Fallacies of Ambiguity

Fallacies of Ambiguity involve some confusion over meaning, specifically over the members referred to by a term used in the argument.

In a syllogism there are, of course, three terms that might be a source of confusion. However, on the principle that all arguments are valid (for their type), ambiguous arguments can best be understood as sorites - that is, as arguments with more than two premisses. Such arguments will have more than three terms. An unstated premiss asserts a (false) relation between the two meanings of the confused term. We can then break the sorites into a chain of syllogisms to locate the premiss that is the source of the error.

The Middle Term (i.e. the term shared by the two premisses) -

These fallacies of ambiguity appear as Deductive arguments, specifically the fallacies of Equivocation and (I believe) Amphiboly. For example:

"All beetles have six legs. John Lennon is a Beatle, so John Lennon has six legs."

We can render the above argument valid (but not sound) by adding the premiss "All Beatles are beetles." The two syllogisms that comprise the sorites are, then, "All beetles have six legs. (All Beatles are beetles). Hence, all Beatles have six legs," and "Since all Beatles have six legs, and John Lennon is a Beatle, it follows that John Lennon has six legs." The error appears in the Minor premiss, so it seems that Deductive ambiguities of this type can be classified as Errors of the Minor Premiss.

The Minor Term (i.e. the subject of the conclusion) -

These fallacies of ambiguity appear as Deductive arguments, specifically the two Distributive Fallacies, Composition and Division. For example:

"Slugs (as a group) are important to forest ecology, so slugs (as individuals) are something you must be careful not to step on."

This example has two missing premisses: "All things important to forest ecology are things you must be careful not to step on," which may be true; and, "All slugs (taken as a group) are slugs (taken individually)," which clearly isn't true. Once again, laying out the sorites in detail will reveal that the false missing premiss, appears as a Minor premiss, so these Deductive ambiguities can also be classified as Errors of the Minor Premiss.

The Major Term (i.e. the predicate of the conclusion) -

These fallacies of ambiguity appear as Inductive arguments, specifically the fallacy of Inappropriate Operational Definition. For example:

"Polish immigrants score poorly on the Stanford-Benet I.Q. test. Apparently Poles just aren't very bright."

Again, this example has two missing premisses. One premiss, "All Polish immigrants are Poles," tells us only that we are making an Inductive generalization from Polish imigrants, taken as a sample, to Poles in general, taken as a population. The premiss is obviously true. The other missing premiss is "All people who score poorly on the Stanford-Benet I.Q. test aren't very bright." is where the error occurs. Performance on the Stanford-Benet test is being taken as an operational measure of "brightness," and one that is known to be misleading and inaccurate in these sorts of cases. The problematic premiss is the Major premiss of the syllogism in which it appears, so, apparently, Inductive fallacies of ambiguity can be classified as Errors of the Major Premiss, similar to other Errors in Observation.

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