Critical Thinking - a Simple and Concise Look 3

This post is one in a series on the book How to Think about Weird Things: Critical Thinking for a New Age by Theodore Shick, Jr. and Lewis Vaughn. (Fifth Edition)

Unless noted otherwise all quotes used in this series are from that book, usually with the page number noted in parenthesis.

The series should be read in order starting with the first post.

"INDUCTIVE ARGUMENTS

Even though inductive arguments are not valid, they can still give us good reasons for believing their conclusions provided that certain conditions are met." (Page 44)

"Using inadequate sample size to draw a conclusion about a target group is a common mistake, A fallacy called a hasty generalization." (Page 45)

"But how large a sample is large enough? Generally, the larger the sample, the more reliably it signifies the nature of the target group. But sometimes even small samples can be telling. One guiding principle is that the more homogenous a target group is in characteristics relevant to the property being studied, the smaller the sample needs to be. We would require, for example, a very small sample of mallard ducks to determine whether they all have bills, because the physical properties of ducks vary little throughout the species. But if we want to know the buying habits of Canadians, we would need to survey a much larger sample - hundreds or thousands of Canadians." (Page 46)

"People differ dramatically in their social or psychological properties, so surveying  a handful of them to generalize about thousands or millions is usually pointless.

Samples must not only be the right size, but also representative - that is, they must be like the target group in all the relevant ways. A sample that is not properly representative of the target group is known as a biased sample. Biased samples make weak arguments. To reliably generalize about the paranormal beliefs of New Yorkers, we should not have our sample consist entirely of members of the local occult club. The members' views on the paranormal are not likely to be representative of those of New Yorkers generally. To draw a trustworthy conclusion about water pollution in Lake X, we should not draw all the water samples from the part of the lake polluted by the factory. That area is not representative of the lake as a whole.

A sample is properly representative of the target group if it possesses the same relevant characteristics in the same proportions exhibited by the target group. A characteristic is relevant if it can affect the relevant property." (Page 46)   

"National polling organizations have perfected techniques for generating representative samples of large target groups - all American adults, for example. Because of modern sampling procedures, these samples can contain fewer than 2,000 individuals (representing about 200 million people). Such small representative samples are possible through random sampling. This technique is based on the fact that the best way to devise a genuinely representative sample is to select the sample from the target group randomly. Random selection is assured if every member of the target group has an equal chance of being chosen for the sample. Selecting sample members nonrandomly produces a biased sample." (Page 47)

"Analogical Induction

When we show how one thing is similar to another, we draw an analogy between them. When we claim that two things that are similar in some respects are similar in some further respect, we make an analogical induction. For example, before the various missions to Mars, NASA scientists may have argued as follows: The Earth has air, water, and life. Mars is like the Earth in that it has air and water. Therefore, it's probable that Mars has life. The form of such analogical inductions can be represented as follows:

Object A has properties F, G, H, etc., as well as the property Z.

Object B has properties F, G, H, etc.

Therefore, object B probably has property Z.

Like all inductive arguments, analogical inductions can only establish their conclusions with a certain degree of probability. The more similarities between the two objects, the more probable the conclusion." (Page 48)

The authors point out the dissimilar traits of Mars such as a thin atmosphere and very little water being available, trapped frozen at the poles. It is extremely unlikely that Mars supports life, especially complex life like human beings, at this time.

Others use analogical induction as well. In testing products on animals the argument is made that the products may have similar effects on humans.

The legal system similarly uses analogies of past cases and legal rulings, known as precedents. These often have tremendous influence on the decisions made by courts and judges. 

"Hypothetical Induction

(Abduction, or Inference to the Best Explanation)

We attempt to understand the world by constructing explanations of it. Not all explanations are equally good, however. So even though we may have arrived at an explanation of something, it doesn't mean that we're justified in believing it. If other explanations are better, then we're not justified in believing it.

Inference to the best explanation has the following form:

Phenomena p.

Hypothesis h explains p.

No other hypothesis explains p as well as h.

Therefore, it's probable that h is true.

The great American philosopher Charles Sanders Peirce was the first to codify this kind of inference, and he dubbed it abduction to distinguish it from other forms of induction.

Inference to the best explanation may be the most widely used form of inference. Doctors, auto mechanics, and detectives - as well as the rest of us - use it almost daily. Anyone who tries to figure out why something happened uses inference to the best explanation. Sherlock Holmes was a master of inference to the best explanation. Here's Holmes at work in A Study in Scarlet: 

I knew you came from Afghanistan. From long habit the train of thoughts ran so swiftly though my mind that I arrived at the conclusion without being conscious of intermediate steps. There were such steps, however. The train of reasoning ran, "Here is a gentleman of a medical ty, but with the air of a military man. Clearly an army doctor, then. He has just come from the tropics, for his face is dark, and that is not the natural tint of his skin, for his wrists are fair. He has undergone hardship and sickness, as his haggard face says clearly. His left arm has been injured. He holds it in a stiff and unnatural manner. Where in the tropics would an English army doctor have seen much hardship and got his arm wounded? Clearly in Afghanistan." The whole train of thought did not occupy a second. I then remarked that you came from Afghanistan, and you were astonished.

Although this passage appears in a chapter entitled "The Science of Deduction," Holmes is not using deduction here because the truth of the premises does not guarantee the truth of the conclusion. From the fact that Watson has a deep tan and a wounded arm, it doesn't necessarily follow that he has been in Afghanistan. He could have been in California and cut himself surfing. Properly speaking, Holmes is using abduction, or inference to the best explanation, because he arrives at his conclusion by citing a number of facts and coming up with the hypothesis that best explains them.

Often what makes inference to the best explanation difficult is not that no explanation can be found, but that too many explanations can be found. The trick is to identify which among all the possible explanations is the best. The goodness of an explanation is determined by the amount of understanding it produces, and the amount of understanding produced by an explanation is determined by how well it systematizes and unifies our knowledge. We begin to understand something when we see it as part of a pattern, and the more that pattern encompasses, the more understanding it produces. The extent to which a hypothesis systematizes and unifies our knowledge can be measured by various criteria of adequacy, such as simplicity, the number of assumptions made by a hypothesis; scope, the amount of diverse phenomena explained by the hypothesis; conservatism, how well the hypothesis fits with what we already know; and fruitfulness, the ability of a hypothesis to successfully predict novel phenomena. In chapter 6 we will see how these criteria are used to distinguish reasonable explanations from unreasonable ones. " (Page 49-50)

That is quite a bit on inductive arguments and abduction, but these are crucial points for understanding the entire model presented by the authors. They just can't be skipped.