“Logic is a Wreath of Pretty Flowers Which Smell Bad:” Skills of Thought, Part 2

In my first year teaching high school, I was required to include a logic unit in my public speaking class. The idea was that, when students wrote and delivered persuasive speeches, they had to actively demonstrate that their reasoning was logical. 

Explaining logic to fifteen-year-olds was challenging. However, it turns out that learning it myself was just more difficult. The first time I taught syllogisms, I got things mixed up and had to reteach it the next day. I vividly remember a student who regularly came in for help, arriving by gleefully saying, “Mr. Hirsch, today NOBODY understood what was going on!” He was right. 

Logic is difficult. Logic can be manipulated. Some forms of logic are particularly prone to misinterpretation. Here is a very simple explanation: 

In deductive logic (like that which made Sherlock Holmes famous), a syllogism has two premises. One of these states a general rule, the major premise: All cats have whiskers. It makes a broad factual statement about a group of things or ideas. The second or minor premise makes a claim that is more specific and focused: Harold is a cat. We can use our Venn diagram to reveal that if the group of cats all have whiskers and Harold exists inside the circle of cats, Harold has whiskers. Simple enough! Well…not exactly. 

Of course, we have to be sure that both of these claims are factual. Are there cats that don’t have whiskers? Do we know that Harold is not a dog or a man who has a beard? Things can get muddy when the Venn diagram is related, but not overlapping. 

Try this one: All cats die. JFK is dead. Does that mean that JFK was a cat? This is a silly example and I am sure you were a step ahead of the very young speech teacher and his students. JFK is never shown to be a cat. We cannot reach a conclusion just because two things share a characteristic - and you can’t create a general rule from one example. 

This is where we often go wrong in our political discourse. We hear from many people that a single example proves a general rule. That is where inductive logic comes in; we draw a general rule by drawing conclusions from patterns we observe. This is the scientific method. 

In class, I used a simple example: I looked at the students’ footwear. I would point out that the boys in the front row were all wearing athletic footwear. Then I would note that the boys in the second row also had athletic footwear on. From these fifteen or so examples, I would conclude that all male students in the high school wear athletic footwear. 

Of course, I would be wrong. There would be a student out there in sandals (we were in Illinois, of course, and some kids would be in sandals and shorts well into the winter). I could make the statement (and be correct) that a majority of boys in school were wearing athletic footwear. Of course, many (usually most) of the women in the room were also wearing athletic footwear. 

That is why it is so challenging to create new generalizations inductively. It is why scientists doing research have a very high burden of proof and why their studies are so carefully scrutinized. 

Too often, in our public conversations, we think we have a general rule and are using deductive logic (although we may not use those labels) when we are in fact using specific examples that may or may not be enough to prove a generalization. 

Just because some people cheat on their taxes, does it mean that everyone does that? Just because some people who came from another country got in trouble with the law, does it mean that every immigrant is going to cause problems? Of course not! 

But politicians and advertisers will try to persuade people with powerful anecdotes and examples. They don’t explicitly say that their story represents EVERYONE or applies ALL THE TIME, but they want their listeners to make that logical leap – incorrectly. One testimonial doesn’t mean much. Ten testimonials are more powerful, but still may not be enough. 

Human beings want things quickly. We have learned, sometimes, that a few examples are all we need. I ate pizza two or three times and had terrible stomach aches afterward. So, I stopped eating pizza for years! Eventually, I had pizza again and found it was delicious and I had no ill effects. What a shame that I missed out on all those pizzas! 

We come to incorrect conclusions when we fail to think logically – and plenty of folks benefit by leading us down this illogical path. Fear and anger can make us less likely to think things through methodically. Lack of time can rush us into drawing poor conclusions. If we are invested in the conclusion or have high hopes that something is true, we may change our thinking to reach conclusions that please us. There are many logical fallacies (which we can discuss later) that can trip up our reasoning. 

In times when people debate what is and is not factual, we must slow down and use the tools that thinkers centuries ago developed. We must be like Mr. Spock and use logic to come to reasonable conclusions – and not be suckered into accepting seductive falsehoods that often benefit those who have a vested interest in fooling us!