The Art of the Reductio

While we'd all like to think we are prone to rational discourse, we nevertheless can be deceived into thinking that just because someone is smart, they are a careful thinker. As the example of Jesus, Paul, and parents everywhere shows---this is not necessarily the case.
The reductio ad absurdum is perhaps one of the most useful and important philosophical arguments. 
The Latin name given to the argument seeks to accurately describe it—that is, it means to “reduce to absurdity.” The point is easy to grasp, I think. 
An argument that is self-refuting is one that can be reduced to absurdity. This argument is a favorite among presuppositional apologists because the PA’s point is that non-Christian worldviews all reduce to absurdity. Although it’s tempting, I will refrain from spending too much time making that association here, but instead make a practical application to that end a bit later. 
So what’s an example of an argument that reduces to absurdity? Consider the following statement: All knowledge is derived from the use of the five senses.
But there’s a problem. The statement makes a knowledge claim which was not derived from the five senses! The claim is a philosophical one that reduces to absurdity because it cannot sustain its own burden. 
Since one could not know via the five senses that all knowledge derives from them, this claim is self-refuting and, therefore, absurd. 
Many don’t realize how this thinking has crept into everyday use. Consider the wayward child who wishes to follow his friends in a risky endeavor, despite knowing the potential consequences: “But everybody will be there!” he protests.
Mom and dad, in their wisdom, reply to the child: “Oh yeah, well if everybody jumped off a bridge, would you do that too?” The point is that if you follow the child’s thinking to its logical conclusion, it creates an absurd situation.
We see this kind of thing in popular New Atheist arguments. “Only the hard sciences provide truth.” Really? Is it true that only the hard sciences provide truth? If so, then the claim is false, because we did not apprehend that truth by using the hard sciences. 
The most common and potentially most recognizable is the post-modernists’ claim that there is no truth. But if it’s true that there is no truth, then it’s also true that there is truth—a glaring contradiction.
As you see, this can be a very powerful tactic, because a surprising number of arguments which seek to set themselves up against the knowledge of God fall into this trap.
Speaking of tactics…
Tactics
One of my favorite authors, Greg Koukl, calls this the “Taking the Roof Off” tactic in his book, Tactics. 
He provides a helpful illustration to set up the study:
If you were visiting Los Angeles and wanted to go to Santa Barbara up the coast, someone might draw a map to guide you to your destination. If, however, you followed the instructions very carefully and took the highway they suggested but found yourself in Riverside, on your way to the desert, you would know something was wrong with the route you were given. In a similar fashion, worldviews are like maps. They are someone’s idea of what the world is like. The individual ideas making up a worldview are like highways leading to different destinations. If you use the map but arrive at a strange destination, either part of the map is inaccurate (the part about the highway you were driving on), or the map itself is the wrong one for the region. I realize that this last option is not likely when you are talking about real maps. I doubt you would try to find your way around New York using a map of Chicago. But this kind of thing happens all the time with worldviews. Sometimes the roads are wrong on otherwise good worldview maps. At other times, worldview maps are inadequate for the actual terrain.1
He is making a grand point here. Many people make this simple mistake at the worldview level—a level which, as Koukl demonstrates below, can lead to undesirable social consequences.
Koukl explains a scenario in which Mother Teresa attempted to lobby for the forgiveness of a criminal. This demonstrates just how important the concept of the reductio is—it can have disastrous consequences in our thinking:
Mother Teresa once appealed to the governor of California to stay the execution of a vicious double murderer. She reasoned that since Jesus would forgive, the governor should forgive. Though the intentions were good, the argument itself proves too much, as our tactic demonstrates. When applied consistently, this view becomes a reason to forgo any punishment for any crime, because one could always argue, “Jesus would forgive.” Emptying every prison does not seem to be what Jesus would advise, since great evil would result. Capital punishment might be faulted on other grounds, but not on this one. Here is the analysis. Claim: If Jesus would forgive capital criminals, then it is wrong to execute them. Taking the Roof Off: On this reasoning, it would be wrong for government to punish any criminal, because one could always say, “Jesus would forgive.” This seems absurd, especially when Scripture states that the purpose of government is to punish evildoers, not forgive them.Therefore: Even though Jesus might forgive murderers, that does not mean it is wrong for the government to punish them.2
In a final example from Greg, it becomes clear that such arguments can literally lead to the difference in mentality between life and death:
Virtually every argument in favor of abortion could equally justify killing newborns if pressed to its logical conclusion. If it’s acceptable to take the life of an innocent human being on one side of the birth canal, why forbid it on the other side? A seven-inch journey cannot miraculously transform a “nonhuman tissue mass” into a valuable human being. When someone justifies abortion by saying, “Women have the right to choose,” use a version of Taking the Roof Off called Trotting Out the Toddler. Ask if a woman should have the right to kill her one-year-old child for the same reason. Since both an unborn child and a one-year-old are human beings, the same moral rule should apply to each. The logic of choice, privacy, and personal bodily rights endangers newborns, not just the unborn. At the University of New Mexico, a student said we should abort children to save them from future child abuse. Former Stand to Reason speaker Steve Wagner “trotted out the toddler” in response. “Should we also kill two-year-olds to save them from future child abuse?” “I hadn’t thought about that,” the student said. And that’s the point. People don’t think about the logical implications of their ideas. It’s our job to help them see where their ideas logically take them.3
A Monkey Wrench
I should point out one liability, here. Not everything that sounds contradictory actually is. In a few moments we’ll examine biblical examples of the reductio, some of which are employed by Jesus himself. 
However, Jesus also taught paradoxical truths. Paradoxes are often surface-level contradictions that are not logically fallacious when examined closely. Many proverbs are like this as well. They are designed to create tension in your thinking for the purpose of making you dig deeper and think harder. 
For example, when Jesus says, “He who is first shall be last,” he is saying something that is broadly logically contradictory. In an undefined sense, if someone is first, he cannot be last. 
However, Jesus’ point was that someone who takes all for himself now (a selfish person) will be placing themselves at the end of the line later. “They have their reward” and are therefore “last” in God’s kingdom. But someone who makes little of himself now for the good of others (a selfless person) will have a greater reward and will be “first” in God’s kingdom. 
What made me think of this point was actually the song I was listening to when finishing up the above section. The song is “Beautiful Terrible Cross” by Selah. The song is named this way, of course, intentionally. On the surface, we don’t normally think of beautiful things as being terrible. In our minds, these are logically contradictory ideas. 
Every line in the song is incredible, but this one in particular serves to make the point: 
Oh, we gained the riches of Heaven Jesus, You paid the horrible cost We stand forgiven and praise You For the beautiful terrible cross
The cross is beautiful because of what we gained; terrible because of what he had to give. The surprise engendered by the title requires us to think deeper about it. Again, it creates a sort of tension in our minds that will not let us rest until we understand what the writer means. In this way, even the title of a song has the potential to say more than some writers can say in an entire song. 
So paradoxes are useful and should not be considered contradictory.4
Biblical Examples 
Let’s have a look at a couple of biblical examples. 
Jesus was quite the philosopher, and often stopped the pharisaical religious leaders in their tracks running reductio ad absurdum arguments on them.
Consider the scene in Matthew 12:9-13. Jesus had just been in an altercation (vv. 1-8) with the Pharisees in which he also used a reductio, although it’s a harder one to spot. 
And when he was departed thence, he went into their synagogue: And, behold, there was a man which had his hand withered. And they asked him, saying, Is it lawful to heal on the sabbath days? that they might accuse him. And he said unto them, What man shall there be among you, that shall have one sheep, and if it fall into a pit on the sabbath day, will he not lay hold on it, and lift it out? How much then is a man better than a sheep? Wherefore it is lawful to do well on the sabbath days. Then saith he to the man, Stretch forth thine hand. And he stretched it forth; and it was restored whole, like as the other.
Here, Jesus takes the Pharisees to task by pointing out the absurdity in their view. On what grounds was Jesus going to heal on the Sabbath? This would apparently be unlawful! And yet, Jesus knew (and so did they) that they’d have no issue rescuing one of their own sheep if it had fallen into a pit on the Sabbath. 
Therefore, the Pharisees’ argument was absurd. 
The Apostle Paul was another sound thinker. He was trained in the halls of Judaisms finest and brought a wealth of knowledge into his discussions with the Grecians. 
One of the Apostle’s most famous encounters found him before the Areopagus in Acts 17. Here are vv. 22-31:
Then Paul stood in the midst of Mars’ hill, and said, Ye men of Athens, I perceive that in all things ye are too superstitious. For as I passed by, and beheld your devotions, I found an altar with this inscription, TO THE UNKNOWN GOD. Whom therefore ye ignorantly worship, him declare I unto you. God that made the world and all things therein, seeing that he is Lord of heaven and earth, dwelleth not in temples made with hands; Neither is worshipped with men’s hands, as though he needed any thing, seeing he giveth to all life, and breath, and all things; And hath made of one blood all nations of men for to dwell on all the face of the earth, and hath determined the times before appointed, and the bounds of their habitation; That they should seek the Lord, if haply they might feel after him, and find him, though he be not far from every one of us: For in him we live, and move, and have our being; as certain also of your own poets have said, For we are also his offspring. Forasmuch then as we are the offspring of God, we ought not to think that the Godhead is like unto gold, or silver, or stone, graven by art and man’s device. And the times of this ignorance God winked at; but now commandeth all men every where to repent: Because he hath appointed a day, in the which he will judge the world in righteousness by that man whom he hath ordained; whereof he hath given assurance unto all men, in that he hath raised him from the dead.
Paul makes a calculated move here. It appears subtle to us, but his audience would’ve immediately felt the force of his point. In vs. 28, he is quoting Epimenides and Aratus, Greek writers and philosophers who wrote these words for Zeus, not Yahweh. 
What is Paul’s point? Throughout the pericope above, Paul is essentially making the point that the Grecians have a contradictory worldview because they are borrowing from the God of the Bible. They worship manmade idols as if they have the power and attributes of Yahweh.
Paul declares the “unknown God” to them, who they’ve erected an altar for. His point is in line with his thinking in Romans 1:19-20. They worship the “unknown god” in ignorance. Yahweh is who they ought to worship, especially given that he gave all men assurance of his identity by raising from the dead (v. 31). 
In one swift move, he has reduced their entire worldview to absurdity by demonstrating that they direct worship toward a god who does not have the attributes required to produce the goods they worship him for.
As you can hopefully see, we should not dismiss carefully thinking about these ideas because they appear to be abstract. If Jesus and Paul used them in the public square with the philosophers and religious leaders of their day, why think we should not do the same? 
In a day where we have many “armchair philosophers,” we should be ready to respond with careful thinking.
Using it in Practice
In Tactics, Koukl provides a helpful grid for using this in real conversation. 
First, distill the idea down to its most basic principle or assertion. Do the work to make sure you understand the claim correctly. 
Second, he suggests giving the idea a “mental test drive.” Ask yourself:
If I follow this principle consistently, what are the consequences? What implications might it have for other issues? Does it take me somewhere that seems wrong, counterintuitive, or absurd? The answers to these questions may not be immediately obvious but often become clear later, after you have given the issue some thought.
Finally, point the problem out to your interlocutor. Allow her the time to think carefully and reflect on the problem for herself, and to the extent possible, help her understand that she will have to modify her thinking in some way to remain consistent. 
By employing the reductio ad absurdum, you join a long list of philosophers, careful thinkers, and concerned parents who all realize that ideas have consequences, and absurd ones should be exposed for their irrationality. 
Whether the issue is justifying juvenile disobedience or defending a woman’s “right” to “choose,” bad ideas must be exposed. The reductio is a tactic that is simple to employ and yet is the death knell to bad thinking. I would invite you to learn more about it and begin to use it in conversation with others.