Advertising and logic

What an interesting advert!

About two years ago, I saw this advert: 

"If Cineplexx does not exist, your wife would be a lord of the rings."

I have been looking at it, for a long period of time. I was standing there in the middle of the mall center, while people were passing by, and some of them (those that were not in a harry) looked for a moment at the point I was looking at - the advert, possibly thinking that I am fond of The Lord of the Rings, and that I am standing there planning to go to see the film.

What is "the logic" and the logic behind this advert?

While I was standing there, I was asking myself "What do the creators of the advert want to tell us?" The fact is that Cineplexx does exist (since the advertisement was placed in a mall where there is a Cineplexx cinema). So what? What are we supposed to do with the rest of the sentence, with "the wife" and "the lord of the rings"? The next days I started a conversation with some of my friends. Suddenly, this advertisement appealed to be anti-feminine for some of them, and the others thought it is romantic (I agree with the last one, but only if Cineplexx does not exist). Why some people found that the advertisement is anti-feminine? Let us see. If we think about "the wife who is a lord of the rings" as the one that is the head of the marriage, I suppose that the men (who support anti-feminism) would like this not to happen. And since Cineplexx does exist (and The Lord of the Rings is showing at Cineplexx), the wife would not be a lord of the rings (i.e. she would not be the head of the marriage) - that is how the authors of the advert believe that everybody would make the conclusion out of the given sentence and the fact that Cineplexx does exist. But is this a right way to make a conclusion? If we denote by \(p\): "Cineplexx does not exist." and by \(q\): "Your wife is a lord of the rings.", then we have \(\neg p\): "Cineplexx does exist." and \(\neg q\): "Your wife is not a lord of the rings." The last two propositions are negations of the propositions \(p\) and \(q\) respectively. Then, "the rule" that the authors would like everybody to implement is \(((p \implies q) \land \neg p) \implies \neg q\). This is behind every logic! It is the same as "If it is a dog, then it is an animal. It is not a dog. Therefore, it is not an animal." 

Later, I found that this kind of fallacy in logical thinking is called Denying the Antecedent. (In conditional statements "if \(p\) then \(q\)", \(p\) is called an antecedent, and \(p\) is a consequent.) Denying the Antecedent happens when the inference rule Modus Tollens is misunderstood, it is not being used properly. The Modus Tollens states \(((p \implies q) \land \neg q) \implies \neg p,\) which is interpreted as "p implies q and q is asserted not to be true, so therefore p must be false." It is a tautology, which means that it is always true regardless the values of \(p\) and \(q\) (true or false for each of them), so there is no place for doubt in its correctness. When we switch the places of \(\neg p\) and \(\neg q\) in Modus Tollens, we get the logical fallacy called Denying the Antecedent.

It is always interesting to explore further. I found that the logical fallacy that is mistaken for Modus Ponens is called Affirming the Consequent. Modus Ponens is the rule \(((p \implies q) \land p) \implies q\), and Affirming the Consequent refers to \(((p \implies q) \land q) \implies p\). An example of an Affirming the Consequent fallacy is, "If someone owns Apple, then he is rich. Bill Gates is rich. Therefore, Bill Gates owns Apple".

Logical fallacies within other advertisements

After identifying a logical fallacy in my advert, it was trilling to look for the others. So, here are some advertisements that I found and "the logic" behind them:

"There are some things money can't buy. For everything else there's MasterCard."

This is a False Dichotomy or False Dilemma. It says that we have only two options that we have to choose from, instead of allowing for other possibilities. In this case we can choose between things that money can't buy and the things that we can buy using the MasterCard (and nothing else). Here is another:

"Marilin Monroe says - Yes, I use Lustre-Creme Shampoo."

This fallacies are widely used in marketing, there are called Appeal to Authority. The reasoning is based on what some authority says on the subject. In this case Marilin Monroe uses Lustre-Creme shampoo, so the advertised shampoo must be good. It is true that most of our knowledge is formed by listening to authorities, books that we learn from are written by some authorities in the particular area, teachers who teach us are trained for the job they are doing, our parents give us advises based on their experience and believes that are formed, I suppose, by listening to authorities. You have to have some background knowledge about the subject or the authority, in order to spot this kind of fallacy. Now, look at this one:

"Costs less then a personal trainer."

(showing a picture of Wendy's backed potato, a small chili and a fresh salad with fat-free dressing, a meal with just 5 grams of fat)

It is a Faulty Comparison or Questionable Analogy. When reasoning by comparison, the fallacy occurs when the analogy used for the comparison is irrelevant or very weak or when there is a more relevant disanalogy. In the advertisement, the low fat meal is compared to a personal trainer, probably on the base that the both have the same effect on someones health, which is very weak argument. A personal trainer will do much more things for you, he will help you to eat and exercise properly, to lose weight, to gain self confidence, to live a healthy lifestyle. It is true that a 99 cents meal is less then a personal trainer, but is it healthy to eat the same meal through a long period of time? 

There is a huge list of fallacies in reasoning, and each of them, unfortunately, can be used in advertising campaigns and might have great negative impact on proper logical people's reasoning.

Epilogue

Two years after I saw the Cineplexx advert for the first time, I was visiting the same mall center, and ... it was there again.