Logic Laws and Flaws

Christian thinkers yield and appeal to logic because it reflects God’s orderly nature. The apostle Paul, making his defense in chains before a Roman governor and a Jewish king, said, "I am not mad, most noble Festus, but speak words of truth and reason. For the king, before whom I also speak freely, knows these things; for I am convinced that none of these things escapes his attention, since this thing was not done in a corner" (Acts 26:25-26).

Logic has basically 3 laws that are foundational to all reason and thinking:

1.   The Law of Identity: A is A.  
   Example: God is God, not something else.

2.   The Law of Non-Contradiction: A is not non-A.  
   Example: God cannot be both personal (having mind, emotions, and will) and impersonal (not personal, like a force).

3.   The Law of the Excluded Middle: Either A or non-A.
   Example: God either exists or does not exist. There is no other alternative.

The basic laws of logic are neither arbitrary inventions of God, nor principles that exist completely outside God’s being. They are not exactly like the laws of nature. God may violate the laws of nature (for example, suspend gravity), but He cannot violate the laws of logic because those laws reflect God’s own nature. Indeed, some scholars think the beginning of John’s Gospel, "In the beginning was the Word (Greek, logos)" is best translated, "In the beginning was Logic (a divine, rational mind)." For example, even God cannot exist and not exist at the same time, and even God cannot validly believe that red is both a color and not a color. When people say that God need not behave logically, they are using the term in a loose sense to mean "the sensible thing from my point of view." Often God does not act in ways that people understand or would do in the same circumstances. But God never behaves illogically. He does not violate in His being or thoughts the fundamental laws of logic.

Summary of Logical Fallacies (Logic Flaws)  

1. Argumentum ad hominem = argument directed at a person rather than the idea being discussed. For example, a person saying: "How can anyone take Ronald Reagan seriously as a president? He was an actor!" It is foolish to evaluate any leader, past or present,  based only on a past occupation. Other factors need to be considered, such as character and achievements. Argumentum ad hominem is almost always against a person. Its logical opposite, Argumentum pro homine, speaks favorably of a person, but makes the same logical mistake. For example, "Ronald Reagan was such a fine actor, he must have been a wonderful president."

2. Argumentum ad ignorantiam = argument to ignorance or lack of proof so far. For example: "Lots of people have taken this drug and it has not hurt them!" Are you sure about that? Just because you do not know does not mean nothing has happened. You need more proof.

3. Argumentum ad logicam = argument to so-called logic, but what is actually invalid proof. For example: "Lots of people have taken this drug and the drug manufacturer’s study proves it is perfectly safe," neglecting to mention that the manufacturer is naturally biased in its own favor and did not conduct its study in an objective way, such as a double-blind study. Sound evidence from an impartial source is needed. 

4. Argumentum ad misericordiam = argument or appeal to pity only, ignoring other relevant facts. For example: "We must outlaw hunting so animals will not suffer!" What about hunters and their families suffering from hunger? 

5. Argumentum ad nauseam = argument to the point of nausea by repetition. For example: People who keep repeating, "But children need their milk!" every time they hear of even a grown child who does not drink milk regularly, no matter what you say—whether lactose intolerance or excessive calories or protein is an issue. Of course, it is not a fallacy to state the truth again and again; what is wrong is to expect repetition alone to substitute for logical proof. 

6. Argumentum ad numerum = argument or appeal to numbers only. For example: "This has to be right because so many people are doing it!" Oh really? Were the Nazis right because so many people voted for them? 

7. Argumentum ad populum = argument or appeal to  popular people. For example: "The coolest people like this so it must be good!" But what does cool really mean, who defines it, and who says that group of people is the ultimate authority? Sometimes bad people become popular. That doesn't make them good.

8. Argumentum ad verecundiam = argument or appeal to unsuitable authority. For example: "Socialism must be the best form of government because Albert Einstein said so!" Einstein was an authority on physics, not politics, but pride can tempt any authority figure to pontificate beyond what he or she should, and foolish hero worship can tempt the public to try to demand that their authorities pontificate like that. 

9. Broken Window fallacy = the fallacy that breaking windows, waging war, and other destructive acts actually benefit society by providing jobs for people repairing windows, making weapons, patching up war wounds and the like. But who wants to be the one having their window broken, their relatives slaughtered, or walking around with an artificial limb—if able to walk at all? Such a society would be parasitic and could not exist for long without producing something good worth producing. Going back to that broken window, the store owner who replaces it now is back to where he or she started before the vandalism. The money he could have spent on something to benefit the economy is now lost for that purpose.

10. Circulus in demonstrando (circular reasoning)/ Petitio principii (begging the question). For example: "I have a right to say what I want so you should not try to silence me." Here is the question begging to be proved rather than merely asserted:  Is having a right to X the same as other people having an obligation to allow you to have X? That is like saying X is true because X is true, but not saying why it is true. 

11. Complex question = a loaded question with a built-in assumption. For example: "Have you stopped beating your cat?" is valid only if the thing presumed true (cat beating) has been established. 

12. Cum hoc ergo propter hoc = "with this, therefore that follows" (Cum hoc for short)/mistaking correlation for causation. For example: "President Clinton had great economic policies; just look at how well the economy did when he was in office!" Perhaps that was because of the policies of the president before him. More proof is needed. 

13. Dicto simpliciter = "simple statement"/Sweeping generalization/Stereotyping. For example: "Teenagers are younger than adults and therefore do not have the maturity to make important decisions."  Teenagers are younger than adults by definition, but that does not mean they are incapable of making important decisions.  The biblical examples of Joseph, Daniel, and Mary the mother of Jesus show that they can. 

14. Equivocation = "to call by the same name" or to use a word that has different meanings but gloss over which meaning is intended. For example: "Women have no need to be afraid of man-eating sharks!" Yes, they do since "man" in that sentence means humans, not just males. C.S. Lewis in The Problem of Pain gives a serious example of the equivocation fallacy:  "'If God were good, He would wish to make His creatures perfectly happy, and if God were almighty He would be able to do what He wished. But the creatures are not happy. Therefore God lacks either the goodness, or power, or both.'  This is the problem of pain, in its simplest form. The possibility of answering it depends on showing that the terms 'good' and 'almighty', and perhaps also the term 'happy', are equivocal." 

15. False Analogy = inappropriate word picture or illustration. For example: "What is the big deal about the early American pioneers killing natives to settle the West? After all, you cannot make an omelet without breaking eggs." But making an omelet has nothing to do with killing and stealing!

16. False Dilemma =  making an either/or statement when there are other options. For example: "Either you buy a large car and watch it guzzle away your paycheck, or you buy a small car and risk being killed in an accident." Really? Are big cars that use lots of gas and dangerous little cars the only cars available? Take the time to find out what your options truly are.

17. False Equivalence = making an argument or claim in which two opposing arguments are made to be logically equivalent when in fact they are not. The confusion comes from one shared characteristic between two or more items of comparison in the argument that is way off in the order of magnitude, oversimplified, or just that important additional factors have been ignored. An apple and orange are both fruits, but it would be wrong to assert they are just the same. An oil stain and an oil spill both involve oil, but one is much more serious than the other.

18. Naturalistic fallacy = assuming nature or whatever is natural is always morally good; trying to bridge the is-ought gap. For example: "Because many species of animals have multiple mates, so should we humans!" Just because, in a fallen world, some species have multiple mates does not mean that humans ought to, especially since our Creator has clearly told us to be faithful for life to one’s husband or wife.  

19. Non sequitur = "it does not follow"/missing steps in the chain of reason. For example: "Thousands of people have seen lights in the night sky that they could not identify. The existence of life on other planets is fast becoming certainty!" The second sentence needs more proof than what the first sentence states. 

20. Post hoc ergo propter hoc = "after this, therefore that follows" (Post hoc for short)/assuming A led to B because A happened first. For example: "The Patriots always win when I put on my lucky red shirt before they play!" Twice in 10 years maybe, but do you really think the Patriots would always win if you always kept your red shirt on?

21. Red herring = a diversion, introducing emotional facts to distract from the issue at hand. For example: "It is claimed that welfare dependency leads to higher crime rates, but how are poor people supposed to keep a roof over their heads without our help?" It is important to help poor people with the necessities of life, but that does not refute the claim that welfare leads to crime. Not all red herrings are bad, however. Notice the red herring that rescued the apostle Paul from evil men who intended to kill him: "When Paul perceived that one part were Sadducees and the other Pharisees, he cried out before the Sanhedrin, 'Men and Brothers, I am a Pharisee, the son of a Pharisee; concerning the hope and resurrection of the dead I am being judged!' When he said this, an argument arose between the Pharisees and the Sadducees, and the assembly was divided. For Sadducees say that there is no resurrection—and no angel or spirit, but the Pharisees confess both" (Acts 23:6-8). Paul, at that point, was taken away by the Romans into protective custody. 

22. Slanting = saying something that is true, but in a misleading way for emotional effect. For example: "The government keeps pouring money into the defense industry" or "The government naturally spends some money on the defense industry." The first sounds extravagant and wasteful; the second sounds minimal. Precise language and numbers are required to make an intelligent evaluation of the issue at hand.

23. Slippery slope = saying one thing inevitably leads to another when it does not (but sometimes it does). A funny example of the slippery-slope fallacy is in the famous musical Music Man, where a con man tries to unload a bunch of musical instruments on an unsuspecting town by asserting, "Trouble, oh we got trouble, right here in River City!  With a capital T, that rhymes with P, and that stands for Pool (as in pool tables).  We gotta figure a way to keep the young ones moral after school!"  He cons the morality-conscious town into believing the only way to keep their teenagers from wasting their time on gaming after school is to get them all into a marching band! A serious example of a true slippery slope is how allowing one group of people to be treated in an inhumane way leads to inhumanity and suffering on a large scale. Think about these famous words from a repentant German pastor (visible in stone at the Boston Holocaust Memorial): "First the Nazis came for the Socialists, but I did not speak out because I was not a Socialist. Then they came for the Trade Unionists, but I did not speak out because I was not a Trade Unionist. Then they came for the Jews, but I did not speak out because I was not a Jew. And then they came for me, but there was no one left to speak for me." (Martin Niemoller spent 8 years in Nazi concentration camps.) 

24. Straw man = fallacy of presenting an extreme version of someone’s point rather than the actual point. For example: "Those Christians think Jesus is the only way, so they think the rest of us are wrong about everything!" Christians do believe Jesus is the only way of salvation from sin because He said so, and proved His claim in many ways, especially by rising from the dead. The Gospel is the Good News of God’s victory through Jesus Christ over Satan, sin, and death on behalf of His people. That should be the central issue of any Christian’s discussion with a non-Christian about Christ’s exclusivity. However, C.S. Lewis wisely observed in Mere Christianity: "If you are a Christian you do not have to believe that all the other religions are simply wrong all through.... When I was an atheist, I had to try to persuade myself that most of the human race have always been wrong about the question that mattered to them most; when I became a Christian I was able to take a more liberal view. But, of course, being a Christian does mean thinking that where Christianity differs from other religions, Christianity is right and they are wrong. As in arithmetic, there is only one right answer to a sum, and all other answers are wrong, but some...are... nearer being right than others." Be sure to represent people and issues accurately, and expect others to as well. 

25. Tu quoque = "you too"/excusing your flawed logic because you accuse your opponent of using the same flaw. For example: "Christians accuse us evolutionists of making unjustified assertions, but they assert a lot of things, too!" An error is still an error, regardless of who makes it. Do not focus on your opponents; focus on truth. Tu quoque is also known as whataboutism, which the Oxford English Dictionary defines as "the technique or practice of responding to an accusation or difficult question by making a counter-accusation," originating in the 1990s from the way counter-accusations often take the form of questions introduced by "What about—?"

Logic is an essential tool for the Christian to “speak the truth in love” (Ephesians 4:15) in a humble, respectful way (1 Peter 3:15).

PS. Teachers, it is very easy to make a quiz based on this material to test your students. Try multiple choice,  fill in the blank, true/false, essay, or a combination.