# Chapter II

## Sabotaging Logical Expressions

I will call a statement a "logical" one, or a "statement of logic" if and only if it implies something about what the logical relation is between certain propositions; and the word or phrase, in virtue of which it has this implication, I will call a "logical expression". Thus for example, any substitution-instance of "P entails Q", or of "P is inconsistent with Q", will be a logical expression. These statements and expressions are even purely logical ones; because "P entails Q", or "P is inconsistent with Q", implies nothing about P and Q except a statement of what their logical relation is. But a statement or expression can be logical without being purely so. For example, "P is a proof that Q" is a logical statement, because it implies that P entails Q, and in it "is a proof that" is a logical expression; but they are not purely logical, because "P is a proof that Q", besides implying what the logical relation is between P and Q, implies other things as well, such as that P is true.

A statement of what the logical relation is between P and Q, is equivalent to certain statements about how rationally conclusive certain inferences are: certain inferences, namely, from the truth or falsity of P to the truth or falsity of Q. The strongest logical statements such as that P entails Q, or that P is inconsistent with Q, imply that certain of these inferences are completely conclusive. The logical relations between P and Q implied by such statements as these are therefore like frictionless pipes along which knowledge can travel, and travel without loss. In virtue of P entailing Q, if you know that P you can arrive at knowledge that Q, by traveling along that logical relation; but even if you did not arrive at this knowledge in that way, your claim to know that Q cannot be consistently denied while your claim to know that P is admitted, if P does entail Q. Again, if P is inconsistent with Q then some one who admits your claim to know that P cannot consistently deny your claim to know that Q is false.

Suppose I say that the proposition Q has been proved. Then I have used a success-word. I might then say that in particular it is the truth of P that proves Q, or is the proof (or a proof) that Q. Here I have used a logical expression. Now let us suppose, however, that in my first remark I was neutralizing the success-word: using the word "proved" without its implication of truth. Then clearly, to be consistent, I must do something, to the logical expression in my second remark, which is like neutralizing a success-word. For that remark implies that P entails Q, and I said that P is true; so I will not be able to go on doing what I began by doing, avoiding the implication that Q is true, if I leave intact that implication of my logical statement.

Similarly with "refuted" and "refutation", for example. Suppose I first say that Q has been refuted, and then say that it is the truth of P which refutes Q, or if the refutation (or a refutation) of Q. In the first remark "refuted" is a failure-word, implying the falsity of Q; in the second, the cognate words are logical ones, since in virtue of them my remark implies that P is inconsistent with Q. But now suppose that in my first remark I was neutralizing the failure-word, taking out its implication of falsity. Then, to be consistent, I clearly must do something, to the logical expression in my second remark, which is like neutralizing a failure-word. Having admitted the truth of P, I will not be able to continue, as I began, avoiding the implication that Q is false, if I allow my logical statement to retain the implication that P is inconsistent with Q.

What consistency requires in such cases is like neutralizing a success- or a failure-word. For I must use a logical expression, and appear by doing so to make a statement of logic, that is, appear to imply something about the logical relation between propositions; but at the same time, I must really not do so.

The process in question cannot be that of neutralizing a success- or a failure-word, however. Some logical words are indeed success-words as well. For example, "(is) proved" and "proof" are such; just because the connection in meaning is so close between saying that Q is proved, and saying that there is some truth P which is a or the proof of Q. Similarly, "(is) refuted" is a logical word as well as being a failure-word, and "refutation" is both too. But on the other hand, success- or failure-words need not be logical words. "Knowledge", for example, is not. That Q is known, implies nothing about the logical relation of Q to any other proposition. And contrariwise, logical words need not be success- or failure-words. For example, purely logical expressions like "entails" or "is inconsistent with" only imply something about logical relations, nothing about cognitive success or failure; and not having any such implication, they cannot be deprived of it.

Nevertheless, we recall, the logical relation between two propositions, which is what a logical statement implies something about, may be a path along which cognitive achievement can travel; and even travel without loss in the case of logical relations like entailment or inconsistency. The practice we are now thinking of, of using logical expressions so as to appear to make a statement of logic, but without in fact implying anything about logical relations, is one which would make such travel impossible. Neutralizing a success-word is a device for wiping out cognitive achievement after it has arrived. Its counterpart for logical expressions would prevent cognitive achievement, if it had to travel along logical relations, which almost all cognitive achievement has to do sooner or later, from ever arriving. It is like blowing up railway tracks, holing water pipes, or cutting power-lines. Let us call it "sabotaging" logical expressions.

This is the second of the two main literary devices by which our authors make irrationalist philosophy of science plausible. The first, the use of success-words (though neutralized), is of course a device which makes directly for plausibility. Sabotaging logical expressions does not do this, but it is an essential auxiliary to the first device. A writer who often took the implication of truth out of "proved", but never the implication of entailment out of "proof", or who often took the implication of falsity out of "refuted" but never took the implication of inconsistency out of "refutation", would be in a position hopelessly exposed to criticism. Our authors have not been so careless.

This will be proved by examples later. Obviously I cannot prove that philosophers of science who are not irrationalist do not sabotage logical expressions as often as our authors do. But I think that my examples will be found sufficiently distinctive of the kind of English our authors write. And anyone who tries to match these examples with examples of the sabotage of logical expressions drawn from the writings of Hempel and Carnap, say, will find that experiment instructive.

But sabotaging logical expressions is not only a device which is for our authors an essential auxiliary to that of neutralizing success-words. It has a most important and distinctive effect of its own, directly on the literary fabric of their philosophy of science, and indirectly in giving that philosophy plausibility. For it generates what I call "ghost-logical statements". To explain what I mean, I need to anticipate slightly.

One way to sabotage a logical expression, and the way which is most common in our authors, is to embed a logical statement in a context which can be broadly described as epistemic. A schematic example, and one not likely to occur in our authors, is this: instead of saying "P entails Q", which is of course a logical statement, to say "P entails Q according to most logicians, ancient, medieval, and modern".

The latter statement, unlike the former, is not a logical statement at all: it implies nothing about the logical relation of P to Q. It is really just a statement, contingently true or false, about the history of logic. Yet at the same time it makes the strongest possible suggestion, not only that a statement of logic is being made, but that one is being made from which no rational person will dissent. The context "according to most logicians (etc.)" sabotages the logical expression "entails"; yet suggestions of logic are so artfully blended with implications of history that the statement is a kind of mirage of a logical statement being made: it is a ghost-logical statement.

Now ghost-logical statements have, while logical statements lack, a characteristic of the utmost importance (and ghostliness): they are absolutely immune to criticism on logical grounds. For consider "P entails Q according to most logicians (etc.)". Suppose some one attempts to criticize it on logical grounds, and suppose that the outcome of his attempt is the most favorable possible for the critic: that is, he succeeds in showing that after all P does not entail Q. What is that to the purpose? Nothing. For the statement he set out to criticize never did imply that P does entail Q.

That statement is also, we see, virtually immune to criticism on historical grounds too. The task of historical criticism of it would be at once so enormous, and so indefinite that, if a critic did set out on that venture, you could rely on his never returning from it. And this virtual immunity even to historical criticism is possessed by very many ghost-logical statements (though of course not by all).

Confronted with our ghost-logical statement, however, a potential critic is not likely to be able to contemplate distinctly either the possibility of logical criticism or the possibility of historical criticism of it. What is far more likely is that his critical powers will be paralyzed, and he will not know how to react to the given statement: for the ghost-logical statements produced by epistemic embedding are typically not only immune to criticism, but actively paralyze it. And the reason is clear. Such a statement is like a statue of Janus, forever pointing the potential critic in opposite directions at once: implying that historical criticism (even if practically impossible) would be relevant, and logical criticism not, while at the same time irresistibly suggesting that logical criticism would be relevant, and historical not.

When our authors use this method of sabotaging a logical expression, their epistemic contexts will be drawn of course from the history of science, not from the history of logic as in the above example. But the result will be the same, namely a ghost-logical statement. And in fact ghost-logical statements are common enough in our authors (and their followers), and peculiar enough to them, to constitute, along with neutralized success-words, a literary hall-mark by which any writing of theirs can be identified as such.

While the neutralizing of success words contributes directly to the plausibility of irrationalist philosophy of science, then, the sabotage of logical expressions by epistemic embedding does not. But it indirectly makes an enormous contribution of its own to the plausibility of our authors: it enables them to make statements, about the relations between the propositions of science, which appear to be statements of logic, and yet which possess absolute immunity to logical criticism. For it generates not logical but ghost-logical statements; and these (as well as being in most cases virtually immune to historical criticism) are always and absolutely immune to logical criticism. How great an advantage in philosophy such immunity is, and how important as an indirect aid to plausibility, no philosopher will need to be told.

Logical expressions, whether purely logical or not, can be divided into strong and weak ones, just as success-words can; and as I have said, some of them are success-words as well. Examples of strong logical expressions are "entails", "proves", "verifies", "has as a special case". Weak ones include "is consistent with", "supports", "confirms", "is a special case or example of". Logical expressions weaker still include "explains" and "solves the problem of". (Here as elsewhere I generally take verbs as my logical expressions, but of course the cognate noun will be a logical expression too).

All the above are in an intuitive sense positive logical expressions. Corresponding to them, and for the most part trivially intertranslatable with them, are negative logical expressions. Strong negative ones include "is consistent with", "disproves", "refutes", "falsifies", "is a counterexample of", "clashes with". Weak negative expressions include "disconfirms", "is an anomaly for", "poses a problem for", "cannot explain", "fails to predict".

In our authors, the sub-class of logical expressions which is most prominent is that of the strong negative ones. The historical reasons for this are obvious. Popper had undertaken, in The Logic of Scientific Discovery, to display the entire logic science without departing once from the vocabulary of deductive logic; and even the positive part of that vocabulary was not needed, he thought, except for the uncontroversial work of describing the `downward' articulation of laws and theories. For the rest, Popper claimed, everything in science could be understood with the aid of "falsification", "refutation", or other expressions implying inconsistency; that is, of the strong negative logical expressions. Our other authors are of course in this respect very much under Popper's influence. It was therefore to be expected, and it is in fact the case, that when any of our authors sabotages a logical expression, it is almost always a strong negative one.

If our authors are willing, as I will prove by examples that they are, to sabotage even strong negative logical expressions, they will be still more willing to sabotage weak ones, negative or positive. And if they sabotage strong negative ones, then this practice will confer on what they write a wider immunity to logical criticism than the same thing would do for other writers of a less `deductivist' tendency: just because our authors make such comparatively little use of logical expressions of any other kind.

What ways are there, then, of sabotaging logical expressions? That is, of seeming to imply something about the logical relation between propositions, without actually doing so.

First, it may be done by enclosing a logical expression in quotation-marks. "P `entails' Q" can be used in such a way, or in such a context, as to suggest, what of course it does not imply, that P entails Q.

This is a tiresome subject, but it cannot be entirely omitted. Popper, and any philosopher of science much influenced by Popper, will sometimes be found sabotaging by quotation-marks some of the weak positive logical expressions at least: for example, "confirms". And Lakatos in particular is forever using quotation-marks to sabotage even the strongest logical words, such as "proof" and "refutation": see his Proofs and Refutations, passim. Most of what was said in Chapter I about Lakatos and quotation-marks could in fact be repeated here, because it happens that most of his victims are logical words as well as being success- or failure-words. But I will add just one short example.

"If a theory is refuted, it is not necessarily false. If God refutes a theory, it is `truly refuted'; if a man refutes a theory, it is not necessarily `truly refuted'" [1].

This example is the more sad, because it seems clear that what Lakatos tried to say was that if God, unlike man, refutes a theory, then it is truly refuted. If so, however, his tic was too strong for him, and he could not say it. For as the sentence came out, we see, even God's refutations were sabotaged by quotation-marks.

Let us leave this depressing topic.

A second way to sabotage a logical expression, and the way our authors use most, is the one I have already mentioned in anticipation: by embedding a statement of logic in an epistemic context.

Of course such embedding need not result in sabotage of the logical expression. It need not even cut off the embedded statement's implication about logical relations. "Everyone knows that P entails Q" is, among other things, a logical statement in my sense, but not a ghost-logical one: it implies that P entails Q, just because of the success-word "knows" in the context. But even if the implication about logical relations is cut off by embedding, there need not result any sabotage of the logical expression. "Some people think that P entails Q", for example, is not logical, since it implies nothing about the logical relation of P and Q; but it is not ghost-logical either, since there is nothing in it to suggest that it does have such an implication. The statement is a plain historical one, and does not pretend to be anything else.

But consider the following schematic examples, in which a logical expression is sabotaged by epistemic embedding. "Any scientist would regard P as entailing Q". "P entails Q on the Copenhagen interpretation". "Given the conceptual scheme of special relativity, P entails Q". "Once R was discovered, though not before, P could be seen as entailing Q". "P does indeed entail Q, once Galileo's paradigm is adopted". "Q was a logical consequence which could hardly be overlooked once P was added to the hard core R of the research programme". "A scientist who accepted P but rejected Q would be regarded by his profession as violating one of its most basic values, consistency".

It is rather easy, isn't it, to sabotage logical expressions by epistemic embedding? For it is being done in these examples fairly effectively, and even with an approach in some cases to our authors' individual styles of sabotage. (You do not need to be an anti-saboteur specialist to see, in the ruins of a logical relation in the last example, a fair imitation of the handiwork of Kuhn). Yet it is being done here under the most unfavorable possible conditions. My `propositions' being mere dummies, "P entails Q" could not help, by its own truth or plausibility, to second the suggestion (the false suggestion) that a statement of logical is being made. The main logical expression used here, "entails", is one of those least easy to sabotage. A weak logical expression such as "confirms" succumbs far more readily to sabotage; as may be seen by the fact that the first example, say, will be still more easily mistaken for a logical statement if we replace "entailing" by "confirming". My epistemic beds were of necessity imaginary, and above all too short to be very lifelike; quite unlike the vast beds of detail, drawn from the actual history of science, which are available to Lakatos, Kuhn and Feyerabend, for suffocating logical expressions. Yet even under all these handicaps, we see, it is not at all hard to set up a suggestion, and a suggestion of almost any degree of strength that might be desired, that P entails Q; even though, because of the epistemic embedding, one has actually implied nothing of the kind. If you were a writer likely in any case to switch from the logic to the history of science and back again, and still more if you considered yourself licensed to do so, and as fast and as often as you like, you could positively leave this trick to work itself.

In some of the above examples there is a hint of another vice as well, something quite additional to the sabotaging of a logical expression. This is what I have elsewhere called "misconditionalization" [2]: that is, for example, saying that if R, then P entails Q, when what you really mean is that the conjunction of P and R entails Q. Misconditionalization, however, is a vicious process performed on logical statements. (It will often turn true ones into false). Sabotage of a logical expression, on the other hand, is a literary device for appearing to make a logical statement, without actually doing so. Misconditionalization can be used to assist the sabotage of logical expressions by epistemic embedding, and in our authors it is in fact sometimes so used. But that is as far as the connection between the two extends.

The examples given above, as well as being schematic, were of the simplest type possible; and this in two respects.

First, the logical relation which was sabotaged was one between particular propositions: between some concrete values of the propositional dummies P and Q. But of course it is equally possible, and for a philosopher it is often more natural, to sabotage the logical relation between P and Q where these are kinds of propositions: where P stands for theories, say, or law-statements, and Q for, say, observation-statements, or again, statements of initial conditions. In other words, the logical statement which is embedded in a ghost-logical statement need not be singular, but may be general, and of any degree of generality. Example: "A scientist would never regard a law-statement as entailing any statement of initial conditions". And in our authors, sabotage by epistemic embedding is in fact more usually of general logical statements than of singular ones.

Second, in the above examples there was no iteration of epistemic embedding; but there easily can be such a thing. A logical statement can be sabotaged, by being embedded in an epistemic context, and then this whole thing, the ghost-logical statement, can in turn be embedded in another epistemic context. Schematic example: "Logicians generally assume that any scientist would regard P as inconsistent with Q". There is no theoretical limit, of course, to how far this `layering' of epistemic contexts, over an original statement of logic, may go. In our authors there is hardly any practical limit either. Moreover the ghost-logical effect of the first embedding, that is, the false suggestion of a logical statement being made, may pass undiminished through the second embedding, or may even be amplified by it. It will depend on the nature of the second epistemic context whether this happens or not. Here is an example in which iteration does amplify, or at least does not diminish, the ghost-logical effect of the first embedding. "Most philosophers of science, since reading Popper, Kuhn, Lakatos, and Feyerabend, have agreed that scientists never regard a theory or a law-statement as falsified by a single observation-statement".

This example is not one which could occur in our authors themselves, of course, though there are plenty of others that do. But in the writings of their followers (those who are doing `normal science', as it were, in the wake of the irrationalist revolution), instances of such iterated epistemic embedding are especially common. And one can easily see why: they make assurance doubly sure. The first epistemic context, "scientists never regard", is sufficient on its own, as we have seen, to confer on what is said total immunity to logical criticism. The second epistemic context, "philosophers of science [...] have agreed", while it amplifies if anything the false suggestion that a statement of logic is being made, at the same time buries the embedded logical statement so deep in sociology, that omnipotence itself might despair of ever dredging it up again. As for ordinary philosophers, as Lakatos calls them (actually of course he calls them "`ordinary' philosophers" [3]), who might be tempted to criticize this remark, let them consider the utter hopelessness of that undertaking.

Historical criticism, if that is what is aimed at, would need to begin with the outer context, about philosophers. Should the critic's work there be ever done, he still has the inner context, about scientists, before him. How can he succeed here? Being an ordinary philosopher he probably does not know enough about the history of science; and if he does, then he also knows that any actual episode in the history of science is so complicated that he will never be able to put it beyond dispute that in it a scientist regarded (say) a law-statement as falsified by a single observation-statement. As for logical criticism of the remark, to which the philosophical critic is more likely to be drawn, it must for a start be long: much longer, at least, than the remark which he is criticizing. Again, it will require much tedious insistence on obviously true statements of logic: statements about the relation between propositions (those mummified objects of the ordinary philosopher's art). It must therefore be boring. But let his logical criticism be ever so good: let him prove to perfection that an observation-statement can be inconsistent with, and therefore can falsify, a law-statement. He has still only wasted his own and others' time, in proving an irrelevance. For it was never said that an observation-statement cannot falsify a law-statement. Only that most recent philosophers of science have agreed that scientists never regard them as doing so. And that is a proposition which is so very far from being a statement of logic, a contribution (whether a true or a false one) to the logic of science, that it actually belongs to the sociology of the philosophy of science.

Such are the joys in store for anyone who would attempt to criticize such a representative expression of irrationalist philosophy of science as we have just been considering. And such are the advantages, correspondingly, to irrationalism, of the sabotage of logical expressions by embedding them in an epistemic context or in more than one. But while this device bestows, on those who are willing to use it, virtual immunity to all criticism, and absolute immunity to logical criticism, I entertain some hopes that it may not be entirely proof against simple exposure, as the deceitful literary device it is. Let us turn to some specific and representative passages of our authors.

The use of epistemic embedding to sabotage a logical expression is less common in Popper than in any of our other authors. Even when he does it, he does it in a more diffuse way than they usually do, and (what may be connected with that) not with quite the same unclouded conscience. Yet, characteristically, it was he who began the practice, and by the authority of his example gave it currency.

His most influential act of sabotage occurs in a part of The Logic of Scientific Discovery which is seldom read, or at any rate remembered, by any but adepts. The instance must have been sufficiently grievous, because even people not otherwise apt to criticize Popper complained of it [4], and what is more remarkable still, Popper himself later said in print that what he had written at this place was "not to my own full satisfaction" [5]. To readers in whom the critical faculty is not entirely extinct, the episode has afforded a certain amount of hilarity. To our other authors, by contrast, what it afforded was a model and a license for their own efforts in the way of sabotaging logical expressions. If what Popper did here was not to his own full satisfaction, it certainly was to theirs.

The propositions in question were unrestricted statements of factual probability: that is, contingent unrestricted propositions of the form "The probability of F being G is = r", where 0 < r < 1. For example, H: "The probability of a human birth being male = 0.9". Concerning such propositions Popper had fairly painted himself into a corner. For he had maintained (1) that some such propositions are scientific; (2) that none of them were falsifiable (i.e. inconsistent with some observation-statement); while he had also maintained (3) that only falsifiable propositions are scientific. (The reason why (2) is true is, of course, that H is consistent even with, for example, the observation statement E: "The observed relative frequency of males among births in human history so far is = 0.51").

Popper draws attention with admirable explicitness [6] to this---to put it mildly---contretemps. He puts it almost equally mildly himself, however. For he insists on calling the conjunction of (1), (2) and (3) a "problem" ("the problem of the decidability" [7] of propositions like H); when in fact of course it is a contradiction. The reader can hardly fail to be reminded of Hume's complaint about the absurdity of the "custom of calling a difficulty what pretends to be a demonstration and endeavoring by that means to elude its force and evidence" [8]. But Popper's `solution' to his problem was far more remarkable than even his description of it, and indeed was of breathtaking originality.

It consists---or I should say, it appears to consist, because there is another interpretation of Popper possible here, though one which makes his situation far less satisfactory still, which will be discussed later---in making frequent references to what it is that scientists do when they find by experience that s, the observed relation frequency of G among F's, is very different from r, the hypothesized value of the probability of an F being G. What scientists do in such circumstances, Popper says, is to act on a methodological convention to neglect extreme probabilities (such as the joint truth of E and H); on a "methodological rule or a decision to regard [...] [a high] negative degree of corroboration as falsification" [9], that is, to regard E as falsifying H.

Well, no doubt they do. But obviously, as a solution to Popper's problem, this is of that kind for which old-fashioned boys' weeklies were once famous: "With one bound Jack was free!". What will it profit a man, if he has caught himself in a flat contradiction, to tell us about something that scientists do, or about something non-scientists don't do, or anything of that sort? To a logical problem such as the inconsistency of (1), (2) and (3) there is of course---can it really be necessary to say this?---no solution, except solutions which begin with an admission that at least one of the three is false. But least of all can there be any sociological solution.

For our purposes, however, what is important about the episode is the following. The pairs of propositions we are talking about are pairs such as E and H. As (2) implies, and as is in many cases obvious, E is consistent with H. But the logical word `falsifies' or its cognates, applied to a pair of propositions, implies that their logical relation is that of inconsistency. So to say that E falsifies H would be to make a logical statement which is false, necessarily false, and obviously false. So Popper will not say that. What he says instead are things which, however irrelevant to his problem, are at least true (even if only contingently true). Such as the following. That "a physicist is usually quite well able to decide" when to consider a hypothesis such as H "`practically falsified'" [10] (namely, when he finds by experience, for example, that E). That "the physicist knows well enough when to regard a probability assumption as falsified" [11] (for example he will regard H as falsified by E). That propositions such as H "in empirical science [...] are used as falsifiable statements" [12]. That given such an observation-statement as E, "we shall no doubt abandon our estimate [of probability, that is, H] in practice and regard it as falsified" [13].

These are the very models of how to sabotage a logical expression by epistemic embedding, or of ghost-logical statements. They use a logical expression, one implying inconsistency, but they do not imply the inconsistency of any propositions at all. They are simply contingent truths about scientists. Yet at the same time there is a suggestion that not only is a logical statement, implying inconsistency, being made, but that one is being made with which no rational person would disagree. This suggestion is in fact so strong as to be nearly irresistible, and it comes from several sources.

First, Popper's references to a rule, decision, or convention, imply that when scientists regard E as falsifying H, they cannot be wrong: and they therefore serve to suggest that they are right. Second, there is the fact that scientists regard E as falsifying H, and that they are unanimous in doing so. How can a reader suppose that scientists, all scientists, are mistaken in regarding E as inconsistent with H? He might almost as easily suppose all philosophers mistaken in regarding a Barbara syllogism as valid. Third, and most important of all: the reader's own common sense---and it is his logical common-sense---emphatically seconds the statement of logic which here appears, by suggestio falsi, to be being made. He knows, as everyone (near enough), knows, that given E, it is rational to infer that H is false. And since scientists, as these statements report them, seem to be saying only very much the same thing, the reader is disposed to think that the scientists are right. And if they are right, it is clearly a point of logic on which they are right.

The suggestion, coming from all these sources, that a logical statement, and a true one, is being made, is so strong, in fact, that to many people it will appear perverse, or at least pedantic, to resist it. What is there, then, to object to, in the statement that scientists regard E as falsifying H?

Simply that its suggestion, that a statement of logic is being made, is false; and that suggestio falsi is not better, but worse, the stronger the suggestion is. The statement is only a ghost-logical statement. It implies nothing whatever about the logical relation between E and H. A logical word, "falsifying", is used indeed, but its implication of inconsistency is sabotaged by the epistemic context about scientists. This is cold-blooded murder of a perfectly good logical expression, in exchange for a handful of sociological silver about scientists.

What makes the case more unforgivable is that the logical expression here sabotaged is not only a strong or deductive-logical expression, but the one which is, of all deductive-logical words, Popper's own particular favorite; and that he had just a few pages before undertaken that, however others might succumb to non-deductive logic, he never would, but that in his philosophy all relations between propositions of science would be "fully analyzed in terms of the classical logical relations of deducibility and contradiction" [14].

I mentioned earlier that all our authors are of a marked deductivist tendency, and that therefore, when they can no longer avoid a weak or non-deductive logical expression such as "confirms", they will sometimes sabotage it by quotation-marks. We have now seen an example of another strategy that our authors use, when non-deductive logic threatens to break into their philosophy. This is, to retain the deductive-logical words, but deprive them of their deductive-logical meaning, by embedding them in epistemic contexts about scientists. A painful spectacle this: like the citizens of a besieged town, when the besiegers are on the point of breaking in, strangling their own children.

We will see later that our other authors repeat on their own behalf, and extend, what Popper did to the logical relation between statements of factual probability and observation-statements. For the present, let us turn to another, and a less special case: the relation between scientific theories and other statements. Here it is possible to display a series of statements, beginning with Popper and extending through our other authors, in each of which "falsifying" or some equivalent logical expression is sabotaged by epistemic embedding. The members of this series are not only linked by strong family resemblance: it is reasonable to believe that, as a matter of history, the other members of the series grew out of the first one.

The better to display both the nature of these statements and the continuity between the members of the series, I will first give a version of my own which will be a composite-photograph, as it were, of many things actually said by one or more of our authors. No one familiar with our authors will dispute the verisimilitude of my versions. But afterwards I will give, for each statement in this list, at least one of the actual passages which have gone to make up the composite version.

1. `Only a low-level corroborated theory will be accepted as falsifying a scientific theory'.
(This is the thesis of Popper which is, I believe, the germ of the following three others).
2. `In the actual history of science, as distinct from the distortions of it by philosophers, theories are never regarded as refuted by reports of observations, or experiments: a scientific theory can be defeated only by another theory'.
(This thesis, although in fact Popperian enough, is more usually associated with our other authors, and is sometimes even advanced by them as a criticism of Popper).
3. `It is often only with the hindsight provided by a later and rival theory T' that a certain experiment is seen as `crucial' against, that is, as a falsification of, an earlier theory T'.
(This thesis is Lakatosian, of course, but is also entirely congenial to Kuhn and Feyerabend).
4. `The anomalies which beset an earlier paradigm are considered intolerable, that is, as logically compelling its abandonment, only after the shift to a new paradigm has been made, and even then only by those scientists who have made the shift'.
(This is Kuhnian, of course, but again entirely congenial to Lakatos and Feyerabend).

(The following are some of the actual passages from which the foregoing composites have been made.

In connection with (1): "[...] the non-reproducible single occurrences are of no significance to science. Thus a few stray basic statements contradicting a theory will scarcely induce us to reject it as falsified. We shall take it as falsified only if we discover a reproducible effect which refutes the theory. In other words, we only accept the falsification if a low-level hypothesis which describes such an effect is proposed and corroborated" [15].

In connection with (2): "[...] a clash [with observation] may present a problem (major or minor) [for a theory], but in no circumstance a `victory' [for observation]. Nature may shout no, but human ingenuity---contrary to Weyl and Popper---may always be able to shout louder. With sufficient resourcefulness and some luck, any theory can be defended `progressively' for a long time, even if it is false". And "[...] a rival theory, which acts as an external catalyst for the Popperian falsification of a theory, here becomes [i.e. on Lakatos's methodology] an internal factor" [16].

In connection with (3): "The anomalous behavior of Mercury's perihelion was known for decades as one of the many yet unsolved difficulties in Newton's programme; but only the fact that Einstein's theory explained it better transformed a dull anomaly into a brilliant `refutation' of Newton's research programme. Young claimed that his double-slit experiment of 1802 was a crucial experiment between the corpuscular and the wave programmes of optics; but his claim was only acknowledged much later, after Fresnel developed the wave programme much further `progressively' and it became clear that the Newtonians could not match its heuristic power. The anomaly, which had been known for decades, received the honorific title of refutation, the experiment the honorific title of `crucial experiment', only after a long period of uneven development of the two rival programmes" [17].

In connection with (4): "Ordinarily, it is only much later, after the new paradigm has been developed, accepted, and exploited, that apparently decisive arguments [against the old paradigm] are developed. Producing them is part of normal science, and their role is not in paradigm debate but in post-revolutionary texts" [18]. Again: "Though the historian can always find men---Priestly for instance---who were unreasonable to resist [a new paradigm] for as long as they did, he will not find a point at which resistance becomes illogical or unscientific" [19]).

Statements such as I have referred to here either quoted or paraphrased will be admitted to be representative of our authors' writings. They even embody a considerable amount of the substance of their philosophy of science, and they certainly exemplify a very characteristic way our authors have of expressing that philosophy. They are a fair sample of our authors' contributions to that enterprise on which they are all engaged, and their contributions to which constitute their main claim on their readers' attention: the enterprise of making known the logic of science.

It is therefore worthwhile to point out that not one of them is a logical statement at all. Not one of them has a single implication about the logical relation between any propositions whatever. They all indeed use logical expressions, and strong ones: "falsifying", "refuting", "decisive argument against", or some cognate equivalent. But every time such an expression occurs, it is sabotaged by being embedded in an epistemic context about scientists: about how scientists `regard', `consider', `take', `see', etc., the relation between certain propositions. In short they are one and all ghost-logical statements, and nothing more.

Enough examples, and sufficiently representative ones, have perhaps now been given, to enable the reader to begin to realize how extremely common in our authors is the sabotage of logical expressions by epistemic embedding. Once you mix the history with the logic of science, the possibilities of such sabotage are limitless; and almost every possibility has been realized. Recall for example Kuhn's willingness to dissolve even the strongest logical expressions into sociology about what scientists regard as decisive arguments; recall that the logical expressions most important to him (namely the positive "solves the problem of", and the negative "is an anomaly for") are weak ones, and are therefore easily sabotaged; recall his express and repeated assertion that what constitutes solution of a problem is paradigm-relative; and you will see that his entire philosophy of science is actually an engine for the mass-destruction of all logical expressions whatever: a `final solution' to the problem of the logic of science. Then there is that variety of iterated epistemic embedding which is an especial pest in Lakatos: `According to sophisticated theoretical conventionalism' (or whatever) `scientists never regard such-and-such as inconsistent with so-and-so', etc., etc. But these are the block-busters of sabotage. The small-arms fire, which almost never stops, is better represented by the following quotation from Popper, in which he is discussing the positive scientific knowledge. Now "positive scientific knowledge" may perhaps be not obviously a logical expression, but a logical expression it must be. "Positive scientific knowledge" must at least entail "well-confirmed theories", for example; and here is what Popper says. "In my view, all that can possibly be `positive' in our scientific knowledge is positive only in so far as certain theories are, at a certain moment in time, preferred to others in the light of our critical discussion, which consists of attempted refutations [...]" [20].

Thus, where the reader expects, and non-irrationalist philosophy would require, the word "preferable", what Popper actually says is "preferred"; and so the logical expression "positive scientific knowledge" is quietly sabotaged, by a context referring only to the actual theory-preferences of people (presumably scientists). There are literally hundreds of sentences in Popper like this. He is about as sensitive to the difference between an evaluative word (like "preferable") and a descriptive one (like "preferred") as Mill in a famous passage [21] showed himself to be to the difference between "desirable" and "desired".

Such examples enable us to understand something which is especially prominent in Kuhn, and which is otherwise baffling: what might be called his `tautological optimism' about science. See his [1970a] Chapter XIII passim, and for the example the following. "If I sometimes say that any choice made by scientists on the basis of their past experience and in conformity with their traditional values is ipso facto valid science for its time, I am only underscoring a tautology" [22].

The reader is dumbfounded: the validity of current science is guaranteed by ordinary scientific behavior plus tautology? There has to be a catch in that! How could Kuhn come to write such a thing? Well, we now know how. If, like Kuhn, you cannot tell the difference between talk about the logical relation of current evidence P to the current theory Q, and ghost-logical talk about what scientists consider to be the logical relation of P to Q, why, then, the connection between valid-science, and what scientists currently consider to be so, will of course seem to you to be perfectly analytic.

It may be worthwhile to add another instance in which it is a weak positive logical expression, rather than a strong negative one, which is sabotaged. (This example is a composite-photograph one, but will easily be recognized as representative). "Scientists consider a theory T' better confirmed than a theory T, if T' explains all that T does, avoids the failures of T, and predicts facts which T does not". This kind of example is interesting for two reasons. One is that, because of the embedded logical statement ("T' is better confirmed (etc.)") is so highly plausible, the sabotage of it by "Scientists consider" is, to a correspondingly high degree, inconspicuous: indeed, it is almost imperceptible. The other reason is, that such ghost-logical statements as this one have a special advantage for deductivist authors. For the embedded logical statement is, of course, one belonging to non-deductive logic, and therefore it would, if asserted naked, entangle the author in non-deductive logic; whereas when it is clothed in an epistemic context about scientists, it leaves one's options open and one's deductivist record unblemished. There is a slight drawback, of course, that one has now not made a logical statement at all! But then, no one is likely to notice that: at least, they never have.

I have not implied, and it is not true, that our authors are the only ones in recent philosophy of science who ever sabotage a logical expression by epistemic embedding. In fact, easily the most influential ghost-logical statement of the century is one which is not usually associated with them at all; though they find it congenial, and, as we might have expected, Popper actually anticipated it. This is `the Quine-Duhem thesis': that "any statement can be held true come what may, if we make drastic enough adjustments elsewhere in the system [...]. Conversely, [...] no statement is immune to revision" [23].

Would-be critics of this thesis have been mystified by its immunity to revision. They would not have been, if they had come to it from a course of reading in our authors, as we do now. For our ears are by now accustomed to detect the fatal premonitory sounds of sabotage---`regarded as', `accepted as', etc., prefixed to a logical expression---and once we hear, in Quine's word "held", the doom of a logical expression again pronounced, we expect immunity to logical criticism to ensue. The thesis means, of course, that any scientific theory can be held to be consistent with any observation-statement, however `recalcitrant', provided we make drastic enough adjustments elsewhere in the system. This thesis is undoubtedly true. But what kind of a truth is it?

It seems to be a statement of logic. For it seems to imply that a certain logical relation, namely consistency, exists between certain kinds of propositions. But look more closely: the thesis does not imply that observation-statements are always consistent with scientific theories. It does not imply that they ever are. It does not imply anything about the logical relation between any propositions whatever.

In fact the thesis is simply the most trivial of contingent truths about humans beings: that given any proposition whatever, a scientist (or anyone) can take it into his head to affirm it, and can then stick to it through thick and thin. Of course, it is true that "any statement can be held true come what may, if we make drastic enough adjustments elsewhere in the system": for the simple reason that any statement can be held true come what may, with or without making `adjustments elsewhere'. Quine's proviso then, (here italicized), was entirely unnecessary for the truth of what he said. Its only function was that of suggestio falsi: to generate the illusion that a statement of logic, and in particular one which implies that certain propositions are consistent with one another, was being made.

A third way to sabotage a logical expression is to embed it in a context which is not epistemic, but of a kind which I will call "volitional". This kind of context makes the logical relation, implied by the logical statement embedded in it, an object not of anything epistemic (such as belief), but of the will. The logical relation between propositions is now spoken of as being, by some one or other, decided or chosen or made to be, entailment, inconsistency, or whatever. Schematic examples: "Logicians, let us make the Barbara syllogism valid"; "I permit P to be consistent with Q"; "I propose a rule making P and Q inconsistent"; "I propose the adoption of a convention to regard P as entailing Q".

This may not seem a very intelligible way to speak. Still, our authors often do speak in essentially this way. And historically this practice too stems, just as epistemic embedding does, from the locus classicus in Popper already discussed, concerning the falsifiability of unrestricted statements of factual probability. So we must return to that.

Our example, it will be remembered, of the propositions here in question, was H, "The probability of a human birth being male is = 0.9". Its unfalsifiability (that is, its consistency with every observation statement) we exemplified by its consistency even with E, "The observed relative frequency of male births in human history so far is = 0.51". And Popper's problem, we recall, was that he had asserted (1) that some unrestricted statements of factual probability are scientific; (2) that none of them is falsifiable; and (3) that only falsifiable statements are scientific.

Now I took Popper's solution, when I wrote about it above, to be a historical report, by Popper, that scientists do in fact act on a convention to regard E as falsifying H. But what he says may also be interpreted in another way, either instead of this, or (as I believe it should be) in addition to it: as Popper himself proposing such a convention.

Lakatos and Kuhn both interpret Popper exclusively in the second way. And some remarks of Popper himself, though made much later, give additional weight to this interpretation. (See the text to footnotes 30 and 31 below).

On my first interpretation, Popper's sabotage of the logical expression "falsifying" was by embedding it in an epistemic context (about scientists). On the second interpretation, it was by embedding it in a volitional context. For we are now to understand him as permitting us to regard E as falsifying H, or as introducing a rule which makes E inconsistent with H.

Popper's `solution' to his problem is, of course, even more amazing on this interpretation than it was on the first. It is bad enough to suggest that you can get yourself out of the contradiction constituted by (1), (2) and (3), by reporting some fact about scientists. But to suggest that you can get out of it by some exercise of your will---by permitting something or proposing something---is even more breath-taking still. It is difficult even to understand such a suggestion. Nevertheless, that does appear to be Popper's main suggestion, and we must make the best we can of it.

To Lakatos and Kuhn, at any rate, this presents no difficulty at all. Far from that, they willingly endorse it, and heartily repeat on their own behalf Popper's exemplary act of sabotage. Lakatos writes: "[...] no result of statistical sampling is ever inconsistent with a statistical theory unless we make them inconsistent with the help of Popperian rejection rules [...]" [24]. Again, he writes: "[...] probabilistic theories [...] although they are not falsifiable [...] can easily be made `falsifiable' by [a] decision which the scientist can make by specifying certain rejection rules which may make statistically interpreted evidence `inconsistent' with the probabilistic theory" [25]. Kuhn similarly writes: "[...] dealing with a probabilistic theory [scientists] must decide on a probability threshold below which statistical evidence will be held `"inconsistent"' with that theory" [26].

The last quotation is well worth the attention of the connoisseur. The logical word "inconsistent" is first sabotaged with quotation-marks, and not by one but by two sets of them. And as though this might still not be quite enough to ensure that the word "inconsistent" no longer means inconsistency, it is sabotaged as well by the volitional context "[scientists] [...] decide [...]". Finally, Kuhn's word "must"---but this is best left for an advanced course in the anti-saboteur college.

In Popper, the logical relation between observation-statements and statements of factual probability is the only one sabotaged by embedding in volitional contexts. It is not so in Lakatos or Kuhn. On the contrary, Lakatos speaks quite generally of "making" propositions "unfalsifiable by fiat" [27]; that is, as though it were possible to do this to any proposition whatever. Equally generally, Kuhn writes, taking up this phrase of Lakatos, that "Scientists must decide which statements to make `unfalsifiable by fiat' and which not" [28].

In these places in our authors, then it is implied that in at least some cases the logical relation between propositions can be made or chosen by, or be in some way subject to, the will. At many other places in their writings the same thing is suggested. For example, when Feyerabend pleads for majority-rule in science [29]. Or again when Lakatos speaks of the scientist's need, when he had deduced a false conclusion from a complex set of premises, to `decide where to direct the arrow of modus tollens' [30]. The will in question, then, may be that of Popper, or of scientists, or of the majority of people. But all our authors imply, by embedding logical expressions in volitional contexts, that logical relations can be subject to some will.

The major difficulty is simply that of understanding how this could be true. When our authors sabotage logical expressions by embedding them in epistemic contexts, the result is a ghost-logical statement; and those, while poor substitutes for logical statements, are at least always intelligible, being usually just historical statements about scientists. But when logical expressions are embedded in volitional contexts, the result is simply unintelligible, at least to `ordinary philosophers'. The word "unfalsifiable", for example, means, in Popper and in all our authors, "consistent with every observation-statement". To "make a proposition unfalsifiable by fiat", then, is to make it, by fiat, consistent with every observation-statement. But how can anyone, whether the majority, or scientists, or even Popper, make it so? Or make the logical relation between propositions, in any other case, to be anything? Logical relations, surely, simply are not subject to the will.

Of course one can decide or choose what proposition a given sentence will on a given occasion express. If I decide, as I can decide, that the next time I utter the sentence "The cat sat on the mat", the word "cat" will mean "bat", then that sentence may not on that occasion express the same proposition as it usually does. But it is certainly not this understanding and ever-present possibility that our authors have in mind. What they imply, and what they undoubtedly mean, is that the logical relation between propositions can properly be spoken of as made, decided, chosen, or the like.

If this were intelligible, it would be inexplicable how Popper ever allowed his original problem, the inconsistency of (1), (2) and (3), to arise. He `solved' it, it now appears, by proposing a rule that would make E inconsistent with H, or by permitting us to regard E and H as inconsistent. But if he can do this kind of thing, why did he not do it in the first place? He could simply have permitted us to regard (1), (2) and (3) as consistent, or proposed a rule that would make them consistent. They aren't, of course, but then he would not be saying that they are: only exercising his will, permitting or proposing that they be so regarded. After all, he is permitting us to regard E and H as inconsistent, or proposing a rule that will make them inconsistent, though they aren't; and he is not saying they are, but only exercising his will and proposing a rule that will make them so. Why postpone the exercise of so sovereign a will?

But the major difficulty, as I said, is simply that of understanding our authors when they embed logical expressions in volitional contexts. The proposition H, again, is consistent with every observation-statement, including E. How then can any choice, decision, rule, or any operation of any will, even the divine will, make H and E inconsistent? This is, as James I said of the Novum Organum, like the peace of God, which passeth all understanding.

There is one important thing which is clear, however, and it is this: if a logical expression is embedded in a volitional context, then it is sabotaged. Thus, for example, it would not be possible for anyone to make P and Q inconsistent (say), or to decide that they are inconsistent, if they are inconsistent. With this much, I believe, even the most voluntarist of our authors would agree. But then it follows that if anyone could make P and Q inconsistent or decide that they are inconsistent, then P and Q would be consistent, not inconsistent. That is, a logical expression, once embedded in a volitional context, cannot retain its implication about logical relations, but must be sabotaged.

Every time, therefore, that our authors embed a logical expression in a volitional context, we have yet another instance in their writings of a logical expression being deprived of its implication about the logical relation between propositions.

The practice of sabotaging logical expressions by embedding them in contexts about scientists, and again Kuhn's `tautological optimism' about science, correspond, in an easily understandable way, to a certain substantive thesis about logical expressions and scientists. Namely, that in the application of logical expressions, the highest authority, or at least some special authority, resides in science; that is, that scientists, whether in virtue of their knowledge or in virtue of their will, have some special authority on statements of logic. If like Kuhn you cannot tell the difference between (for example) the logical statement "P entails Q", and the ghost-logical statement "Any scientist would regard P as entailing Q", then you will think it out of the question that on matters of logic there could be any authority higher than science, or even any authority independent of science. And if you think this, then, since a statement of what the logical relation is between two propositions is equivalent to certain statements about how rationally conclusive certain inferences are, you will think that science has some special authority on questions of the rational conclusiveness of inferences.

It is interesting, therefore, to find that this thesis is actually affirmed by Kuhn. He writes: "To suppose that we possess criteria of rationality which are independent of our understanding of the essentials of the scientific process is to open the door to cloud-cuckoo land" [31].

Beliefs about the rational conclusiveness of inferences are, I take it, among `criteria of rationality'. But if so, then Kuhn's thesis is not only false but the exact reverse of the truth. For we do possess, all of us, and by the million, criteria of rationality, and correct ones at that---that is, true beliefs about the rational conclusiveness of inferences---which are entirely independent of our understanding of science.

Everyone (or near enough) knows that "Socrates is mortal" is entailed by "All men are mortal and Socrates is a man". That the former does not entail the latter. That "Socrates is mortal" is less probable in relation to "Socrates is a man", than it is in relation to the conjunction of that proposition with "All men are mortal". That "All men are mortal" is more probable in relation to "Socrates is a man and Socrates is mortal", than it is to the first conjunct of that proposition alone. And so on. Such logical knowledge may properly be called "natural", since everyone (near enough) possess it. Obviously, too, everyone has enormous amounts of it. And it is clearly independent of the understanding of science. For such knowledge has been and is now possessed by a great many people who never so much as heard of science. To paraphrase Locke, God did not deal so sparingly with mankind as to make them barely two-legged, leaving it to scientists to teach them which inferences are rationally conclusive, or to what degree.

It may be said that natural logical knowledge, though it does not require acquaintance with actual science, nevertheless is knowledge of at least some of "the essentials of the scientific process": which were Kuhn's words. In a sense of course this is true: namely, in the sense that scientists do have natural logical knowledge and could not do their work if they did not. But in that sense natural logical knowledge is knowledge of at least some of the essentials of the legal process too, and of the haircutting process; for it is true of lawyers and barbers, too, that they have natural logical knowledge and could not do their work if they did not. Taken in this attenuated sense, then, Kuhn's thesis would be true. But then it no longer implies, what Kuhn appears to have meant by it, that on matters of how rationally conclusive inferences are, scientists have some authority which other people lack.

Our authors, as I said in Chapter I, do not neutralize success-words all the time. Mixed strategy forbids it. Besides, they need to have these words on hand, with their success-grammar intact, as weapons to repel the different neutralizations which may be made of them by other people: people who are not licensed, as our authors are, to kill scientific success with words. It is all right for Popper to call scientific knowledge conjectural, but a mere undergraduate who in an essay called knowledge a poached egg, or said that knowledge entails falsity, would no doubt be given by our authors the sharp reminders he deserves about the meaning of some common English words. He might even be reminded (since this is clearly no time to be neutralizing) that knowledge entails truth. Well, it is just the same with the sabotage of logical expressions. Our authors by no means do it all the time. Mixed strategy forbids that; and besides, they need the logical expressions on hand, with their implications about logical relations intact, to use against other and unlicensed saboteurs of logic. They need them too, no doubt, for the humdrum task of correcting the mere errors that undergraduates make in their logic exercises.

Popper writes: "I had introduced in Chapter VIII of [The Logic of Scientific Discovery] a methodological rule permitting us to neglect "extreme improbabilities" [32]. And he continues: "Certain sorts of coin behavior [he means, for example, a million heads in a row] are incompatible with the coin's being fair (given our rule) and that is that [...]" [33].

It is just as well that Popper introduced this rule. Otherwise we might have gone on indefinitely just neglecting extreme probabilities in our old bad way: that is, without his permission. But at least until Popper introduces a rule of higher type, permitting no else to introduce other rules of the first type, other people may introduce other such rules. `With one bound Jack was free' is a good game, but it has the drawback that any number can play.

Popper tells us that he has had students who thought at first that "All men are mortal and Socrates is mortal" entails "Socrates is a man"; but that he succeeded in getting them to acknowledge this error [34]. But such a student might not have been by any means so docile on this point, it seems to me, if he had read a little more widely in his teacher's writings.

He might have said: `I have introduced, in my logic exercise, a methodological rule permitting us to deduce "Socrates is a man" from "All men are mortal and Socrates is mortal". Given our rule, this premise is incompatible with Socrates' not being a man; and that is that".

Or suppose the subject were an inductive argument: say, "All the observed ravens have been black, so at least one of the unobserved ravens is black". Here Popper would urge upon the student his famous discovery, that such an argument is invalid. But why should the student tamely submit to this? If he wants to sabotage logical expressions, his teacher has given him ample precedent. And is he bound to sabotage only those logical expressions, and only in those places, that his teacher's example had previously authorized? Surely not. He might, then, choose a suitable epistemic context, and say for example, in the best ghost-logical style, and with plausibility: "Any ornithologist would regard that argument as valid". If he prefers sabotage by volitional embedding, he may simply propose a rule making this inductive argument valid; or perhaps his whole class, or the undergraduate body, will propose such a rule. Again the students would have Popper's precedent to justify them; and just as there is no special authority over logicals relations attaching to Popper's will, so there is no special lack of authority attaching to undergraduate wills. More simply still, the students might make a point of writing, in all their essays, never that inductive arguments are invalid, but always that they are `invalid'; and see what objection their teacher could consistently make to this practice.

A pupil so apt as this one would oblige Popper, or any of our other authors, to fall back on doing what ordinary philosophers do, or try to do, all the time. That is, to use only un-sabotaged logical expressions, and to talk plain English about the logical relations which exist between propositions, independently of `scientists' or anyone else's `regards', `proposals', and bedding generally. There would then be no embedding of logical expressions in either epistemic or volitional contexts, no enclosing them in quotation-marks, in fact no sabotage of logical expressions at all; at least for a little while.

While this lucid interval lasted, there would be a respite, too, from another maddening feature of the English of some of our authors: a feature which, though it is distinct from their sabotage of logical expressions, could not have come about but for that, and could not subsist if sabotage were dropped. I mean the practice, so common in Lakatos especially, of speaking in such a way as to weld logical and causal relations into one solid mass of confusion. For example, the application to scientific theories of expressions such as "is defeated", "is eliminated", "is removed", "is abandoned", as though these causal expressions were logical expressions like "is falsified", only perhaps stronger; and as though, consequently, the logical relation between propositions could have causal power.

It is very easy to see how this practice came in. P's falsifying Q cannot itself have any share of causal power; for example the power to cause abandonment of belief in Q. But of course P's being regarded as falsifying Q can have a share of causal power, just as the knowledge or belief that P falsified Q can. And our authors, by their constant sabotage of logical expressions, have succeeded in blurring the distinction between P's falsifying Q and its being regarded as doing so. But the practice is one which is deplorably well-adapted to reinforce, at the same time as it expresses, the conflation of the history with the logic of science.

There may then be an interpretation of the thesis of the theory-dependence of observation which it is true and does not support irrationalism. My own suspicion is that there is not, and that on the contrary "Observation-statement O depends on theory T" is always just a ghost-logical statement in an indeterminate or fetal stage of development, and that the right regimen for it is abortion or exposure. Anyway, for the opponents of irrationalist philosophy of science there is nothing more urgently required than to focus critical attention on this quasi-logical/quasi-causal relation of dependence or ladenness, of which so much has lately been made.

## Appendix to Chapter II

Helps to Young Authors (II)

Sabotaging logical expressions

Q: This is a fair coin.
P: It has just been fairly tossed 1000 times and it came down "heads" 900 of those times.

How to rewrite the sentence: Q is consistent with the true observation-statement P, but very improbable in relation to it.

Lakatos:
Q is `falsified' by P.
Popper:
(Either) Scientists, by a methodological convention, regard Q as falsified by P.
(or) I introduce a methodological rule permitting us to regard P as incompatible with Q.
Kuhn:
A scientist who did not, in view of the anomaly P, reject Q, would be regarded as violating one of the most basic values of his profession: consistency.
Feyerabend:
The theory Q, though `refuted' by the anomaly P and a thousand others, may nevertheless be adhered to by a scientist for any length of time; and `rationally' adhered to. For did not the most `absurd' of theories, heliocentrism, stage a come-back after two thousand years? And is not Voodoo now emerging from a long period of unmerited neglect?