Chapter 7 Chapter 6 On Induction

In almost all of our discussions above, we have been trying to figure out what is our material through knowledge of existence.Are there any things in the universe that we know they exist because we know them?So far our answer has been: we know our sense-data and perhaps ourselves.We know that these exist, past sense-data in memory, and we also know that they have existed in the past; this knowledge furnishes us with the data. But if we are to be able to draw inferences from these materials—if we are to know the existence of matter, the existence of other people, the existence of the past or the existence of the future long before our personal memory begins, then we must Know some general principle by which we can draw the above inferences.We must know that the existence of a certain kind of thing A is a sign of the existence of another kind of thing B, either at the same time as A, or a little earlier or a little later than A. For example, the sound of thunder is a sign of the pre-existence of lightning.If we did not know this, we should never be able to extend our knowledge beyond the sphere of our personal experience; which, as we have seen, is very limited.The question we have to consider now is whether it is possible to expand knowledge in this way?If possible, how to achieve it?

Let us take a case that no one doubts.We all believe that the sun will come out tomorrow.why?Is this belief simply a blind product of past experience, or is it a valid belief that can be tested?It is not easy to find a standard to judge whether such a belief is reasonable or not.But at least we can be sure of what sort of general belief (so long as it is true) that justifies the judgment that the sun will rise tomorrow, and many other similar judgments on which our actions are based. Obviously, if someone were to ask why we believe the sun will rise tomorrow, we would naturally answer "Because it always rises every day."We firmly believe that it will come out in the future because it always came out in the past.If anyone asks us why we believe it will continue to come out in the future, then we have to appeal to the laws of motion: we will say that the earth is a rotating body, and such a body will never stop as long as it is not interfered by external forces. It rotates, and there is no external force interfering with the earth between today and tomorrow.Of course, it is possible to wonder how we can be so sure that there was no external interference, but such doubts are not of our interest.The question that interests us is whether the laws of motion will still be valid tomorrow.If someone asks this question, we are in the same position as when someone asked the question about the sunrise.

The only reason we have for believing that the laws of motion will continue to be valid is that they have been valid so far as past knowledge enables us to judge.It is true that the laws of motion are more likely to be supported by the mass of evidence obtained in the past than for the sunrise, because the sunrise is only a special case in which the laws of motion operate, and such cases are innumerable. .But the real question is: is the fact that a law has worked in the past enough examples that it will work in the future?If not, it is evident that we have no grounds for predicting that the sun will rise again tomorrow, that we will not be poisoned by our next meal of bread, or any other prediction which controls our daily lives without our being consciously aware of it.It should be noted that all these expectations are mere probabilities; then we need not look for a proof that they must be fulfilled, but only a reason for the opinion that they might be fulfilled.

In dealing with this issue, we must first make an important distinction, without which we can quickly descend into hopeless chaos.Experience has shown us that hitherto certain identical sequences and concurrences have often repeated themselves, and this is one reason why we expect the same sequence or concurrence next time.Generally speaking, food tastes what it looks like, and when we find a familiar look combined with an unusual taste, our prophecy received one of the most serious shocks.By habit, the things we see come to be associated with a certain sense of touch which we expect when we touch them; Any sensation we touch.When uneducated people go abroad for the first time, they are astonished in disbelief to find that their native language is not understood.

This ability to connect is not limited to humans; animals are also extremely strong.If a horse goes one way too often and you try to tell him to go another way, he will resist.Livestock look forward to feed when they see the person who feeds them regularly.We know that all these shallow expectations of uniformity can be misleading.The man who feeds a chick every day and feeds it all its life can at the end wring the chick's neck, which shows that it is better for the chick to have a more refined view of the uniformity of nature. Although such expectations can be wrong, they exist.The mere fact that a certain thing has happened several times makes animals and men expect it to happen again.So our instincts of course lead us to believe that the sun will come out tomorrow, but we are no better than a chick whose neck has been strangled unexpectedly.Therefore, it is one thing for the uniformity of the past to form expectations about the future. After the question of the validity of the expectations is raised, whether there is any reasonable basis for these expectations to have weight is another question; we must distinguish between the two.

The question we must discuss here is whether there is any reason to believe in the so-called "uniformity of nature."To believe in the uniformity of nature is to believe that everything that has happened or will happen is an instance of some general law to which there are no exceptions.The shallow predictions we have considered are subject to exceptions and, therefore, disappoint those who entertain them.But science has traditionally held—at least as a practical hypothesis—that general laws with exceptions can be replaced by those without exceptions. Balloons and airplanes are exceptions to the general rule that "objects fall in the air if they are not supported."But the laws of motion and gravitation not only account for the fact that most objects fall, they also account for the fact that balloons and airplanes can rise; thus, the laws of motion and gravitation do not make them exceptions.

If the earth suddenly collided with a massive body which disrupted its rotation, the belief that the sun would rise tomorrow would be false; but the laws of motion and gravitation would not be violated by such an event.It is the task of science to find out such uniformities as the laws of motion and gravitation which, so far as our experience knows, have no exceptions.Science has been exceptionally successful in this area, and this uniformity has been considered valid so far.This brings us back to the question: Given that they have always been valid in the past, is there any reason for us to assume that they will always be valid in the future?

We have argued that we have reason to know that the future will be like the past because what was once the future has continually The experience of the future, that is, the experience of having a time in the past that was the future, which we may call the future of the past.But such an argument is actually based on unresolved issues.We have experience of past futures, but not of future futures, and the question is: Is the future of the future similar to the future of the past?This question cannot be answered by looking at the past and the future alone.Therefore, we have to look for some kind of principle, so that we know that the future is obeying the same laws as the past.

In this question, inferring the future is not the most fundamental thing.This problem arises when we apply laws that are valid in experience to things in the past that we have not experienced--for example, to geology or to the theory of the origin of the solar system.In fact, the question we must ask is: "If you find that two things are often connected together, and you know that there has never been an example where only one of them appears but not the other, in a new instance, if one of them does that give us good grounds for anticipating the occurrence of the other?" The reliability of all our predictions about the future, all the results we obtain by induction are, in fact, the same as our daily life. All beliefs on which to base must depend on our answer to this question.

First, it must be admitted that the fact that we find that two things are always together and never apart is not in itself a sufficient proof that they will also be together in the next example we shall consider.At best we can only hope: the more times certain things are found together, the more likely it is that they will be found together next time.If they are found together enough times, then probability is almost equal to certainty.It can never quite reach inevitability, for we have seen that, despite its frequent repetitions, sometimes;Probability, therefore, is all that we should be after.

It may be objected to this view which we have advanced, and maintain that we know that all natural phenomena are governed by laws; and that sometimes we can see from observation that only one law can fit the facts in our example.There are now two possible answers to this insight.The first answer is that even if there were some law without exceptions that could apply to our example, we can never be sure in practice that we have discovered the law, nor can we be sure that it is a law without exceptions. law.The second answer is that the command of the law itself seems to be only probable; and our belief that it will be valid in the future or in past instances which we have not The principle discussed is based on this. The principle we are now considering may be called the principle of induction, and its two parts may be expressed as follows: (A) If it is found that a certain thing A and another thing B are connected together, and they have never been found to be separated, then the more cases A and B are connected, the greater the number of cases in new cases (of which the presence of one) the greater the probability that they are connected. (b) In the same case, a sufficient number of connected instances will bring the probability of a new connection almost to a certainty, and will make it infinitely nearer to a certainty. As stated above, this principle can only be used to test our expectations in individual new cases.If things of the kind A and things of the kind B are known to be related often enough, and if there are no instances of them not being related, then things of the kind A and things of the kind B are always related—we would also like to know that there can be a This possibility is supported by this general law.The probability of the general law is obviously less than the probability of the special case, because if the general law is true, the special case must be true; but at the same time, the general law is not true, but the special case can still be true.But the probability of a general law, like that of a particular instance, can be increased by the repetition of the instance.We may therefore restate the two parts of the principle of universal law as follows: (A) If the number of instances in which A and B are found to be connected, the greater the probability that A and B will be connected forever (if no unconnected instances are known). (B) Under the same circumstances, when the number of instances where A and B are connected is large enough, it is almost certain that A and B are connected forever, and this general law can be infinitely close to necessity. It should be noted that probability is always relative to a certain material.In our case the material is simply those known instances of A and B coexisting.Perhaps some other material may also be taken into account, since they may alter the probability considerably.For example, someone who has seen many white swans can argue from our principles that, from the data available, perhaps all swans are white.This can be regarded as an argument with perfect reason.The fact that some swans are black doesn't disprove the argument, because something can happen despite the fact that some material would make it improbable.In the case of the swan, it may be known that the colors of many animals are characterized by great variations;But this knowledge counts as new material, and by no means proves that we have miscalculated the probabilities of past material.The fact, therefore, that things often fail to meet our expectations, does not prove that our expectations may not be fulfilled in a particular case or group of cases.Thus, in any case, the principle of induction cannot be opposed empirically. However, the principle of induction is likewise not empirically demonstrable.It is conceivable that experience may justify the principle of induction in the cases which have been considered; but as regards the cases which have not been considered, it is only the principle of induction which can justify those inferences drawn from the known to the unknown.All arguments based on experience, whether of the future, or of an as yet unexperienced part of the past, or of the present, must presuppose the principle of induction; Take the unresolved issue as an argument.We must, therefore, either accept the principle of induction on the basis of its internal evidence, or abandon all justification for our anticipation of the future.But if the principle of induction were really unsound, there would be no reason why we should expect the sun to rise again tomorrow, or that bread is more nutritious than stones, or that we should fall to the ground when we jump off a roof.When we see what seems to be our best friend coming towards us, we shall have no reason to think that within him is not the heart of our sworn enemy, or the heart of a complete stranger.All our actions are based on those associations which were valid in the past, and we therefore think them likely to be valid in the future; this possibility is only valid by the principle of induction. The general principles of science, such as the belief in the validity of laws, the belief that everything happens for a reason, rest as wholly on the principle of induction as the belief in everyday life.All these general principles are believed because mankind has discovered countless instances of their truth, and no instance of their falsity.But this also provides no evidence that they will be true in the future, unless we first admit the principles of induction as premises. Thus all knowledge which experience tells us about something we have not experienced is based on a belief which experience can neither confirm nor deny; but this belief, at least in its The more concrete aspects of application seem to be ingrained in us, as are many facts of experience.The existence of beliefs of this kind and their justification—induction, as we shall see, is not the only instance—has given rise to some of the most difficult and most debated problems in philosophy.In the next chapter we shall briefly consider how this kind of knowledge is accounted for, what is its extent, and what is its degree of accuracy.