Current Issue: Spring 2007 (Vol I)
A Humerous Introduction to Induction
To Hume it may concern, we’ll be discussing the Problem of Induction.
Suppose I say: “All spirits contain alcohol. Gin is a spirit. Therefore, gin contains alcohol.” This argument is completely uncontroversial. It is what we call the sound deductive argument. It is a valid argument because the conclusion necessarily follows the premises. If the premises are true, the conclusion can be nothing but true; the negation of the conclusion would imply a contradiction. It is sound because this particular argument’s premises happen to be true. All spirits do indeed contain alcohol and gin is indeed a spirit. Therefore, gin must contain alcohol.
Now consider the following: Nick is an air-guitarist and he is sweet; all my friends who are air-guitarists are sweet; every single air-guitarist I know or with whom I have come into contact is sweet—therefore, it is highly likely that the next air-guitarist whom I meet will be sweet. This is what is known as an inductive argument. We make this sort of argument all the time. For example: I have dropped a cube of sugar into hot tea and it has dissolved every single time. I have tried it with white sugar, brown sugar, green tea and Earl Grey. I reasonably assume that the next time I drop a cube of sugar into hot tea, it too will dissolve. In fact, I take it a step further and generalize, claiming that every cube of sugar dissolves in hot tea.
But somehow this last argument seems stronger than the one preceding it about my air-guitaring peers. We are more confident that sugar will dissolve in hot tea every time than we are that the next air-guitarist we meet will be really sweet. Why? Because the former has a natural connection whereas the latter seems accidental. It may or may not be the case that there is something inherent in each air-guitarist that makes him or her awesome and radically sweet. However, the connection between the two events, (1) dropping the sugar cube into the hot tea and (2) the sugar dissolving, seems to be a necessary connection. It is not only that (2) always follows (1); it is more than that. There is something in the very nature of sugar and hot tea such that (1) necessarily brings about (2). But as we shall see, the Problem of Induction and the Humean philosophy on which it is based will reject this line of reasoning.
Now people can make some pretty ridiculous arguments. Suppose you are in Italy and you see two families fighting each other. During a lull in the violence, you ask one side, “Why are you fighting that family?” and they respond:
“Because they’re Capulets.”
“Well why do you fight Capulets?” you persist.
“Because we’re Montagues.”
“Why do Montagues fight Capulets?”
“Because we’re feuding.”
“Why are you feuding?”
“Because we’re fighting.”
“Why are you fighting?”
“Because they’re Capulets.”
After shaking your head in disbelief, you think to yourself, “What a bad argument!” It is bad because it is unreasonable, and it is unreasonable because it is circular.
It is precisely this circularity that can be found in inductive arguments such as the one above about sugar dissolving in tea. Suppose you ask me, “How do you know sugar dissolves in tea?” I will respond,
“Because in past instances it always has.”
So you continue: “How do you know it’ll happen again?”
“Because future events resemble similar past events.”
“How do you know the future resembles the past?”
“Because in past instances, the future has always resembled the past; so too now, the future will resemble the past.”
Here we find another instance of circular argumentation. To say that the conclusion about sugar dissolving in tea is “reasonable” is to give all circular arguments a revolutionary new status as reasonable. If we are intellectually honest and consistent, the inductive conclusion that we have drawn about sugar, or about anything else we experience in a similar fashion (namely, all of science!) ought to be deemed unreasonable. It is unreasonable because it is circular, and it is circular because it presupposes the very principle it invokes: namely, the Principle of the Uniformity of Nature (PUN). We can thank David Hume for bringing this problem to our attention. Because of PUN, it is unreasonable to assume that future puns will be just as funny as past puns (present pun intended).
There are two important things to remember about PUN. The first is that it is not analytically true, meaning that it is logically consistent to hypothesize that the course of nature may not be uniform. Nevertheless, we do in fact invoke PUN all the time in order to make claims about unobserved matters of fact.1 . portant point to remember. From a single observed set of data, we use PUN to make a proposition about all other unobserved instances of that same state of affairs. In all of our inductive arguments, we assume that unobserved things will resemble observed things. The problem is that this assumption can only be established using the assumption itself. In the past, our future predictions based on past observation have been vindicated subsequently by the then present states of affairs; but what is to say that our future predictions will be vindicated by the still more future states of affairs? In the words of Bertrand Russell, “We have experience of past futures, but not of future futures, and the question is: Will future futures resemble past futures?”2 We argue for the validity of induction with induction. We argue from past experience that past experience is a good foundation for making future judgments.
To prevent circularity, one would have to base PUN on reason rather than experience. One could do this by a demonstration using deductive reasoning from a priori self-evident premises, such as the one that gave us “Gin contains alcohol.”
For Hume, deductive arguments can only be justified if the conclusion necessarily follows the premises; by accepting the premises of a sound argument and rejecting the conclusion, a contradiction would have to result. So, for example, if we accept the first two premises of the above argument concerning alcohol and spirits, and then proceed to deny that gin is a spirit, we would be involving ourselves in a contradiction. The two propositions “Gin is a spirit” and “Gin is not a spirit” are clearly contradictory. One must necessarily assent to the former conclusion if he accepts the premises. But the two propositions “The future has resembled the past” and “The future will not resemble the past” imply no contradiction. Other possible future instances of sugar cubes not dissolving in hot tea are not excluded by all the other past instances in which sugar cubes did dissolve. Therefore, it is not by necessity that one concludes that sugar dissolves in hot tea, but by invoking PUN and thereby “evidently going in a circle and taking that for granted which is the very point in question.”3 After all, there is no way to prove that the natural laws that govern the way things behave, like gravity for example, will not change tomorrow. The only data we use to infer that nature is uniform are past instances of similar conjoined events. We call them “regularities” because we assume PUN, but we have not established this deductively.
It is because of this circularity that PUN cannot be established inductively either. To say that all my past experiences of inferential thinking have been vindicated—that is to say, that past inductive premises were followed by inductive conclusions that turned out to be true—carries no weight in justifying PUN. This premise’s rational justification is under question just as much as the conclusion it seeks to prove. All we can prove inductively is that PUN has been true up until now. But we cannot prove that it will continue to be true.
But who cares about any of this? Are we going to walk off buildings because we have no rational justification for believing that the law of gravity will stay intact?
“But who cares about any of this? Are we going to start making bets at the pool hall that when the cue ball hits the red billiard ball it will turn into a chicken instead of roll on the table?”
Are we going to start making bets at the pool hall that when the cue ball hits the red billiard ball it will turn into a chicken instead of roll on the table? Why doesn’t Hume stick his hand in the fire if he doesn’t trust inductive inferences that teach the rest of us the burning potential of fire?
The anticlimactic answer is that Hume does in fact expect you to heed your inferential conclusions. In fact, he thinks you can do nothing but heed them. Inferring inductively is instinctual and indispensable to both goal oriented action and scientific inquiry. When we see two events constantly conjoined with one another, we call one of them “cause” and the other “effect.” Hume does not completely do away with this concept of cause and effect. He just transfers the idea from the natural realm into the psychological. The intuitive “causal power” that one thinks is contained in the cue ball hitting the billiard ball, or the sugar dissolving in the tea, is merely transferred from the object to the mind:
This observation of repeated sequence generates—causally generates—in the mind a custom or habit. This custom of habit, in turn, itself generates—again in a causal manner—the feeling of necessitated transition; and it is upon the pattern of this impression that our ideas of causal connection have come to be modeled.4
Induction is not so much a thinking process to which we can choose to adhere, but rather a natural explanation for how we actually think. Induction, then, rests on custom, not reason.
But what difference does it make whether it is custom or reason that makes us behave as we do when we trust science, supply people with medicines, etc? As long as it works we will continue to do so, and the matter becomes irrelevant.
Yet the problem is relevant to all of us, for the following reason: the most important issues in life—among them religion, morality, testimony, intelligibility of the world— are under attack. If Hume is right, then in addition to subverting justification for our most commonly held beliefs, induction ceases to be a reason for believing the things we believe. It becomes a psychological explanation for how we believe the things we believe. The intelligibility of the universe is reduced to impressions imposing themselves upon us and our interpretation of those impressions that are not reasoned but hard-wired into us. We believe in cause and effect not because it is true, but because we cannot do otherwise.
The stakes are high. For example, if Hume is right, we believe that a man cannot give birth to a child not because nature reveals this to us, but because of a custom or habit that has been embedded into us through repeated observations of a man’s anatomy. There is no natural law we interpret. Rather than interpreting it, we create it. A great reversal takes place: reason is a slave to the passions and not the other way around. Hume’s morality is rooted in our psychology. When nature is no longer intelligible, any kind of natural law to which the reason conforms ceases to exist. “The good” ceases to be reasonable but is reduced to what gives us pleasure: “Tis in vain to pretend, that morality is discover’d only by a deduction of reason. Actions do not derive their merit from a conformity to reason, nor their blame from a contrariety to it.”5 Anyone digging for the roots of relativism can begin their excavation here.
While there may be several possible solutions to the problem of induction, I think that the most effective is the “Nomological” justification. John Foster’s “Nomological- explanatory solution” (NES) is an argument from the best explanation of ordinary experience. Ordinary experience reveals a regularity in the world around us that begs for an explanation. According to NES, a natural law (also referred to as objective regularity or natural necessity) provides this explanation.
Let us consider two possible worlds: (1) a world in which experienced regularity corresponds to actual regularity explained by a natural law; (2) the alternative world, posited by Hume, which is devoid of natural law and in which experienced regularity does not correspond to any actual regularity. In the first world we need not look further than the natural law for an explanation of our experienced regularity. In the second, Humean world, however, each and every experience of regularity is a skewed representation of an actually irregular world. But this very skewage reveals itself with regularity: because it is present at each experience of regularity, it itself is a regularity that begs explanation. In fact, even if (contrary to all our experience) we discern absolute irregularity in the world around us, it would be reasonable to expect this irregularity regularly. Such a world is one in which irregularity is regular! For this reason, regularity is inescapable.
Now that we have established that natural law is the best explanation for our experience of regularity, the only other option for the Humean (save resorting to an “explanation” of regularity based on some sort of absurd coincidence) is to contend that the laws of nature are efficacious for only a limited span of time. For example, is it not possible that the law of gravity has been intact up until now but will change tomorrow? I do not deny that this is possible. However, I do believe that the burden of proof here rests upon the objector. He must provide an explanation that is as good as, if not superior to, temporally-unrestricted laws. But any such laws that would be restricted to a particular temporal period are, in Foster’s words, “more mysterious, inherently more puzzling” than those that are temporally universal.6 Although time- restrictive laws explain past regularities just as well as universal laws, they also beg a further explanation as to why they are time-restrictive in the first place.
Is it possible that these laws are time-restricted? Perhaps it is possible. It may also be possible that I will turn into a penguin tomorrow, or that I am the world’s best air- guitarist. I think it is safe to say that if the laws dictating how things behave in certain circumstances change, then the natures of those things change as well. This, however, is a metaphysical question, and as such it must be considered at length on its own terms. All of this aside, one must now show me why it is more reasonable to explain regularities by irregular accidents than by regular laws. Until then, I’ll maintain my belief in the universal laws of nature. After all, even if I can’t guarantee one-hundred percent that the next air-guitarist I meet will be sweet, I can say with certainty that my tea-with-sugar will be.
1. “Matters of fact” here means anything that is not a relation between ideas. In other words, the way the world is as we experience it. Relations between ideas are analytical—they are knowable independent of observation. You don’t need to take a survey of bachelors to know that “bachelors are unmarried men.” But in order to know that there is a table in your room, you need either to perceive it, remember it, or have someone testify to it.
2. Bertrand Russell, Problems of Philosophy, 65.
3. David Hume, Enquiry Concerning Human Understanding, no. 30.
4. Norman Kemp Smith, The Philosophy of David Hume, 373.
5. David Hume, Treatise of Human Nature: BK III “Of Morals,” 509-510.
6. John Foster, “Induction, Explanation and Natural Necessity” in Michael Huemer, Epistemology: Contemporary Readings, 338.
Andrew Meszaros is a senior in the school of Arts and Sciences majoring in Philosophy. He enjoys studying a variety of epistemologies and metaphysics. He likes Triscuits©, air-guitaring, Beethoven, and long walks on the beach.