Well, according to De Morgan’s laws, ¬(A∨B) is indeed equivalent to ¬A∧¬B. So if P(¬(A∨B)) is high (because P(A∨B) is low), P(¬A∧¬B) is high. However, conjunctive arguments usually rely on an assumption of independence, while disjunctive arguments assume mutual exclusivity. I’m not sure whether these properties can be transformed into each other when switching between disjunctive and conjunctive arguments.
I’ve usually seen them both conditionalized, implicitly or explicitly.
The conjunctive argument is often presented something like “you need all of A,B,C,… . A is moderately likely, and even when A is true then B is moderately likely, and when … . But this means that the end result is not likely at all!”
Similarly for disjunctive: “Any of A,B,C… is sufficient. A is moderately likely, and even if A isn’t true then B is moderately likely, … . So the end result is very likely!”
Well, according to De Morgan’s laws, ¬(A∨B) is indeed equivalent to ¬A∧¬B. So if P(¬(A∨B)) is high (because P(A∨B) is low), P(¬A∧¬B) is high. However, conjunctive arguments usually rely on an assumption of independence, while disjunctive arguments assume mutual exclusivity. I’m not sure whether these properties can be transformed into each other when switching between disjunctive and conjunctive arguments.
I’ve usually seen them both conditionalized, implicitly or explicitly.
The conjunctive argument is often presented something like “you need all of A,B,C,… . A is moderately likely, and even when A is true then B is moderately likely, and when … . But this means that the end result is not likely at all!”
Similarly for disjunctive: “Any of A,B,C… is sufficient. A is moderately likely, and even if A isn’t true then B is moderately likely, … . So the end result is very likely!”