Modal Scope Fallacy

A fallacy of necessity 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. Using the formal symbolism in modal logic, the ''de dicto'' expression $\Box (Bx\rightarrow\neg Mx)$ is a tautology, while the ''de re'' expression $Bx\rightarrow \Box\neg Mx$ is false.

See also

* ''De dicto'' and ''de re'': Context of modality
* Modal logic

References

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{{Formal Fallacy

Necessity
Necessity