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.