Modal fallacy

The modal fallacy or modal scope fallacy is a type of formal fallacy that occurs in modal logic. It is the fallacy of placing a proposition in the wrong modal scope, most commonly confusing the scope of what is necessarily true. A statement is considered necessarily true if and only if it is impossible for the statement to be untrue and that there is no situation that would cause the statement to be false. Some philosophers further argue that a necessarily true statement must be true in all possible worlds.

In modal logic, a proposition

P

{\displaystyle P}

can be necessarily true or false (denoted

◻

P

{\displaystyle \Box P}

and

◻

¬

P

{\displaystyle \Box \lnot P}

, respectively), meaning that it is necessary that it is true or false; or it could be possibly true or false (denoted

⋄

P

{\displaystyle \diamond P}

and

⋄

¬

P

{\displaystyle \diamond \lnot P}

), meaning that it is true or false, but it is not logically necessary that it is so: its truth or falseness is contingent. The modal fallacy occurs when there is a confusion of the distinction between the two.

A fallacy of necessity is an informal fallacy in the logic of a syllogism whereby a degree of unwarranted necessity is placed in the conclusion.

Description

In modal logic, there is an important distinction between what is logically necessary to be true and what is true but not logically necessary to be so. One common form is replacing

p

→

q

{\displaystyle p\rightarrow q}

with

p

→

◻

q

{\displaystyle p\rightarrow \Box q}

. In the first statement,

q

{\displaystyle q}

is true given

p

{\displaystyle p}

but is not logically necessary to be so.