Reflections: In this chapter, we will focus on the three major kinds of inductive arguments. We will first examine arguments based on analogy. We will then turn to cause-and-effect reasoning. Finally, we will look at statistical reasoning and learn how to assess two common forms, the statistical syllogism and the inductive generalization. These can be very persuasive methods of argument--the use of an analogy, for example, can be transformative.

Goals: My goals here are to help you acquire the tools to tackle the three most powerful forms of inductive reasoning. Since these are so powerful, it is easy for us to fall under the sway of any of these arguments. Being able to stand back and assess these forms of inductive reasoning can not only be important for your personal life--it can also be instrumental on a societal level and in helping others. We look at three forms: first, analogies; secondly, cause and effect reasoning; and, thirdly, statistical syllogisms and inductive generalizations.

The Big 3 of Induction:

Analogies, Causal Reasoning, and Statistical Arguments

Arguments from Analogy
Arguments based on an analogy are one of the most important kinds of inductive reasoning. Analogies can be found everywhere from politics to religion, and in all aspects of our lives. An analogy consists of a comparison between two things in which, on the basis of certain similarities, a principle or characteristic of the one term is then applied to the other term and asserted as true in that case as well. In law these take the form of precedents (previous cases decided by a court of law or made into law by a legislature

Form of an Argument from Analogy

A is like B in terms of characteristics p, q, r.
A also has characteristic "z."
So, B has characteristic "z" also.

Assessing an Analogy
If you allow the analogy off the ground, the argument is generally successful. If, however, the weight of the differences of the two terms is greater than that of the similarities, the analogy falters. That is, the argument is not as powerful if the differences outweigh the similarities. Every time you see an analogy you should ask, "What are the similarities? What are the differences?"

The Fallacy of False Analogy
Occasionally someone sets out a false analogy. This is a fallacy in which two terms are being compared for the purpose of making an inference resting on that comparison--and yet there are no real similarities at all, other than trivial ones.

Steps to Analyzing an Analogy

1. Clarify the terms of comparison. Note exactly what is being compared to what.
2. Write it out like an equation setting out the comparison.
3. State the principle or characteristic attributed to the one term that is being applied to the other term.
4. List the similarities.
5. List the differences.
6. Survey the two lists. Add any omissions to your lists.
7. Weigh similarities and differences.
8. Assess the Analogy.

Assessing the Use of an Analogy: Structuring the Analysis

1. What is at issue? What principle or conclusion is being drawn from the analogy?
2. Exactly what is being compared? Set out the terms of the analogy.
3. What are the relevant similarities and differences? List them both.
4. Critically examine the lists, weighing them to see the strength of each side (similarities and differences).
5. How would you attack the analogy? (What are its weaknesses?)
6. How would you defend the analogy? (What are its strengths?)
7. If this is an analogy you intend to use, see if you can modify it to minimize weaknesses and boost strengths.
8. If this is an analogy you are evaluating, make note of the relative strengths and weaknesses and decide if the analogy is successful--or if it's a detriment.
9. Remember: Similarities make the analogy and differences break the analogy.
10. You are now are in a position to question whether the conclusion (the principle being drawn) can be said to follow with credible support.

Analogies and Hypothetical Reasoning in the Law
In order to help prepare a student for the practice of law, one teaching technique is to use a hypothetical case (alias Hypo). In hypothetical law cases, a scenario or story is presented, with the task of deciding how it is to be evaluated given the existing laws and precedents

Legal Precedents
One of the most powerful uses of analogies is in the law. The use of a precedent can have a definitive effect on an argument, positively or negatively.

Potential Legal Precedent:

1. Research. Study the case being litigated. Seek out the details of the case and determine what legal alternatives exist.
2. Examine Potential Precedents. Find cases that are similar. Find potential precedents that: (a) have strong similarities to show applicability and, (b) have rulings favorable or useful to the current case.
3. Show the Analogy Holds. Show strength of similarities merit the application of the principle from the precedent to the present case. The lawyer can then assert that this new case warrants the same decision.

Cause-and-Effect Reasoning
The second major kind of inductive argument is cause-and-effect reasoning. in causal reasoning. Cause and effect arguments present us with probability, not certainty. It is claimed that the stated condition will result in a particular effect. How likely it is becomes the issue.

False Correlations
Sometimes people draw causal connections between events that are unrelated. We see it in post hoc reasoning where an inference is drawn that something causes another thing to happen just because it happened at an earlier time. Of course, the fact that one thing precedes another does not necessarily mean they are related. To think they are is to draw a false correlation. To assert such a relationship requires more evidence than the temporal sequence of when the two events happened. Rather, we need to show that there are causal--not just temporal--links between them.

Arguments Based on Statistical Studies. Three key aspects:

Date	⇒	What is the date of the study?
		Is it still relevant?
Size	⇒	How big was the sample group?
Diversity	⇒	How diverse is the sample population? Is it representative of the target population?

Two Major Ways to get Sufficient Diversity in A Sample Study

1. Representative Sample. A representative sample is obtained by trying to match the sample group with the target population. Try to keep a balance of the major aspects to consider (like gender, age, race, religion, education, class, geography).

2. Random sample. A random sample is not obtained by carefully orchestrating a sample group taking into account the relevant factors (like age, gender, nationality, class). In a random sample, each member of the target population has an equal chance of being studied.

Fallacious Use of Statistics

• Hasty Generalization → If the size is simply too small, a generalization from it could result in the fallacy of Hasty Generalization.
• Biased Statistics → If the size is sufficient, a random sample will likely result in a sample representative of the target population.

Confronting Problems in Statistical Studies
When the study is in doubt, basically we have these choices: (1) throw it out (in the event of serious concerns) or (2) examine the study's margin of error. Every study contains a margin of error. Because the inference from the sample study to the target population contains a wedge of doubt, this ought to be reflected in the conclusion. That is, instead of going from x% of the sampled group to x% of the target population, a margin of error should be added to the conclusion. This would mean that your conclusion would change to "x plus or minus z% of As are Bs," (where z is some little number, usually 5 or lower).

The smaller the margin of error z, the better. Remember the margin of error means the range goes from -z% to +z%, which is a range of 2z. This means if your margin of error is 3%, then the range is 6% and a margin of error of 5% will give a range of 10%, which is significant range. For example, 32% plus or minus 5% means the range goes from 27% to 37% -- a range of ten percentage points!

Two Forms Of Statistical Arguments
There are two prevalent forms of statistical arguments: (1) statistical syllogisms and (2) inductive generalizations.

Form of a statistical syllogism

x% of A is a B.
p is an A.
Therefore, p is a B.

The second major kind of statistical reasoning is called an inductive generalization.

Form of an inductive generalization

x% of A's polled (or sampled) are Bs.
Therefore, x% of all As are Bs.

In a strong Inductive Generalization, watch for date, size and diversity. Be sure the poll is recent, the size not too small, and the sample group representative of the target population. The issue of diversity (that the sample represents the larger group) is crucial.