Most people are capable of using logic. Most people, however, don’t know why or how the logic works, because they just use the language which evolved to include logical constructs. We have no problem understanding simple things like the statement “I will cut the grass and edge the sidewalk” is only really true if you both cut the grass and you edge the sidewalk, and that “I will cut the grass or I will edge the sidewalk” is fully true if just one of those things is done, and still true if you do both, and “If you cut the grass, I will edge the sidewalk” is not true if you only cut the grass unless I also edge the sidewalk. Now, I know the gears are turning for some of you. I have had folks argue over “inclusive or” versus “exclusive or” statements. My example was inclusive, but there can be an exclusive one like “you will cut the grass or I will take away your Xbox”, in which the assumption is that only one of them will be true and that if the statement was uttered with the other meaning, it would be misleading to say the least. Logic can get more difficult, however, if you lose track of meaning. For example, if I said “I did cut the grass, I cut it from the list of stuff I was going to do today”, the meaning of the word “cut” is different in that statement than what was implied earlier. Logic depends on truthful intentions to have the mathematical precision to determine what reasoning is sound. Misleading intentions can be used to twist statements that are logically consistent into arguments that are absurd. We have all been a victim of the “but you just said…” ploy in which this tactic is used to push the desired meaning over the stated meaning of some idea that presents an obstacle to what they want to believe. (e.g. “You just said you beat that woman you were racing against, so you admit you beat women!”) But there is a particular area of logic that is not obvious to a lot of people, and is used a lot by politicians who want to fool or scare people, and subsequently repeated by their base that makes up the echo chamber that reverberates the bad logic until repetition alone convinces them that the logic is sound.
The fallacy is called “affirming the consequent”, and it goes like this: “If you cut the grass, I will edge the sidewalk. I have already edged the sidewalk; therefore you must have cut the grass”. Pretty obviously a fallacy, right? What about this way: “If all illegal immigrants were criminals and rapists, someone will be raped by an illegal immigrant. In the news today, a woman was raped by an illegal immigrant. Clearly, Trump is right that all illegal immigrants are rapists”. The logical form of the “if…then…” statement is termed as follows: If [antecedent], then [consequent]. While the antecedents may lead to the consequents logically, the consequent has no such relationship with the antecedent. The relationship between the antecedent (if) and the consequent (then) is such that if the antecedent is true, the consequent must be true for the whole statement to be true, but the consequent may still be true even if the antecedent is false without affecting the truth of the statement. “If the temperature drops, it will rain” does not preclude rain without a temperature drop in order for the claim to be true, but it does preclude the possibility that the temperature does drop but it does not rain and have the statement still be a true statement. In other words, the if…then… construct is logically the same as “either [consequent] or not [antecedent]”, as in “either someone will be raped by an illegal immigrant, or not all illegal immigrants are rapists”. Perhaps an even simpler example of how the consequent is independent might be “if I am a mile tall, then 1+1=2”. In this one, the consequent is true whether the antecedent is true or not, which it is clearly not. By including the antecedent, I appear to be making the claim that the consequent depends on the antecedent, but as you can see, that would be a misleading claim. Even when the consequent clearly does follow from the antecedent (e.g.,if all men are mortal and Socrates is a man, then Socrates must be mortal), the consequent is not bound by the antecedent (Socrates could be mortal even if some men are immortal or Socrates is not a man, and the statement would still be valid, because if he were both, he must be mortal).
The fallacy of affirming the consequent is pervasive in the media and politics, because it makes the logically absurd sound reasonably logical for anybody who does not want to bother with considering if it is logical at all. Here are some examples I hear a lot.
If blacks are more likely to be criminals, then the prisons will have more blacks.
If all Muslims are out to destroy Americans, then we will catch groups of Muslims trying to do us harm.
If someone hates Christianity and all Christians, then they will oppose imposing Christian values on non-Christians
If someone loves and supports [insert enemy], then they will want to protect the rights of people we accuse of being in league with that enemy.
If people hate morality, they will oppose attempts to legislate morality.
If people are likely to be criminals themselves, then they will demand constitutional rights for the accused.
If someone made a lot of money by working hard, then they will be rich.
Take any of these perfectly good if…then statements and you can find examples of them being turned backward to form a false statement that is widely accepted as true by people who find it comforting to think it must be so (i.e., if they are rich, they earned the money; if they oppose government religion, they hate Christians, etc.). Hardly a day goes by in which I do not hear these very statements used to “prove” the fallacy. I have, in fact, been told that pointing out logical fallacies is “just liberal thinking”. I don’t deny being liberal, but “conservative” and “liberal” are values positions, not logical positions. The fact that someone might see logic as opposed to their values simply indicates that their values are not logically consistent. It is easier, for example to avoid living up to the burden of your values if you simply believe that you already have. So here are some alternates to satisfy the conservatives that I am not totally blind to problems of using this construct for liberal ends:
If hiring and promotion in an industry are biased against women, women will have lower average pay.
If hiring in an industry is biased against minorities, unemployment will be higher for that minority.
If most police are racists, more minorities will be harmed by police.
If your “religious” views were actually motivated by hate, you would cite religion when opposing changes to the status of others you do not agree with.
If you just want to shoot somebody, then you will own a gun.
As well as the value neutral:
If you are wrong, then I may be right.
To conclude, I want to again point out that this sermon is about how to catch bad arguments and not fall victim to them. If I was wrong in thinking that readers of this site are basically logical thinkers, some will assume that I actually agree with the implied arguments which I have identified as “fallacies”, which are arguments that sound to some like they are logical, when they are not. It is quite possible for some arguments that are fallacies happen to have true conclusions, but what makes them fallacies is that the logic was bad and does not justify the conclusion. For example, the argument “If the clock is working, then when I look at it at noon, it will display 12 o’clock; At noon, it displayed 12 o’clock, therefore the clock is working.” Is bad whether the clock works or not, because the truth of the conclusion was not guaranteed by the truth of the premises.