An inductive argument is intended to provide only probable support for its conclusion, being considered strong if it succeeds in providing such support and weak if it does not. Inductive arguments come in several forms, including enumerative, statistical, analogical, and causal. In enumerative induction, we argue from premises about some members of a group to a generalization about the entire group. The entire group is called the target group; the observed members of the group, the sample; and the group characteristics we’re interested in, the relevant property.
An enumerative induction can fail to be strong by having a sample that’s too small or not representative. When we draw a conclusion about a target group based on an inadequate sample size, we’re said to commit the error of hasty generalization. Opinion polls are enumerative inductive arguments, or the basis of enumerative inductive arguments, and must be judged by the same general criteria used to judge any other enumerative induction. Statistical syllogisms begin with a statistical generalization about some group or category and reaches a conclusion about some specific member of that group or category.
We evaluate a statistical syllogism by examining: (1) whether the statistical generalization it begins with is well-founded, (2) the strength of the statistical claim (is it a near-universal generalization, or a weaker claim about ‘a majority’ of members of the group? ), and (3) whether the individual about which a conclusion is being reached is in fact likely to be typical of the group as a whole. In analogical induction, or argument by analogy, we reason that since two or more things are similar in several respects, they must be similar in some further respect.
We evaluate arguments by analogy according to several criteria: (1) the number of relevant similarities between things being compared, (2) the number of relevant dissimilarities, (3) the number of instances (or cases) of similarities or dissimilarities, and (4) the diversity among the cases. A causal argument is an inductive argument whose conclusion contains a causal claim. There are several inductive patterns of reasoning used to assess causal connections. These include the Method of Agreement, the Method of Difference, the Method of Agreement and Difference, and the Method of Concomitant Variation.
Errors in cause-and-effect reasoning are common. They include misidentifying relevant factors in a causal process, overlooking relevant factors, confusing cause with coincidence, confusing cause with temporal order, ignoring a common-causal factor, and mixing up cause and effect. Crucial to an understanding of cause-and-effect relationships are the notions of necessary and sufficient conditions. A necessary condition for the occurrence of an event is one without which the event cannot occur. A sufficient condition for the occurrence of an event is one that guarantees that the event occurs.