Chapter One, Tutorial Four

Further Concepts for Deductive
Logic

Deductive logic is concerned with *more* than arguments and their validity
and soundness. This final tutorial for chapter one takes up further concepts
defined in terms of (logical) possibility.

We begin with a notion related to that of meaning: logical equivalence. Very roughly, the idea here is that two sentences are logically equivalent when they both express the same idea.

For example, the following two sentences say the same thing in different ways:

Neither Sandy nor Tim passed the exam.

Both Tim and Sandy failed the exam.

So, we will say they are logically equivalent; they express the same idea.

But, again, this rough definition is vague. We need something more precise. And as a first step towards this exactness, we define "logical equivalence" in terms of possibility.

Think about the Sandy and Tim example. These two sentences can be seen to
say the same thing because if one of the two is true, then the other must
also be true. (It's *inescapable* that one be false if the other is true!)
So, we can give a definition like that for validity in terms of what is possible
and not possible:

The two members of a pair of sentences are *logically equivalent*
if and only if it is not possible for one of the pair to be true while the
other is false.

Now, test this idea of logical equivalence. Which of the following sentences
is logically equivalent to

"**No student doesn't like
logic**"?

Click on the answer:

Correct!

Try one more. Which of the following is logically equivalent to "Beth
and Jerry did not *both* receive a diploma":

Yes! "It's not the case that both received a diploma" means "either just one received a diploma or neither did". Choice 1 is the way to say this.

One final point: We see from these examples one *benefit* of logic.
**We start to get very clear on meaning and thus practice at being very
precise in our thinking. **

Now, click below to continue this tutorial.