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Modal (Scope) Fallacy

(also known as: fallacy of modal logic, misconditionalization, fallacy of neccessity)

Description: Modal logic studies ways in which propositions can be true or false, the most common being necessity and possibility.  Some propositions are necessarily true/false, and others are possibly true/false.  In short, a modal fallacy involves making a formal argument invalid by confusing the scope of what is actually necessary or possible.

Example #1:

If Debbie and TJ have two sons and two daughters, then they must have at least one son.

Debbie and TJ have two sons and two daughters.

Therefore, Debbie and TJ must have at least one son.

Explanation: We are told that Debbie and TJ have two sons and two daughters, so logically, by necessity, they must have at least one son.  However, to say that Debbie and TJ must have at least one son, is to confuse the scope of the modal, or in this case, to take the contingent fact that applies to the specific case that is conditional upon Debbie and TJ having the two sons and two daughters, to the general hypothetical case where they don’t have to have any children.  Therefore, if they don’t have to have any children, then they certainly don’t have to (necessary fact) have at least one son.

Example #2:

If Barak is President, then he must be 35 years-old or older.

Explanation: Technically this is fallacious.  There is no condition in which someone necessarily is a certain age.  More accurately, we would say:

It must be the case that if Barak is President, then he is 35 or older.

The “must” in this second statement covers the whole condition, not just the age of the president.

References:

Curtis, G. N. (1993). The Concept of Logical Form. Indiana University.



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