Chapter 12

1. Chapter 12 • CAUSAL REASONING

2. Chapter 12 • Inductive arguments are often based on more than analogy. • Frequently, they involve reasoning from effect to cause and from cause to effect. • The word “cause” can have various meanings. • Logicians distinguish between necessary and sufficient conditions for the occurrence of an event to underscore two of those meanings. • A necessary condition is something in whose absence an event cannot occur; a sufficient condition is a circumstance in whose presence an event must occur. • We can infer “necessary condition” from effect. We can infer effect from ‘‘sufficient condition.” • Another related sense of the word is a factor that is critical or crucial in the occurrence of some phenomenon. • There are two types of this sense of cause: remote causes and proximate causes. • When we speak of “root” causes, we are referring to remote causes.

3. Cause • To block a negative thing, “cause” means any necessary condition. Remove that cause and the thing doesn’t happen. To create a positive thing, “cause” means sufficient cause; all necessary conditions must be present. • Cause may also mean “increase the probability of” as in “smoking causes cancer.” • It may also mean the incident or action that, in the presence of normal conditions, triggers an event, as in the “cause” of a suspicious fire. This type of cause may be “proximate”as in “A causes B” or “remote”as in “A causes C; C causes D; D causes B.”

4. Chapter 12 • Every assertion that a particular circumstance was the cause of a phenomenon implies the existence of a causal law, a general truth about the way things work. • It is not deductive, however, and cannot be discovered by a priori reasoning: it can only be discovered through experience, a posteriori. • We say that A causes B after observing that whenever there is an A, there will be a B.

5. Chapter 12 • Inductive generalization is the process of arriving at universal propositions from the particular facts of experience. • If I hit a forehand at a sharp angle, winning the point, I could think that making the same shot will win another point (by analogy) or I could think that making such shots will always win points (by inductive generalization). • Unlike argument by analogy, the conclusion is not about one further event, but about all such events. Such general conclusions are called inductions by simple enumeration. • If some effect followed some cause repeatedly, we could infer that the effect will again follow the cause, by analogy. If we can enumerate a large number of instances where the same effect follows the cause, we can infer a causal law, but this inference must be tested. A single instance of the cause not followed by the effect will disprove the law. • Due to the similarity between these inductions and analogies, similar criteria for appraisal apply.

6. Chapter 12 • John Stuart Mill’s five “canons” represent a more powerful method of induction, not as limited as simple enumeration. • These five methods of inductive inference, though now very old, are still widely used: • 1. The Method of Agreement • 2. The Method of Difference • 3. The Joint Method of Agreement and Disagreement • 4. The Method of Residues • 5. The Method of Concomitant Variation

7. Mill’s Canon

8. Mill’s Canon • 1. The Method of Agreement - • Find the one cause common to all instances of a phenomenon. Not always easy. The absence of a cause is sufficient to disprove causality. The presence of a common cause suggests, but doesn't prove, causality. The common "cause" may in fact be an effect of the phenomenon. • 2. The Method of Difference - • Given some phenomena (contracting a disease) isolate a single difference (bitten by mosquito) that produces the phenomena. This is a powerful method. • 3. The Joint Method of Agreement and Difference - • Half the kids in Kiryas Joel were given a probable hepatitis A vaccine. They didn't get hepatitis. Many that did not get the vaccine did get hepatitis.

9. Mill’s Canon • 4. The Method of Residues - • The weight of the cargo is the weight of the laden truck minus the weight of the empty truck. Variations in the orbit of Uranus suggested the existence of Neptune. • 5. The Method of Concomitant Variation - • Two phenomena may vary directly (up or down together) or inversely (one up, the other down). Quantitative measurements are required to show concomitant variation. No inference possible on which P is causal. (High birth rates caused more storks.)

10. Chapter 12 • Though Mill believed that his methods could discover and prove causal relations, modern logicians believe that he was wrong. • Things cannot have only one circumstance in common, or every circumstance except one for that matter—and we cannot examine all possible circumstances to find out. • Mill’s formulations refer to the set of all relevant circumstances, but they give no clue as to how these are to be sorted out from the others. • Nevertheless, Mill’s methods are effective paths to discovery; and they are still central to science when used with causal hypotheses about the circumstances being investigated.

11. Chapter 12 • A. The Limitations of Mill’s Methods- • It takes much a priori knowledge to narrow down possible causes to a testable few. Successful testing can only determine with high probability (never with certainty) that a causal relationship exists. • B. The Power of Mill's Methods - • These are "profoundly important" as "instruments for testing hypotheses"—the subject of the next chapter.

12. Questions for Discussion • 1. What are some of the meanings of the word “cause” identified in this chapter? Come up with examples of each to demonstrate the differences between these senses. • 2. What is Induction by Simple Enumeration? What are its limitations? • 3. When is the Method of Agreement most effective? What are its most serious limitations? What other methods can we use to conduct a more refined search for causes? • 4. What distinguishes the Method of Residues from the other methods? • 5. Which method should we use when we cannot possibly eliminate the possible causes of a phenomenon? Why does this method work when others fail?