November 18, 2005

Inductive Reasoning Defined

Logicians divide logical reasoning into two categories: inductive and deductive. Inductive reasoning is based on generalizing from our existing knowledge or experience. David Kelley, The Art of Reasoning 453 (1998). The premises “of an inductive argument are not offered as conclusive evidence for the truth of their conclusions, but as evidence for the likelihood or reasonable probability of the conclusion’s truth.” Douglas Lind, Logic and Legal Reasoning 9 (2001). Inductive reasoning generally takes one of two forms, inductive generalization or reasoning by analogy. Id.

Inductive generalization involves drawing a general conclusion from a number of particular instances. Lind, supra at 15. The process of inductive generalization stems from science; scientists hypothesize certain outcomes and test them by repetition. Ruggero J. Aldisert, Logic for Lawyers: A Guide to Clear Legal Thinking 6-2 (1992). If the scientist observes something to be true in every instance in a test, then he can infer that is true in other instances as well. Id. Inductive generalization is therefore based on the concept of probability. A “conclusion reached by inductive reasoning is not considered a truth; rather, it is a proposition that is more probably true than not.” Id. at 6-6.

Inductive reasoning may also be based on analogy. Reasoning by analogy is based on the argument “that because the two examples are like in many ways they are also alike in one further specific way.” Anthony Weston, A Rulebook for Arguments 19 (3d ed. 2000). In other words, the advocate claims “that since some percentage of one or more things (the sample) possesses a property, an inference can be made that some similar thing or things (the target) are likely to have that property as well.” Lind, supra at 10. Analogies require a “relevantly similar example.” Weston, supra at 21. Analogical reasoning is used to determine whether precedent is controlling. See generally, Edward H. Levi, An Introduction to Legal Reasoning (1949). The “steps are these: similarity is seen between cases; next the rule of law inherent in the first case is announced; then the rule of law is made applicable to the second case.” Levi, supra at 2. It is also used in numerous other ways in legal reasoning.

Reasoning by enumeration (inductive generalization from enumerated examples) and reasoning by analogy are similar. But in reasoning by enumeration, the argument is based on reviewing numerous instances of the same thing. For example, an inductive generalization might be reached about the color of horses by examining many horses. If one million horses are 7 examined and none are white, one might conclude that horses are not white. In contract, reasoning by analogy involves comparing different things that have some similar attribute. One might, for example, analogize a donkey to a horse and conclude that if no donkeys are white, then no horses are white. These examples make clear that the outcome of inductive reasoning is not necessarily true as a matter of logic; much depends on the comparison, the sample, and the breadth of the conclusion.

Testing Inductive Logic

When analyzing an inductive argument, the advocate should first “[i]dentify the two things being compared (A and B) and the property (P) that is being attributed to B in the conclusion.” David Kelley, The Art of Reasoning 498 (3d ed. 1998). The advocate should then look for “the property (S) that is supposed to make A and B similar.” To assess the strength of an inductive generalization, consider the size of the sample relative to the size of the target. If the analysis is based on a complete set, then the conclusion will be strong. But if a complete set is not used for the analysis, the conclusion may be weak. The advocate must test the strength of the conclusion by examining the sample’s size and its representativeness. The advocate should also consider the strength and number of any counterexamples. Weston, supra at 10-18. In a search for counterexamples, look for prototypical cases, but also “referents close to the borderline of the concept, because many generalizations are true only of prototypical cases, not of atypical” ones. Kelley, supra at 458-459.

Evaluation of the strength of an analogy is based on similar considerations. The advocate should consider the size of the sample, the percentage of the sample that has the property, the similarities or positive resemblances, the relevance of the similarities or dissimilarities, the diversity within the sample, and the breadth of the conclusion. Lind, supra at 11-12. Analogies 8 “do not require that the example used as an analogy be exactly like the example in the conclusion.” Weston, supra at 21. Instead, the analogy requires “relevant similarities.” Thus, the advocate should analyze whether the analogy is based on relevant or irrelevant similarities.

Whether an argument is based on the fallacy of a false analogy is often subject to debate. The analogy may be rejected if the comparison is based on irrelevant or inconsequential similarities or ignores dissimilarities. Corbett & Connors, supra at 69. United States v. Leonard, 494 F.2d 955 (D.C. Cir. 1974) illustrates one such argument. A federal circuit court of appeals analogized paid informers and accomplices who give testimony against their cohorts to witnesses who are granted immunity. The comparison was based on the notion that all had an interest in testifying against another at trial beyond mere truth-telling. Id. quoted in Lind, supra at 98. But the Wisconsin Supreme Court later characterized the analogy as “questionable,” concluding that it lacked a “rational basis.” Linse v. State, 286 N.W.2d 554 (1980) in Lind, supra at 97-98. A Maryland appellate court’s attack on an analogy exemplifies another argument of this kind. In Conyers v. State, 691 A.2d 802 (1997), the appellant argued that the same rules should apply to in-court identification procedures as are applied to pre-trial identifications. The court called this a false analogy because the policy concerns raised by overly suggestive pre-trial identifications are absent in court where the identification is inherently suggestive since the defendant is always sitting at the trial table. Conyers, in Lind, supra at 102-103.

These examples illustrate both the rhetorical strength of analogies and some strategies to refute them. The advocate can explain why the point of comparison is not relevant. Or the advocate can point out that there is no empirical or logical basis for the conclusion that the comparison is based on factors that are the same in the relevant aspect. These strategies allow 9 the advocate to diminish the analogy’s force as an argument by laying bare the logic or lack thereof that forms the underpinnings for the comparison.

The fallacy of faulty generalization may also mar a conclusion based on inductive reasoning. Corbett & Connors, supra at 68-69. If a conclusion is based on inadequate evidence, then the generalization is faulty. The advocate should determine whether the evidence that has been used as the basis for the generalization is relevant, whether it is representative, and whether it is numerous enough to permit the conclusion. Id. at 68. To the extent that evidence in support of a generalization is based on accepting authority of some kind, the advocate should evaluate whether the authority is biased or prejudiced, incompetent, or outmoded. In addition, the advocate should check to see if the authority has been inaccurately quoted, misinterpreted, or quoted out of context. Id. Any of these can be a basis for undercutting the grounds for the generalization. Id.

Watch for Part 3 and Part 3 in future issues of Lorman Legal Update. To read Part 1 in this series please click here. This article was originally published in For the Defense.