How To Argue: Inferring from Examples

The most important components of any informal arguments are the patterns of inference they make, the logical chain that connects the reasons, or evidence in the argument, to the conclusion, or claim.

Without this chain of inference, the vital justification for accepting the claims on the basis of the reasons, the argument fails to carry itself.

This post deals with reasoning from the basis of examples, and shall shortly deal with two sorts of inference from example, arguments from generalization and arguments from classification, and at this post can be noted both deductive and inductive forms of these.

Also to be discussed here are the various tests of these arguments that must be met for their validity, for this post deals with logical inferences which do not follow necessarily, and so must meet certain requirements of minimal strength and certain basic criteria of soundness, in order for them to carry with confidence, in going from here to there.

First are generalizations, which draw upon particular instances of something to make an overarching conclusion about the broad category those examples are said to belong to.

The argument in this case is made that what happens to be the case with the instances discussed is also true for the overall class of things named, relating the parts to the whole.

This is normally an inductive inference when we cannot completely account for every part of the whole, when the enumeration of the parts is not total. Were the accounting for these to be complete, the argument would follow deductively.

Unfortunately, this is usually not the case, so the justification for accepting the claims on the basis of the evidence is that the parts are representative of the entire category.

There are two sorts of generalization that we make:

First are statistical generalizations, in which we sample a portion of an entire population, and the inference here is that what’s the case with the sample taken is probably also true of the population in total.

There are tests we use to assess the validity of this inference, such as the typicality of the sample obtained, and its size in relation to the population as a whole. The more representative and the larger the sample, the better.

Then there are anecdotal generalizations, in which an overall statement about the complete set is made on the basis of a few specific cases noted.

For this sort, the tests we use are the number of examples, whether or not there are any notable counterexamples, and whether the anecdotal examples are truly typical of the category they are said to belong to.

Either of these must be tested, because the argument does not follow deductively, for the fallacy of composition, assuming a priori that the entire category is necessarily like the components that make it up.

The Hasty Generalization, reasoning one’s way to a premature conclusion on the basis of insufficient data, must also be avoided.

Next are inferences from classification, in which we attempt to draw a particular statement from a portion of a broad category of things, and here we argue that what is the case for the entire category is also the case for the instance under discussion.

To assume that this follows necessarily is to commit the fallacy of division, for we are arguing inductively under imperfect conditions, unlike those situations where the enumeration is complete, in which case the argument would follow with certainty, an uncommon occurrence indeed, since even simple enumeration can result in error when overcounting and undercounting happen, as is usually the case at least to some extent in conducting a census, election tally, poll, or survey.

Arguments from classification serve the purpose of making a statement more immediate and graspable, ‘hitting close to home’ for the audience, so to speak, the opposite purpose of an argument from generalization.

Finally, the tests we must apply to arguments from classification, in order to avoid the fallacy of division, is to ask ourselves if the instance cited is truly part of the general class, and to answer the question of whether or not it is atypical for the category it belongs to.

[Last Update: 2012/01/18 - Text Clarification; Meaning Unchanged]

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