Modal scope fallacy

A fallacy of necessity (fellacia necessitas)is a fallacy in the logic of a syllogism whereby a degree of unwarranted necessity is placed in the conclusion.

Example:

a) Bachelors are necessarily unmarried.

b) John is a bachelor.

Therefore, c) John cannot marry.

The condition a) appears to be a tautology and therefore true. The condition b) is a statement of fact about John which makes him subject to a); that is, b) declares John a bachelor, and a) states that all bachelors are unmarried.

Because c) presumes b) will always be the case, it is a fallacy of necessity. John, of course, is always free to stop being a bachelor, simply by getting married; if he does so, b) is no longer true and thus not subject to the tautology a). In this case, c) has unwarranted necessity by assuming, incorrectly, that John cannot stop being a bachelor. Formally speaking, this type of argument equivocates between the de dicto necessity of a) and the de re necessity of c). The argument is only valid if both a) and c) are construed de re. This, however, would undermine the argument, as a) is only a tautology de dicto--indeed, interpreted de re, it is false.

Another example of fallacy by necessity stated less formally:

"There are a lot of car accidents on this road. We must reduce the number of car accidents. There would be no car accidents if we closed the road. Therefore we must close this road." The necessity of reducing the number of car accidents is extended to imply the necessity of closing the road; clearly ignoring other plausible solutions to the problem of car accidents.