1. If p, then q.

2. p.

3. Therefore, q.

Modus ponens is deductively valid - given that both premises are true, the conclusion will always be true.

Now, consider the following argument form:

1. If p, then q.

2. q.

3. Therefore, p.

This argument form is called affirming the consequent. It is deductively invalid. Both premises can be true while the conclusion is simultaneously false. This often happens as the result of a failed attempt at modus ponens.

Here is a concrete example of affirming the consequent:

1. If a person is a Communist, then they are an atheist.

2. Bob is an atheist.

3. Therefore, Bob is a Communist.

This argument is deductively invalid, since it is possible that Bob is not a Communist even if both premises are true.

The preceding argument attempts to reason in modus ponens, as follows:

1. If a person is an atheist, then they are a Communist.

2. Bob is an atheist.

3. Therefore, Bob is a Communist.

This argument is deductively valid. However, premise 1 is false. Many atheists are not Communists. To know whether any given atheist is a Communist, particularly in the West where there are relatively few Communists, more information is needed.

The application of these lessons to CARM, and conservative Christian apologetics in general, is left as an exercise to the reader.