Validity and possible situations

Now, when we’re thinking about whether an argument is valid or not, it can help to think in terms of possible situations (ways things could have been or could have gone). In this step, we look at this strategy and note a crucial challenge we face in testing for validity.

Possible situations

Thinking about validity in terms of possible situation, we’d say:

• an argument is valid if and only if there is no possible situation in which all of the premises are true and the conclusion is false

The reason it can help to think in terms of possible situations is simple: if we can think of and describe a possible situation (a way things could be or a way things could have gone) in which the premises of a particular argument would be true and the conclusion false (what’s called a counterexample), then we can conclude that the argument is not valid (invalid). If we can’t think of such a situation, that gives us some reason to think the argument is valid.

A crucial challenge

Crucially, however, this test for validity isn’t conclusive. Finding a counterexample does show conclusively that an argument is not valid. But failing to find one—at least where we just apply our imaginations in looking for counterexamples in an unsystematic way—doesn’t always show beyond doubt that an argument is valid. The trouble is that we might just have overlooked a counterexample that’s there to be found. We’ll find a solution to this particular important problem later in the course.

A quick note on possibility: When you think about whether there is a possible situation in which premises are true and conclusion false, you should allow in even remote possibilities. What we’re interested in is logical possibility, which in this context means anything that is possible, with the only restriction being that we keep the meanings of the words in the sentences we’re looking at constant. Considering this wide range of possibilities means that we’re setting the standard for validity very high, and if we find arguments that are valid we can have a very high level of confidence in them.

(If you’d like to find out more about kinds of possibility, take a look at the additional material linked below. Note that this is optional content, and you don’t need to cover it to follow the main thread of the course.)