Humans have a natural ability to do logic predicated on learning rules from their environment. Training in mathematics improves your logic — and makes you more effective in an argument (at least the polite sort). It’s often humorous when somebody does not follow those rules. In the show Parks and Recreation, actress Amy Poehler plays the director of the Parks and Recreation department in a small town in Indiana. At one point a citizen, at a town meeting, says this. “I found a sandwich on a bench in one of your parks! (pause) Why wasn’t there any mayonnaise on it?” Something that sounds like a complaint about littering turns in a completely unexpected direction. Occupy Math starts with this because the fact that this condiment twist in the citizen’s complaint was funny means that there is hope in a moderately awful situation.
Occupy Math found a book in the library at the University of Kansas many years ago entitled “A Guide to Rhetoric”. That was the early 1980s and “rhetoric” was almost a pejorative term. The book was not long, so Occupy Math sat down and read it out of curiosity. It was a textbook for a class that was no longer offered on how to argue clearly and persuasively. There were some nice tricks: if you make your voice go down at the end of a sentence it makes it sound like you are stating a fact. Make you voice go up and it expresses doubt or turns the sentence into a question. Tricks aside, it was mostly an applied logic textbook. Up until finding that book, Occupy Math had assumed that logic was the property of mathematicians, who used it to chop through difficult symbolic thickets to essential truth, and philosophers who seemed to use it for all sorts of things, including confusing people to death. Subsequently, Occupy Math’s view of philosophy has softened and he now think of math as the biggest of the fields of applied philosophy.
Any shmoe with a computer, dot arrgh.
The internet has lowered the bar for entry into public discourse so that anyone with a computer (still an elite group, but a much larger elite group) can join in. Simultaneously, the idiotic revolution to make education “relevant” means that learning to argue logically and persuasively is no longer widely taught as a core skill. The “relevance” demand is reappearing today in the form of expectations that students be prepared for jobs. While it sounds like a good idea, the problem is that the jobs change much faster than the education system and what is actually needed is to teach people how to think clearly, solve problems, and have confidence in themselves. Rhetoric (persuasive, logical argument) is exactly such a general skill. You see, once you gain some mastery of rhetoric, it affects the way you listen and learn, think and plan. It make you a more effective person, a person equipped with a high-fidelity BS detector. At least some skill in rhetoric is one of the side effects of leaning math, when it is taught well.
The causus belli for this edition of Occupy Math was a keynote presentation “Sex and Love with Robots” at the 2017 Foundations of Digital Games (FDG) conference and things that happened subsequently on Twitter. One heartening outcome is that the community is objecting firmly to the improper conduct. Click the link for a calm summary of events and the community response. Occupy Math is a colleague of the researcher who was attacked, so he must declare a potential lack of objectivity. Following firmly the editorial principle of looking for the silver lining and lighting a single candle instead of cursing the darkness, Occupy Math will look at and critique a few really bad ways of arguing.
First up: Ad hominem arguments
The Ad hominem attack is the error in which you go after the person making the argument instead of directly addressing the argument. In point of fact, a brilliant person can say something idiotic and someone you’ve never heard of can present a correct, subtle, incisive argument; this means that the identity of the person making the argument is at most a secondary factor. The keynote speaker who motivated this post did not answer a Twitter critique of his address; rather, he attacked the person making the criticism.
A prominent recent example of an ad hominem argument is a series of attacks on female members of the video game industry. Occupy Math spent five years in the trenches of the creation-evolution debate-and-or-shouting match. A common tactic on both sides of the debate, especially when not doing too well on the logic and evidence front, was to attack the other person. This spans a spectrum from the almost relevant attack on a person’s credentials to loud declarations of idiocy and assignments of destinations in the afterlife. Occupy Math was consigned to the fire in the afterlife dozens of times. It is not only a lack of desire to go to the dark place that makes Occupy Math think this is not a useful method of figuring out how the universe works. The antidote is to try really hard to directly address the claims the person is making, not irrelevant aspects of the person themselves.
Occupy Math’s favorite example of this is a parody of reasoning that appears in many arguments. “I cannot hear any fireworks. That means it cannot be the Fourth of July. We can then conclude that today is Christmas.” This is a ridiculously exaggerated version of a common logical error with several names. Basically the error is to assume that there are only two possibilities. This argument is at the core of much of creationism. People who believe in biblical literalist young-earth creation often arrive at the conclusion that if they can disprove “evolution”, then that will prove they are right. It won’t. The human brain is somewhat wired to want two choices, a useful but often inaccurate simplification. The antidote is to make a habit of asking yourself, “are there other possibilities?”.
Post hoc, ergo propter hoc
This logical error was the title of a West Wing episode (Season 1, Episode 2). The fictional president translated the error into English: “After it, therefore because of it.” Let’s give an example with a high emotional content. Occupy Math has heard people say “This neighborhood went to hell after the black people moved in.” The assertion was literally true. The implication that the black people somehow caused the neighborhood to decay was false. Lots of people moved in and the unifying principle was affordability of housing. The world changed, the local employer went broke, the community’s average income went down, and so did house prices.
“The blacks” were not the only new type of people moving into the community. There were low-income white folk, Hispanics, a few people with grandparents from India, you know: Americans. A cultural history of bigotry made the new people in the neighborhood with ancestors from Africa undesirable to the longer-term residents and set up the logical fallacy that somehow the brown-skinned were responsible for declining conditions. Occupy Math’s take home? Studying logic and rhetoric might help you notice your own bigotry. More on why it might not help later in the post.
Correlation and Causation
A more general form of Post hoc, ergo propter hoc is to believe that, when two things are correlated, one is causing the other. This logical error is also connected to false duality; “one causes the other” ignores the possibility that both events are responding to some more fundamental cause — or even that the correlation might result from random chance. The comic XKCD provides a thoughtful view in 23 words.
This error is also at least partially centered in our history. Since correlation and a causal link happen together fairly often, the pattern-finder that helped our primitive ancestors survive holds this logical fallacy firmly in place as a useful heuristic rule. It’s not a bad rule, it is just completely wrong sometimes. The antidote is to remember that the belief that correlation implies causation is sometimes useful but not reliable.
The Plural of Anecdote is not Evidence
This error is one that an example of has appeared in Occupy Math before. The particular phrasing used in the section heading is due to David B. Fogel, a deeply respected colleague, from a well-done keynote speech. A really common logical error is to find a few examples of something and then to offer those as proof that whatever the thing is is universally true. This is disrespectful of the entire profession of statistics (Dr. Fogel’s PhD is in statistics) and also a good way to be wrong with jet-propulsion. Politicians, demagogues, salesman, and cult leaders are among those that exploit this error to the hilt. The antidote is two part — check for more cases than the ones presented and ask yourself if the conclusion makes any sense at all.
Product testimonials are a good example of an institution that exploits this logical error. Someone says that this type of makeup changed their life? Look for online comparisons of satisfaction with types of makeup and also ask yourself, “would I find any sort of makeup life-changing?” Maybe you would, but if you don’t then the testimonial is not relevant to you, personally.
The Fallacy of Relevance
Occupy Math provides lots of links in his posts that either provide context or supporting evidence. This is a habit leaned while writing scientific papers and enhanced and re-skinned for blogging with help from his editor. Another remarkably common logical error is to authoritatively cite facts and evidence that are not germane. Example: “Bob Blogs has fifteen years experience as a longshoremen and so he has my vote for Sheriff!” Occupy Math suspects that many people in the hypothetical district are longshoremen, meaning the ad is not a bad one for Mr. Blogs’ campaign to run, but the logical connection between loading ships with goods and law enforcement is prominent through its absence.
The recent controversy concerning a memo about the suitability of women to be software engineers was built on the fallacy of relevance. While a good deal of evidence was cited, it was not evidence about women who apply to be software engineers. It was evidence about the general population of women (that was not the only problem with the document, but it is the problem relevant to Occupy Math’s current post).
Why do people hold vehemently to obviously false positions?
Occupy Math’s answer is “because we don’t teach enough math and we don’t teach it properly”, but that answer is selfish, biased, and not really well supported by logic and evidence. Yes, if we taught people a lot more math, and stopped using Pavlovian conditioning instead of discourse and well-chosen examples, things would get better. However, the problem is much deeper than that. The part of the story that Occupy Math has not told is one he has decided to outsource to The Oatmeal. Briefly, the evolutionary advantages of solidarity and avoiding hesitation have granted human beings minds that are logically defective — but in ways that are sometimes quite helpful. Please read the linked The Oatmeal. Occupy Math quite enjoyed it and it makes an excellent point.
Taking positive action
Occupy Math uses anecdotes all the time in teaching. He thinks they are valuable tools for setting the scene. While an anecdote cannot be used to establish universal truth, anecdotes have a big role to play. First of all, an important point is that math also needs existence results. A story about a person’s experiences is an anecdote — but if it makes you aware of a possibility you were not aware of before they are performing a valuable role in the discourse. In fact, anecdotes are useful tools for avoiding false duality and correlation/causation errors. Anecdotes are examples and that is an important role in discourse.
The XKCD comic to the left is entitled “duty calls”, an instant classic because it captures in one panel one of the great new addictions of the internet. Many of us have heard the trumpet that is audible to the character in the comic. Occupy Math takes up his quill in response to this siren call and feels the martial spirit that stirs when idiotic or hateful things appear on his screen. Given that, it is worth considering if you should join in and, once you decide to go ahead, how to join in. Occupy Math strongly recommends polite logical argumentation supported by evidence. Many people are there for the fight, not the point, and calmness and good manners can de-escalate things, at least sometimes. This post has highlighted several errors: avoid them. Polish your rhetorical style. Do the reading and learn the background. Not only will the tone of arguments you participate in trend upward, you will become more effective in life.
The list of logical errors in this post is far from exhaustive; they were chosen because Occupy Math encountered them recently. It is also important to note, with thanks to my editor for suggesting it, that logical correctness is not a get-out-of-needing-social-skills-free card. Are there particular logical fallacies you would like called out? Is there a domain of discourse that needs to be examined or turned over so light and air can get in? Please comment or tweet!
I hope to see you here again,
University of Guelph,
Department of Mathematics and Statistics