Modal scope fallacy

Afallacy of necessityis afallacyin the logic of asyllogismwhereby 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 atautologyand 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 thetautologya). 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 thede dictonecessity of a) and thede renecessity of c). The argument is only valid if both a) and c) are construedde re.This, however, would undermine the argument, as a) is only a tautologyde dicto– indeed, interpretedde re,it is false.Using the formal symbolism inmodal logic,thede dictoexpression$\Box (Bx\rightarrow \neg Mx)$is a tautology, while thede reexpression$Bx\rightarrow \Box \neg Mx$is false.

See also

• De dictoandde re:Context of modality
• Modal logic

References

• Curtis, Gary N., "Modal Scope Fallacy",The Fallacy Files,retrieved22 October2014
• Bradley, Raymond;Swartz, Norman(1979), "Problems with the use of" it is necessary that "; the modal fallacy; absolute and relative necessity",Possible Worlds: An Introduction to Logic and Its Philosophy,Hackett Publishing Company, pp. 330–332,ISBN978-0-915144-60-0
• Swartz, Norman,More on "The" Modal Fallacy,retrieved22 October2014
• Franzén, Torkel,Eternal Questions: Free Will and Divine Omniscience,archived fromthe originalon 2007-07-08,retrieved22 October2014