On Affirming the Consequent

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.



About UncleJoe

I'm a middle aged male who has attended a seminary as well as receiving a degree in philosophy from a secular university neither of which would particularly impress you if I said which. I have pondered and puzzled questions of faith and the lack thereof for many years. I don't not claim to be holy, or an expert on everything, simply observant and interested. I'll make bold statements about what I see as the way things are, and you don't have to take my word for it. Call me on it. I am here for the discussion.
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4 Responses to On Affirming the Consequent

  1. vapidatious vapidatious says:

    Sitting here on my antecedent, reading this has given me a pounding consequent! Why is it that geniuses can take, what is to me, the simplest ideas and complicate the hell out of them? It probably has something to do with the fact that they are smart. Trust me, that is a compliment. I am green with envy. However, that doesn’t help the fact that just about every word of this sermon went shooting right over my head! I am fascinated though that the thinker in my noodle immediately began deconstructing the text and breaking it down to something A little more simple that I can more easily understand. With just a little effort, a couple of bloodshot eyeballs and a teensy migraine, it all came into focus and i understood it completely. Also i have to agree. Although, I would have said, “folks tend to believe what they want to believe in order to make it alright to believe in what they want. And, you damn well better believe it too!”
    Am I completely wrong UncleJoe?

  2. UncleJoe UncleJoe says:

    You are not wrong, but there is more to it. There are mental games that make someone feel like they have discovered a fundamental truth they can then defer to instead of thinking something through. If they depended on a fallacy of logic to arrive at their new belief, then it is a problematic belief.
    Were the examples of what it looks like clear enough to spot the pattern?

  3. vapidatious vapidatious says:

    To answer your question; Yes the pattern is clear enough to spot. Of course, for me, I had to read it 3 times to understand it. But, now that I do, I am going to have to argue the degree to which people arrive at a belief based on faulty logic. I have always been bothered by the extreme number of people who seem to be incapable of understanding consequent. The number of people I have spoken with in my entire life who think problems through can be counted on both of my hands and feet. Most either can not, or will not, measure the degree to which their actions will effect the future. As an example: almost everyone I spoke to on the topic of Iraq were absolutely certain that WE needed to go in and remove Saddam Hussein from power. No matter the argument I made, or questions I asked, their minds were made up. “Really, you think they actually have weapons of mass destruction? You believe that we are the right country to go into a Muslim nation and set up a democracy? You aren’t concerned that it will turn into another Vietnam? Don’t you think there are at least 10 other important global problems that we should be attending to before worrying about this?” Asking these questions and making arguments that Iraq could most certainly wait only made their eyes glaze over!

    In the realm of politics, the lack of concern about where an individuals ideals will lead the whole of a free nation and world are almost non-existent! It is so frustrating that I quit discussing politics years ago. Even among like minded people, that utter lack of foresight is inescapable. This is not to say that all political arguments fall within the antecedent/consequent, but most do. Another example? Okay, as long as you are asking. I was having dinner with friends. When dinner was over I got up to stretch my legs and about 5 minutes later one of my friends came out to join me. She told me that a political debate had broken out and was getting very passionate and heated. I told her that I quit discussing politics years ago and was glad I didn’t have to excuse myself as well. She asked, “why do people have to get so loud and obnoxious? Why can’t we just have a calm, intelligent conversation on the subject?” So, I said, “Fine, go ahead and hit me with it.” In that instant her voice raised 3 octaves and her volume went strait to shrill, and she screamed at me, “That whore, Hilary, did you know she took over 200 million dollars from Saudi Arabia, who are supporting the Taliban, and that the entire world media is covering it up so that Bitch can get elected?” After collecting my jaw from the ground and slowing my brain back below light speed, I asked, “Where, on earth, did you get that?” She replied, “WikiLeaks! Don’t you listen to WikiLeaks?” Within that statement there are more than one antecedent/consequent. Therefore, more than one affirmation, and in one fraction of a second before I started to tear into that fur ball of horseshit, I suddenly remembered why I stopped discussing politics, (which is, by the way, going to be my point… eventually).

    Folks are folks. They want what they want, and they want it right now! They are either incapable of recognizing that their actions have consequences, or they just don’t care. Since I find it hard to believe that the inordinate number of folks I have known who don’t, at least seem to, think it through are really that stupid, I am forced to believe the latter, they just don’t care. They aren’t going to think it through because it may end up changing there stance on something. I think they don’t believe the argument because of the logic, (or their inability to see the fault in it). I think they accept the logic because their minds are already made up and it is the best they have to support their position. If someone else believes it and gets on their band wagon, all the better.

    When trying to determine why someone either believes or is trying to make others believe the affirmation, never forget:

    We want the world and we want it Now. NOW… NNNOOOOOOOWWWWW!!!

  4. UncleJoe UncleJoe says:

    The situation you are describing is a different mental construct than a particular logical fallacy. It is a different critter altogether. It describes the kind of “reasoning” often employed by apologists. Apologists are not people saying they are sorry. It is a word to describe those people who defend a belief system to nonbelievers. Many beliefs we hold are not based on facts at all, and for some of them, that is the only way it could be. For example, I may believe that chocolate ice cream is inherently better than strawberry ice cream. There is no fact that can support of refute this because it is a value judgment, not a measurable truth. Good and evil can be derived logically from value based assumptions, but there is no logical proof of those assumptions. Also, there are uncertainties pertaining to any perceived facts which we can only deal with by a value judgment on credibility.
    The method of “reasoning” that predominates errors in this arena is “wishfull thinking” or “magical thinking”. Fans of Disney recognize that this is the plot of many a children’s tale: “If you want it really bad and make yourself believe it, then it will be true.” A famous apologist use of this notion is called “Pascal’s Wager”. Roughly stated, it says “If I believe in God, and I am wrong, then when I die I will be nothing and incapable of regretting the decision, but if I do not believe and I am wrong, then I will suffer for the decision, ergo it is wiser to believe in God.” For this to be a valid point, you must subscribe to the notion that belief is more important than truth. That facts do not matter, only what you choose to believe. “who would want to live in a world where there is no God?” logically asks whether suicide is a good value to adopt upon being convinced in the lack of a Supreme Deity, but those who say it mean “why would anyone allow themselves to consider the possibility that something they wish to believe is wrong?”
    I am certain that for people who think this way, upon reading this post they would draw the conclusion that I do not believe in God and want to convince them there is no God and the only reason they could give would be that I suggested that they consider what it would mean to entertain the notion and examine its merits.
    So, what people entrenched in a political thought process are wont to do is to consider the credibility of any source of data that challenges their belief as worthless, so that they can maintain the illusion that their thinking is consistent with “valid” data, and those who cite those “facts” as being beholden to the propagandists spouting the data that lacks credibility because it must be from a source incapable of recognizing truth. It is not unique to one side or the other, even if one side has managed to monetize the process far more effectively than the other.

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