EQUATING IMPERFECT KNOWLEDGE WITH SCIENCE IS QUESTIONABLE
1. The traditional opinion concerning imperfect knowledge, if it exists, equates such knowledge with the body of highly probable hypotheses. This opinion rests on the assumption that scientists try to render theories probable in the light of experience.
This latter assumption has been under the ceaseless barrage of devastating arguments from the pen of Sir Karl Popper during the last three decades or so. His alternative assumption is that scientists try, not to render theories probable, but to refute them; events which are erroneously considered as raising the probability of a given hypothesis are, he adds, failed attempts to refute that hypothesis. If one holds to the traditional opinion about imperfect knowledge while replacing the traditional assumption concerning the activities of scientists with Popper’s alternative assumption, one comes up with he amended traditional opinion: imperfect knowledge is the body of hypotheses we have unsuccessfully tried our best and cleverest to refute.2. Does Popper equate imperfect knowledge with the body of severely tested and still unrefuted hypotheses? Almost all of Popper’s commentators say, yes, of course, in print as well as in conversation. I have found no sufficiently clear-cut answer to this in Popper’s own written or spoken material. Moreover, the traditional opinion equates science with the body of highly probable hypotheses. Does Popper wish to equate, instead, science with the body of unrefuted though severely tested hypotheses? For years I answered this question in the negative. Today I know I had been reading my own wishes into his writings. Re-examining his works I find no sufficiently clear-cut answer to this question in his written works.1 Dismissing the question of the authorship of this opinion until its rightful owner stakes a claim, the question of the truth of this opinion remains and deserves study quite apart from the fact that its popularity is on the increase: is it true that
science = imperfect knowledge = the body of well tested yet unrefuted hypotheses?
3.
What is common to the old-fashioned equation of imperfect knowledge with the body of probable hypotheses, and the newly fashioned equation of imperfect knowledge with the body of hypotheses which thus far have stood up to severe tests, is that they both enjoy the respectability of being backed by a philosophy of science. Perhaps one may put it like this: the possibility of splitting traditional philosophy of science into two parts, one of which has been reformed and one, basic, which has remained intact, is what makes the opinions adumbrated here so very important. We do have a basic equationimperfect knowledge = scientifically attested (rational) belief, and a reformed one,
probable hypothesis
(the old-fashioned view)
scientifically attested (rational) belief
well-tested-but-as-yet- unrefuted hypothesis (the newly fashioned view)
Popper does assert that scientifically attested (rational) belief may be equated with the body of well-tested-but-as-yet-unrefuted hypotheses, though he is (regrettably systematically) ambiguous as to whether he advocates such an equation. In Chapter 7 I have criticized this equation to my satisfaction; here I wish to criticize the more fundamental, and as yet unchallenged equation,
imperfect knowledge = scientific knowledge.
As an alternative to this equation I propose the following hypothesis. Imperfect knowledge is that contention which would be perfect knowledge if certain conventional and unquestioned contentions were unquestionable. Moreover, all claims for imperfect knowledge are so understood, and therefore they become null and void the moment conventional and unquestioned claims upon which they hinge turn out to be untrue. Furthermore, the criterion given here can easily be expanded to become partially graded: a sociological (semi-institutional) criterion for the conventionality of an opinion can be given. This will render the present view highly refutable, and it may be refuted, but not so easily that I can say how.
It may also be used with ease to engender examples which refute the popular equation of imperfect knowledge with scientific knowledge.When rejecting the equation, imperfect knowledge = science, as I intend to do here, as well as the equation, science=the body of well tested though unrefuted hypotheses, as I have done elsewhere, I reraise the questions of demarcation of both imperfect knowledge and of science. In the present chapter I only refute the equation of imperfect knowledge with science and try to demarcate imperfect knowledge.
4. Let us consider perfect knowledge first. In his Preliminary Discourse to Natural Philosophy of 1831, Sir John Herschel has a small but interesting presentational difficulty, which he solves in a manner still acceptable today. He wishes to explain his claim that scientific knowledge is perfect knowledge, and is at pains to distinguish it from common and imperfect knowledge. I understand Herschel to say that perfect knowledge is perfect certainty, to be sharply distinguished from common and imperfect certainty which is the merest feeling of certainty. However strong the feeling of certainty is, it may accompany theories which are objectively open to doubt; scientific knowledge, he says, is perfect knowledge which permits no doubt, and which should be endorsed with centainty because it is demonstrable. He calls this mathematical certainty, to distinguish it from the mere certainty of one’s feelings, which he calls psychological certainty. Scientific knowledge, then, according to Herschel, is perfect knowledge, which is mathematical certainty, which is demonstrability. Scientific knowledge is nowadays considered imperfect, but the rest of Herschel’s analysis is still generally accepted. Now we may feel certain regarding imperfect knowledge or even regarding the merest conjecture. And thus, not only perfect knowledge but also imperfect knowledge may be demarcated not psychologically but more objectively. The question is, what is objective imperfect knowledge, whether scientific or otherwise?
It may perhaps be gratuitous to note that were imperfect knowledge identified with the feeling of certitude, than all bona fide claims for imperfect knowledge would be acceptable.
Yet this should lead to a slight modification of our initial premises. We have initially assumed that some claims for imperfect knowledge are not acceptable. We now have to strengthen this: some claims for imperfect knowledge are bona fide yet not acceptable.5. Numerous philosophers have recently reaffirmed the view that ordinarily claims for knowledge, as well as for certainty, are not claims for perfect knowledge, yet they are in some (weak) sense objective. This makes claims for perfect knowledge made by mathematicians, some theologians, some philosophers, and even some scientists, not ordinary but, one might say, extraordinary. In any case, since claims for perfect knowledge are very clear, we may ignore them and center on the question, what are the objective claims for imperfect knowledge? Can we have objective certainty yet only imperfect knowledge? What, in such cases, is the objective grounds for claims for imperfect knowledge? Can we not adhere to the traditional opinion which identifies knowledge with objectivity and thus imperfect knowledge with partial objectivity?
6. Herschel endorses the opinion, which is already endorsed by Dr. Watts almost a century earlier, and whose beginnings can be traced to Bacon’s preface to his collected works of two centuries earlier, namely the opinion that there are objective degrees of rational belief. According to this opinion, we ought to believe a theory to the extent that it is supported by evidence (empirical evidence, usually), and suspend judgment concerning its truth to the extent that it has not been so supported. In other words, a theory is objective to the degree that it has objective empirical backing and should be held to the degree that it is backed. Unfortunately, this does not help us to understand what is ordinarily meant by claims to (imperfect) knowledge: the concept of degrees of imperfection of knowledge and the concept of partial proof are not clear, nor is the identification of these with the concept of partial belief.
Admittedly, the concept of partial belief is somewhat clearer. Yet, historically, it was the clearer concept which was clarified first. A criterion for the degree of our belief in a given theory which can apply to ordinary circumstances was proposed by William Hyde Wollaston and reported by Michael Faraday (‘On Mental Education’): the nearer to certain one is that a theory is true, the more one will be willing to bet on it even against high odds. Thus, the assigning of high probability is the measure of high confidence in the truth of a proposition, and partial belief or a degree of belief is partial confidence or a degree of confidence. Admittedly even regarding rational belief this clarification is not sufficient, since it only clarifies the concept of belief, rational or irrational. This, no doubt, was a difficulty felt by various writers, and fairly early in the day.7. Faraday reports that when Wollaston told him of his criterion, namely that the degree of one’s belief in a proposition may be reflected in his betting quotient on the truth of that proposition, Faraday was not very happy with it: he said, one is foolish to bet. Wollaston answered him, it is not an actual betting but a hypothetical betting that he had in mind. To this one might add a stronger argument of a more modern stock: people do gamble all their lives, not only when they invest in the stock exchange but when they make any investment whatsoever, in the broadest sense of investment: in a significant sense all action involves gambling.
This can be reformulated thus: fair betting quotients are necessary, not sufficient, conditions for an acceptable bet. When we elicit what one thinks is the fair betting quotient we do not force or even recommend a gamble, but merely decide one necessary condition for it.
This is, I think, quite acceptable to all parties. However, this only shows that we may elicit on some occasions what even a nonbettor may think a fair betting quotient is. It does not show that we can always elicit a fair betting quotient, it does not show that a fair betting quotient indicates one’s degree of belief, it does not show that one’s degree of belief is one’s rational degree of belief (one may be under the influence of, say, an optimistic mood in the neighborhood), and it does not show that rational degree of belief equals current scientific opinion equals imperfect knowledge.
There is an enormous analytic literature on all this. The chief question the literature rests on is, how can we measure the degree to which one may believe a proposition given one’s present knowledge of facts. The other questions are only lightly touched upon. Keynes, for example, only implies - however clearly - most of the identities listed in the above paragraph. Even if one assumes that all arguments in the literature are valid, one can still wonder whether rational belief equals imperfect knowledge.
IL