III. THE LIMITS OF INFERENCE
Note 81: "The question in what cases we may believe that which goes beyond our experience, is a very large and delicate one, extending to the whole range of scientific method, and requiring a considerable increase in the application of it before it can be answered with anything approaching to completeness. But one rule, lying on the threshold of the subject, of extreme simplicity and vast practical importance, may here be touched upon and shortly laid down."
The rule Clifford has in mind will be discussed below, but here it should be remarked that his opening question - "in what cases we may believe that which goes beyond our experience" - is a basic one, and covers many problems of the philosophy of science, such as relates to scientific methodologies; the problem of induction; the questions what characterizes good statistics and what is probability, and more.
Also, he is right that these are difficult questions to answer rationally, and he would have been right had he added that each science has its own methodological problems, while what makes a science into science is a core of tested rational methods to learn from experience and to objectively test, control and where possible and necessary improve and revise any results of these rational methods.
An excellent modern text that contains much relevant knowledge and ideas of these kinds is:
Stegmüller: Probleme und Resultate der Wissenschaftstheorie und Analytische Philosophie. (Four thick or some 25 thin volumes. I have been told it has been translated, but never saw the translation, that contains the words "philosophy of science" in the title. Much recommended to anyone interested in rational belief of any kind!) Text.
Note 82: "A little reflection will show us that every belief, even the simplest and most fundamental, goes beyond experience when regarded as a guide to our actions. A burnt child dreads the fire, because it believes that the fire will burn it to-day just as it did yesterday; but this belief goes beyond experience, and assumes that the unknown fire of to-day is like the known fire of yesterday. Even the belief that the child was burnt yesterday goes beyond present experience, which contains only the memory of a burning, and not the burning itself; it assumes, therefore, that this memory is trustworthy, although we know that a memory may often be mistaken."
Precisely - the experience we really have is limited to "the specious present", which has an extent of a few seconds at most. And as I pointed put before: There simply is no possibility of testing a theory without predictions which go beyond known experience, nor is a theory any use to guide one's actions if it doesn't go beyond such experiences as one has or remembers. Text.
Note 83: "The question is not, therefore, "May we believe what goes beyond experience?" for this is involved in the very nature of belief; but "How far and in what manner may we add to our experience in forming our beliefs?" "
Indeed. I shall below discuss Clifford's - consciously partial and superficial - recommendation, and here refer the interested reader to my On The Logical Principles Of Scientific Explanation. Text.
Note 84: "And an answer, of utter simplicity and universality, is suggested by the example we have taken: a burnt child dreads the fire. We may go beyond experience by assuming that what we do not know is like what we do know; or, in other words, we may add to our experience on the assumption of a uniformity in nature. What this uniformity precisely is, how we grow in the knowledge of it from generation to generation, these are questions which for the present we lay aside, being content to examine two instances which may serve to make plainer the nature of the rule."
The principle Clifford proposes is: "We may go beyond experience by assuming that what we do not know is like what we do know; or, in other words, we may add to our experience on the assumption of a uniformity in nature."
Actually, there are somewhat better formulations and motivations. Clifford himself provides a better formulation than "assumption of a uniformity in nature", which is too general and unspecific in many cases, namely "what we do not know is like what we do know", which merely counsels us to rely (rather than not) on whatever we have established by careful reasoning and experimentation.
Next, the kind of principle Clifford has in mind has been formulated several times explicitly, possibly first by the Chinese. Here is a beautiful quotation from Robert Temple's "The genius of China" (that popularizes Joseph Needham's work):
"Isaac Newton formulated his First Law of Motion in the eighteenth century. It stated that 'every body continues in its state of rest, or uniform motion in a right line, unless it is compelled to change that state by forces impressed upon it.
Needham's researches have now established that this law was stated in China in the third or fourth centuty BC. We read in the Mo Ching: 'The cessation of motion is due to the opposing force... If there is no opposing force ... the motion will never stop. This is as true as that an ox is not a horse." (p. 161)
Furthermore, Newton's First Law of Motion was closely related to a methodological principle Newton formulated himself as follows below, namely as his Third Rule of Reasoning, as Clifford undoubtedly knew.
Newton's Rules of Reasoning minus his comments are as follows, where it should be realised that in the following quotation Newton meant by "experimental philosophy" what we call "natural science" and that a shorter version of "which admit neither intensifcation nor remission of degrees" is "which are invariant". Newton added these rules to the second edition of his Principia, in 1714:
Rule I : We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances.
Rule II : Therefore to the same natural effects we must, as far as possible, assign the same reasons.
Rule III : The qualities of bodies, which admit neither intensification nor remission of degrees, and which are found to belong to all bodies within the reach of our experiments, are to be esteemed the universal qualities of all bodies whatsoever.
Rule IV : In experimental philosophy we are to look upon propositions inferred by general induction from phenomena as accurately or very nearly true, notwithstanding any contrary hypotheses that may be imagined, till such time as other phenomena occur, by which they may be either made more accurate, or liable to exception.
So what Clifford proposes is much like Newton's Rules II to IV, simplified to their common essence.
Finally, I have shown elsewhere these rules can be mostly argued rationally with the help of probability theory, and note here that there is a principle at the bottom of them that can be stated simply thus:
- Human beings can learn from experience.
For if they can, they must use such knowledge as they believe they have to find more and to correct what was mistaken - and that they can do so is shown by scientific technology: The very many thousands of human artifacts made with the help of scientific theories, that show these theories are far bettter tools to explain and improve the world than the far less rational or tolerant religious or political creeds. Text.
Note 85: "But this is the kind of assumption which we are justified in using when we add to our experience. It is an assumption of uniformity in nature, and can only be checked by comparison with many similar assumptions which we have to make in other such cases."
Yes, but as I pointed out in Note 84, it is usually more sensible to make the assumption more specific: What will probably happen is like what mostly happened so far.
Furthermore, the Chinese version I quoted above has the nice feature that it suggests the following form and principle:
- Things will continue to happen as they did before, unless there is a reason they don't.
Hence, if we know of no reason that what has been happening so often before will happen again, then our best guess about what will happen is that it will happen again.
Perhaps it is well to also briefly indicate the reasons why this is rational to believe:
First, see Note 84. Next, supposing that theories are attempts to explain features of things in each and any circumstances, to the extent that our theories have been reliable in the past and to the extent that they have good evidence, they may be relied upon to keep working if there are no intervening reasons. Text.
Note 86: "But is this a true belief (..)? Can it help in the right guidance of human action?
Certainly not, if it is accepted on unworthy grounds, and without some understanding of the process by which it is got at. But when this process is taken in as the ground of the belief, it becomes a very serious and practical matter."
Well, it certainly is a belief that in very many distinct known cases has been true in the past, to the best of our knowledge.
Furthermore, as I pointed out in Note 59, the whole notion of human scientific knowledge of reality, that has produced so much technology, discoveries and inventions that would not exist without it, and that surely shows that mankind has some real knowledge about the real world they are all part of, is based on the possibility of guessing that certain general statements are true, that represent some real feature(s) of some real thing(s) in general, in all circumstances and at all times, and until we have found evidence this is not so in some circumstances, for some reason.
And in the end the best argument for the scientific method, for science, and for rational thinking are the very many discoveries and inventions that would not exist without science, and that were wholly beyond the grasp or dreams of all systems of religious faith and all Holy Books supposedly informed by divine infinite knowledge. Text.
Note 87: "Whereas the acceptance of the spectroscopic method as trustworthy has enriched us not only with new metals, which is a great thing, but with new processes of investigation, which is vastly greater."
This is a point Clifford made before, but which stands repeating: Far more important than actual results, which are always particular, are general rational methods and tools by which new results can be found. Text.
Note 88: "We find also that men do not, as a rule, forge books and histories without a special motive; we assume that in this respect men in the past were like men in the present; and we observe that in this case no special motive was present. That is, we add to our experience on the assumption of a uniformity in the characters of men. Because our knowledge of this uniformity is far less complete and exact than our knowledge of that which obtains in physics, inferences of the historical kind are more precarious and less exact than inferences in many other sciences."
Here we have an application of Clifford's rule - say: "what we do not know is like what we do know" - to the science of history. Actually, we need not make "the assumption of a uniformity in the characters of men", but only need to count or get a good approximate idea of the number of forged histories and of the number of non-forged histories. As a matter of fact, the latter - especially if restricted to such books as have been seriously considered and discussed by historians and other intelligent knowledgeable men - is far greater than the former, and all that remains is to apply Clifford's rule to this to get his conclusion. Text.
Note 89: "We may, then, add to our experience on the assumption of a uniformity in nature; we may fill in our picture of what is and has been, as experience gives it us, in such a way as to make the whole consistent with this uniformity. And practically demonstrative inference—that which gives us a right to believe in the result of it—is a clear showing that in no other way than by the truth of this result can the uniformity of nature be saved. No evidence, therefore, can justify us in believing the truth of a statement which is contrary to, or outside of, the uniformity of nature."
This is not quite true, and the main reason is that, since Clifford lived, the rise of quantum mechanics has made it necessary to assume that there are real chance processes in nature. Put otherwise: The "assumption of a uniformity in nature" can only be retained in the sense that what remains uniform is a statistical distribution of otherwise principially unpredictable events. Text.
Note 90: "If our experience is such that it cannot be filled up consistently with uniformity, all we have a right to conclude is that there is something wrong somewhere; but the possibility of inference is taken away; we must rest in our experience, and not go beyond it at all. If an event really happened which was not a part of the uniformity of nature, it would have two properties: no evidence could give the right to believe it to any except those whose actual experience it was; and no inference worthy of belief could be founded upon it at all."
Again, this is not quite so. What does seem true to me is sketched in Notes 84 - 86, to which I can add the following:
What we seek are adequate explanations of natural things, events and processes, and to do so we need sufficient experience of what we try to explain to know that we can be more certain than not that quite a few things remain invariable, and can can be predicted and foreseen from a proper interpretation of their past, if this is known and well understood.
Furthermore, to explain anything at all we must have some idea what it may be like, and the only way we can find such an idea is by using our imagination about what we believe we know has happened in nature so far.
Finally, it is a tested and often verified truth that things will continue to happen as they did before unless and until there is a reason they don't, and this truth we may use both to derive and to test predictions, and indeed we normally do and did so even if we are not conscious of this. Text.
Note 91: "Are we then bound to believe that nature is absolutely and universally uniform? Certainly not; we have no right to believe anything of this kind. The rule only tells us that in forming beliefs which go beyond our experience, we may make the assumption that nature is practically uniform so far as we are concerned. Within the range of human action and verification, we may form, by help of this assumption, actual beliefs; beyond it, only those hypotheses which serve for the more accurate asking of questions."
Yes, here Clifford is again quite right, and argues along the lines of my comments in this section.
Also, his idea that there are "hypotheses which serve for the more accurate asking of questions" is sensible - and indeed one often must make suppositions, see whether these are confirmed, and then take it from there to try to account imaginatively to explain such results as one found. (For more see my On The Logical Principles Of Scientific Explanation.) Text.
Note 92: "We may believe what goes beyond our experience, only when it is inferred from that experience by the assumption that what we do not know is like what we know."
No, not quite, for there is a slight complication: We also know from experience that many things can't continue to do what they did for a long time. Men die eventually; a piece of iron that is bend and bend again eventually breaks; elastic bands remains elastic a long time but then grow brittle, and so on.
But Clifford is right that these facts are also known from experience, and that to suggest that something will end that has gone for some time we need some evidence to the effect that something like it has ended. Text.
Note 93: "We may believe the statement of another person, when there is reasonable ground for supposing that he knows the matter of which he speaks, and that he is speaking the truth so far as he knows it."
Precisely - and usually, as men are on average, more to the point: We need not believe a statement of another person, however honest and sincere that person may be, if we have no reason to believe he knows of what he speaks and no reason to believe that he is honest. Text.
Note 94: "It is wrong in all cases to believe on insufficient evidence; and where it is presumption to doubt and to investigate, there it is worse than presumption to believe."
And this is Clifford's dictum plus another very memorable claim that may be restated thus: You have no right to claim any rational belief in cases where you have no right to doubt and investigate, and about cases where you never doubted nor investigated. Text.