A logical argument by analogy analysis

 

Similarity in several respects between discrete cases. A logical argument by analogy relies upon an inductive inference from the supposition that things are similar is certain known respects to the likelihood that they are also similar in some further unknown respect. Example: “Jennifer enjoys listening to the music of Beethoven, Mahler, and Bartok. Susan and Harold also like Beethoven, Mahler, and Bartok. Chris enjoys listening to Beethoven and Mahler. Therefore, Chris would probably like the music of Bartok, too.” The degree of reliability achieved by such an argument depends upon the extent and nature of the similarities that hold between the instances in its premises and the new case in its conclusion. Also see DPM, Keith J. Holyoak and Paul Thagard, Allison Barnes and Paul Thagard, and Amélie Frost Benedikt. Analogical reasoning simplest variety of inductive reasoning is argument by analogy, which takes note of the fact that two or more things are similar in some respects and concludes that they are probably also similar in some further respect. Not every analogy is an argument; we frequently use such comparisons simply to explain or illustrate what we mean. But arguments by analogy are common, too. Suppose, for example, that I am thinking about buying a new car. I’m very likely to speak with other people who have recently bought new cars, noting their experiences with various makes, models, and dealers. If I discover that three of my friends have recently bought Geo Prizms from Burg and that all three have been delighted with their purchases, then I will conclude by analogy that if I buy a Geo Prizm from Burg, I will be delighted, too. Evaluating Analogies Of course, this argument is not deductively valid; it is always possible that my new car may turn out to be an exception. But there are several considerations that clearly matter in determining the relative strength or weakness of my inductive inference:

1. Number of instances. If five friends instead of three report their satisfaction with the model I intend to buy, that tends to make it even more likely that I will be satisfied, too. In general, more instances strengthen an analogy; fewer weaken it.
2. Instance variety. If my three friends bought their Prizms from three different dealers but were all delighted, then my conclusion is somewhat more likely to be true, no matter where I decide to buy mine. In general, the more variety there is among the instances, the stronger the analogical argument becomes.
3. Number of similarities. If my new purchase is not only the same make and model from the same dealer but also has the same engine, then my conclusion is more likely to be true. In general, the more similarities there are between the instances and my conclusion, the better for the analogical argument.
4. Relevance. Of course, the criteria we’re considering apply only if the matters with which they are concerned are relevant to the argument. Ordinarily, for example, we would assume that the day of the week on which a car was purchased is irrelevant to a buyer’s satisfaction with it. But relevance is not something about which we can be terribly precise; it is always possible in principle to tell a story in the context of which anything may turn out to be relevant. So we just have to use our best judgment in deciding whether or not some respect deserves to be considered.
5. Number of dissimilarities. If my friends all bought Geos with automatic transmissions and I plan to buy a Geo with a standard transmission, then the conclusion that I will be delighted with my purchase is a little less likely to be true. In general, the fewer dissimilarities between instances and conclusion, the better an analogical argument is.
6. Modesty of conclusion. If all three of my friends were delighted with their auto purchases but I conclude only that I will be satisfied with mine, then this relatively modest conclusion is more likely to be true. In general, arguments by analogy are improved when their conclusions are modest with respect to their premises. ©1997, 1998, 1999 Garth Kemerling. Questions, comments, and suggestions may be sent to: [email protected].com Inductive Inferences When an argument claims merely that the truth of its premises make it likely or probable that its conclusion is also true, it is said to involve an inductive inference. The standard of correctness for inductive reasoning is much more flexible. An inductive argument succeeds if its premises provide some legitimate evidence or support for the truth of its conclusion. Although it is therefore reasonable to accept the truth of that conclusion, it would not be completely inconsistent to withhold judgment or even to deny it. Inductive arguments, then, may meet their standard to a greater or to a lesser degree, depending upon the amount of support they supply. No inductive argument is absolutely perfect or entirely useless, although one may be said to be relatively better or worse than another in the sense that it recommends its conclusion with a higher or lower degree of probability. In such cases, relevant additional information often affects the reliability of an inductive argument by providing other evidence of the likelihood of the conclusion. It should be possible to differentiate arguments of these two sorts with some accuracy already. Remember that deductive arguments claim to guarantee their conclusions, while inductive arguments merely recommend theirs. Or ask yourself whether the introduction of any additional information, without changing or denying any of the premises, could make the conclusion seem more or less likely; if so, the pattern of reasoning is inductive. Truth and Validity Since deductive reasoning requires such a strong relationship between premises and conclusion, we will spend the majority of this survey studying various patterns of deductive inference. It is therefore worthwhile to consider the standard of correctness for deductive arguments in some detail. A deductive argument is valid when the inference from premises to conclusion is perfect: If the premises of a valid argument are true, then its conclusion must also be true. It is impossible for the conclusion of a valid argument to be false while its premises are true. (Considering the premises as a set of propositions, we will say that the premises are true only when each and every one of those propositions is true.) Any deductive argument that is not valid is invalid: it is possible for its conclusion to be false while its premises are true, so even if the premises are true, the conclusion may be either true or false. Notice that the validity of the inference of a deductive argument is independent of the truth of its premises; both conditions must be met in order to be sure of the truth of the conclusion. Out of eight distinct possible combinations here, only one is ruled out: Premises Inference Conclusion True Valid True XXXX Invalid True False Valid True False Invalid True False The only thing that cannot happen is for a deductive argument to have true premises and a valid inference but a false conclusion. Some logicians designate the combination of true premises and a valid inference as a sound argument; it is a piece of reasoning whose conclusion must be true. The trouble with every other case, in which either one of the premises is false or the inference is invalid or both, is that it gets us nowhere. The conclusions of such arguments may be either true or false, so they are entirely useless in any effort to gain new information.

 

 

 

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