From: JASA 20 (September 1968): 65-70.
On July 20, 1963 F. Schmeidler and others from the Munich University Observatory were on the shores of Great Slave Lake in Canada seeking to obtain eclipse plates of the star field within six radii of the sun. As often happens in the astronomy business, clouds came up at the last minute and no usable results were obtained. One might wonder why the German astronDmers 'were out fighting mosquitoes in Canada. They were there because recent attempts had failed to verify the earlier observations confirming Einstein's Relativity prediction that a ray of light just grazing the sun would be shifted 1.75 seconds of arc. In fact recent data had yielded results significantly different from that predicted. Also a re-examination of the reduction method used in earlier experiments had raised some questions as to the evidence supplied by them. This example illustrates one characteristic of the scientific method about which there is almost universal agreement. This characteristic is the testing of a theory or hypothesis by means of an experiment or observation.
*Robert D. Jewell is on the philosophy faculty at the University of Calgary, Calgary, Alberta, Canada. Paper presented at the annual meeting of the American Scientific Affiliation at The King's College, August 1965.
The problem under discussion is not whether data
collected which is in accord with the predicted results
of theory does in fact tend to confirm the theory, the
problem is rather the degree to which such collected
data entitles us to conclude that the theory is true.
Einstein's relativity theory, for example, when first
presented predicted the results of the Michelson-Morley
experiment. But one would not be on very safe ground
if he concluded that the theory were true on the basis
of this evidence alone for it is known that Einstein
used this data in constructing the theory. It is for this
reason that other conclusions of the theory such as the
star shift are important. Even though such a shift had
been predicted in 1804 by Johann Soldner it had never
been actually investigated. Hence, if the shift were
found to actually occur it would then confirm
Einstein's theory to a considerable degree. Unfortunately, this is only one of many different
kinds
of examples.
In one case a certain type of experiment may bear
almost the whole weight of supporting a theory, in
another seemingly similar case scientists may regard it
as of almost no consequence. Furthermore the value
of a particular kind of experiment may vary from one
science to another. Sometimes it might appear as if
the determination of the degree of confirmation were
a cult ritual which no accumulation of facts could allow
the outsider to understand without first being initiated
into the tribe. It would thus be valuable to all concerned if a general theory of confirmation could be
devised so that one could in each case know how much
a given experiment or observation would support the
theory. With the advent of a highly developed
probability calculus and later of game theory it was
hoped that such a theory of confirmation was within
reach. While the application of these theories has
helped in the attack upon problems in the area of
confirmation of scientific hypotheses, they have also
revealed certain new difficulties.
Some Suggested Analyses of
Scientific Confirmation
In order to elicit these difficulties let us suppose that some confirmation function, C, has been agreed upon so that we may say that the evidence, e, confirms a proposition or hypothesis, P, to a certain degree determined by C, i.e., c (p,e) = x. (This is merely a supposition, for at the present there is no agreement among philosophers of science as to the proper function. The problem under discussion may be stated without the specification of a particular function, however.) Suppose further that one is faced with a choice of several actions based upon certain information. An example might be that of a drug company planning to produce a new drug. The company has the choice of several different manufacturing processes and it wants to know which one yields a product safe enough for human consumption to be placed on the market. In this case the company has several possible actions (aj) before it-one for each manufacturing process-and several possible outcomes (om) of each action as well as the scientific evidence, e, which determines the probability of each outcome. So the probability of a certain outcome might be symbolized by c(o,e & a). But, as the example of a drug for human consumption is intended to indicate, there is also the problem of the utility or disutility accrued by a particular outcome. If, for example, with the use of one process the probability were high that one sample out of a thousand would be fatal, the utility of that outcome would be negative. As a result this would outweigh the value gained from the healing powers of the drug. The application of the notion of utilities to the theory is not very difficult in principle as can be seen from the illustration at hand. Since killing a person is to be avoided at all costs, considering the mere probabilities would not be enough; the value of each outcome must also be considered and not only the outcome of healing, but also the outcomes of cost of manufacture as well as harm to health. The utility of one particular action, ai, then is the sum of the utilities of the various possible outcomes of that action. U (aj,e)=c(o1,e& aj) X it, + . . . + c(om, e & aj)X um., where ui= the value of outcome oi.
Those who are proponents of the pragmatist or instrumentalist school of thought feel that the correct analysis of confirmation in science is the one which involves the computation of certain utilities. Their conclusion rests on the grounds that the final test of any theory is its usefulness. The pragmatist view in general is probably familiar to all educated Americans, especially those who are close to Christian circles since there has been considerable criticism of it from some of these circles. In the case of confirmation, however, there is something to be said for it prima facie. A decision to accept a theory is an action of a certain sort and it is an action with important consequences to the person involved, qua scientist, as well as, qua person.
Although it is hazardous to make such statements, it would appear that for present-day philosophers of science an analysis along these general lines is the leading candidate. One might hope then that the utilities could be specified and defended in some non-subjective fashion so that the description of science as a purely rational endeavor could be retained. Today, however, there seems to be a growing pessimism as to whether this latter objective can be fulfilled. For when it comes to determining the values of the utilities of the various actions it looks as though one is involved in value theory or ethics and thus has left philosophy of science pure and simple. The pessimism has gone so far that in an address on this subject at the University of Pittsburgh not too long ago a noted philosopher of science, Carl Hempel, was heard to say-humorously, to be sure, but still intending a serious point-that perhaps the preachers were correct after all when they claimed that the conclusions of science involve a value judgment, a judgment which could not be made purely within the rationally defined procedures of science.
Another widely accepted solution in this same tradition has come from game theory. It is the "minimax" procedure which says that one should act according to the rule that will minimize the maximum risk. It seemed for a while that the difficulties of making assumptions outside the scope of science proper did not arise when such a procedure was applied. Nevertheless the minimax principle does involve a metaphysical assumption. The minimax principle can be understood as recommending that one select the rule "for which the largest of the (statistically defined) probability estimates of the losses that might be incurred in a given context as a result of following this rule is no greater than the largest of the corresponding risks." This is a typical statement from the literature. R. C. Jeffrey in "Valuation and Acceptance of Scientific Hypotheses" (Philosophy of Science 23: 230246 (1965) ) has pointed out that when a player uses this seemingly cold and objective mathematical recommendation he is really making a rather massive metaphysical assumption for he is assuming that this is, for him, the worst of all possible worlds, one which is, so to speak, out to get him. Similarly the most obvious alternative, the "maximin" procedure would assume that this is the best of all possible worlds for the player using it.'
Because of such difficulties in the pragmatist theories some have turned to the hope mentioned earlier that certain utilities could be specified for the sciences which would be completely impersonal and free from the onus of falling under ethics. The general debate between this approach and the pragmatic one is not new. For instance, a similar debate occured between W. K. Clifford and William James with Clifford arguing that any hypothesis ought to be rejected until there is adequate evidence for concluding that it is true and James arguing that there are important decisions that we have to make before adequate evidence is available. A problem that arises here is that in the human predicament it is not always easy to decide when the evidence is adequate to determine truth. The meaning of "truth" in science is not difficult: an hypothesis is true if it correctly describes what is the case, if it corresponds with the facts. The difficulty is that the truth of a theory cannot be determined directly in spite of the fact that the definition of truth is clear and simple; for it is the nature of a scientific theory to go beyond the known facts. If theories did not provide for the prediction of things which were not presently known, they would be of little interest, especially the very abstruse theories of mathematical physics. Hence it would appear that the human being must search for marks such that if an hypothesis has them, they will count as adequate evidence that the hypothesis is true.
Perhaps then utilities could be found which would count as marks that an hypothesis were true and would thus relieve some of the disapprobation which often falls upon the use of utilities in the context of confirmation. Some so-called purely scientific utilities have already been suggested. They are familiar to the scientist although often they are used quite vaguely. In the forefront of present thought are the utilities of increased simplicity, addition of new informational content, increased inner connection of the parts of the general theory, and the explaining of observational reports and empirical laws. And indeed, some progress has been made in giving these utilities a precise formulation. This general sort of attempt, as the debate between Clifford and James shows, takes one into the area called by some the "ethics of belief." (As the paper has so far been focusing upon the notion of utilities and their relation to action and the ethics of belief it may be well to warn at this point in the discussion that the notion of a theory's being true or false is not in question. The problem concerns only the evidence a scientist uses to decide if a theory is true, that is, how he confirms the assertion that an hypothesis is true.)
Much still needs to be done technically before the "purely scientific" utilities approach can be presented in a fashion adequate to the accepted procedures of science, but even at this stage of its development one may ask how these requirements could be justified as utilities leading to truth. This is a relevant and important question for with the addition of utilities to confirmation theory the spector is raised of a theory's turning out to be highly confirmed merely because of the great utility which would be attached to it if it were true when, in point of fact, it actually has little support. The danger of this approach has been evident ever since James argued that even if a person knew there were no god it would still be better to believe that there were, for more good consequences would, follow from the latter belief. Furthermore, there are metaphysical questions raised by some of the purely scientific utilities, for example, how do we know that the universe is such that it is more likely to be explained truly by simpler rather than more complex theories?2
If the above has been successful in indicating some of the problems now being discussed in the area of confirmation of scientific hypothesis there should be little need to expand greatly on the possible implications for the Christian. One of the more difficult obstacles the Christian apologist has faced in recent times has been that of dealing with the rejoinder, "Your religion involves value judgments unsupported by rational evidence, while science deals with facts and with theories supported (confirmed) by those facts." Present research indicates that, on the contrary, all is not so simple in science itself, that perhaps there has been an "extra-scientific" or even "non-rational" element of value hidden in science all along and only now is this fact being brought to light. (Note that the word "non-rational" should, when used in this context, be distinguished from the word "irrational." This point is also important if one is to avoid begging the question as to the actual status of the confirmation procedures presently in use in science.) And in the event that this element should turn out to be fully rational-which now appears unlikely-that rationality has, up to now, been taken only on faith, for it may be said that it was not known that science was fully rational without remainder. It should also be emphasized that the discussion of utilities and values involved in confirmation is coming from within science and philosophy of science and not from people particularly sympathetic with Christian theism. This gives, I believe, the line of investigation being discussed in this paper an suspect accusations that having (or practicing) a notation-that a science involves a value judgment, or that the scientist as an individual cannot escape himself, but is a mass of predilections.
Such an introduction as the one being given here should warn that besides the theories already discussed there are other approaches which have been suggested as to the proper rational reconstruction of the confirmation procedures used by science. Two others will be mentioned by way of example. The first is similar to the procedure involved in the notion of a crucial experiment. At the risk of oversimplification one might describe this view of Karl Popper as denying that an hypothesis is ever confirmed to any degree whatever, rather it is merely tested and rejected if it fails the test. Popper's view has been criticised extensively, especially on the grounds that having passed a series of tests is taken, in practice, as having lent inductive confirmation to the future correctness of an hypothesis. For example, A. J. Ayer has nicely expressed this by asking: "Why reject an hypothesis merely because it has been falsified once-perhaps this is just an infantile disease which many good hypotheses catch early in their lives, but to which they are immune from then on?" It may be though that Popper's account is descriptive of what has actually occurred many times in the history of science. Yet not withstan ding the fact that what has actually occurred in the history of science is both intrinsically interesting and suggestive of methods for rational reconstruction as well as of possible use for apologetics,3 those working in this field are more concerned with the problem of discovering a rationally defensible confirmation theory. For this reason, and also because of the kind of criticism already indicated, Popper's theory will not be discussed further at this time.
On the other side of the ocean Toulmin has argued
that there is no such thing as confirmation of a theory
in scientific practice at all, that what look like experiments intending to confirm a theory are really only
attempts to determine the scope of the theory. This
suggestion seems to run the risk of reducing all theories
to ad hoc ones, since they would not really be taken
as projecting beyond the evidence already piled up for
them. One would have to wait until the theory were
tested in this new area before he could say that the
theory applied. This raises an even deeper problem,
for without the confirming ability of induction how
could one decide of any experiment whatever, other
than the one used in the initial test, that it was not
actually an extension of the scope of the theory? In
such a case then a theory could never be used to
predict at all because a prediction would always be an
extension of the scope of a theory.
There is one more major alternative which will be
presented in this paper. Although still in a state of
development it appears to offer several advantages. It
follows the inductive approach espoused by Reichenbach and makes use of a theorem from statistics known
Bayes' Theorem. The use of the theorem of Bayes
of i is not unusual in this connection. As applied here the probability-written
P(H & E, T)
in quasi set theoretic given hypothesis (of a certain kind),
H,
with a certain kind of confirming evidence,
E,
is a of member of the class of true hypothesis, T, is P (H,T) x P(H &
T,E)/P(H,T) x P(H & T,E) P(H,T) x P(H & 7,E).
The first item of importance is
P(H & TE),
the probability that untrue hypotheses (of the same sort) - will have this kind of
confirming evidence, which is, of course, an inverse measure of the confirmatory value
of the evidence. The term,
P(H & T,E),
can be determined by deduction alone and has a value of I while
P(H,T) is
a logically determinable function of
P(H,T) since T is the complement of T-and hence is determined as soon as
P(H,T) is
determined.
The problem in applying Bayes'Theorem which has been an objection to its use is the term,
P(H,T),
called variously "the antecedent, or prior probability" that - an hypothesis of this sort is true. It is the probability
r of the truth of an hypothesis before any confirmatory experiments or observations are made. The frightening
name, "prior probability" has caused some writers either to go into hysteria or to exhibit symptoms of withdrawal
in the presence of Bayes' Theorem when it is used in this connection. One need not have this reaction, however,
for several useful suggestions have been made for handling prior probabilities. Interest in the use of this
theorem comes from the suggestion that the prior probabilities be determined by simple enumerative
induction, a procedure already accepted in scientific methodology. In practice, one merely examines the
history of science inductively to see which kinds of hypotheses have been successful in the past. Quite a list
of these prior probabilities has been drawn up and they can be classified into several categories. A presentation
of this list would lead too far afield, especially since it is the principle of justifying items on the list by
induction that is of interest here; thus only three somewhat controversial examples from the category of the origin of the hypothesis will be mentioned: the circumstances of publication, e.g., where it is published; the
education of the author of the hypothesis; and his established competence, or authority, in the field. It
should be noted that in applying this suggestion to use simple induction in the establishing of
prior probabilities one does not have to obtain a high probability, it is only necessary that it be greater than zero, for any
non-zero probability can finally be swamped out by piling up higher and higher confirming evidence (i.e., P (H & TE) will become smaller and smaller).
Implications for the Christian
The last proposed theory, that Bayes, Theorem be applied inductively, has several advantages. It is a fruitful theory in that inductive investigation can sug gest new characteristics of true theories. It is a power ful theory for it can incorporate many, if not all, of the valid insights of the other theories (by inductively establishing their soundness). And not the least of its advantages is that it is an objective theory. When determining scientific utilities it does not depend upon beliefs, bias, or prejudices whether they be aesthetic, social, or whatever; rather it allows the proposed utilities to be tested. This latter characteristic of the theory is important not only because it provides a way of preserving science's ability to discover truth, but also because it provides a possible protection for the practicing scientist who is a Cbristian.4 Admittedly it is rather difficult today for a citizen of the Western world to believe that there is a real danger of a bias being built into science which could be used to bar an hypothesis suggested by a Christian from consideration by science. There is, however, enough evidence from the history of science in the Soviet Union to indicate that this danger is not completely imaginary.
Two points must be made at this juncture. The first is the general point that there is more work to be done on all the theories that have been presented before definitive conclusions can be drawn from them. The second point applies more specifically to the inductive theory and its relevance to the Christian: The use of Bayes' Theorem is based upon induction and induction is very much in question in philosophical circles today. It is not enough of a defence of induction to say that science itself is based upon induction for this would not defend the position, but would merely show that an attack upon induction is an attack upon science itself.5 The situation today is worse than that indicated by a mere questioning of induction. There is a very prevalent attitude toward induction which if it were to gain dominance would undermine the objectivity of induction. Indeed, it is in reality an attack upon the objectivity of induction and is all the more pernicious for it is presented in the guise of a defence of inductive reasoning.
Two forms of this position have so far appeared: The earlier form is in the tradition of linguisticism, e.g., A. J. Ayer (The Problem of Knowledge-Penquin Bks. -pp. 71-75), Paul Edwards ("Russell's Doubts About Induction" Mind LVIII (1949)), and P. F. Strawson (Introduction to Logical Theory-London), and it merely asserts more or less blatantly that what we mean when we use the word "rational" is, among other things, that the person follow, when appropiate, inductive patterns of reasoning. The later and more disguised-but no less cavalier-form has been best expressed by J. Katz in The Problem of Induction and its Solution (Chicago) and can probably be most easily understood as a modem form of psychologism, especially since it tries to appeal to Hume's Treatise. This latter form seems to be based upon a principle something like the following: (1) "A person cannot be blamed for what he cannot help doing." (This principle need not be debated here.) To it they add a premise and draw a conclusion: "Since (2) a person cannot help but reason inductively (3) the proposition which is the result of inductive reasoning is therefore justified." This latter is a non sequitur and would be of little concern except that it is rarely stated explicily; it is only tacitly accepted. Even granting the second premise, it would only follow that a person ought not to be blamed for holding the inductive proposition; it does not follow that what is expressed by the proposition is true, that one has been shown to have adequate evidence for it, or that what has been asserted by the proposition has been justified. (Again it may be well to point out that the issue here is not whether induction is justified, but rather what would count as a valid justification.)
It is as if one were to argue, in the year 1984 after Orwell's "double-think" had obtained complete psychological success in making everyone so that they could not help but believe that grass is pink, that therefore the proposition, grass is pink, is justified. This illustration is not as far fetched as it might seem, for both forms of these so-called justifications are really invalid arguments from authority, in the one case from the authority of the language we use, in the other from the authority of the users of the language-or as the positivists used to say, "of the scientists of our culture circle." That this is an argument from authority can easily be seen from the fact that many human beings do not reason inductively in the appropriate circumstances, rather they reason invalidly or fallaciously. Yet this does not bother the proponents of the view; they have already picked as the standard those who reason as they do. It is not so far then from this position to Orwell's 1984. It is only accidental to the position that what is now believed is valid. (One cannot help wondering if these sorts of arguments do not indicate a worship of man, for now man is the standard of rationality, rather than man being under a standard of rationality.)
This discussion of justification may seem to the reader to be about a rather recondite philosophical battle deep down in the darkness of philosophical induction, a long way from the bright and fair world of practicing science, but it reveals, I think, a well entrenched tendency in modern thought which is of potential danger even to the practicing scientist who is a Christian. For if these authorities of our culture circle can decree by argumentum ad populum, which inductive, or anti-inductive, rule is "rational" they can just as easily (and just as subtly) decree what utilities are "rational" and hence what hypothesis of science are even worth taking seriously. And since the Christian is in the minority, both in the world and in the West, it would not be surprising if these authorities were at some future date to determine grounds of confirmation, which would leave the Christian theist in the wrong a priori. They might even be able, by such means, to delude him into rejecting elements of his own position which actually have as much going for them.
This paper has considered confirmation theory in the sciences by attempting to sketch in outline several contemporary accounts of the subject. Most of the time has been spent in this presentation, but enough has been said in the way of critical comment to indicate that even though these accounts are still very much in the works they contain possible dangers. It is for this reason that I would hope that Christians will become interested and work in this area not only for scholarly and apologetic purposes, but also in order to ascertain how the criteria for confirmation are to be established so that the Christian who labors in science may avoid thinking that his science must, in some particular case, make him question special revelation and so that he may more properly perform his task of bringing glory to the Creator in the investigation of His revelation in nature.
1Having raised the subject of game theory, I cannot refrain from remarking in passing that, upon careful reading, Pascal's "wager" does not appear to be as trivial as some later presentations have made it out to be. It is really quite in keeping with the tenor of modern philosophy of science, for one of Pascal's major weapons is the consideration of the risks involved in assuming that the world is a certain way.
2Science actually does use simplicity, and similar criteria, but one would like better grounds for accepting them than those just given. The inductive approach from the history of science which will be discussed later seems to be the best proposal so far given for avoiding these metaphysical problems; however, even here more careful investigation is needed to make sure that these problems do not arise again at some deeper level.
3Jt might be both interesting and profitable if an examination were made of the history of science in the light of present work in confirmation theory, especially of the infamous conflicts between the "church" and science. For example, it is now conceded that Galileo did not understand the experimental method (see Galileo Galilei by Ludovico Geymonat (N.Y., 1965), and that the Copernican system was mathematically equivalent to the Ptolemaic one. Also the biological, as distinct from the philosophical, theory of evolution might also be amenable to such an analysis in terms of confirmation. One wonders bow much of the historical content of its propositions is actually confirmed by the experimental evidence available. Since contemporary phenomena provided the only empirical data it might be discovered that the only confirmed propositions of biological evolution are those which predict present day biological phenomena.
4There may be some Christians who would hesitate in accepting this protection from the fear that the position's being inductive places it too much in the tradition of empiricism. What is the origin of this fear and is it well founded? There are two pressures acting upon the Western Christian today which tend to influence him against an inductive approach. One is idealism from India which, coming through European philosophers such as Hegel, affected irrevocably the great "Christian idealists". The idealists' influence over Christian thought is still almost overwhelming especially their ideas of evidence, of logic, of infinity, and of system. This influence still exists even among many Christians who reject idealism as a system. (Interestingly enough, this idealism has had through Hegel an historically verifiable influence on pragmatism, the traditionally great enemy of Christian idealism. Indeed pragmatism has actually taken up some of its doctrines, e.g., the coherence definition of truth.)
The other pressure comes from ancient Greek rationalism which even began to influence the church soon after Apostolic times and whose view that man can in some way come to know, a priori, almost anything, including the material world, appears again and again, whether in Descartes or Leibnitz, Galileo or Eddington. When, however, the Christian realizes that these pressures are acting upon him and becomes aware that their origins are pagan he should not then rule out the inductive approach, a priori, but should judge it on its own merits, on the adequaty of its account of confirmation.
5Making this point does have another use, though, which is of some value; it indicates that an inductive analysis of confirmation drags no new metaphysical assumptions into science.