Chapter Four, Tutorial Four
Validity and Logical Consistency in SL

In this chapter we will consider two concepts that involve sets of sentences.

Validity in SL

First consider the following argument (and carefully note the antecedent!):

Bob will attend law school if he scores well on the LSAT's.    (S>B)
As it turns out, he scores very well indeed on the LSAT's.    (S)
_________________________
He will attend law school.    (B)

It's pretty clear that this is an example of a valid argument. It has the right form.

Name that form!

 

But we can say more about being valid than just that it has the right form. Roughly the idea of validity is that the truth of the conclusion is inescapable given the premises.

But as usual, we gave the official definitions in terms of possibility. Let's try to recall, an argument is valid if and only if ______. If and only if what??? Select the correct way to fill in the blank:

  1. it is not possible for the conclusion to be false while the premises are all true.
  2. it is not possible for the premises to be false while the conclusion is true.
  3. It is not impossible for the premises to be true and the conclusion to be true.