Apologetics to the Glory of God

An Informal Introduction to Covenantal Apologetics: Part 29 – Problem of induction.

By C.L. Bolt

By induction we refer to singular and general predictive inferences. When humans think, they do not limit themselves to thinking only about what is immediately apparent to them. In fact, we often go beyond what is currently present to our senses, memories, and reasoning and make inferences; we infer things from what we have experienced in the past or are currently experiencing. For example, if we ate bread on Monday, Tuesday, and Wednesday and found that it nourished us, then we would at least expect that bread will nourish us on Thursday as well. We may even go so far as to say that we know that bread will nourish us on Thursday. To predict that the bread will nourish us on Thursday is a singular predictive inference.

We might go even further than this and claim that bread in general nourishes us! To predict that bread will nourish us in general is a general predictive inference. Some have argued that if we are going to expect bread to nourish us at any single point (like Thursday) then we already have an expectation that bread in general will nourish us.

Unfortunately the use of “predictive” can confuse what we are actually doing in these instances, because induction is not always performed strictly with respect to what will happen in the future. It may even be better to speak of moving beyond experience. So for example, a person who has been in over a hundred fields that were all full of black crows has experienced black crows, but when asked, “What color are crows?” he will move beyond his experience in answering, “Crows are black.” He has not experienced all crows; he may not have even experienced half of all crows, but the man feels warranted in stating that crows are black. For the sake of our example, he means either that all crows are black, or that crows in general are black.

Or take the nature of rock. Think of the rocks you have experienced. You may have formed a belief that rocks are hard. Now, there may be some rocks that are not hard, but if that actually is the case, then it is some rather strange rock! At any rate, you can concede that some rocks may not be hard, and still state that rocks in general are hard. You may want to stick with all rocks being hard though. Rocks, by nature, are hard. And if it is the case that rocks are hard by their very nature, then a particular rock will likewise be hard.

When people go to toast something for breakfast, they will likely choose the bread over some gravel from their driveway. Why? Well, bread nourishes, and rocks are hard. We might even say that a person who chooses the gravel over the bread has something terribly wrong with him. He is very confused, or worse, he is insane. At any rate, people act as though they know something about things they have not experienced, whether that is bread, crows, gravel, or any number of hundreds of thousands of other entities and events. We are not claiming that anyone “knows the future” in the popular sense of the phrase, but certainly people act as though they know something about the future. The future is merely one example of something beyond present experience. We are talking about the future in the case of the bread, but we are not necessarily talking about the future in the case of the crows and rocks, unless we are just referring to our future experience of them.

One worry that is already lingering in the backs of the minds of quicker readers concerns sample size. If we pick out one or two sheep that are white, we might infer that all sheep are white, but this would be a false conclusion, and a bad inference. Why? Because the size of the sample we selected to draw an inference from was much too small to be representative of the total number of sheep. With a better sample size we may have run across a few black sheep even if they did not have three bags full of wool. But what we are discussing here is different from concerns about sample size. What we are drawing attention to is that even with a fair sample size, we as humans move in our thoughts and behavior from what we presently experience to expectations or knowledge based upon that which we do not presently experience. For example, we obtain an acceptable sample of sheep and make knowledge claims about particular sheep, or sheep in general, or all sheep. It is this aspect of induction that we will be focusing upon here.

Another concern is that if we make some universal claim with respect to any kind of entity or type of event we may find ourselves easily proven wrong. For example, we may want to say that all bread nourishes, but it may be the case that the next piece of bread you eat makes you sick for some reason! Universal claims – claims about everything in some given case (like bread, every piece of bread) – are usually not made through induction, but we do not necessarily want to say that they cannot be. What we do want to say is that all that it takes to overturn a universal claim is one counterexample. So with respect to induction, most people do not want to claim anything like certainty with respect to an inductive conclusion, since they believe it is at least possible that some counterexample will turn up, and in many cases we do know of counterexamples from previous experience. For example, we may observe that deer are brown and believe deer to be brown until we find an albino, but we consider the albino an exception rather than a norm. From this we might say that the next deer you encounter will probably be brown, or that deer in general are brown. Here we have weakened an inductive conclusion to allow for exceptions to a regularity.

There is a difficult question that comes up when we think about induction. We have seen some potential problems with induction in the examples of sample size and overstated inductive conclusions, but these are hardly fatal problems. These types of problems are more like concerns, and they are concerns which simply lead us to be cautious in our use of induction. We can fix them and have only briefly alluded to how we can (and do) fix them.

However, there is a potentially fatal problem for induction. It is not found in sample size or an overstated conclusion. Instead, it is found in the premises of an inductive argument. More specifically, it is found, or not found, between the premises of an inductive argument and between those premises and the conclusion. We have discussed skepticism as a problem of connection. What we are asking now is what connects the premises and conclusion of an inductive argument or line of reasoning together. What is it that ensures us that particular experiences are related to one another and especially to whatever experience we have not had but are reasoning about? What is it that allows us to move from our present experience to something outside of present experience? For example, we said that the bread nourished us on Monday, Tuesday, and Wednesday. But what is it that connects these individual experiences together? Perhaps they are independent from one another. If they are, then there is certainly no reason to conclude that the bread will nourish us on Thursday. And if these individual experiences are connected together by something else so that we can reason from them to the conclusion that we have not yet experienced, then what is this something else?

Now we are beginning to encounter a famous skeptical problem known as the problem of induction. We need to take a moment to clarify what the problem of induction is not before moving on to describe what it is in more detail. First, the problem of induction is not a problem concerning sample size, for the problem of induction still applies even when a sample is acceptably representative. Second, the problem of induction is not a problem concerning our lack of certainty regarding inductive conclusions, for the problem of induction still applies even when we fix overstated conclusions by weakening them. Third, the problem of induction is not a problem concerning whether or not we should initially or should continue to use induction, for it seems clear that people do in fact use induction by force of habit or custom whether it is in the end rationally justifiable or not, and this takes us into our discussion of the problem itself.

The problem of induction can be stated in different ways. Some have taken the problem of induction to call into question human rationality due to the use of induction by humans, some have taken the problem of induction to call into question our ability to know anything through induction, and others have taken both of these or something similar to them as constituting the problem of induction. What exactly is the problem? Again, it is a problem of connection. Or if you prefer, we can think about this as another instance of the problem of the one-and-many, because we have a plurality of premises that do not even probably establish a conclusion if there is no unity between those premises. If there is no such unity or connection between the premises themselves or the premises and the conclusion, then there is no way for us to move beyond our present experience in terms of expectation or knowledge. We are stuck, in other words, with whatever is present to the senses, memories, and reasoning. We cannot make singular or general predictive inferences at all. Or at least, we do not have any reason for doing so. However, we continue to do so in every day experience. Some have looked at our predicament and believe us to be irrational since we attempt to move beyond present experience without any reason or justification for doing so. Some say that the lack of this justificatory element of knowledge means that we cannot have any knowledge of anything that is not a part of our present experience. Some say both. There have been some popular and noteworthy attempts to solve this problem.

An initial response to the problem of induction is to exclaim that it is clearly the case that people “cannot know the future.” But this response misses the point, as has already been discussed. We are not speaking of the future per se, but of future experience. We do not even necessarily need to use this language. Next, a response is offered that there is something connecting the premises to one another and it is obvious what it is! Since we have experienced the same things happening over, and over, and over again in the past, it is completely reasonable to assume that these same sorts of things will continue to happen in the future. We might say that “the future will be like the past;” at least in the relevant sense. For example, gravity has held us in the past, and so it is reasonable to think that it will do so in the future. Another similar response is to say that particular entities have particular natures and properties. For example, rocks are hard. To sum these two responses up we can say that nature exhibits regularities; there is such a thing as the uniformity of nature. Therein do we find our unifying principle for the many particulars of experience.

Of course, we don’t want to say that this uniformity of nature is some sort of absolute uniformity to which there are no exceptions, because then we would run into our previous problem of rendering our inductive conclusions too strong and making them subject to swift refutation through even one counterexample. We might nevertheless say that nature exhibits regularities; things tend to be the same as they always have been even if there are exceptions here and there. This premise of the argument would be sufficient to connect the other premises together so that they are no longer independent. Instead, they are tied together because they are part of nature, and there is a uniformity of nature. While this uniformity of nature is not absolute, it is enough for us to arrive at a probable conclusion. So then, bread nourished me on Monday, Tuesday, and Wednesday, and the future resembles the past, so bread will nourish me on Thursday as well. In fact, bread is generally nourishing. Or, every rock I have ever come across is hard, and there is a uniformity of nature, so the next rock I come across, and probably every other rock I ever come across, will be hard also. It seems that we have solved our supposedly fatal problem of induction. Not only can we definitely hold onto our inductive expectations, but we can know things through induction and are rational in our use of induction.

It should be added that some have said that induction is at least pragmatically justified. By this is meant that induction works. There are some problems with this position. For example, what do we mean by “works”? What does induction work for? If it is irrational or we cannot know anything through it, then it certainly does not work in those respects. There are many things that people have believed work and have continued to rely upon them because of this belief even though the beliefs or activities “justified” pragmatically in this way have nothing to do with what is actually occurring. For example, an ancient civilization might have sacrificed a virgin annually so that the sun would continue to appear for the remainder of the year. What do you know, the virgins were sacrificed, and the sun continued to rise! So the pragmatic approach to the problem of induction has some other worries that we will now set aside. For now, note that the uniformity of nature is being assumed here in this pragmatic response, since it is taken to be the case that induction worked in past experience and will continue to do so in future experience.  

Others have said that we as humans do not use induction anyway, or that if we do, it is not really that important since knowledge does not come through induction and because we can sidestep the problem of induction by using deduction. In this theory someone will think up and believe a proposition which will then be tested in order to try and disprove it. Once the proposition in question has been tested, it is rational to continue to hold onto it. It should be noted that there are some problems with this view as well, and many of them are too involved to go into in this short introduction. For example, one should notice that we cannot ever come to know the truth through this method, since we have not inductively gathered data in an effort to establish a conclusion directly and initially based upon that data. Also, the proposition in question could always be refuted by the next attempt to disprove it. Those who defend this view are trying to say that it is rational to hold these beliefs anyway, so long as they actually describe something about the world and have been tested to make sure that they do not immediately fail. However, this method also assumes a uniformity of nature because it assumes that those things already tested will remain as they were when they were tested.

Each of the above examples of responses to the problem of induction relies in some way or another upon the uniformity of nature. The uniformity of nature is proposed as a means of connecting the premises to one another for the sake of establishing inductive conclusion. Through adding this premise into induction we are able to go beyond present experience in order to have expectations about that which we have not experienced and even to have knowledge about it. We noted that we can weaken our inductive conclusions to being probable, but here too we rely upon the uniformity of nature to establish that the premises are related to the conclusion to establish its probably being true. To say that induction will continue to work beyond our present experience of it working likewise assumes the uniformity of nature. Finally, to ditch induction for an approach which essentially starts with the conclusion and then attempts to disprove it assumes a uniformity of nature especially with respect to that which has already been tested. In some way then, each of these rather different attempted answers to the problem of induction relies in some way upon the uniformity of nature. It is to this topic that we turn next.

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One response to “An Informal Introduction to Covenantal Apologetics: Part 29 – Problem of induction.”

  1. ZaoThanatoo Avatar

    I can tell this one is your favorite so far…

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