreed. But, this much being agreed, any empiricist who is also a deductivist, as all our authors are, condemns himself, not just to irrationalism, but to unseriousness, about science.


Hostility to non-deductive logic, and the sabotaging of non-deductive-logical expressions, are among the inevitable consequences of our authors' deductivism. But there are also two marked and characteristic features of our authors' writings which, although not inevitable consequences of their deductivism, can only be explained by reference to it, or to that cast of mind which acknowledges only deductive-logical relations between propositions.

One of these features, and one which is at first sight surprising in deductivists, is this: an extreme lack of rigor in matters of deductive logic.

As evidence of this fact, I could of course cite again all the cases, already mentioned in Chapter II, in which a deductive-logical expression is sabotaged by our authors; all the cases, for example, in which they say that one proposition or kind of proposition `falsifies' another, when they know well enough that the two are not inconsistent. But obviously it would be preferable, if it is possible, to draw here on entirely independent evidence; and this is not only possible but easy. I will give three instances of the extreme lack of rigor of which I speak. All three are drawn from Popper, who is the most rigorous of our authors.

(1) Two scientific theories can be inconsistent with one another. This fact is too obvious to need examples to prove it. Nor has any philosopher assumed this obvious truth more often than Popper does. His writings are full of references to incompatible, or conflicting, or competing, or rival, scientific theories. Nor is this an accident. For his entire philosophy of science in fact arose (as we saw in Chapter III) from contemplating, over and over again as in a nightmare, the overthrow of Newtonian physics by a rival theory; this kind of episode in the history of science has always remained his principal concern; and he thinks (as we saw in Chapter II) that the overthrow of one scientific theory always requires the presence of an incompatible theory.

At the same time, it is an immediate and obvious consequence of the account which Popper gives of the logical form of scientific theories, that one scientific theory cannot be inconsistent with another.

This account was given by Popper in his [1959], and has since then been taken for granted in all his writings. According to it, any scientific theory, and equally any law-statement (for Popper always lumps these two together) is what we may call "a mere denial of existence". That is, it is a proposition which denies the existence of a certain kind of thing, and which does not assert the existence of anything.

"(x)(Raven x => Black x)" will suffice as an example of this class of propositions. Since it is logically equivalent to "There are no non-black ravens", it denies the existence of a certain kind of thing; and since, for the same reason, it would be true (as philosophers say) "in the empty universe", that is, if nothing at all existed, it does not assert the existence of anything. Hence it is a mere denial of existence.

That Popper does conceive scientific theories and laws as mere denials of existence, the following quotation is sufficient to establish. "The theories of natural science, and especially what we call natural laws, have the form of strictly universal statements; thus they can be expressed in the form of negations of strictly existential statements, or, as we may say, in the form of non-existence statements (or `there-is-not' statements). For example, the law of conservation of energy can be expressed in the form: `There is no perpetual motion machine', or the hypothesis of the electrical elementary charge in the form: `There is no electrical charge other than a multiple of the electrical elementary charge'. In this formulation we see that natural laws might be compared to `proscriptions' or `prohibitions'. They do not assert that something exists or is the case; they deny it. They insist on the non-existence of certain things or states of affairs, proscribing or prohibiting, as it were, these things or states of affairs: they rule them out" [3].

But now, two mere denials of existence cannot be inconsistent with one another. For in the logically possible case of the empty universe, all such propositions would be true.

Hence Popper, while he constantly assumes that two scientific theories, or two law-statements, can be inconsistent with one another, gives an account of the logical form of such propositions which immediately has, by the most elementary deductive logic, the consequence that they cannot.

(2) Let us call the conjunction of Newton's laws of motion with his inverse-square law of gravitational attraction, "Newtonian physics". And let us consider the question of whether Newtonian physics in this sense is falsifiable; the question, that is, whether there is any observation-statement which is inconsistent with Newtonian physics.

Even allowing for the differences in detail which exist among philosophers as to what counts as an observation-statement, it is obvious enough that the answer to this question is "no". There can be no observably non-Newtonian behavior, on the part of billiard balls or of anything else. (There could, of course, be non-Newtonian behavior, for example a billiard ball coming to rest with no forces acting on it; but then, that there are no forces acting on this ball, is a theoretical generalization, and hence cannot be part of an observation-statement). That Newtonian physics is unfalsifiable, is also evident from the fact that, however oddly billiard balls might behave on a given occasion, Newtonian physics could form part of the deductive explanation of this behavior, by being combined with other propositions, perhaps about hidden masses, or about the presence of forces other than inertia and gravitation.

Newtonian physics (in our sense) is evidently a scientific theory. This fact, along with its unfalsifiability, is a refutation of Popper's famous thesis that falsifiability is a necessary condition of a theory's being a scientific one. This criticism of Popper was made by Lakatos [4].

Popper's reply is given in the following paragraph. "Suppose that our astronomical observations were to show, from tomorrow on, that the velocity of the earth (which remains on its present geometrical path) was increasing, either in its daily or in its annual movement, while the other planets in the solar system proceeded as before. Or suppose that Mars started to move in a curve of the fourth power, instead of moving in an ellipse of power 2. Or assume still more simply, that we construct a gun that fires ballistic missiles which consistently move in a clearly non-Newtonian track [...]. There are an infinity of possibilities, and the realization of any of them would simply refute Newton's theory. In fact, almost any statement about a physical body which we may make---say, about the cup of tea before me, that it begins to dance (and say, in addition, without spilling the tea)---would contradict Newtonian theory. This theory would equally be contradicted if the apples from one of my, or Newton's, apple trees were to rise up from the ground (without there being a whirlwind about), and begin to dance around the branches of the apple tree from which they had fallen, or if the moon were to go off at a tangent; and if all of this were to happen, perhaps, without any other very obvious changes in our environment" [5]. (I have here substituted the word "track" where, I take it, "tract" is a misprint in the original).

That Popper's reference to missiles which move in a "clearly non-Newtonian track" was a flagrant begging of the question, I need hardly state. The question, which Lakatos had answered in the negative, was, precisely, whether there is any such thing as a "clearly", that is observably, non-Newtonian track.

But the principal defect of the paragraph just quoted is much more simple and amazing than this. Consider the proposition: "There was no whirlwind about; the apples which had fallen from my tree rose from the ground and began to dance round the branches of the tree; and this happened, perhaps, without any other very obvious change in the environment". It might be doubted, in view of the remarkable last clause, whether this proposition is, as it needs to be in order to be relevant at all, an observation-statement. But we do not need to decide that. For it is not only obvious, it is blazingly obvious, that this proposition, whether it is observational or not, is not inconsistent with Newtonian physics. The same is true, and equally obviously true, of the proposition: "The cup of tea in front of Popper began to dance, without spilling the tea". The same is also obviously true of every one of the other examples which Popper gives. Yet he brazenly asserts that any of these propositions, and indeed "almost any statement about a physical body which we may make [...] would contradict Newtonian theory".

One can scarcely believe one's eyes while reading this paragraph of Popper. What beginning student of deductive logic would not be ashamed to assert such transparent logical falsities as these? (He would never be tempted to do so, however, because they have not the smallest particle of plausibility to recommend them). What editor would print such palpable untruths, if they came to him from an `ordinary philosopher'? It is difficult, in fact, to imagine a more brutal contempt for deductive logic than is displayed by this impudent list of so-called falsifiers of Newtonian physics.

If the paragraph quoted above was not mere bluff (as I believe it was), then it testifies to the survival, in an unlikely quarter, of a belief which was very common in the two preceding centuries, and which has only recently been almost entirely extinguished: the belief that Newtonian physics is a guarantee against the occurrence of---just about anything disagreeable. In the mid-18th century Dr.Johnson refused for six months, on a mixture of Anglican and Newtonian grounds, to believe the reports of the Lisbon earthquake. In the mid-19th century it was widely believed that Newtonian physics, as developed by Laplace in particular, guaranteed the stability and permanence of the solar system (at any rate until `the trumpet shall sound'). That this belief survived to some extent even up to the mid-20th century, is strongly suggested by the irrational hostility with which Immanuel Velikovsky's theories were received in 1950. Now, of course, when theories like his have become respectable, this belief is almost extinct. But even when it was at its height, say among 18th-century Anglicans, I never heard of anyone who believed that Newtonian physics was a logical guarantee of decent behavior on the part of his teacup.

(3) My third example also concerns Newtonian physics, in the same sense as before. In this case the question is, what logical relation does Newtonian physics bear to Kepler's laws of planetary motion?

An answer which has often been given to this question, and which has been still more often implied, is that Newtonian physics entails Kepler's laws. It is obvious that this is not so. Kepler's laws entail that the planets and the sun exist; but Newtonian physics has no such entailment.

Popper gives a different answer. Newtonian physics, he says, is actually inconsistent with Kepler's laws. It "formally contradicts" [6] them; "from a logical point of view, Newton's theory, strictly speaking, contradicts both Galileo's and Kepler's [...]" [7].

This answer to the above question has become an article of faith among irrationalist philosophers of science. Feyerabend [8], Kuhn [9], and many others [10] repeat it. Yet it is obvious that this answer too is false: strictly speaking, and formally, Newtonian physics is not inconsistent with Kepler's laws.

Kepler's laws are purely kinematic; that is, they simply ascribe certain motions to certain bodies, and say nothing whatever about the mass of anything, or about any force exerted by or on anything. And it is easily seen that no purely kinematic proposition is inconsistent with Newtonian physics. Take any purely kinematic proposition: for preference, here, such a highly `non-Newtonian' one as, say, "The planets describe rectangles with the sun as center". This proposition is so far from being inconsistent with Newtonian physics, that it could be deduced from and explained by Newtonian physics, in conjunction with certain contingent assumptions about the forces to which the planets are subjected, the mass of the planets, their cohesiveness, and so on. Some at least of these auxiliary propositions would of course be false in fact. Their conjunction with Newtonian physics would therefore be false in fact too. But that conjunction, obviously, need not be logically false; as it would have to be, if the hypothesis of rectangular orbits were actually inconsistent with Newtonian physics. And the same is equally true of any other purely kinematic proposition, such as Kepler's laws.

The examples which have just been given, of carelessness, or something a good deal worse, regarding deductive-logical relations between propositions, are characteristic of our authors. They are in fact characteristic of them in two senses. One is, that other examples of the same kind can easily be supplied from their writings [11]. The other is, that there is no parallel to these examples in the writings of non-irrationalist philosophers of science. In particular, one would look in vain in the writings of the `inductive' logicians, for anything corresponding to the carelessness, in matters of deductive-logical relations between propositions of science, which has just been illustrated from our deductivist authors.

Now this is, at least at first sight, surprising. One expects a deductivist to be a severe judge of logical morals, and not only of other people's: his own logical conduct one would expect to be above reproach. He is the last person one would expect to assert or imply that a certain deductive-logical relation exists, in cases where it does not, or does not exist, in cases where it does. And on the other hand such sloppiness would not be at all unexpected from `inductive' logicians. After all, they are `soft on logic'. For example they wish to palliate those inductive propensities which erring man shares with the brute creation, and which deductivists think should only be reprehended. Indeed, the entire enterprise of `inductive' logic appears (at least to its critics) intended to conceal, by a fig-leaf of system, the naked indecency of affirming the consequent. Why then is it precisely the deductivists, and not the `inductive' logicians, whose deductive logic turns out to be bad? Why is it that, while Popper's philosophy of science furnishes a steady stream of examples of indifference to elementary deductive logic, the philosophy of Carnap or of Hempel does nothing of the kind? I believe I can answer this question.

Deductivism, it is to be remembered, is a variety of perfectionism: it is an `only the best will do' thesis. And, at least in very many domains, perfectionism is especially apt to produce performance which is actually further from perfection than the average for that domain. In politics, for example, perfectionism is wisely recognized as having brought into being the very worst societies. In philosophy each of us knows someone whose standards are so extremely high that he never does any philosophy at all. In morals the ancient perfectionist doctrine, often revived, that all evils are equally evil, is at once recognized by any person of common sense as sure to have disastrous moral effects in practice. And so on.

Nor is the inner mechanism of these causal connections at all hard to perceive. It is this. The perfectionist, by his exclusive concentration on the ideal, is prevented from attending to the differences which exist among cases in which that ideal is not satisfied: even though such cases may include all the actual ones (the ideal being so high), and even though the differences are very great between some of these cases and others.

This gives us a reason to anticipate that deductivists will be, in practice, uncommonly careless in matters of deductive logic. But it does not on its own quite cover the particular case before us. For here the errors are all of one particular kind, and of a kind which is still rather surprising. Our authors' carelessness never takes the form of implying that some specific deductive-logical relation does not exist, in cases where it does. In always takes the form, as in the three examples given above, of implying that a specific deductive-logical relation exists, in cases where it does not. This cannot be explained just by the tendency of perfectionism to result in general carelessness. On the contrary, it is somewhat surprising in perfectionists. For its moral analogue (for example) would be, a perfectionist whose neglect of the differences between actual evils often carried him to the point of positively mistaking actual evils for ideal goods. This is not what one expects from perfectionists. How is this particular kind of carelessness to be explained?

Popper, as we saw in Chapter II above, rejected the belief that there are propositions of science "the analysis of [whose] relations compels us to introduce a special probabilistic logic which breaks the fetters of classical logic" [12]. In opposition to such views, he undertook to show that, even in the apparently intractable cases, the logical relations between the propositions of science can always be "fully analyzed in terms of the `classical' logical relations of deducibility and contradiction" [13].

Well, let us consider what the result of actually carrying out this undertaking. What is the actual `classical' logical relation between, for example, one scientific theory and another, in those cases in which they are intuitively and rightly called "competing" or "rival" theories? The relation cannot be contradiction or contrariety. For as we have seen, two scientific theories (taking their logical form to be what our authors say it is) cannot be inconsistent. The relation cannot be sub-contrariety, since any two rival theories might both be false. There cannot be logical equivalence between them, or over-entailment either way; for in any one of those cases it would be quite wrong to call the two theories competing. But these six are the only deductive-logical relations possible between two contingent propositions, apart from independence. The logical relation, therefore, between any two competing scientific theories, in independence.

What is the classical logical relation between, for example, Newtonian physics and any observation-statement? Not inconsistency, as we have seen, Not sub-contrariety, since both could be false. There is no entailment either way. So the answer to this question, too, is: independence.

What is the classical logical relation between Newtonian physics and Kepler's laws of planetary motion? Not inconsistency, as we have seen, Not sub-contrariety, since both could be false. There is no entailment either way. So the `classical' answer to this question, too, is independence.

What is the classical logical relation (to go back to a class of examples which was, as we know, of peculiar importance to Popper) between H, "The probability of a human birth being male is 0.9", and E, "The observed relative frequency of males among births in human history so far is 0.51"? Again the answer is, of course, independence.

Evidently, this is going to be an excessively uninteresting philosophy of science! Yet the four questions just asked are ones intensely interesting to any philosopher of science, and are in fact typical of the questions which interest him. But if he insists on confining his answers to classical or deductive-logical relations, then the only answer which he can give with truth to any of them is the uninteresting one, "independence". This answer is uninteresting, because almost any two propositions are logically independent: for example, almost any two non-competing scientific theories (the Copernican theory and Darwinism, say), as well as any two competing theories, are independent. And the ultimate reason for that, of course, is that the classical logical relation of independence is extremely unspecific: it comprehends indifferently logical relations which are in fact of the utmost diversity. Hence by giving just the same answer in all of the four examples above, obvious and important logical differences among those cases are suppressed: the fact, for example, that while in the last case given above, E disconfirms H, Kepler's laws do not disconfirm Newtonian physics.

Confronted, then, with almost any interesting question about the logical relations between propositions of science, a philosopher who is resolved to confine his possible answers to deductive-logical relations, is faced with an extremely painful choice. He absolutely must: either give no answer at all; or give an answer which is true but excessively uninteresting both to himself and others; or give an answer which may be interesting but is false.

Now our authors, as I have said, always in fact choose the third kind of these alternatives. This is explicable, but on only one hypothesis, to the nature of which the first two alternatives just mentioned provide the clue. For the three alternatives may be reduced to just the following two: a deductivist philosopher must either give a false answer, or suffer painful under-exercise of his logical faculty. Our authors' characteristic kind of carelessness, of attributing to a pair of propositions a deductive-logical relation which they simply do not possess, is therefore a case of vacuum-activity in Lorenz's sense [14].

The commonest case of vacuum-activity is that in which a dog, long deprived of both bones and of soil, `buries' a non-existent bone in non-existent soil (usually in the corner of a room). This behavior-pattern is innate in dogs, and if deprived for too long of its proper objects, it simply `discharges' itself in the absence of those objects. After a certain point, bone-free life is just too boring for dogs.

Just so, our authors are philosophers of science, and have a built-in need to answer interesting questions about the logical relations between propositions of science. But what can be said with truth in answer to such questions, without `breaking the fetters of classical logic', is painfully uninteresting; while our authors are resolved to permit themselves no other kind of answer. After a certain point, however, life without interesting logical relations is just too boring for philosophers. Sooner or later, then, another and more interesting deductive-logical answer discharges itself, although in entire disregard to the absence of its proper objects. Then, for example, Kepler's laws and Newtonian physics are called "inconsistent"; although anyone who is not under the same compulsion as the deductivist easily sees at once that those two propositions are in fact merely independent.

This phenomenon can equally well be looked at, of course, from the other end. The dog engaged in his vacuum-activity, if he could write, might say, exactly in the style of Lakatos, "I am `burying' a `bone'". If he were more Popperian he might write either "I introduce a methodological rule permitting us to regard this as bone-burying", or "Any similarly-deprived dog would regard this as burying a bone". His ghost-behavior corresponds to their ghost-logical statements.

The apparent paradox, of deductivists whose deductive logic is sloppy, and `inductive' logicians whose deductive logic is not, is thus resolved. Our authors, by their determination to acknowledge no other than deductive-logical relations, are self-condemned, when they come to almost any interesting question about the relation between propositions of science, to being totally silent, totally uninteresting, or totally wrong. Faced with the first two dread alternatives, a philosopher's reaction will not be long in doubt. The `inductive' logician, on the other hand, is from the start under no such compulsion. That is why he can write about the relations between propositions of science, without having to produce a stream of elementary mistakes in deductive logic.


There is another feature of our authors' writings, a feature even more pronounced and characteristic of them than their carelessness about deductive logic, the explanation of which also lies in their deductivism. This is, their levity or enfant-terriblisme.

The levity of Feyerabend is too `gross, open, and palpable', to require that instances be given here to prove it. In Against Method it is in fact so omnipresent that he has managed to entangle himself in a certain `paradox of levity' which is, as far as I know, entirely original. Feyerabend enjoins the reader of that book [15], indeed he pleads with him [16], not to take anything he reads there too seriously. But this injunction and this plea are among the things he reads there. How seriously, then, ought the reader to take them?

Lakatos' fame as a philosopher of science rests principally on his [1970]. He there claimed, among other things, to give an account, more accurate than anyone else had given, of the actual history of science. Yet that essay contains several episodes from the history of science, episodes complete with circumstantial detail, which are, Lakatos calmly tells us in footnotes [17], fabrications of his own. Perhaps it will be said that this instance is not characteristic: a mere isolated outcrop of levity. Even if it were so, this particular way of wasting paper is not one which would even suggest itself to a philosopher who was in earnest with his subject. But in any case there are in Lakatos many instances of levity which are indisputably characteristic. One is the long footnote in Proofs and Refutations about proof in mathematics. This begins with the remarkable understatement, that "Many working mathematicians are puzzled about what proofs are for if they do not prove". And Lakatos goes on to quote, with relish, the mathematician G.H.Hardy, as follows: "`proofs are what [...] I call gas, rhetorical flourishes designed to affect psychology, pictures on the board in the lecture, devices to stimulate the imagination of pupils'" [18]. As academic humor, this may be allowed to pass (combining as it does self-contempt, and the contempt of others, in the prescribed unequal proportions); as serious philosophy of mathematics, not.

Most people suppose that Popper is far removed, at least in this matter of levity or enfant-terriblisme, from those intellectual progeny of his to whom I have just referred. Indeed, there are at the present time many youngish philosophers of science in whose writings Popper is made to serve (since they know next to nothing of any philosopher of science before him) as their standing and cautionary example of the unbearable gravitas which characterized philosophers of science in the dark ages. But this is merely a measure of the ignorance of such persons; the truth is exactly the opposite. The Logic of Scientific Discovery was no less an enfant-terriblisme first book than Language, Truth and Logic, or A Treatise of Human Nature.

The simple and sufficient proof of Popper's levity is this: that he is always saying `daring' things that he does not mean. For example he says, and says, as we have seen, with all possible emphasis, that there is no good reason to believe any scientific theory. But he is not in earnest. He does not really believe that there is no good reason to believe that his blood circulates, or that the earth rotates and revolves, or that his desk is an assemblage of molecules---or a thousand other scientific theories which could as easily be mentioned. Confront him with members of the Stationary Blood Society, who are in earnest when they say that there is no good reason to believe that the blood circulates, and Popper would find the difference manifest enough between real irrationalism, and his own `parlor-pink' version of it. Indeed, even as things are, Popper every now and then notices, to his alarm, that what Hume called `the rabble without doors' shows some tendency to agree with him, that there is no good reason to believe any scientific theory: at these points, the reader of Popper is about to receive another lay-sermon on the deplorable growth of irrationalism, relativism, etc. In other words, Popper's daring irrationalist sallies are meant to be tried, like a baron under Magna Carta, only by a jury of his peers, and for the same reason: the other people might not understand.

The levity of Popper and his followers concerning science bears a marked analogy, therefore, to a species of political levity which is excessively familiar: what Kipling called "making mock of uniforms that guard you while you sleep". For who are the pet aversion of Popperites, as policemen are of parlor-pinks? Why, ordinary flesh-and-blood scientists, of course! Any contact with living scientists always leaves a Popperite far more Feyerabendian than it found him. It can be relied on to bring him out in fury of what we may call `criticismism'. Scientists, he finds to his horror, are dogmatic, uncritical, authoritarian, etc., etc. So they are, of course. They are also people of the very same kind, by and large, as those who have erected what Popper himself once called, in a moment of self-forgetfulness, "the soaring edifice of science" [19].

It is the frivolous elevation of the `critical attitude' into a categorical imperative of intellectual life, which has been at once the most influential and the most mischievous aspect of Popper's philosophy of science. That it is frivolous, should be evident from the tautology that it is only valuable criticism which is of value; not criticism as such. The demand that scientists in general should be critics and innovators, rather than mere followers, is even, in its extreme forms, self-contradictory; like the implicit demand of those educationalists who want every child to be exceptionally creative. (Before they complain of the rarity of any great critical faculty in scientists, Popperites should read Hume on what he called those "thoughtless people" who complain of the rarity of great beauty in women [20]). Even in its non-extreme forms, however, the apotheosis of the critical attitude has had, as its principal effect, simply this: to fortify millions of ignorant graduates and undergraduates in the belief, to which they are already only too firmly wedded by other causes, that the adversary posture is all, and that intellectual life consists in "directionless quibble" [21].

In the most marked contrast possible to all of this, the writings of the `inductive' logicians are entirely free of levity. These philosophers take science not as furnishing materials for mere `critical discussion', but seriously. They have nothing of our authors' bohemian contempt for, or disbelief in, success. On the contrary, scientific success is treated by them as the obvious though wonderful fact which it is. They never say daring things that they do not mean about science.

The levity of our authors, and the absence of levity in the `inductive' logicians, is sufficiently obvious as a fact. But why do I say that the explanation of it lies in the fact that our authors are deductivists, while the `inductive' logicians are not? The main part of my answer is this: that deductivism, the thesis from which all the disagreements between these two groups of philosophers spring, is a proposition which can recommend itself only to the minds of enfant-terribles or other extreme doctrinaires, and more specifically, that deductivism is a thesis of an intrinsically frivolous kind.

Consider the argument to the conclusion "I will win a lottery tomorrow", from: "There is a fair lottery of 1000 tickets, to be drawn tomorrow, in which I hold just one ticket or none". Here everyone would agree that the premise is no reason to believe the conclusion. Anyone who said the same thing, however, about the argument to the same conclusion from the above premise minus its last two words, would find few to agree with him. On the contrary, the difference in logical value between the two arguments is so manifest, that such a person would be thought to display an almost unheard-of degree of logical blindness or perversity. But let us change the premise again, so that it now ends with "[...] in which I hold just 999 tickets". Anyone who said that, even here, the premise is no reason to believe the conclusion, would evidently thereby announce himself as one of those hopeless doctrinaires with whom rational argument, and even `critical discussion', is effort thrown away.

The deductivist, however, must say that in all three of these arguments the premise is no reason to believe the conclusion. For all three are invalid, and incurably so. This is enough to show that deductivism is one of those theses which, although anyone under pressure of philosophical argument might momentarily reconcile himself to it, would not be adhered to willingly and with knowledge of its consequences, by anyone except an enfant-terriblisme or an extreme doctrinaire.

Suppose I have come to know that P, "I hold just 999 of 1000 tickets in a fair lottery to be drawn tomorrow"; and suppose that, as a result of acquiring this knowledge, I have come to have a higher degree of belief than I had before in the proposition Q: "I will win the lottery tomorrow". Suppose that I am then reminded by someone of the fact that R, "It is logically possible that P be true and Q false"; and suppose I fully accept this truth, and add it to my stock of knowledge. I acknowledge, in other words, that although I hold nearly all tickets in this fair lottery, I might not win it. Suppose, finally, that on account of adding this truth R to my premise P, I come to have a lower degree of belief in Q than I had before being reminded of R.

In that case, it will be evident, I am being irrational, and more specifically I am being frivolous. Irrational, because R is a necessary truth, and hence its conjunction with P is logically equivalent to P itself, while two arguments cannot differ in logical value if their premises are logically equivalent and they have the same conclusion. And my irrationality is of a frivolous kind. My conclusion Q is a contingent proposition, saying only that the actual world is thus-and-so. My additional premise R is a proposition true in all possible worlds. But a proposition true in all possible worlds cannot tell in the slightest degree for or against any proposition just about the actual world. (If it could, why ever leave the armchair at all? Why not do all our science a priori?). Yet after having allowed my degree of belief in the contingent Q to be raised by the contingent P, I have allowed it to be depressed again by the addition to P of a premise R which, where the conclusion of this argument is contingent, as it is here, cannot weigh anything at all. To do this is light-mindedness on my part; and it would be light-mindedness in anyone else to demand it of me.

Let us change the example to one in which the argument is inductive. P is now "All the many flames observed in the past have been hot", and Q is "Any flames observed tomorrow will be hot". Suppose that I have come to know P, and that, as a result of acquiring this knowledge, I have come to a higher degree of belief in Q than I had before. Suppose I am then reminded by someone of the fact that R, "It is logically possible, however many may be the `many flames' referred to in P, that P be true and Q false". And suppose that I fully accept this truth, and add it to my stock of knowledge.

Now, if on account of adding this truth R to my premise P, I come to have a lower degree of belief in Q than I had before, then I am being irrational in exactly the same frivolous way as in the case of the lottery. For here too the additional premise R is a necessary truth, while the conclusion of the argument Q is contingent. Therefore R cannot tell in the slightest degree against or for Q. Yet having allowed my degree of belief in the contingent Q to be raised by the contingent P, I have allowed it to be depressed again by the addition to P of a premise R, which cannot weigh anything at all in an argument about whether flames will be hot tomorrow.

Yet it is precisely this piece of light-mindedness that the deductivist demands of me. The deductivist, Hume for example, tells me that P is no reason to believe Q; and of course, if that is so, then I should indeed lower my degree of belief in Q. But I ask him, why is P no reason to believe Q, or why should I lower my degree of belief in Q? Is Hume about to remind me of some quite other contingent fact S, which I have neglected, and which tells against Q, perhaps even making it probable that some flames tomorrow will not be hot? Hardly! So I repeat my question: why should I lower my degree of belief in Q? Forsooth, Hume tells me, just for this reason: that a man who infers Q from P, or from P conjoined with any other observation-statement "is not guilty of a tautology" [22]; that given P, and any other observational premise, "the consequence [Q] is nowise necessary" [23]; that, whatever our experience has been, "a change in the course of nature [...] is not absolutely impossible" [24]; that past and future hot flames are `distinct existences', that is, that the one might exist without the other; and so on.

This, and nothing else in the world, is what Hume finds to object to in my inductive inference from P to Q. This is the whole of his answer to the question, why I should lower my degree of belief in Q. Yet it amounts just to this, that the inference from P to Q is invalid, and remains so under all observational additions to its premises; or in other words just to R, that it is possible for P, and any other observation-statement to be true, and Q false. But this is a necessary truth. And therefore to demand, just on this account, that I should lower my degree of belief in the hotness of tomorrow's flames, is mere frivolity.

Of course exactly the same is true of Popper. If I have, as Popper says I should not have, a positive degree of belief in some scientific theory, what can Popper urge against me? Why, nothing at all, in the end, except this: that despite all the actual or possible empirical evidence in its favor, the theory might be false. But this is nothing but a harmless necessary truth; and to make it as a reason for not believing scientific theories is simply a frivolous species of irrationality. Yet it is this proposition, that any scientific theory, despite all the possible evidence for it, might be false: a proposition loudly announced by the fall of Newtonian physics; amplified ever since by morbidly sensitive philosophic ears; endlessly reapplied and reworded; insisted on to the exclusion of every other logical truth about science, and mistaken for a reason for not believing scientific theories; it is this proposition, so treated, which may be said to be irrationalist philosophy of science.

This phenomenon is so far from being new, that it appears to be a perennial feature of sceptical or irrationalist philosophy. To furnish a reason for doubting all contingent propositions among others, Descartes appears to have thought it sufficient if he could establish the logical possibility of an all-deceiving demon [25]. The sceptics of later classical antiquity were fully conscious of the dependence of their entire philosophy on expressions such as "might" and "possibly", and they appear to be constantly guilty of taking logical truths involving such expressions as grounds for doubting contingent propositions [26]. And among recent irrationalist philosophers of science, along with neutralized success-words and sabotaged logical-expressions, an unfailing literary diagnostic is, the use of the frivolous or deductivist "might". Such philosophers can be absolutely relied on to try to cast doubt on the truth of contingent propositions, by the enunciation of mere logical truths about the possibility of their falsity.

In Hume's Treatise, Abstract, and first Enquiry, deductivism, conjoined with the incurable infallibility of induction, led to scepticism about induction. The latter two books, were, of course, rewritings of Book I of the Treatise: "a juvenile work", as Hume tells us, "which the Author had projected before he left College" [27]. It is therefore not surprising that in the central argument of those books, concerning induction, the key premise should have been the enfant-terrible thesis of deductivism. But Hume, unlike our authors, did not remain a deductivist enfant-terrible all his life. In the one philosophical work of his maturity, which is also his best, the Dialogues concerning Natural Religion, the incurable invalidity of induction is maintained as firmly as ever. But at the same time, in that book, inductive scepticism, and therefore by implication deductivism, are rejected very early, and with a summariness which is well-proportioned to their frivolity [28].

Hume did better than that, however. Late in his life he made precisely the contemptuous dismissal that any rational inductive fallibilist must make of inductive scepticism, and by implication of deductivism. This was on his deathbed, in a conversation with Boswell on the subject of immortality. Boswell, almost desperate for some hint of consolation, "asked him if it was not possible that there might be a future state. He answered, It was possible that a piece of coal put on the fire would not burn; and he added that it was a most unreasonable fancy that he should exist for ever" [29]. I earnestly commend this remark, of their founding father and favorite deductivist, to irrationalist philosophers of science. For it, and not the deductivist levity of the Treatise or of their own writings, expresses exactly the response of a rational man to contingencies which are recommended to his belief just on the impertinent ground of their possibility.

Of course I do not say that every philosopher who is a deductivist is frivolous. I do say that deductivism is intrinsically a thesis of a deeply frivolous nature; that it is the premise from which flow all the irrationalist consequences of our authors' philosophy of science; and that the levity which their philosophy exhibits so markedly is therefore to be explained, as their irrationalism is, by the influence on their minds of deductivism. But it is no more to be inferred from the fact that deductivism is frivolous, that all deductivists are frivolous, than it is to be inferred from the fact that patience is a virtue, that all the patient are virtuous. And in the one case or in the other, the conclusion would be false in fact; for even among our four authors there is one who, in this respect, stands apart from the others.

Kuhn shares with our other authors, as he must, their boundless contempt for `inductive' logic. His remark about "cloud-cuckoo land", for example, quoted in Chapter II above (see the text to footnote 30), is a thinly-veiled contemptuous reference to it. But setting this point aside, his writings are entirely free from the levity which disfigures the writings of our other authors. His philosophy of science is not daring; only shocking. He had no time at all for criticismism, and to epater les bourgeois is the least of his concerns. His admiration for `normal science' is so pronounced that it brings out Popper and his followers in a perfect rash of Spocks [30].

The reason is, that Kuhn is in earnest with irrationalist philosophy of science, while the others are not. He actually believes, what the others only imply and pretend to believe, that there has been no accumulation of knowledge in the last four centuries [31]. And he even bids fair, by the immense influence of his writings on `the rabble without doors', to make irrationalism the majority opinion. `This was the most unkindest cut of all' for our other authors, and is in fact the real ground of the offense which Kuhn has undoubtedly given them; as distinct from the avowed but manifestly spurious ground mentioned at the beginning of the book. For the cruellest fate which can overtake enfants-terribles is to awake and find that their avowed opinions have swept the suburbs.

There are, unfortunately, grounds for believing that the deductivist cast of mind is, like priesthood, indelible; or at least that deductivism, and the levity which is its natural consequence, can never be entirely erased from any mind in which they have once taken hold.

Consider again the fair lottery to be drawn tomorrow, in which I hold just 999 of the 1000 tickets. Imagine this case to be described by a contemporary philosopher: one who was formerly a deductivist, but who has since `put away the toy-trumpet of sedition' in philosophy. This philosopher, in other words, has arrived at the prodigious pitch of learning which enables him to say, and to believe, what non-philosophers believed all along: that, in this case, while it is possible that I will not win a lottery tomorrow, it is probable that I will.

Now, will there not be, even so, a faint apologetic smile accompanying the word "probable", but not the word "possible", if our ex-deductivist is speaking? If he is writing, will there not be sabotaging quotation-marks around "probable", though not around "possible"? Almost to a certainty there will. A contemporary philosopher can hardly rid himself, even if his life depended on it, of the feeling that the possibility of my not winning the lottery is `objective', in some sense in which the probability of my winning it is not.

It is essentially the same in the inductive case. The contemporary philosopher will admit easily enough, once it is pointed out to him, that it is a mere logical truth that tomorrow's flames may be unlike past ones; and that therefore this cannot be a reason to doubt that they will be like them. Yet in spite of all his efforts to prevent it doing so, this logical truth operates on his mind as though it were such a reason, and a weighty one. So obsessive is our endless re-enactment of the death of Newtonian physics, and so permanently disabling is `modern nervousness' in the philosophy of science.

That this state of mind is a confused one, it can hardly be necessary to say. Probabilities are no less objective than possibilities. On any philosophy of probability, alternatives which are equally probable can be called, with equal propriety, equally possible; and for one alternative to be more probable than another, it is logically sufficient that there be, for every way in which the second can be realized, an equally possible way in which the first can be realized, but not conversely. Anyone, therefore, who is hyper-sensitive to possibilities, but at the same time is insensitive to all difference in magnitudes between probabilities, is certainly in a deeply-confused mental state; even, one would think, a pathological state. Yet this is, in some degree, the actual mental state of most philosophers of science at the present time, and is to a pre-eminent degree the mental state of deductivist philosophers of science, such as our authors.

If it is true that any philosopher who was once a deductivist will carry at least some tincture of deductivism to his grave, then the prospects are so much the worse for there being any future philosophy of science which is free from the levity and other vices of irrationalism. For there can scarcely be any contemporary philosopher of science who is not either a deductivist or an ex-deductivist.

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