A Puzzle at the Logicians' Club
The Logicians' Club has an unusual tradition, but then it's an unusual club whose membership is restricted to perfect logicians who make no mistakes. The odd tradition is that every year the club hires an outside firm―last year it was Acme Novelties and Party Supplies, Inc.―to award gifts to a randomly chosen set of members of the club as part of a celebration of the club's founding. How many gifts are awarded depends upon the funds in the club's coffers that year, as well as the price of the gifts chosen to be awarded, though at least one gift is awarded every year. Acme selects the gift or gifts and keeps both their number and nature secret from all members of the club.
Once the gift for a year has been selected, Acme announces the recipients of the gifts on Founding Day. At the celebratory dinner, Acme representatives distribute small, sealed envelopes to every member of the club. Inside each envelope is a folded card, inside of which is printed the name of every member of the club who is to receive a gift―with one exception: no member is informed by Acme that he or she is to be a gift recipient, and violation of this rule is grounds for the company losing the club's future business. Moreover, all members of the club are sworn to never inform or even hint to any other member of the club that he or she is a gift recipient, and violators are immediately expelled from the club.
This secrecy is not merely to surprise the gift recipients, as an additional rule requires said recipients to request their gifts. In addition, any designated member of the club who fails to request his or her gift in time is expelled as unfit for membership in a club for perfect logicians. As you can imagine, members of the Logicians' Club are strongly motivated both to receive the gifts, which can be highly valuable, as well as to maintain membership in such a prestigious club.
Each morning, starting with the first day after Founding Day, members of the club may submit a request to Acme to receive their gift. However, only those members who have been chosen by Acme will actually receive a gift, and any others are immediately expelled from the club. Each afternoon, Acme announces to all members of the club how many gift requests were made that morning and who submitted them. Moreover, the number of mornings open to gift requests is determined by the number of gifts to be awarded that year, for instance, if only seven gifts were to be awarded then a week's worth of mornings would be allotted for gift requests.
Last year, the rules were followed to the letter, and no member informed any other member of that member's status as a designated gift recipient, and Acme strictly followed its instructions. Nonetheless, every member who had been duly chosen received a gift, and no members were expelled. How did the chosen members of the club manage to figure out that they were selected by Acme, since neither Acme nor any other club member so informed them? Keep in mind that each member of the club is a perfect logician and knows that all other members are also perfect logicians.
On the first four mornings after Founding Day, no members requested a gift. On the fifth morning, at least one member requested a gift, but perhaps more. If you can determine how many gifts were awarded last year without looking at the Solution linked below, you are certainly Logicians' Club material!
In the Mail: Scrutinizing Argumentation in Practice
This is an anthology edited by Frans van Eemeren and Bart Garssen, with papers by van Eemeren, Garssen, Jeanne Fahnestock, Henrike Jansen, and many others. The book has parts dealing with scientific arguments, political arguments, legal arguments, arguments in education, and personal argumentation. The papers included in the book are from a conference held in 2014, so this is not for the beginner. Since part of what I do here is to scrutinize arguments in practice, I'm very interested in it and hope to learn something useful.
The Illogic Behind Conspiracy Theories
You'll see him in your nightmares, you'll see him in your dreams.
He'll appear out of nowhere but he ain't what he seems.
You'll see him in your head, on the TV screen
And, hey buddy, I'm warning you to turn it off!
He's a ghost, he's a god, he's a man, he's a guru.
You're one microscopic cog in his catastrophic plan
Designed and directed by his red right hand.
―Nick Cave, "Red Right Hand"
Rob Brotherton, author of the new book Suspicious Minds―see the "New Book" entry, below―has a recent article on the psychology of conspiracy theories (CTs) in the Los Angeles Times. I'm in the middle of the book currently and hope to have a review ready soon, so stay tuned. In the meantime, if you're interested in the book or its topic, check out the article. Read the whole thing―it's short―then I have some comments.
Brotherton starts the article as follows: "The Internet is often accused of fueling conspiracy theories, but it also serves as an outlet for mindless conspiracy bashing." I'm not in favor of "mindless" conspiracy bashing, either; I prefer "mindful" conspiracy bashing. However, I'd like to see some evidence of all this "mindless conspiracy bashing" on the internet, or anywhere else for that matter. The kind of lists that Brotherton goes on to cite don't fit the bill because none of them dismisses "all conspiracy theories (and conspiracy theorists) as crazy", as he puts it. A better grounded charge is that some of the lists are politically biased since they list only right-wing theories―were there no crazy left-wing theories in 2015?
Brotherton goes on to write: "You don't have to be crazy to believe conspiracy theories." No, but it helps. As a philosopher, the question that popped into my mind when I read this was: what do you mean, "crazy"? Brotherton seems to assume that it's impossible that most people could be "crazy", since the only evidence against the claim that conspiracy theorists (CTists) are "crazy" that he cites is survey evidence that most people believe one or more CTs. However, suppose that what you mean by "crazy" is "irrational", which is surely one meaning of the word. That most people are irrational at least some of the time, about at least some things, is not unlikely at all. Also, I assume that Brotherton would not deny that at least some CTs and CTists are irrational. In fact, as I may discuss in more detail in the review to come, Brotherton's own book supports these claims.
I agree entirely with Brotherton's point that the human mind's hyper-active pattern-detecting and cause-seeking mechanisms mean that "we are all―yes, all―wired to feel the lure of" CTs. Understanding these psychological mechanisms helps to explain why many people succumb to that lure, but not everybody does.
Finally, while it's true that there are real conspiracies, such as Watergate, for every real conspiracy there are a thousand false CTs. Just as a matter of pure statistics, you are likely to be right 99.9% of the time if you simply dismiss all CTs as "crazy". Now, I'm not recommending that strategy, but many CTs are so obviously irrational on their face that they can and should be so dismissed. To quote Christopher Hitchens: "What can be asserted without evidence can also be dismissed without evidence."
Source: Rob Brotherton, "The logic behind conspiracy theories", Los Angeles Times, 1/19/2016
Resource: Quote-Unquote: Christopher Hitchens
"Demography has more to do with crime increasing or decreasing than any one policy," said Michael Maltz, an emeritus professor of criminal justice at the University of Illinois at Chicago. "A politician is always looking to embellish his own record to the best that he can. If there's something that gets better during his administration he'll take credit for it."
Source: John Fritze & Doug Donovan, "Fact check: O'Malley lays claim to an ambitious record in Md.", The Baltimore Sun, 4/18/2015
I don't want to pick on former Mayor of Baltimore and ex-Governor of Maryland Martin O'Malley, who at this point is a very long shot to get the Democratic nomination for President. Not only that, but O'Malley was reduced to pathetically begging for time from the moderators of the most recent Democratic debate, who seemed more interested in front-runners Hillary Clinton and Bernie Sanders. However, a claim that O'Malley made in the debate illustrates a common logical problem in political rhetoric. Here's his answer to a question posed by moderator Lester Holt about crime in Baltimore: "I drove our incarceration rate down to 20-year lows, and drove violent crime down to 30-year lows…."
It's clear from O'Malley's choice of words that he is claiming to have through his policies or actions brought about―"I drove down"―the low incarceration rate and lower level of violent crime in Baltimore. However, violent crime was decreasing nationwide during the time period that O'Malley was mayor, and surely he could not plausibly claim that his policies caused a national decline in violence. Thus, the question is raised: how much, if any, of the decline in violent crime in Baltimore was the result of O'Malley's policies, and how much of it was simply the city's share in the national decline?
This is much the same logical mistake as in the previous entry on the Republican debate, though Bush claimed that the reduction in gun violence in Florida was due to specific policies, whereas O'Malley was not specific about what led to the lower crime rate in Baltimore though he claimed credit for whatever it was. In general, when politicians, such as Mayors, Governors, or Presidents, run for office they take credit for any good thing that happened during their term of office, while denying blame for the bad things. However, officeholders both benefit and suffer at the hands of events that are beyond their control.
O'Malley is probably no worse about making such dubious causal claims than any other politician running for office, but we need to be skeptical when we hear them. It is much harder than most people realize to identify the causes of crime, or to affect its rate with legal or police policies. So, when a politician claims to have lowered crime, or one blames an opponent for higher crime rates, we need to ask some critical questions: What was happening to the crime rate nationwide during the relevant period? How did the crime rate change in similar cities or states?
Source: "Democratic debate transcript: Clinton, Sanders, O'Malley in South Carolina", CBS News, 1/18/2016
- The sixth Republican Presidential debate was just held―that's right, sixth! I missed a couple because there just wasn't anything new or interesting in them. In this most recent one, moderator Maria Bartiromo asked Florida ex-Governor Jeb Bush the following:
Bartiromo: … Governor Bush, gun rights… What is the harm in tightening standards for not only who buys guns, but those who sell them?
Bush: …I think we need to focus on what the bigger issue is. It isn't law-abiding gun owners. Look, …we…have a reduction in gun violence because in Florida, if you commit a crime with a gun, you're going away. You're going away for a long, long while. And that's what we should focus on is the violence in our communities. …
Source: Team Fix, "6th Republican debate transcript, annotated: Who said what and what it meant", The Washington Post, 1/14/2016
Bush is here claiming that the fact that "you're going away"―that is, you will go to prison "for a long, long while"―if you use a gun to commit a crime in Florida caused the reduction in gun violence in the state. The word "because" signals that this is a causal claim. However, how do we know that the imprisonment policy is responsible for causing the drop in gun violence? Bush is not explicit about when this policy was adopted, but presumably it was adopted before and was in place during at least part of the reduction; otherwise, it would be clear that the policy could not be responsible for the reduction.
The Washington Post's Fact Checker has a helpful annotation in its transcript of the debate to this part of Bush's answer―see the Source, above. Here's the relevant part:
Some types of gun violence decreased while Bush was governor of Florida, but not all. … Overall crime decreased while Bush was governor of Florida from 1999 to 2007. The downward trend continued after he left office, and is consistent with crime rates overall in the country. This is not an exhaustive look at gun violence in Florida, but we crunched the numbers in three key categories of gun violence to see how they fared between 1999 and 2006…. Murders by firearm were at three per 100,000 in 1999, then four per 100,000 in 2006. But it increased to 4.4 per 100,000 in 2007…. Aggravated assaults with firearms and gun robberies went down while Bush was in office….
It appears that the career of gun violence in Florida during Bush's term was checkered, with some types going up and other types declining. However, if we assume that there was an overall decline in violence with guns, is it possible that Florida's "tough" gun crime policies have caused or at least contributed to said reduction? Yes, it's even plausible. But as the Fact Checker points out, the downward trend in Florida was part of a larger national reduction in crime. For this reason, it's impossible to know how much if anything "tough" sentencing policies may have had to do with this reduction. Plausibility is not enough: a causal conclusion is not warranted by Bush's evidence.
Fallacy: Non Causa Pro Causa
…And a New Taxonomy
The Fallacy Files now has a new, improved Taxonomy of Logical Fallacies. To see the new Taxonomy, you can simply click on the link on the Main Menu to your left. The old, legacy Taxonomy is still available from the "How to Use the Taxonomy" page. As explained on that page, the old Taxonomy was almost impossible to update, and is out of date as a result. The new version is far from perfect, but will be easy to update. As usual, if you find any broken or missing links, or other problems with the page, please let me know.
A New Book for a New Year
I just got my hands on a copy of psychologist Rob Brotherton's new book Suspicious Minds: Why We Believe Conspiracy Theories. I'm a bit put off by that subtitle since I, for one, don't believe conspiracy theories. However, as with newspaper and magazine titles, book titles and subtitles are often imposed upon writers by their editors and publishers. A New York Times review makes the same claim as the subtitle:
It turns out we are all conspiracy theorists. Brotherton attacks the stereotype, which he says was popularized by the historian Richard Hofstadter in his influential essay “The Paranoid Style in American Politics,” of conspiracy theorists as a small band of tinfoil-adorned loonies―the paranoid fringe. Brotherton’s main argument is that we all possess a conspiracy mind-set to some extent, because it is hard-wired into our brains. “Suspicious Minds” details the various psychological “quirks and shortcuts” that make us susceptible to conspiracy theories.
Source: Adrian Chen, "‘Suspicious Minds,’ by Rob Brotherton", The New York Times, 12/31/2015
I'm willing to accept that "we all possess a conspiracy mind-set to some extent" because "various psychological 'quirks and shortcuts'…make us susceptible to conspiracy theories", but it just doesn't follow that "we are all conspiracy theorists". That's just factually wrong. It's like claiming that everyone has sexual desires and attractions of the sort that lead to people cheating on their spouses or lovers―which is no doubt true―therefore everyone cheats on their spouse or lover―which is obviously false. We may all be potential cheaters but we are thankfully not all actual ones.
I hope the book doesn't live up to its misleading subtitle. I won't promise anything, but I may review it later this year.
Resource: Rob Brotherton, et al., The Psychology of Conspiracy Theories. The author's website.
Solution to a Puzzle at the Logicians' Club: Five gifts were awarded to Logicians' Club members last year.
To see this, think about what would happen if Acme chose to award only one gift that year, and suppose that the designated recipient was Jim Lucky. Then, at the Founding Day dinner, all of the other members of the club would receive a card with only Mr. Lucky's name on it, while Jim himself would receive a blank card. Since Jim knows that at least one gift must be awarded, he doesn't have to be a perfect logician to figure out that he is that person. Moreover, only one morning will be allotted for Jim to request his gift, that is, the morning of the day after Founding Day, so Jim will request his gift that morning.
Now, consider what would happen if there were only two gift recipients. On Founding Day, everyone else would receive a card with both recipients' names on it, but each recipient would receive a card with only the other recipient's name. Suppose that those two members are Jim Lucky and Jane Happy. Now, Jim has received a card with only Jane's name on it. However, for all he knows Jane is the only gift recipient that year. So, he will not apply for a gift the morning after Founding Day. Similarly, Jane received a card with only Jim's name on it, and is in the same situation he is. Therefore, neither one would submit a gift request on the first morning. Nor, of course, would anyone else in the club.
On the afternoon of the day after Founding Day, both Jim and Jane will be informed that no one requested a gift that day. However, being perfect logicians, each will realize that if only the other had been selected to receive a gift, he or she would have requested it that morning. Thus, two people were selected for gifts, and those two people must be Jim and Jane. Moreover, the next morning is the last one to request a gift. Therefore, both Jim and Jane will request their gifts on the second morning after Founding Day. No other member will submit a request that morning for fear of expulsion.
If you follow out this reasoning for three recipients, you will see that all and only those three will submit their requests on the third morning. Similarly, if there are four designated recipients, exactly those four will submit requests on the fourth morning.
To generalize: if n recipients are designated, then those and only those recipients will submit their requests on the nth morning, and no requests will be submitted on earlier mornings. This is because each of the n designated recipients will receive a list of n - 1 members on Founding Day, since it will be missing only the member's own name. On the afternoon of the n - 1st day, they will be informed that no one submitted a gift request that morning. Then each will realize that there must be n chosen recipients, and that they are among those chosen. Therefore, on the following morning of the nth day, they will all submit their requests.
Since we are given that at least one recipient submitted a request on the fifth morning, we are entitled to conclude that a total of five members submitted their requests on the fifth morning and received gifts last year. All of this, of course, is based on the assumption that the members of the Logicians' Club are perfect logicians who make no mistakes, which is why in reality the club has no members!
Source: William Poundstone, Labyrinths of Reason: Paradox, Puzzles and the Frailty of Knowledge (1988). The puzzle is based on one from pp. 84-86 & 90-91.