Inductive Argument Forms

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Introduction

While inductive reasoning promises less certainty than deductive argument, it makes up for this in the wide range of application that it has in our lives. Inductive arguments attempt to support the probable truth of their conclusions. The basis of inductive argument rationales is our confidence in the patterned quality of our experience (See Logical Structure in Deductive and Inductive Reasoning). Remember that the Principle of Induction identifies the assumption that nature is uniform. From observed regularities, we build up theories about all kinds of things, from the nature of the dungbeetle to the explanation for music and reason in human beings. In other words, we can have not only biology, physics, and chemistry, but also psychology, sociology, and anthropology and many other fields that depend upon induction in their method of inquiry. While the patterns we observe in different disciplines depend upon different empirical methods, at root, the process of induction drives a good deal of theory building across these disciplines. Let's call this "induction in the sciences".

Then there's ordinary induction -- the kind of inference based on a claim about a pattern in your experience. You rely implicitly on numerous regularities in your experience. Our confidence in the rising of the sun, the reliability of building materials (especially of the floor and building that are probably supporting you right now), the regularities of nature, are all arguably a product of an inductive process. But at the local level, you expect the refrigerator to keep working, and you don't suspect the floor boards in the morning. All of this is based on your justified confidence in the reliability of patterns in physical processes.

With psychological processes, people have particularly keen inductive awareness. If we're looking for clues that we can trust someone, we look for specific things that we believe (rightly or wrongly) predict trustworthiness. Between the errors in our perception and the mistakes in our model of what a trustworthy person is, we probably miss a few and misjudge a few others. But at the heart of our thinking lies a prediction, in this case, that someone is trustworthy. Over time, you can keep track of your record. So here an ordinary judgment, the assessment of someone's trustworthiness, is the product of our ability to recognize and understand some patterns in our experience (especially experience that reveals the characteristics that predict trustworthiness).

We use inductive inference to build up our confidence in which stores to shop at, which advice to take about new music or clothes. We use inductive inference to assess how we are doing at some task. For example, suppose I had convinced myself that I was on track to becoming a great golfer. There's a lot of information about the pattern of accomplishment that leads to becoming a great golfer. It's a pattern. To the extent that I'm honest with myself, I would have to acknowledge that there was little evidence that my game was fitting the pattern. Maybe that's one of the most important things about inductive reasoning: you can often establish conditions that would at least disprove your hyposthesis (in this case, that I was becoming a great golfer).

Now we can see that the scope of inductive evidence encompasses all of our experience and even, to some extent, hypothetical experiences that we feel confident reasoning about, such as thought experiments. Inductive reasoning emerges as we try to fit information and careful observation (evidence) to the patterns of experience we already rely on and to a reliable and testable theory. Whether we're talking about a theory in a scientific discipline, a consequence of "induction in the sciences" or a personal theory you have as a result of ordinary induction, we usually identify a pattern of reasoning from a pattern.

Common Patterns of Argument Found along with Inductive Reasoning

Rather than treat inductive reasoning as fundamentally pattern based (as we did with deductive validity), it makes more sense to say that inductive reasoning involves the "fitting" of data or experience to a (predictive) theory. Then we can say that there are various ways of expressing that "pattern in nature" that the Principle of Induction presumes we will find. Edit!

Specific Case to Generalization

A basic inductive method is to accumulate evidence to demonstrate a pattern from which we can then generalize. So, if you're in a new a town, you might start to accumulate experiences with people that help you make an inductive generalization about the people in that town. A simple inductive inference might be:

Premise 1: In 19 of 20 interactions with people in my new town, people were friendly.
Premise 2: This is much higher than the percentage of friendly interactions in my old town.
Conclusion: My new town is friendlier than my old town.

Likewise, as you accumulate experiences of any kind that fall into a reliable pattern, you are making an inductive generalization from specific instances.

Generalization to Specific Case

We can also use the inductive generalizations we have accumulated evidence for in order to infer that some specific new claim, which falls under the generalization, is true.

Premise 1: People in my new town are friendly (inductive generalization or principle based on previous specific cases).
Premise 2: Ms. Smith lives in town.
Conclusion: Ms. Smith is probably friendly.

Specifics to a new specific case

Finally, induction can underlie an inference from one specific case to another, though technically this is just the result of applying an intermediate generalization and combining the first two types of inference. The pattern would be to infer a generalization from specific cases and then apply that generalization to a new specific case.

Analogies

If something utterly bewildering were to happen to you or if someone suggested a point of view to you that seemed, at first, obviously wrong, the first thing you would try to do to make sense of it or to defend your intuitions about the view you oppose would be to find points of resemblance between the new experience or view and something already familiar to you. You would seize on these resemblances and then see if you could understand the new experience by inferring more about its nature from the old. After all, if the carpet of our experience has a pattern, then maybe the points of comparison between two different areas of experience is a good basis for inferring additional similarities. In doing so, you would be making use of inductive analogical reasoning. The power of analogical reasoning in our experience is hard to overstate.

The search for resemblances in experience is perhaps the most important shared practice of poets, philosophers, and scientists, but it is equally valuable to us all in our everyday experience. Wordsworth looked for "hidden resemblances" between nature and the mind, scientists use resemblances between and among physical systems to both suggest new experiments and to help them conceptuahze the results of old ones, and philosophers use analogies to speculate about things beyond their experience. We will look at a famous philosophical analogy for the existence of God shortly, but first we need to learn a bit about what analogies are and how they work.

An analogy is a set of particular resemblances between two things that are otherwise dissimilar. If you have only one point of resemblance, you have a simile. If the resemblances are extensive, you have an allegory. Analogies are somewhere between similes and allegories. The most typical way to use them in reasoning is when you need to convince your audience that they should adopt a particular way of thinking about some issue (we will call it the "disputed case") because it is similar to some other issue about which they have a settled (presumably justified) way of thinking. We call the settled case the "analogue."

The schema for analogical argumentation looks like this:

Premise 1: The disputed case resembles the analogue in the following ways (X, Y, and Z).
Premise 2: We have justified beliefs about the analogue.
Conclusion: We are justified in having similar beliefs about the disputed case.

Using an analogy, someone might argue for the conclusion that "We ought to prevent the harms caused to women by pornography," by claiming that pornography harms women in an analogous way that civil rights violations harm people. The points of resemblance might be: 1) that a person's civil rights are violated when a stereotype is promulgated about them and, 2) in both cases people are harmed by discriminatory judgments made about them or are treated in a harmful manner on the basis of that stereotype and, finally, 3) in both cases, a person's potential and abilities are systematically underestimated by this distorted public perception. You might then say that since we have justified beliefs about the undisputed case (that we ought to protect people from civil rights violations), then we should have similar beliefs about the disputed case.

Analogies depend for their argumentative force on two underlying principles (or norms of rationality) about how to think about similarities. The first is the now familiar Principle of Induction: that nature has uniformities. The second is a claim that we ought to think about "like cases alike".

Our example above concerns a moral issue. In everyday discussions, perhaps that is the most common use of analogies -- to argue that because someone agrees that they should do X in siutation A, therefore they should do X in situation B. The primary ground for arguing for such an inference is a belief that situations A and B (whether they are "treatment of pornography" and "treatement of civil rights violations" or any other comparison) are similar in ways that are relevant to the decision.

But analogies are used in many other ways in reasoning, not all of which are argumentative. For example, you can use an analogy "heuristically" - as an aid to explicating, discovering or problem-solving. If I tell you that finding good ideas for papers is analogous to fishing (you have to be prepared, know where to look, relax,.. .etc.), I am probably less interested in arguing about it than just explicating my view about writing. Likewise, the famous extended analogy (an allegory, really) given by Plato in The Republic, the Allegory of the Cave, is a means of communicating a vision of the true relationship between an enhghtened person and his or her society. It is not really an argument, though it is clearly a view supported by his writings.

In scientific reasoning, we also rely on analogy. When we test drugs on animals, we are reasoning about effects from the similarities between their biological systems and our. Scientists frequently build models to explore hypotheses. For example, a population theorist might model natural selection in a computer program by establishing points of similarity between the behavior of the program and some population of organisms. We might measure the mutation rate, the reproductive rate, etc. and mimic it in the computer program. The scientists could then test hypotheses by means of an inductive inference between the two analogous systems.

It is important to realize that analogies do not depend upon extensive similarities. No one, least of all a scientist, would mistake a computer program for a population of bacteria or fruit flies. The key to judging an analogy (and responding to it) is to focus on relevant similarities and differences. The strength of the inductive inference from the analogue to the disputed case is directly proportional to the relevance of the features captured by the comparison. It will not do to draw an analogy between an individual's finances and a government's and then argue by analogy that just as individuals should not spend more than they earn, governments should not. While it sounds like a common sense comparison, most economists agree that there are too many differences between one type of budget and another to use the same principle for each. Good analogies do not just depend upon similarities in general, but upon "relevant similarities and differences."

To practice the skill of judging "relevant similarities and differences" consider the following analogy:

Maternity leave should be granted to employees with medical leave benefits because having a child is a medical event analogous to other medical conditions and family emergency situations are covered by health benefits. Delivering a baby is an extraordinarily complex medical event, with profound physical and emotional variables. Caring for a newborn requires the same complete attention as caring for a sick family member -- something leave benefits usually cover. Since employees with medical and family leave benefits do not usually lose their jobs if they become ill or care for ill family members, there is no good reason why prospective mothers should not expect to come back to work after having children.

Here the analogy between having a baby and medical illness is used as the basis of an inductive inference to the conclusion that we ought to allow maternity leave as a covered benefit, at least one which allows an employee to return to her job after having a child. The relevant similarities are spelled out. but notice that there are differences as well. You could argue that having a baby is a personal choice that you need to take responsibility for. Maybe having a baby is like taking up a very time consuming hobby -- an odd, but possibly persuasive counter analogy to the example. Of course, the maternity leave defender could argue that any number of personal choices are covered by medical leave, such as the consequences of smoking or not exercising. Interestingly, some people today are arguing that medical insurance plans should reflect the cost of these lifestyles choices, so that argument strategy might backfire. The analogy is debatable, but its strength depends upon the claim that sufficient and relevant reasons for allowing medical leave apply to maternity leave. Again, the underlying logic of the analogy is that we ought to think alike about like cases.

William Paley's Famous Analogy for the Existence of God

William Paley was a pre-evolutionary theologian who offerred an analogical argument for the existence of God which has become so famous that it is often referred to as "The Argument from Analogy for the Existence of God." The young Charles Darwin, when he was planning to become a parson, was very much taken by Paley's argument, but as we know, he came to doubt it later in light of his study of biology (some of which involved "analogies" among the morphologies of related species of animals). Paley's argument is far from extinct, however. It has been revived by latter day creationists, who refer to themselves as "design theorists." Before the publication of Origin of the Species, another naturahstically oriented thinker, David Hume, wrote Three Dialogues on Natural Religion, which contain criticisms of arguments like Paley's. Along with Paley's argument, which is quoted below, I have provided a paraphrase of Hume's criticism. Notice the use of analogies in both cases.

Paley, from Chapter One of Natural Theology.
In crossing a heath, suppose I pitched my foot against a stone and were asked how the stone came to be there, I might possibly answer that for anything I knew to the contrary it had lain there forever; nor would it. perhaps, be very easy to show the absurdity of this answer. But suppose I had found a watch upon the ground, and it should be inquired how the watch happened to be in that place, I should hardly think of the answer which I had before given, that for anything I knew the watch might have always been there. Yet why should not this answer serve for the watch as weU as for the stone? Why is it not as admissible in the second case as in the first? For this reason, and for no other, namely, that when we come to inspect the watch, we perceive - what we could not discover in the stone ~ that its several parts are framed and put together for a purpose, e.g. that they are so formed and adjusted as to produce motion, and that motion so regulated as to point out the hour of the day; that if the different parts had been differently shaped from what they are, of a different size from what they are, or placed after any other manner or in any other order than that in which they are placed, either no motion at all would have been carried on in the machine, or none which would have answered the use that is now served by it. . . . This mechanism being observed - it requires indeed an examination of the instrument, and perhaps some previous knowledge of the subject, to perceive and understand it; but being once, as we have said, observed and understood " the inference we think is inevitable, that the watch must have had a maker-that there must have existed, at some time and at some place or other, an artificer or artificers who formed it for the purpose which we find it actually to answer, who comprehended its construction and designed its use. (William Paley, Natural Theology, Chapter 1, page 1)

Paley considers a series of objections to this analogy between the watch and the watchmaker. For instance, he explains why the inference is no weaker because we had not seen the watch made. He also develops the analogy by imagining that we observe that the watch has the power to produce another watch from itself. This gives his analogy more credibihty by developing more points of comparison to living organisms. Through a long series of considerations he supports the original inference against many potential objections.

David Hume raises a number of objections to Paley's argument, however. In doing so, he demonstates some of the classic stratgies for responding to analogies. First he says (or has one of the characters in Three Dialogues Concerning Natural Religion say) that while we would infer the watchmaker from the watch, the universe is so much more vast and less available to our comprehension that we would only be making a guess to suppose that it is the product of a creator. He is saying, in effect, that the vastness of the universe is a relevant different between the analogy and analogue. Second, he offers his own analogy.

Now, if we survey the universe, so far as it falls under our knowledge, it bears a great resemblance to an animal or organized body, and seems actuated with a hke principle of hfe and motion. A continual circulation of matter in it produces no disorder: a continual waste in every part is incessantly repaired: the closest sympathy is perceived throughout the entire system: and each part or member, m performmg its proper offices, operates both to its own preservation and to that of the whole. The world, therefore, I infer, is an animal; and the Deity is the SOUL of the world, actuating it, and actuated by it. (" From the online edition of David Hume, Dialogues Concerning Natural Religion, p. 170 in the Kemp Smith edition. From http://www.anselm.edu/homepage/dbanach/dnr.htm.)

Hume uses other argument strategies as well, such as accepting Paley's premises and general conclusion but showing that they lead to other possibilities than Paley suggests. The universe may have its watchmaker God, Hume allows, but is this God perhaps just a technician, possibly a bad one? The argument might not lead to a God with the attributes wanted by those who advance the analogy. Also, as many people work on a watch, so the watchmaker might be a coUection of gods, but Paley's specific conclusion is that there is one God.

In your discussion of this and other analogies, you might reasonably come to the conclusion that the strength of the resemblance in an analogy depends not just on the points of similarity and difference, along with their relevance to the issue, but also on the overall difference between the two things compared. What makes everyday reasoning with analogies so useful is that we often find very close analogues to illuminate a disputed case. Part of Hume's objection, it seems, is that conjectures about the universe as a whole are pretty difficult to make from ordinary experience. While neither Hume nor Paley would have known it in their time, contemporary physics shows us that physical systems that are very, very small (quantum sized) and very, very large (galaxy and universe sized) both behave differently from the "medium sized" world we live in. So while heuristic analogies between the orbits of electrons and planets have been helpful at some stages of science, they may be deceptive if taken too literally.