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The argument against materialism mentioned at the end of the previous section was concisely formulated by J. B. S. Haldane. Haldane  puts it thus: ". . . if materialism us true, it seems to me that we cannot know that it is true. If my opinions are the result of the chemical processes going on in my brain, they are determined by the laws of chemistry, not of logic."16
The argument (retracted by Haldane in a paper "I Repent an Error" 17) has a long history. It can be traced back at least to Epicurus: "He who says that all things happen of necessity cannot criticize another who says that not all things happen of necessity. For he has to admit that the assertion also happens of necessity."18 In this form, it was an argument against determinism rather than against materialism. But the close relationship between the arguments of Haldane and Epicurus is striking. Both indicate that if our opinions are the result of something other than the free judgement of reason,19 or the weighing of reasons, of the pros and cons, then our opinions are not worth taking seriously. Thus an argument that leads to the conclusion that our opinions are not arrived at in this way defeats itself.
Haldane's argument (or more precisely, the second of the two sentences quoted above) cannot be upheld in the form here stated. For a computing machine may be said to be determined in its working by the laws of physics; but it may nevertheless work in full accordance with the laws of logic. This simple fact invalidates (as I pointed out in section 85 of my unpublished Postscript) the second sentence of Haldane's argument as it stands.
However, I believe that Haldane's argument (as I will call it in spite of its antiquity) can be so revised as to become unexceptionable. Although it does not show that materialism destroys itself, I suggest that it shows that materialism is self-defeating: it cannot seriously claim to be supported by rational argument. The revised argument of Haldane could be put more concisely, but I think it is clearer if developed at length.
I will represent the revised argument in the form of a dialogue between an interactionist and a physicalist.
Interactionist I am quite prepared to accept your refutation of Haldane's argument: the computer constitutes a counter-example to this argument as it stands. However, it seems to me important to remember that the computer, which admittedly works on physical principles and at the same time also according to logical principles, has been designed by us — by human minds — to work like this. In fact, a great amount of logical and mathematical theory is being used in the making of computers. This explains why it works according to the laws of logic. It is far from easy to construct a piece of physical apparatus that works according to the laws of physics and, at the same time, according to the laws of logic. Both the computer and the laws of logic belong emphatically to what is here called World 3.
Physicalist I agree, although I admit only the existence of a physical World 3 to which, for example, books on logic and mathematics belong, and, of course, also computers: this World 3 of yours is in fact part of World 1. Books and computers are products of men and women — they are designed; they are products of human brains. Our brains in turn are not really designed — they are largely the products of natural selection. They are so selected as to adapt themselves to their environment; and their dispositional capacities for reasoning are the result of this adaptation. Reasoning consists in a certain kind of verbal behaviour and in acquiring dispositions to act and to speak. Apart from natural selection, positive and negative conditioning through the success and failure of our actions and reactions also play their role. So does schooling; that is to say, conditioning through a teacher who works upon us — somewhat like a designer who works on a computer. In this way we become conditioned to speak and to act and to reason rationally or intelligently.
Interactionist It seems that you and I agree on a number of points. We agree that natural selection and individual learning play their role in the evolution of logical thinking. And we agree that a reasonable or a reasoning materialism is bound to assert that a well trained brain, like a reliable computer, is built in such a way that it works in accordance with the principles of logic and with those of physics and electro-chemistry.
Physicalist Precisely. I am even prepared to admit that if this view cannot be upheld, then Haldane's argument would actually upset materialism: I would have to admit that materialism undermines its own rationality.
Interactionist Do computers or brains never make mistakes?
Physicalist Of course computers are not perfect. Nor are human brains. This goes without saying.
Interactionist But if so, you need World 3 objects, such as standards of validity, which are not embodied or incarnated in World 1 objects: you need them to be able to appeal to the validity of an inference; yet you deny the existence of such objects.
Physicalist I do deny the existence of non-corporeal World 3 objects; but I do not quite see your point yet.
Interactionist My point is quite simple. If computers or brains may fail, what do they fall short of?
Physicalist Of other computers or brains or of the contents of books on logic and mathematics.
Interactionist Are these books infallible?
Physicalist Of course not. But mistakes are rare.
Interactionist I doubt that, but let it be so. I still ask: if there is a mistake — mind you, a logical mistake — by what standard is it a mistake? Physicalist By the standards of logic.
Interactionist I fully agree. But these are abstract non-corporeal World 3 standards.
Physicalist I do not agree. They are not abstract standards, but the standards or principles which the great majority of logicians — in fact, all except a lunatic fringe — are disposed to accept as such.
Interactionist Are they so disposed because the principles are valid, or are the principles valid because logicians are disposed to accept them? Physicalist A tricky question. The obvious answer to it, and at any rate your answer, would seem to be "logicians are disposed to accept logical standards because these standards are valid". But this would admit the existence of non-corporeal and thus of abstract standards or principles whose existence I deny. No, I have to give a different reply to your question: the standards exist, so far as they exist, as states or dispositions of the brains of people: states, or dispositions, which make people accept the proper standards. You may now, of course, ask me "What else are the proper standards but the valid standards?" My answer is "certain ways of verbal behaviour, or of connecting some beliefs with others; ways which have proved useful in the struggle for life, and which therefore have been selected by natural selection, or learned by conditioning, perhaps in school, or otherwise".
These inherited or learned dispositions are what some people would call "our logical intuitions". I admit that they exist (as opposed to abstract World 3 objects). I also admit that they are not always reliable: logical errors exist. But these mistaken inferences may be criticized, and eliminated.20
Interactionist I do not think that we have made much progress. I have long admitted the role of natural selection and of learning (which I, incidentally, should certainly not describe as "conditioning"; but never mind the terminology). I also would insist, as you seem to do now, on the importance of the fact that we often approach truth by way of the elimination and correction of error; and like yourself, I am inclined to say that the same holds with mistaken inferences as opposed to valid inferences: we learn of an inference, or a certain way of drawing inferences, that it is invalid if we find a counterexample; that is to say, an inference of the same logical form, with true premises and a false conclusion. In other words: an inference is valid if and only if no counter-example to this inference exists. But this statement (which I have emphasized) is a characteristic example of a World 3 principle. And although the emergence of World 3 can be, partly, explained by natural selection, that is to say, by its usefulness, the principles of valid inference, and their applications, which belong to World 3, cannot all be explained in this way. They are partly the unintended autonomous results of the making of World 3.
Physicalist But I stick to my point that only the physiological dispositions (more precisely, dispositional states21) exist. Why should not dispositions evolve or develop which I may describe as dispositions to act in accordance with a routine? For example in accordance with what you call the logical standards of truth and validity? The main point is that the dispositions are useful in the struggle for survival.
Interactionist That may sound all right, but it seems to me to avoid the real issue. For dispositions must be dispositions to do something. If we ask what this something is, you seem to indicate that your answer would be "to act in accordance with a routine". But can we not then ask "What routine?" — and this, I think, would lead us back to World 3 principles.
But let us look at the matter from another angle. The property of a brain mechanism or a computer mechanism which makes it work according to the standards of logic is not a purely physical property, although I am very ready to admit that it is in some sense connected with, or based upon, physical properties. For two computers may physically differ as much as you like, yet they may both operate according to the same standards of logic. And vice versa; they may differ physically as little as you may specify, yet this difference may be so amplified that the one may operate according to the standards of logic, but not the other. This seems to show that the standards of logic are not physical properties. (The same holds, incidentally, for practically all relevant properties of a computer qua computer.) Yet they are, according to you and me, useful for survival.
Physicalist But you say yourself that the property of a computer which makes it work according to the standards of logic is based upon physical properties. I do not see why you deny that this property is a physical property. Surely, it can be defined in purely physical terms. We simply build a logical computer, which is a physical object. Then we define the relations between its input and its output as the standards of logic. In this way we have defined a standard of logic in purely physical terms.
Interactionist No. Your computer may break down. This may happen to any computer. Incidentally, you could just as well choose as your standard a particular copy of a logical text book. However, it may have mistakes in it, either printing mistakes or others. No, standards belong to World 3, but they are useful for survival; which means that they have causal effects in the physical world, in World 1. Thus the abstract World 3 property of a computer which we can describe by saying "its operations conform to logical standards" has physical effects: it is "real" (in the sense of section 4 above). This causal action upon World 1 is precisely the reason why I call World 3, including its abstract objects, "real". If you admit that conformity with logical standards is useful for survival, you admit the usefulness of logical standards, and so their reality. If you deny their reality, why is the similarity between useful computers and the difference between a useful computer and a useless one not to be found in their physical similarity or dissimilarity but in their ability or disability to work in accordance with logical standards?
Physicalist I am still unconvinced. Is usefulness for survival purposes according to you a property belonging to World 1, as I think, or do you count it as belonging to World 3?
Interactionist It depends. The usefulness of a natural organ I am inclined to count as a property belonging to World 1 objects, while that of man-made tools may be a property belonging to World 3 objects.
Physicalist But the brain, and its states and processes, are World 1 objects; and so are verbal expressions such as statements or theories. Could we not simply accept a suggestion of William James's and call a theory true if it is useful? And could we not similarly call an inference valid if it is useful?
Interactionist You can, of course, but you do not gain anything. Admittedly, truth is useful in many contexts; it is so especially if one adopts the World 3 aims and purposes of a scientist, a theoretician; that is, to explain things. From this point of view, valid inference is particularly valuable or "useful", because we can look at explanation as a certain kind of (usually abbreviated) valid inference. But although we can say that in this sense truth is useful, it leads to great trouble if we try (with William James) to identify truth and usefulness.
Physicalist How does it lead to trouble?
Interactionist If one thinks of a true theory as useful, then one does so mainly because of the usefulness of its true informative content. But a theory may be true even if its informative content is negligible, or nil: a tautology like "All tables are tables" or perhaps "1 = 1" is true; but it has no useful informative content. This has its repercussions on the usefulness of validity.
A valid inference always transmits truth from the premises to the conclusion and retransmits falsity from the conclusion to at least one of the premises. Is this perhaps enough to show its instrumental value? It is not, for the premises may be true and useful but the conclusion may be true and useless, as I have just shown. The point is that the informative content of a validly derived conclusion can never exceed that of the premises. (If it does a counterexample can be found.) But the informative content can deteriorate in a valid inference. In fact, it may be zero. For example, a valid conclusion drawn from some highly informative and useful theory may be just a tautology like "1 = 1", which is not informative and therefore no longer useful.
Thus a valid inference always transmits truth, but not always usefulness. It cannot therefore be shown that every valid inference is a useful instrument, or that the routine of drawing valid inferences is as such always useful.
You might wonder why you as a physicalist could not say that it is not so much every particular valid inference that is useful but the whole system of valid inferences; that is to say, logic as such. Now, it is indeed true enough that it is the system — logic — which is useful. But the problem for the physicalist is that it is just this that he cannot admit; for the point at issue between him and the interactionist is precisely whether such things as logic (which is an abstract system) exist (over and above particular ways of linguistic behaviour). The interactionist here takes the commonsensical view that valid inference is useful — and this, indeed, is one of the reasons why he admits its reality. The physicalist is prevented from accepting this position.
So far the dialogue. In it I have tried in brief to state some of the reasons why a materialist theory of logic and with it of World 3 does not work.
Logic, the theory of valid inference, is indeed a valuable instrument; but this cannot be made clear by an instrumentalist interpretation of valid inference Nor can, I think, such ideas as that of the informative content of a theory (an idea that depends on that of deducibility or valid inference) be made clear as long as we do not transcend the materialist point of view — the point of view that admits only the physical aspects of World 3.
I do not claim that I have refuted materialism. But I think that I have shown that materialism has no right to claim that it can be supported by rational argument — argument that is rational by logical principles. Materialism may be true, but it is incompatible with rationalism, with the acceptance of the standards of critical argument; for these standards appear from the materialist point of view as an illusion, or at least as an ideology.
I think that the argument of this section concerning validity can be generalized.
Some people assert7 that all argument is ideological and that science is just another ideology. This is clearly a self-defeating relativism. It is sometimes connected with the thesis that there is no such thing as a pure standard of validity, or a pure theory, but that all knowledge works in the interest of human interests — such as socialism and capitalism. Reply: are computers in a socialist Utopia to be constructed differently from those in a capitalist society? (Of course, they may be differently programmed; but this is trivial, as they will always be differently programmed if used to solve different problems.)
16 See J. B. S. Haldane , reprinted in Penguin Books (| 1937], p. 157); see also Haldane
17 , p. 209.
18 2 J. B. S. Haldane , See also Antony Flew . A more recent rejection of what I call Haldane's argument, due to Keith Campbell, can be found in Paul Edwards, ed. [1967 (b)) vol.5, p. 186. See also J.J.C. Smart , pp. 126f. (and Antony Flew , pp. 114-15) where further references will be found, and section 85 of my (unpublished) Postscript.
3 Epicurus, Aphorism 40 of the Vatican Collection. See Cyril Bailey  pp. 112—113. This may well have been Epicurus's central argument against determinism, and for his theory of the "swerve" of the atoms.
19 Cp. Descartes, Meditation IV; Principles I, 32 — 44.
20 s My physicalist seems to me to do somewhat better here than those materialists for whom truth is ensured by direct causation rather than by the elimination of error, e.g. by selection (partly by natural selection). See also section 23 below.
21 6 See Armstrong , pp. 85-8.
7 Perhaps under the influence of Thomas Kuhn's The Structure of Scientific Revolutions .
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