Modus tollens is a way of arguing in formal logic that focuses on denying the consequent in syllogisms. A formal example follows: If p, then q. Not-q. Therefore, not-p. Some people have either misunderstood or deny the validity of the argument from this abstract example alone, so I will provide a specific example from Christian apologetics:
1. If naturalism is true, then persons do not think about anything.
2. Persons do think about some things.
3. Therefore, naturalism is false.
In this example, p represents “naturalism is true,” and q represents “persons do not think about anything.” Since denying q is, literally, “not-persons do not think about anything,” we must introduce the concept of logical equivalence. If it is not the case that persons do not think about anything, it is the case that persons do think about some things! Of course, the conclusion then follows. The reason the logic works is because since we accept (1), we know that persons wouldn’t be thinking about anything if naturalism were true. However, since persons are thinking about some things, it cannot be the case that naturalism is true (since if it were true, well, you get the idea).
MT is particularly confusing when negatives are involved (because then we have introduced double negatives). I once had an argument criticized strongly because nothing follows by affirming the consequent. He was right, of course, in that nothing follows by affirming a consequent. But I denied the consequent. Here is an example:
1. If God does not exist, objective moral values do not exist.
2. Objective moral values do exist.
3. Therefore, God exists.
His mistake was in thinking (2) being “positive” entailed an affirmation of the consequent. A careful reading of the form, however, shows that q would be “objective moral values do not exist.” Not-q, then, would literally be “not-objective moral values do not exist,” or in language, “it is not the case that objective moral values do not exist.” In logical equivalence, then, it would be (2). But as we have seen, that is simply denying the consequent, or MT!
The application for Christian apologetics is to be very familiar with basic forms of logical thought, interpret the major premise correctly, and apply logical equivalence to the discussion. It is only with this full understanding of an argument that one can critique it.