Inside logic #3

Conditionals

In the airport-kissing example, the first premise of your reasoning is a sentence containing the word "if."

Sentences using "if" in this way are called conditionals, where the "if" part is the antecedent and the "then" part is the consequent.

We will use the symbol > to represent conditionals, placing it between the antecedent and consequent:

he kisses her nicely > she is going to marry him.

We also will simplify by using capital letters to stand for simple statements. So let K stand for "he kisses her nicely" and M stand for "she is going to marry him". The conditional first premise then is represented by K> M. Using these abbreviations, we can say you reason from

and

to the

There are many other examples of reasoning that have the same "form" as your reasoning here. The symbolic representation is used to make the form clear and precise, enabling us easily to find common patterns in diverse examples. To see this, let us consider another story.

Suppose that as you sit at the airport you notice another couple sitting across from you. They are glum. It appears they have been arguing. Suddenly you hear the woman say angrily, "Well, then. If you will not confess, I'm leaving you." Wow. He must have done something awful. The man turns away from her, picks up a newspaper and pulls out the Sports section. The woman begins to gather her stuff. You think:

She's going to leave him!

*

Once again you have reasoned to a conclusion. Once again you have two premises:

If he will not confess, then she's going to leave him.

He will not confess.

To represent your reasoning in this terrible story, let the letter W stand for "he will not confess" and let L stand for "she is going to leave him". In this case you reason from

and

to the

As in the first story, your reasoning is valid: if the two premises are true, the conclusion must be true. (Of course the premises may not be true, as before, but nonetheless your reasoning is good based on the premises.)

There is a common pattern in your reasoning in the two stories. In each story, the premises consist of a conditional and the antecedent of the conditional:

the two premises in the reasoning about the kiss: K>M and K

the two premises about the woman leaving: W>L and W

And in each story, the conclusion is the consequent of the conditional first premise:

conclusion in the first story: M

conclusion in the second story: L

Notice the similarity in the pattern of reasoning in the two stories. We can say that your reasoning has the same form in the two examples.