A Vindication of Scientific Inductive Practices

North American Philosophical Publications

A Vindication of Scientific Inductive PracticesAuthor(s): Brian EllisSource: American Philosophical Quarterly, Vol. 2, No. 4 (Oct., 1965), pp. 296-304Published by: University of Illinois Press on behalf of the North American PhilosophicalPublicationsStable URL: http://www.jstor.org/stable/20009179 .

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American Philosophical Quarterly Volume 2, Number 4, October 1965

IV. A VINDICATION OF SCIENTIFIC INDUCTIVE PRACTICES

BRIAN ELLIS

THIS

essay is divided into four parts. The first is a discussion of the attempts of Reichenbach

and Salmon to find a pragmatic justification of induction. The presuppositions of this approach are set out, and it is shown that the rational pre ferability of using certain inductive rules might be demonstrated in this way only if it is assumed that the things with which we have to deal are theoret?

ically isolated, i.e., that we can say whatever we

like about them, without it affecting, in any way, our understanding of the rest of nature.

It is also shown (in Section II) that where the rational preferability of using certain inductive rules might be demonstrated (i.e., where our

subject matter is theoretically isolated), the know?

ledge of which rules we are to use does not help us at all to decide what predictions we should make.

Therefore, no vindication of induction which pre? supposes the theoretical isolation of the subject

matter of our inductive arguments can possibly succeed. On the contrary, it appears that theoretical involvement (as opposed to theoretical isolation) is a necessary condition for the possibility of rational non demonstrative argument.

That being the case, the question of what kind of theoretical involvement is rationally preferable arises. It is shown (in Section III) that if a given sequence of events (e.g.,

a sequence of results of

observations) is, as it stands, in conformity with

currently accepted scientific theory, we are faced with two, and only two, rational alternatives for

projecting this sequence (into the future) :

(a) to project it in such a way that the projected sequence is in conformity with currently accepted scientific theory, or

(b) to devise an alternative theoretical framework

that accounts for the original sequence of events,

and for everything else that could be accounted for on

the original theory, and to project the sequence in

conformity with this alternative theoretical frame?

work.

But this is now an accurate account of scientific inductive procedures. The alternative (a) describes the ordinary case of using accepted theories to make

predictions, and (b) describes the procedure of a

Galileo or a Newton in making a theoretical break?

through. Hence it seems that we have found a

vindication of scientific inductive practices. Some attempt to clarify this proposal for vindi?

cating scientific inductive practices is made in Section IV.

Section I

The Scope of the Pragmatic Justifications of Induction

The problem of induction has two parts. First, there is the problem of justifying scientific methods of predicting the unknown. Second, there is the

problem of justifying scientifically based beliefs about the unknown, and showing that, for the

most part, at least, they are true beliefs. The first

part has come to be known as the problem of

vindicating induction, and the second that of

validating induction.1 H. Reichenbach's pragmatic justification of in?

duction2 was an attempt at vindication only. It

was not, nor was it claimed to be, anything other

than a justification for using certain principles of

inference?principles upon which, he considered, all scientific methods of predicting the unknown

were based. It was not a proof that all, most, or

even some conclusions drawn using these principles must be true.

Very briefly, the argument attempted to show:

(a) that there is a certain class of inductive rules

(convergent rules) persistent use of which must

1 For a discussion of this distinction, see J. J. Katz, The Problem of Induction and its Solution (Chicago, University of Chicago Press,

1962), ch. II. 2 H. Reichenbach/Z&jten?Tzc?? and Prediction (Chicago, University of Chicago Press, 1938), sec. 42; Theory of Probability (Berkeley,

University of California Press, 1949), sec. 87.

296



A VINDICATION OF SCIENTIFIC INDUCTIVE PRACTICES 297

eventually yield knowledge of probabilities, pro? vided only that such knowledge is possible, and,

(b) that there are no other rules that share this

property.

Then, since it is more rational to adopt a pro? cedure that must eventually succeed in achieving our agreed aims, if our aims are

capable of achieve?

ment, than to adopt one that need not succeed in

any circumstances, the persistent use of convergent rules is vindicated.

This argument has been seen to fall short on two accounts. First, it did not succeed in selecting a particular inductive rule. Indeed, the class of inductive rules vindicated by Reichenbach's argu?

ment is so wide that every hypothesis concerning probabilities is consistent with some choice of

convergent rule.3

Second, as probability is explicated by Reichen?

bach, the argument failed to show that knowledge of probabilities is worth having. For, crudely, if

"probability" is understood to mean the practical limit of a sequence of relative frequency estimates

(long-run relative frequency), it seems that knowl?

edge of such limits can be of no real interest, unless we can be assured that these limits are now

being approached. But then, it seems, in order to gain such assurance, we must already have solved the

problem of validating induction. For this assurance concerns our beliefs, not merely our methods.

We may put this objection by saying that Reichenbach's vindication of induction fails to deal with the problem of the short run which is,

necessarily, our only real concern. The question of what may happen in the indefinite future may have a certain speculative and dreamy charm. But the

only question of real importance is what is going to happen tomorrow, next year, or in the next

couple of generations.

However, W. Salmon seems to have shown how

both of these objections can be met. The class of

convergent inductive rules may be narrowed down

to the so-called straight rule if only it is demanded that the various probability estimations yielded by the consistent use of a convergent rule (at any

particular time) must be mutually compatible, whatever language is used to describe observed events.4 The problem of the short run may then be overcome by another pragmatic justification.5 Using an argument akin to Reichenbach's, Salmon claims to have shown that the only permissible short-run rule is the straight rule: Estimate the relative frequency in any finite initial segment of a relative frequency series to be as near as possible to the (assumed known) long-run relative fre?

quency.6

Now, we shall not question the validity of Reichenbach's and Salmon's arguments here. But we must consider what they legitimately claim to have done. They have sought a single principle of inductive inference that possesses certain un?

doubtedly desirable formal characteristics, and

they have shown that the only principle having these characteristics is that of straight induction.

They have not shown that all or even most scien? tific methods of predicting the unknown are based

upon the acceptance of this or any other single inductive principle. Nor have they shown that scientific methods of predicting the unknown (i.e., scientific inductive methods) must yield mutually consistent predictions, whatever language is used to describe events. (Indeed, it is evident that scientific inductive methods do not have this highly desirable property. For, if they did, scientific research would be better done by computers.)

Also, and this is most important, they have not shown that if the straight inductive principle is

accepted, there is no question as to how, or in what circumstances, it should be applied. Yet this

is far from evident.

Consider, for example, the simple case of tossing a coin, which we have examined carefully and found it to be homogeneous in substance and sym? metrical in figure. If 550 heads appeared in a

sequence of 1,000 throws, then the straight in?

ductive rule, ordinarily applied, would instruct us to predict that the long-run relative frequency of

heads would be 55/100. But, even if no one had ever tossed a coin before, such a projection of the

3 Reichenbach himself made this point, but although he attempted to resolve the difficulty by means of his concept of

descriptive simplicity, he never really succeeded. For a full discussion, see W. Salmon, "The Predictive Inference," The Philosophy of Science, vol. 24 (1957).

4 This condition, it will be noted, includes Salmon's linguistic invariance as well as his normalizing conditions. See: W. Salmon, "Vindication of Induction," Current Issues in the Philosophy of Science, ed. H. Feigl and G. Maxwell (Holt, Reinhart and Winston,

New York, 1961), pp. 245-264. 5 W. Salmon, "The Short Run," Philosophy of Science, vol. 22 (1955). 6 In fact, Salmon has not shown this. He has succeeded only in restricting the class of permissible short-run rules to that

of the convergent ones. However, his argument may be extended, on analogy with his own extension of Reichenbach's, and the class of permissible rules may thus be narrowed down to the straight ones.



298 AMERICAN PHILOSOPHICAL QUARTERLY

sequence would be absurd. For, in the first place, the occurrence of the observed sequence is in con?

formity with our present concepts of physical symmetry and mechanical causation (in the sense

that it is the kind of result that is to be expected by anyone who shares our conceptual and theoretical

framework). In the second place, the projected limit of 55/100 is inconsistent with this framework.

For, if the limit 55/100 were seriously entertained, some modification of currently accepted views of

physical symmetry or mechanical causation must

be envisaged. For example, we might have to

suppose that facial markings affect mechanical

behavior. But this supposition would certainly have

far-reaching theoretical repercussions. Therefore,

we cannot accept the projected limit of 55/100, unless we are prepared to make radical revisions to our theoretical and conceptual framework.

It seems clear, therefore, that some restriction

must be placed upon the range of applicability of

straight inductive rules. For the above example shows that the use of straight inductive rules is

not always the most rational policy. It may be thought that in this case the use of

straight induction is illegitimate, only because it fails to take into account the many other straight inductive arguments that might be brought to bear on the same issue. In other words, it might be

suggested that, if due account were taken of these

other (concatenated) arguments, a more acceptable conclusion would be reached.

But this reply is demonstrably inadequate, as is

shown by the following argument:

(1) Scientific theories have a legitimate role in deter?

mining what probability judgments we should

make (i.e., it is rational to be guided by currently

accepted scientific theories in making predictions).

(Hypothesis) (2) There are no determinative rules for scientific theory

construction. That is, there are no rules which

determine uniquely what theory should be con?

structed on the basis of what evidence (where "evidence" is understood to mean "known facts

about particulars").

(Hypothesis) (3) An inductive rule is any determinative rule for

making probability judgments solely on the basis

of evidence. (Definition of "inductive rule" which

accords with Reichenbach's and Salmon's usage.)

(4) If all rationally made probability judgments could be justified simply by reference to inductive

rules and evidence, then propositions (1) or (2)

must be false. But we are assuming (i) and (2) to

be true. Therefore, it cannot be the case that all

rationally made probability judgments can be

justified solely by reference to inductive rules and

evidence.

(Modus Tollens)

It follows that no vindication of induction which succeeds only in showing the rational preferability of using certain inductive rules can possibly solve the general problem of vindicating scientific in?

ductive practices. At best, it can only demonstrate the rational preferability of using these rules where there are no relevant theoretical considerations. In other

words, the most that a pragmatic justification of induction can possibly do is to show the rational

preferability of using certain inductive rules to make probability estimates about things that are

theoretically isolated.

Section II

The Vacuousness of the Pragmatic Justifications

Quite apart from the above general restriction on the scope of Reichenbach's and Salmon's vindications of induction, it can be shown that even where there are no relevant theoretical con?

siderations, i.e., where the things we are dealing

with are completely isolated theoretically, the mere

acceptance of straight inductive rules is utterly powerless to guide us in making predictions. Con?

sequently, where there is no relevant background of scientific theory, every prediction is as good or as bad as every other, and each can be justified on

the basis of straight inductive rules. Moreover, it is possible to show that this is so, even without

introducing such odd predicates as "grue" and "bleen" (as Goodman did in making a similar

point).7 Hence, our actual practice of applying straight inductive rules cannot possibly be justified

by any theory o? predicate-entrenchment (as Goodman

hoped). Suppose that a computer is turning up numbers

on a screen, and that the first five numbers to

appear are 1, 2, 3, 4, 5, in that order. An observer

will naturally expect that if the computer con?

tinues to operate, the numbers 6, 7, 8, . . . will

subsequently appear on the screen in serial order.

But what is the rational basis for this expectation ? Let us suppose that our observer has read Reichen?

bach's and Salmon's arguments and has become

convinced that using straight inductive rules is the

only rationally justifiable inductive policy. Is he, 7 N. Goodman, Fact, Fiction and Forecast (The Athlone Press, University of London, 1954), ch. II and IV.




even so, in any position to justify the actual use that he makes of these rules ? Of course, he may

argue that since in each case an = n, where an is

the nth number to appear on the screen, then in future too, an = n. And, since this accords with

the inductive policy which is rationally preferable to all others, this is the most rational prediction that can be made in the circumstances. However, he could equally well argue that since in each case

an= (n? i) (n ?

2) (? ?

3) (n ?

4) (n ?

5) + n

where an is the nth number to appear on the screen,

then, in future too,

an = (n? 1) (n

? 2) (n

? 3) (n

? 4) (n

? 5) + n

And, this prediction also accords with straight inductive policy.8

Hence, if the prediction a% = 6 is rationally preferable, on straight inductive grounds, so also is the prediction a% =

(5! + 6) = 126. Indeed, it

is not difficult to show that there are infinitely many predictions that can be made, strictly in accordance with straight inductive policies, all

mutually incompatible. That being the case, the mere assurance that straight inductive rules are

rationally preferable to others, does nothing to vindicate the actual use that we make of these

rules, at least, in the kind of case envisaged. Now, the logical situation is not changed, if in

place of 1, 2, 3, 4, 5, the computer throws up the numbers 1, 1, 1, 1, 1. We can argue that since in

each case an = 1, so in general an = 1. But we

can also argue that since in each case

an = (n? 1) (n

? 2) (n ?

3) (n ?

4) (n ?

5) + 1

so, in general,

an = (n

? 1) (n

? 2) (n

? 3) (n

? 4) (n

? 5) + 1.

Hence, the prediction a6 = 1 is no better placed

than the prediction a6 = 121.

Again, the logical situation is apparently not

changed essentially, if in place of the computer sequence, we consider any natural sequence of

events. Suppose, for example, that instead of

watching numbers thrown onto a screen, we are

observing the variations in brightness of a Cepheid Variable star (the first ever observed) and measur?

ing the time-intervals tn from maximum to maxi?

mum. Tabulating our results, we might obtain

the sequence:

tx = 4 days

t2 = 4 days

?3 = 4 days

?4 ?

4 days

t5 = 4 days

If we can argue that t6 = 4 days on the basis

of straight induction, we can also argue that

t6 =

124 days on precisely the same grounds. For while it is true that for each n, (n

= 1 to n = 5),

?n = 4 days, it is also true that for each n, (n

= 1 to ? =

5),

*n = ( (? ~

0 (* -

2) (? -

3) (* -

4) (? -

5) + 4) days.

It is obvious that similar considerations would

apply to any set of quantitative results. The actual length of the sequences considered is quite irrelevant to the structure of the argument. For the plain mathematically demonstrable fact is that

any finite initial segment of a sequence can be continued in infinitely many ways, provided only that there is no prior constraint on the complexity of the generating functions that may be employed. Consequently, unless we are

prepared to supple?

ment the straight rules of induction by some other

principles or rules (such as a principle of sim?

plicity), the knowledge that we are to use only straight rules of induction can give us no guidance at all in making quantitative predictions.

Now what applies to quantitative results also

applies to non-quantitative ones. The fact that the first V members of a given sequence of objects all

possess the property 'P' need not imply (even according to straight inductive canons) that the next member of the sequence an + x will also

possess the property 'P'. For the sequence of results

ax is P, a2 is P, a3 is P, . . . , an is P can be con?

tinued in any way we please, and whatever way

we choose, there will be an appropriate rule to

generate the extended sequence. It is not even

necessary to introduce such odd predicates as

"grue" and "bleen" as Goodman did in making a similar point.9

All of this can be done entirely within our

present language. Thus, the prediction an + x is (? might be justified in the following way. Suppose

that when the first result ax is P is obtained, the

sequence of results a2 is P, a3 is P, . . . , an is P,

an + x is (?, an + 2 is Q,? -is envisaged. Then in

each case, up to an is P, the results obtained 8 The reader can readily see that the complex sequence runs: i, 2, 3, 4, 5, 126, 727, . . . 9

Op. cit.




would be seen to conform to the envisaged sequence. They would be seen to be alike in this respect. Consequently, we should, entirely in accordance with straight inductive rules, predict that in future too the results obtained will conform to this

sequence. Consequently, we should predict that an + x is Q.

It follows then, quite generally, that the Reichen bach-Salmon vindications of straight induction fail to deal with the problem of vindicating the actual use that is made of straight inductive rules. For these vindications fail to account for the fact that it is one thing to state a rule, and another to state how that rule is to be applied.

In reply to objections made along these lines by S. Barker,10 Salmon proposed to restrict the class of projectible predicates to purely ostensive ones.11

A purely ostensive predicate P being any which can be defined ostensively, whose positive and

negative instances for ostensive definition can be indicated non-verbally, and such that things

possessing P resemble each other in some observable

respect. Thus, "blue" and "green" are

purely ostensive predicates (according to this definition),

while "grue" and "bleen" are not. Hence, the Goodman paradox is avoided. But this reply is

hardly adequate. In the first place, it puts a severe

limitation on the scope of the pragmatic justifica? tions of induction. There are many predicates, e.g., "is ten years old," "has a momentum of 10

gm.cm./sec," "is electromagnetic," which are

clearly not purely ostensive but which, we feel, are

projectible. Therefore, while the restriction to

purely ostensive predicates succeeds in eliminating Goodman's "pathological" predicates, it also eliminates some perfectly normal ones.

Second, it is not evident that such predicates as

"is a term in the sequence generated by f (n)" cannot be taught purely ostensively, even when f is a fairly complex function. At least, if simple sequences can be defined purely ostensively, it seems to be only a contingent matter, depending on

how intelligent we are, whether or not complex sequences can also be. Therefore, according to

Salmon's defence, if we are not very intelligent, then only simple applications of inductive rules are justified (since, to us, only simple predicates are purely ostensive). If we are very intelligent, then quite complex applications of inductive rules are justified (since, now, quite complex predicates

may be learned purely ostensively). If we are super beings with super intelligence, then, presumably, knowledge of inductive rules is utterly useless. For, to such beings, simple and extremely complex applications of inductive rules are equally justified. Salmon's reply to Goodman and Barker therefore

works only on the assumption that we are not

very intelligent. Third, the requirement that projectible pre?

dicates be purely ostensive seems in one sense to be ad hoc. Even if, in fact, it were our practice never to use other than purely ostensive predicates in applying inductive rules, then what would be the vindication of this practice? Therefore, even if the first and second of these objections can be met, the problem of vindicating our practice of applying straight inductive rules in the way that we do remains unsolved.

Section III

Theoretical Involvement as a Necessary Condition

for Rational Non-Demonstrative Argument

Consider the sequence of cases discussed in the last section. It will be noticed that the "odd"

applications of straight inductive rules seem to become progressively more irrational. Intuitively, at least, that is what we would say. In the first

computer case, for example, we should not be

greatly astonished to find the number 126 appear on the screen

immediately after the number 5. After all, we know that computers can be pro?

grammed to generate extremely complex sequences, and it would not conflict with anything else we think we know about the world to suppose that the computer has indeed been programmed to

generate a complex sequence which happens to

begin: 1, 2, 3, 4, 5, . . .

Of course, we might argue that there are limits to the complexity of the sequences which even

computers are able to generate. Moreover, even

if there were no such limits, extremely complex sequences like those described are neither mathe?

matically nor physically interesting and, hence, are unlikely to be programmed for any purpose other than trickery. In other words, we might attempt to justify our expectation that the se?

quence, 1, 2, 3, 4, 5, will be continued 6, 7, 8, ... in terms of the psychology and interests of

computer programmers. Even so, it would lead to

10 S. Barker, "Comments on Salmon's 'Vindication of Induction'," Current Issues in Philosophy of Science, ed. Feigl and Maxwell (Holt, Rinehart and Winston, New York, 1961), pp. 257-260.

11 W. Salmon, "On Vindicating Induction," Philosophy of Science, vol. 30 (1963).



A VINDICATION OF SCIENTIFIC INDUCTIVE PRACTICES 3OI

no basic conflict with our understanding of the world to suppose that the sequence, i, 2, 3, 4, 5,

would indeed continue, 126, 727, . . . and so on.

In this sense, then, the computer sequences are

theoretically isolated. If it were not for such incidental information as we may possess concerning the

structure of computers, and the interests of com?

puter programmers, we should, indeed, have no

grounds whatever for preferring one continuation

of the sequence to any other.

The theoretical isolation of the computer sequences (which admittedly is imperfect) stands in striking contrast to the theoretical involvement of what I have called natural sequences. For all that the use of straight inductive rules can tell us, the sequence of time-interval measurements (be? tween maxima in star brightness variations) might be expected to continue in any way at all. But if the sequence were in fact to continue in some

"irregular" fashion (that is, in a way that is

radically different from what we should ordinarily expect), this would at once pose an immense theoretical problem.

So long as the sequence is "regular," we can

see that a detailed quantitative explanation might be forthcoming in terms of accepted laws and theories. Perhaps, we do not yet have a completely satisfactory explanation of the variations in bright? ness of Cepheid Variables. Nevertheless, the law of brightness variation that we suppose applies to these stars is such that we are able to imagine several possible explanations conforming to

accepted laws and theories. But if the law of

brightness variation were highly complex, it would be difficult to suggest any hypotheses compatible with accepted laws and theories which could

possibly lead to the generation of such a sequence. Hence, we must contemplate the possibility that

extraordinary laws, quite unlike any others known

to us, are involved in the detailed explanation. Either that, or else that our theoretical picture of stellar constitution is grossly inaccurate. We might, for example, contemplate the possibility that stars have a structure comparable in complexity and

organization to a computer. But in any case we

must consider making radical revisions or additions to the structure of our physics.

Now, if a sequence of events, physically so isolated as the brightness variations of a distant

star, is so heavily involved theoretically, the con? trast between theoretical isolation and theoretical involvement is even more striking when we turn

to consider more everyday sequences. The dis

covery of a substance which, chemically and

physically, possessed all of the known character? istics of lead but which, spectrographically, was

utterly different from lead would have far

reaching though unforeseeable theoretical reper? cussions. If green things everywhere turned blue, and blue things green, we should be completely at a loss to account for such happenings. (That is, if

things really were discovered to be grue and bleen, the ramifications of this discovery would extend

throughout physics, chemistry, and physiology.) If the length of the day, as measured on ordinary clocks, suddenly began to show enormous varia?

tions, this too would have shattering theoretical

consequences.

Clearly, if sufficiently many such devastating things were actually to occur, the whole edifice of scientific achievement would come tumbling to the ground, and, for a time at least, anyone's

guess as to what would then happen would be as

good as anyone else's. Science can take a few

shocks; but after sufficiently many, they would cease even to be shocks. For the scientific structure,

against which they appeared as shocks, would cease to exist.

In any world where such things have actually occurred in sufficient number, rational argument

concerning future contingencies would become

impossible. Sequences would occur, but they would have lost their theoretical involvement. Con?

sequently, we should all be in the position of the man watching the computer. Indeed, our position would be somewhat worse than his, since we should have no knowledge of the structure of the com?

puter, or of the interests of computer operators. In a world where every sequence is theoretically isolated from every other, every projection into the future is as sound as every other.

We may, therefore, conclude that theoretical

involvement is a necessary condition for rational

non-demonstrative argument. This is really the

lesson to be learned from the Goodman paradoxes. The paradoxes arise only because we vaccillate in our way of regarding such terms as "emeralds"

and "green." Thus, on the one hand, we are

invited (by Goodman in presenting his example) to agree that all evidence that emeralds are green is, at the same time, evidence that all emeralds are grue. (To comply,

we must take "evidence"

to mean "straight inductive evidence," and we must disregard the theoretical commitments made

by the use of the terms "emeralds" and "grue.") On the other hand, it is suggested that the con




elusion that, after a time t all emeralds will be

blue, is absurd. (But it is so only if "emeralds" and "blue" are not taken to be meaningless,

theoretically uncommitted terms, but to refer to a certain kind of stone and a certain color re?

spectively.) Now, since no rational inductive policy can be

self-defeating, it follows that the only permissible inductive policies are those whose use would not

destroy the theoretical involvement of our con?

cepts. For, without theoretical involvement,

rational non-demonstrative argument is impossible. We may therefore argue:

(a) It is irrational to reject any scientific theory solely on the basis of future or otherwise unobserved

possibilities. (For, if this were rational, all scientific

theories could be rejected without further ado, and then, as we have seen, rational argument

concerning future contingencies would be im?

possible.)

(b) Therefore, if any given sequence of events already conforms to currently accepted scientific theory, then it is irrational for anyone to prefer any

projection of the sequence that does not conform

to the currently accepted theory unless they have

an alternative and so far equally satisfactory theoretical framework.

(For to do so is to take up a position requiring the

rejection or revision of scientific theories solely on

the basis of future or otherwise unobserved con?

tingencies. If this were a rational procedure,

then, as before, rational argument concerning future contingencies would be impossible.)

Section IV

Discussion

The vindication of scientific inductive practices proposed at the end of the last section is open to a number of objections and is clouded by some

ambiguities. First, the use of the term "conformity" needs to be explained. When we say that something conforms to our current conceptual and theoretical

framework, we mean that it is the kind of thing that is to be expected by anyone who shares this frame?

work. Thus, if a coin is tossed, we should expect it to land heads or tails; both results are in con?

formity with our conceptual and theoretical frame? work. But if the coin should cease to be a coin and be transformed before our eyes into a butterfly, then this result would not conform to this frame?

work. If people really believed that such a thing had happened, their faith in scientific achievement would be shattered.

There is, however, no hard line to be drawn be? tween conformity and disconformity. The examples taken are extreme ones. Between these extremes

there are many intermediate and borderline cases.

A disconforming sequence is any which we should

judge to be either physically impossible or physically incongruous; a physically impossible sequence being any which conflicts directly with some accepted law or theory, and a physically incongruous one being any which we should judge to be inexplicable on the basis of accepted laws and theories. The "odd"

projection of the sequence of brightness variations discussed in Section II is an example of a physically incongruous sequence.

If a sequence of events neither conforms nor

disconforms to currently accepted theory, then it is theoretically isolated. The best examples of theoret?

ically isolated sequences that I have been able to construct are the computer sequences discussed in

Section II.

Now, not only is there no sharp distinction between conformity and disconformity but different scientists may disagree about what conforms to

what. Thus, certain results which Count Rumford

thought were utterly fatal to the Caloric Theory were not in fact taken to be so by his contempor? aries. And it is hard to put this down either to

ignorance or dishonesty. Nevertheless, it is in this sense that we say that if any sequence of observed events is already in conformity with accepted scientific theory, it is irrational to project this

sequence in any way that will bring it into dis?

conformity with this theory. If, in fact, the sequence is so short, or the theoretical involvement so

tenuous that several conformable projections are

possible, then the choice between them is arbitrary. And, in the limit, where there is no theoretical

involvement at all, no one projection is to be

preferred to any other. Where there is a dis?

agreement about conformity, then we also have a

disagreement about who is being rational. Now it may be objected that if, as I have argued,

the possibility of making rational decisions about the future depends upon the existence of a theoret? ical superstructure then, in the pre-theoretical

stages of human development, such decisions would have been impossible. It is doubtful whether

there ever was such a stage of human development, at least while men were still recognizable

as men.

But if there were such a stage, I see no reason

why this conclusion should not be accepted. There

was, after all, a time when the intellectual leaders

among men were seriously concerned whether the




sun would rise the following day and they pro?

pitiated their gods to ensure that it did so.

It may also be objected that my argument is

incomplete since I have justified the use that is

actually made of inductive rules by reference to

the currently accepted theoretical superstructure,

but I have not explained why this superstructure should, in general, be accepted in preference to

any other. This is quite true. And if this objection could not be met, it would prove a serious

objection to my proposed vindication of scientific inductive practices.

Consider first the case of a man who has a real alternative theoretical framework to offer us, who can show that presently observed sequences of events are as much, or more, in conformity with

it than with our present theoretical scheme, and who is able to make predictions on the basis of his alternative scheme different from those that we

should make, but which are subsequently borne out by experience. Such a man has made a

theoretical break-through in science. If it involved sufficient revision of accepted theory, then it might be compared with the seventeenth century break?

through in astronomy and dynamics. Now,

obviously, he is not obliged to accept the theoretical

superstructure that has so far been evolved. He has something demonstrably better to offer us.

I want to say that such a man has succeeded in

changing our standards of rationality. Consider the theoretical break-through which led to the overthrow of the Caloric Theory of heat and its

replacement by the Kinetic Theory. If, today, a man were to use the Caloric Theory of Heat to make predictions in situations where there are

heat-work exchanges, then he must be either

ignorant or irrational. If he is unaware of the nature of the events which led to the replacement of the Caloric Theory, then he is ignorant. If he is aware of these events, and still persists in using the Caloric Theory (I do not mean a revised version of the Caloric Theory), then he is simply irrational. For he would, knowingly, be making predictions which, if true, must lead to the rejection of

currently accepted and, so far, satisfactory theories

of heat and work. Hence, by implication, he must be prepared to reject such theories solely on the basis of future (unrealized) possibilities.

Next, consider the case of the man who has no

real alternative theoretical framework to offer us

but who, nevertheless, refuses to accept our current

standards of rationality, even though he is

thoroughly informed about all phases of the history

of science. Such a man cannot be rational. If he

accepts no theoretical framework at all, then to

him, all events are theoretically isolated, and he is in no position to make rational predictions. He is genuinely in the position that Hume imagined all men to be. If he accepts any other theoretical

framework, e.g., that of 200 years ago, then, as we

have seen, his method of reasoning is such that he is prepared to reject theories that have so far

proved to be entirely satisfactory solely on the basis of future possibilities.

Since this is an important point, it deserves

emphasis. Consider the case of two men, A and

B, arguing about the likely outcome of an experi? ment in which heat-work exchanges are involved. A is a Caloricist who views the production of work in a heat engine as due to the falling of heat from a higher to a lower (temperature) level, much as

work is produced in a water mill by the falling of water from a higher to a lower level. B is a

Kineticist who views the production of work as

due to the conversion of heat into work. Let us

suppose that their predictions differ. What reason

do we have for preferring B9s prediction to ^4's? We may admit at once that anything might happen. But the following points must be granted :

(i) It would be irrational for me to accept or reject

any theory solely on the basis of what might

happen.

(ii) ^4's Caloric Theory cannot be accepted on the

basis of what has happened. (I am assuming that A 's theory is the historically accepted theory

of the i83o's, not a radically revised theory.)

(iii) B9s Kinetic Theory can be accepted on the basis of what has happened.

(iv) There is, as yet, no other theory that can be

accepted on the basis of what has happened.

From these four propositions it follows at once that we must accept B9s reasoning if we are to

behave rationally. If we accept ^4's reasoning then

we are committed to accepting A9s theory and

rejecting B9s theory entirely on the basis of future

possibilities. If we reject B9s reasoning but do not

accept A9s, then again we are in the position of

rejecting a theory simply because of the logical possibility that anything might happen. If we do not accept any reasoning, then obviously the

possibility of rational argument is precluded. Therefore, if we are rational beings we have no

alternative but to accept B9s reasoning until some

alternative and so far equally satisfactory theory is proposed.




The difficulty remains, however, of saying what counts as an alternative and equally satisfactory

theory. If there are no grounds for rejecting theories other than:

(a) inconsistency,

(b) conflict with experiment or observation, or

(c) incompatibility or incongruity with other

already accepted laws or theories,

then the construction of an alternative theory

might seem to be an easy matter. Could we not

follow the method of goropising described by L. S.

Feuer12?viz., make any hypothesis we like, and

then, for each new piece of contrary evidence that comes to hand, make a special ad hoc hypothesis to account for it? Could we not construct "theories

without analogies" after the fashion of N. R. Camp? bell's famous example?13 Yet, if the construction

of alternative theories is such an easy matter, then

almost any conclusion about the unknown that we may care to draw could be justified by reference to some (ad hoc) theoretical superstructure. And

hence, our proposed vindication of scientific in? ductive practices is seriously incomplete.

It is not evident that "goropising" is in fact such an easy method of constructing

a "satisfactory"

alternative theory. For typically, "goropising" leads in a few steps to hypotheses that are incom?

patible or incongruous with other already accepted laws or theories. Nevertheless, a residual problem remains: we must either show that the grounds (a) to (c) are sufficiently restrictive to make the

construction of alternative and so far "equally satisfactory" theories generally a matter of great

difficulty; or else, we must say what principles in addition to (a), (b), and (c) are involved in the selection of theories; and then, we must justify using these principles in the way that we do.

University of Melbourne

12 L. S. Feuer, "The Principle of Simplicity," Philosophy of Science, vol. 24 (1957). 13 N. R. Campbell, Foundations of Science (New York, Dover, 1957), p. 123.



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A Vindication of Scientific Inductive Practices

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