Jiro comments on On Walmart, And Who Bears Responsibility For the Poor

[Jiro]

You are making a logic error: thinking that { not(A) is_not (B) } necessarily implies { (A) is (B) }

If A and B have truth values, then { not(A) is_not (B) } does necessarily imply { (A) is (B) }. (Although “democratic system of governance” does not have a truth value, “X is a democratic system of governance” does have a truth value.)

[nshepperd]

In the case of A and B being things like a “democratic system of governance” I think we’re more likely to be talking about set membership: “x∉A ⇒ x∉B” does not imply “x∈A ⇒ x∈B” (though it implies “x∈B ⇒ x∈A”)

[Lumifer]

If A and B have truth values

You mean if A and B are boolean values. In that case, yes, but that’s a special case not applicable here.