Valid Patterns Using Conditional Claims

Introduction
Conditional claims can act as the anchor of very powerful arguments. The following basic forms can become the basis of fairly elaborate arguments. Though the content of the claims can be very different, there are only a few basic patterns. We will use P, Q, and R to represent various independent clauses.

Conditional claims don't tell us anything about the actual presence or absence of the conditions. That's why we call them hypothetical. The following argument patterns make additional assertions that allow us to draw conclusions with certainty. It is the specific relationship between the assertions and clauses within the conditional claims that allow us to make such strong conclusions.

Modus Ponens

Modus ponens literally means "the mode of affirming."

If P, then Q. P. Therefore Q.

The symbolic form looks like this;

The first two lines are premises. The last line is the conclusion.

Example. If it is raining, then it is cloudy. It is raining. Therefore, it is cloudy.

How does it work? Recall that "sufficient" means "all that is required." So we know that the sufficient condition "it is raining" is all that is required to guarantee that "it is cloudy." And whenever "it is raining" it is necessary that "it is cloudy." Now what we are doing is making the definite assertion that indeed "it IS raining." Knowing that the sufficient condition actually is present allows us to draw the conclusion "It is cloudy" with certainty.

If you're looking outside right now and thinking, "Yeah, but it's not raining!" review validity.

It's called the mode of affirming because it affirms Q by affirming P.