or in symbols:
P → Q ¬Q ∴ ¬P
or in settheoretic form:
("P is a subset of Q. x is not in Q. Therefore, x is not in P.")
The argument has two premises. The first premise is the conditional "ifthen" statement, namely that P implies Q. The second premise is that Q is false. From these two premises, it can be logically concluded that P must be false. (Why? If P were true, then Q would be true, by premise 1, but it isn't, by premise 2.)
Consider an example:
Another example:
Just suppose that the premises are both true. If Lizzy was the murderer, then she really must have owned an axe; and it is a fact that Lizzy does not own an axe. What follows? That she was not the murderer.
Suppose one wants to say: the first premise is false. If Lizzy was the murderer, then she would not necessarily have to have owned an axe; maybe she borrowed someone's. That might be a legitimate criticism of the argument, but notice that it does not mean the argument is invalid. An argument can be valid even though it has a false premise; one has to distinguish between validity and soundness.
See also: modus ponens, affirming the consequent, denying the antecedent..
Search Encyclopedia

Featured Article
