A Short Course

The Possible Worlds Method of Determining Validity

The possible worlds method uses the principle that an argument is deductive (and therefore valid) if it is logically impossible for its basic premises to be true and its conclusion false. If there is any conceivable situation where the premises are true and the conclusion is false, then the argument is not valid.

Using the possible worlds method one trys to find a logically possible world where the premises are true, but the conclusion is false. Such a world would be a counterexample and show the argument to be invalid.

Some arguments, like syllogisms, are inherently valid when constructed properly. It is important to keep in mind in these cases that the premises must be true to establish the truthfulness of the conclusion.

Some arguments are not valid, but the premises nevertheless do support the conclusion. If the premises are true these can be very strong arguments. The possible worlds method can be used to evaluate the strength of an invalid argument. If the conclusion is found to be true in most of the logically possible worlds, then the argument is inductive. The higher the ratio of the number of possible worlds where the conclusion is true to the number of possible worlds where the conclusion is false, the stronger the argument.

As an example of this method consider the following argument where the premises are all true and the conclusion is true, but the validity is in question.

P1 If an object floats on top of a liquid, then the object is less dense than the liquid.
P2 Oranges float in water.
C Orange peels are less dense than water.

A logically possible world could have oranges where the peels were more dense than water and the insides were much less dense than water. In this world both premises would still be true, but the conclusion would be false.

The argument is invalid, even though all of the statements are true.