Scope Fallacy

Taxonomy: Logical Fallacy > Informal Fallacy > Ambiguity > Amphiboly > Scope Fallacy

Subfallacies:

Quote…

[A]n adjective placed before two juxtaposed nouns is apparently the servant of either master. So "Fabulous Christmas Bargains" is taken to mean fabulous…bargains for Christmas, whereas "Continental Holiday Brochures" are brochures for continental holidays. It is no answer to say that commonsense will guide us to the right interpretation; bargains for a wonderful Christmas and continental leaflets for holidays are both real concepts. And what of the shop's apology based on "Temporary Assistant Shortage"?―is this a shortage of temporary assistants…or a temporary shortage of assistants (whether they are permanent or not)? It will be realised that this seemingly pithy form of expression is always technically open to two meanings, is sometimes actually so, and is occasionally bizarre….1

…Unquote

Example:

All that glitters is not gold.
This rock glitters.
Therefore, this rock is not gold.

Analysis

Exposition:

Logical terms such as "not" have a scope, that is, a part of the statement in which they occur that they affect logically. For example, "not" logically negates some part of the statement, or the statement taken as a whole, and this is its scope. Unfortunately, in natural languages such as English, the scope of a word such as "not" is frequently ambiguous.

In the artificial languages of logic, scope ambiguity is avoided by conventions for interpreting statements, and by introducing additional punctuation2 to indicate scope. Contrastingly, in natural languages, while there are various grammatical devices to indicate scope, ambiguity is still frequent. Often, natural language is disambiguated by common sense knowledge that we bring to our interpretations. For instance, in the Example, above, we automatically reject the meaning of "all that glitters is non-gold" for the first premiss because that would make it false―see the Analysis, below. Thus, scope ambiguity in natural language is often not obvious until pointed out, or exploited for humor.

Usually, scope ambiguity takes the form of a "broad" and "narrow" scope, as in the Example, where the broad scope often is the entire sentence, and the narrow scope is some smaller part of it. Since this is a type of structural ambiguity, and not equivocation on the meaning of words, scope ambiguity is a type of amphiboly.

The following types of logical and grammatical categories have scope, and are therefore liable to ambiguities of scope in natural languages:

Scope ambiguities, as ambiguities in general, are linguistic boobytraps which can cause people to fall into fallacy. Of all amphibolies, scope ambiguities seem to be those most likely to cause fallacious reasoning, especially in philosophical and pseudo-philosophical arguments.

Analysis of the Example:

The familiar saying "all that glitters is not gold" is amphibolous because the scope of the negation—"not"—is ambiguous. There are two possible scopes, and thus two possible interpretations of the saying:

  1. Narrow scope: "Not" negates the predicate "is gold", so that the saying is equivalent to: "All that glitters is non-gold." This is the most literal interpretation of the statement, since the negation actually occurs in the middle of the predicate: "is not gold". However, since gold does glitter, this interpretation makes the saying into a falsehood.
  2. Broad scope: "Not" negates the entire rest of the sentence, that is: "all that glitters is gold". In other words, the proposition is equivalent to: "Not all that glitters is gold." This, of course, is the correct interpretation, meaning that some things that glitter are non-gold, for instance, fool's gold. Or, in another cliché, don't judge a book by its cover.

The Example trades upon this ambiguity since, in order for the premiss to be true, the negation must have wide scope. However, in order for the argument to be valid, it must have narrow scope. Because it can't have broad and narrow scope at the same time, the Example is unsound: either it has a false premiss or the argument is invalid.

Imagine a prospector picking up a gold nugget and, recalling the famous saying, reasoning according to the argument in the Example. Seeing that the nugget glitters, he discards it as not being gold. The old saying, which is a logical boobytrap, has led him to throw away a gold nugget.

Notes:

  1. Basil Cottle, The Plight of English: Ambiguities, Cacophonies and Other Violations of Our Language (Arlington House, 1975), pp. 33-34.
  2. Usually parentheses.
  3. See the Quantifier-Shift subfallacy, above.
  4. See the Modal Scope subfallacy, above.