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October 22nd, 2021 (Permalink)

What is rationality, and why are people saying terrible things about it?

Quote: "Rationality ought to be the lodestar for everything we think and do. (If you disagree, are your objections rational?) Yet in an era blessed with unprecedented resources for reasoning, the public sphere is infested with fake news, quack cures, conspiracy theories, and 'post-truth' rhetoric. … Many act as if rationality is obsolete―as if the point of argumentation is to discredit one's adversaries rather than collectively reason our way to the most defensible beliefs. In an era in which rationality seems both more threatened and more essential than ever, Rationality is, above all, an affirmation of rationality."1

Title: Rationality

Subtitle: What It Is, Why It Seems Scarce, Why It Matters

Comment: The subtitle is made up of three distinct questions that are addressed in the book. The first and third questions are philosophical, whereas the second is sociological, or perhaps political. The first question is an obvious one to ask, if not to answer, but the others are more surprising. That the book would ask the second question is a sign of the times, since it assumes that rationality really does seem scarce―I'm not suggesting it doesn't, as it certainly seems so to me―but I'm not sure that it's any scarcer now than it used to be. The third question is also a sign of the times: is it really necessary to explain why rationality matters? Perhaps the fact that some people today don't seem to understand why is part of the reason it seems so scarce.

Author: Steven Pinker

Comment: Pinker is a psychologist―or, to use the modern jargon, a "cognitive scientist"―but he's the author of one of the best books of philosophy I've ever read, namely, The Blank Slate2. As I mentioned in the comment on the subtitle questions, the first and third questions are philosophical, so Pinker's previous book makes me eager to read this new one.

Summary: The first chapter, "How rational an animal?", is the only one I've read in full, thanks to an online sample. It deals with two topics: first, arguing that human beings are, indeed, rational animals, and explaining why. However, its second part gives examples of ways we can also be irrational animals, some of which may be familiar to Fallacy Files readers: the Cognitive Reflection Test3, the Wason card test4, and the Monty Hall problem5. Pinker also gives a version of the "Linda" problem; if you're not familiar with it, try the following one―it's mine, so don't blame Pinker:

Lynnda is a 28-year-old vegan whose preferred pronoun is "s/he". S/he attended Evergreen State College and majored in Intersexional Studies. S/he has four tattoos and lives with three cats. Which of the following is most probable?

  1. S/he is a real estate agent.
  2. S/he is a barista at a local coffee house.
  3. S/he bowls in a local bowling league when not working as a real estate agent.
  4. S/he attends protests against police violence when not working as a barista at a local coffee house.
  5. S/he voted for Donald Trump in the last election.


Judging mostly from their titles, subjects of the remaining chapters are: logic, probability theory―Bayes' theorem gets its own chapter, as it well should―rational choice theory, statistical decision theory, game theory, correlation and causation, and the final chapter appears to be the one that addresses the question of why rationality matters. This may sound like pretty heavyweight material, but Pinker is very good at explaining difficult matters in a comprehensible way.

Comment: I don't need any convincing that rationality matters, but I'm skeptical about the value of trying to convince those who are not already convinced. How are you supposed to do that? By appealing to their reason? If they don't trust reason, how can that work? You might as well try to stand up by pulling on your own hair.

However, there may be some who have heard the attacks on rationality, are confused by them, and may benefit from understanding what rationality is, why it is important, and why those attacks are fallacious. You can't reason directly to the conclusion that reason works―that's obviously circular―but you can reason indirectly that the arguments against it are not cogent. Once the confusing nonsense is swept away, natural rationality should do the rest. People are rational animals, and logical fallacies and cognitive illusions only show that we are not perfectly so. Also, the more we learn about the mistakes we make, the better we can learn to avoid those mistakes, becoming more rational in the process.

The Blurbs: The book has a strange endorsement from Jonathan Haidt: "If you've ever considered taking drugs to make yourself smarter, read Rationality instead." How many people is the antecedent true of? Is that a big potential readership? Will reading the book actually make you smarter, or will it make it obvious that it's irrational to take drugs for that purpose?

Date: 2021


Disclaimer: This is a new book and I haven't read it yet, so can't review or recommend it. However, its topic interests me, and may also interest Fallacy Files readers. The problem is a work of fiction, and any resemblance of Lynnda to persons living or dead is totally coincidental and distinctly unfortunate.


Notes:

  1. "Preface".
  2. Steven Pinker, The Blank Slate: The Modern Denial of Human Nature (2002).
  3. Versions of two of the three problems that make up the test are given here: I'm with Stupid, 6/21/2012. Here's a link to the article discussed in the entry: Jonah Lehrer, "Why Smart People Are Stupid", The New Yorker, 6/12/2012.
  4. I mentioned the Wason test in passing here: Are you intelligent but irrational?, 11/11/2009.
  5. I mentioned the Monty Hall problem in passing here: Playing with Your Mind, 9/21/2021.

October 16th, 2021 (Updated & Corrected) (Permalink)

Fact Checks, Vast Majorities, and Outright Falsehoods

The ratings systems of professional fact-checking groups often come in degrees1. For instance, PolitiFact's "Truth-O-Meter" has six ratings: True, Mostly True, Half True, Mostly False, False, and Pants on Fire!2 Similarly, The Washington Post's Fact Checker uses a system of five symbols: a Geppetto Checkmark for "claims that contain 'the truth, the whole truth, and nothing but the truth'", and one to four "Pinocchios" for various degrees of falsehood3.

In the previous entry in this series4, I criticized some of the professional fact-checking groups for using ratings―such as "Pinocchios" and "Pants on Fire!"―that suggest those so rated were lying. In this entry, I examine a different problem with such systems, namely, that they treat truth and falsity as if they come in degrees.

Fact-checkers may be tempted to use such systems because they fail to logically analyze what they are checking into distinct factual claims before rating them. If, for instance, someone asserts a logical conjunction of two claims, one of which is true and the other false, it may be tempting to rate the claim "half true". For instance, if I claim that it is raining and the sun is shining, but as a matter of fact it is raining and overcast. We know from the truth conditions of conjunctions that the statement as a whole is false when one conjunct is false. So, either the conjunctive statement should be separated into two distinct claims, each to be rated on its own, or it should be rated "false" rather than "half true".

A factual claim of the type that can be checked at all is either true or false, and never both. So-called half-truths are not half true, but wholly true. This doesn't mean that half-truths are not misleading; in fact, they can be more misleading than whole lies. The very fact that they are true, but not the whole truth, may mislead even more effectively than a lie would. A true claim isn't the whole truth because it leaves out important context, and it's a perfectly fine public service for fact-checkers to supply such missing context, but it shouldn't be reflected in the ratings system, except in a rating such as: "True, but missing important context".

Fact checkers may also be tempted to use degrees of truth to rate vague claims. For instance, if Barry is balding we may be tempted to say that the claim that he is bald is "half true"―or is it half false?―but if Barry really is in the twilight zone between bald and not bald, then the claim is neither true nor false. It's the nature of vague words, such as "bald", that their meaning is not sufficiently fixed to answer certain questions, such as: "Is Barry bald?" Later in this entry, we'll see an example of how it can be possible to check claims for truth and falsity even when they contain vague language. However, if a claim is so vague that it's not clear whether it's true or false, it's best to either ignore it, or point out that it's too vague to rate and explain why.

These rating systems are an open invitation to bias in rating factual claims. A fact-checker rating a false claim made by someone whose politics the checker agrees with is likely to downgrade the rating from False to Mostly False, or even Half True, or to give it less than four Pinocchios, let alone "Pants on Fire!". Similarly, a checker rating a true claim made by someone whose politics the checker dislikes is likely to find some excuse to downgrade it to Half True, or even to Mostly False. Let's look at an example of this process.

In the previous entry4, I used an example from PolitiFact, though I'm sure that I could have found just as good an example, and possibly an even better one, elsewhere. For this entry, I intentionally avoided PolitiFact so as not to pick on it. Instead, the example I have chosen is from The Washington Post's Fact Checker column5.

Earlier this year, the District Attorney of San Francisco, Chesa Boudin, made the following claims during a television interview:

Like the majority of Americans, I grew up with an immediate family member incarcerated. The majority of Americans have an immediate family member who is either currently or formerly incarcerated, so I have that in common with the vast majority of people in this country.6

The interviewer did not call into question these rather alarming claims, or even ask where Boudin got them. Of course, it's hard to fact check statistical claims in the middle of an interview*. Moreover, I haven't seen any sign that the program did any follow-up reporting itself. One public service that fact checkers can provide is to check such claims when the news media fail to do their jobs. It appears that a skeptical viewer's question initiated The Post's fact check.

The claim that the majority of Americans have an immediate family member incarcerated either now or in the past is a surprising one, let alone that the vast majority do. It's in just such moments of surprise that one's skeptical immune system should be engaged. The reason why you are surprised at a claim is that it goes against your own experience or knowledge. Of course, your own experience is limited, and what you think you know may be wrong. Some surprising things turn out to be true, but many turn out to be false, and the purpose of fact checking is to separate the two.

As mentioned above, an often neglected step in fact checking is logically analyzing complex factual claims into their true-or-false components. In this case, Boudin made three distinct factual claims:

  1. He himself had an immediate family member incarcerated.
  2. The majority of Americans have an immediate family member who is either currently or was formerly incarcerated.
  3. The vast majority of Americans have an immediate family member who is either currently or was formerly incarcerated.

I don't think there's any doubt that the first claim is true, so we won't waste any further time on it7. Rather, it's the second and third claims that call for checking. Though obviously logically similar, those two claims are distinct. The word "vast" is the only difference between the two sentences, but there is a difference, if not a vast one, between a majority and a vast majority.

The second claim is true if, and only if, greater than half of Americans have an immediate family member who is either currently or was formerly incarcerated. So, if just over 50% of the American population fits the bill, then the claim is true.

The third statement makes a logically stronger claim, that is, if it is true then the second claim will also be true, but not the other way around. In other words, a "vast" majority is a majority, but not every majority is vast. For this reason, Boudin's second claim could be true while his third one was false.

There are two vague words in these claims:

  1. "Immediate": What exactly is an "immediate" family member? Presumably, parents, children, and siblings would count. What about grandparents or grandchildren? Do the family members have to live together to be "immediate"?
  2. "Vast": The "vast" majority of some class is obviously greater than a simple majority, but how much greater is unclear. Is 55% a "vast" majority? How about 60%? No doubt 95% would be a vast majority, but what about 90%? 85%?

So, both of the claims are vague, but that doesn't automatically rule out rating them as definitely true or false. While vague terms have borderline cases―such as the aforementioned Barry―they also have clear-cut cases, such as Barry's hairy brother, Harry, who has a luxurious head of hair. Though "Barry is bald" is neither true nor false, "Harry is bald" is clearly false. So far, we don't know whether the two claims in question are like "Barry is bald" or "Harry is bald", so we can't stop here.

Now that we've laid the logical foundation for checking these claims, let's proceed to examine The Post's fact check. How can these two claims be checked? Obviously, we need to know what percentage of the American population has had an immediate family member incarcerated. Unfortunately, there don't seem to be any official statistics that could answer this question. Instead, the only way to do so is to look at surveys that ask people whether they have had an immediate family member in jail or prison. The Fact Checker mentions two such surveys:

  1. The FWD.us Survey: This survey was funded by FWD.us, a political group that started out campaigning for immigration "reform"8, but has since added incarceration "reform" to its causes. It also supports the silly "people first language" doublespeak project9, but let's not hold that against the survey.

    Here's the exact wording of the question asked by the survey:

    Many people have been held in jail or prison for a night or more at some point in their lives. Please think about your immediate family, including parents; brothers; sisters; children; and your current spouse, current romantic partner, or anyone else you have had a child with. Please include step, foster, and adoptive family members. Confidentially and for statistical purposes only, have any members of your immediate family, NOT including yourself, ever been held in jail or prison for one night or longer?10

    According to the report: "The data show that 45 percent of Americans have ever had an immediate family member incarcerated.11"

  2. The CNN/KFF Survey: This survey was paid for and conducted by Cable News Network and the Kaiser Family Foundation, a non-profit organization primarily focused on national health care12. In a survey on race, the following question was asked: "Have you or any of your family members or CLOSE friends ever been incarcerated, or not?13" 39% of respondents answered "yes".

The Fact Checker claims that these two surveys are incomparable because of the difference in question wording, but that's incorrect. The CNN/KFF question is logically broader than that asked by the FWD.us. CNN/KFF asked about all family members, not restricting it to immediate ones, and included close friends. Since those who have had immediate family members incarcerated are included in those who have had family members or close friends incarcerated, the latter set is larger than the former. Instead, we see the opposite result in the surveys: 39% answered the broader question affirmatively as contrasted with 45% answering the narrower one "yes". This is inconsistent, which means that at least one of these survey results must be wrong.

Now, I don't know which survey is wrong, but it isn't necessary to decide. Despite their incompatible results, the two surveys agree on one thing: less than 50% of Americans have had an immediate family member incarcerated. This means that both of Boudin's claims are false.

Apparently, the Fact Checker asked Boudin himself or a spokesperson for the source of his statistics and was informed that they were based on the FWD.us survey5. Then, the checker proceeded to check the claims against the study's findings as though the question were whether Boudin reported the paper's claims correctly, though what the checker was supposed to check was whether those claims were true or false.

Relying on the FWD.us survey, the checker concluded: "The overall rate of Americans who have had an immediate family member behind bars, 45 percent, is remarkably high but not quite a 'majority' and far from a 'vast majority.'5" So, both of Boudin's claims were false, according to the very survey that his spokesperson cited.

Despite this finding, the Fact Checker spends the remainder of the column making excuses for Boudin and ends up awarding him a single Pinocchio, which is the lowest "false" rating available. Both of Boudin's claims were false, no matter which survey you consider, and his claim that the "vast majority" of Americans had had immediate family incarcerated was outrageously false. Yet, here's the Fact Checker rating and its explanation:

The Pinocchio Test

Boudin said the "majority" or "vast majority" of Americans currently have or previously had an "immediate family member" behind bars. The study he was citing backs him up to an extent―it found the rate was 45 percent overall, and 63 percent for Black Americans―but it's just shy of a majority of Americans. However, the researchers also asked about extended "family members you feel close with." When including those relatives, 64 percent of Americans, or nearly two-thirds, have had family in jail or prison. It's always a good idea for policymakers to read the underlying research, so errors like this can be avoided. For a light stretching of the facts, Boudin gets One Pinocchio.5

This is the sort of excuse-making you would expect to hear from a spokesperson for Boudin, not from an independent, objective fact-checker. Is 45% "just shy" of a vast majority? Did Boudin claim that the "vast majority" of Black Americans had had an immediate or extended family member incarcerated? No.

Here's the Fact Checker's description of what "One Pinocchio" is supposed to mean:

Some shading of the facts. Selective telling of the truth. Some omissions and exaggerations, but no outright falsehoods.3

What is an "outright falsehood" if these claims are not outright false? One meaning of "outright" that may apply here is "completely" or "totally"14, which brings us back to where we started: degrees of truth and falsity. Apparently, Boudin's claim that the vast majority of Americans have had immediate family in jail or prison was not false enough for the Fact Checker. What would it take to make it outright false: no Americans having immediate family behind bars? That would be absurd.

Both of the controversial claims made by Boudin are outright falsehoods, and one outrageously so, even based on the survey that was supposed to justify them. Using the Fact Checker's own criteria, these claims deserved at least three Pinocchios for "significant factual error and/or obvious contradictions.3" Of course, it would be better to drop the Pinocchios and simply label them both "false", tout court.

My criticism here is entirely of the fact check's rating and its explanation, not of the research that went into the body of the article. By presenting the facts, the article allows readers to come to their own conclusions about Boudin's claims, and judge for themselves whether "one Pinocchio" is a reasonable rating. This is a genuine public service that I don't mean to denigrate.

That said, fact checks such as this give fact checkers a reputation for bias. One thing that The Washington Post and other checkers should do to restore their reputations is stop using such rating scales. Instead of Pinocchios and Pants-on-fires, they should either switch to simple true and false or drop the ratings entirely and simply present the facts as Annenberg does, then let the reader be the judge.


*Correction (10/18/2021): Originally, I wrote: "Of course, it's hard to fact check statistical claims in the middle of an interview, especially when it's a friendly, 'softball' interview such as this with no significant skepticism expressed about anything Boudin said." I based this claim on the latter part of the interview in which the incarceration claims occurred, but the interviewer did express some skepticism about Boudin's claims about crime in San Francisco early in the interview, so I shouldn't have characterized it as "friendly" or "softball". My apologies to the interviewer and to readers for the mischaracterization.


Reader Response (10/18/2021): David Hawkins raises an important issue:

In this post you criticize the fact checkers for treating truth and falsity by degrees. "In this entry, I examine a different problem with such systems, namely, that they treat truth and falsity as if they come in degrees." However, further down in the post the grievance seems to be repeated. Both of the controversial claims made by Boudin are outright falsehoods, and one outrageously so. The implication here seems to be that the outrageously false claim is even more false than the outright false claim.

I also recall from the "Fact-Checkers ≠ Lie-Detectors" post that the subjectivity issues taken with the term "ridiculous" that could be applied here to the term outrageous. What is the evidence that the second claim itself was outrageously false? Is 1 + 1 = 11 a ridiculous or outrageous falsehood relative to the outright falsehood of 1 + 1 = 3. To your point, both of these answers on a math quiz would be marked incorrect, and qualifying the truth or falsehood of a statement in any way seems to be judging them by degrees, this includes the various fact-checking ratings systems, ridiculous, outrageous, and reasonable.

I certainly didn't intend that interpretation of the word "outrageously". The meaning of the word I had in mind was "in a shocking way15". I don't think that an outrageously false claim is somehow more false than a more plausible one, just that it's more obviously false. The same is true of "ridiculous". You're right that such judgments are subjective, and what's obvious to me may not be obvious to you, or to the producers and reporters of the television show where Boudin made the false claims.

It's a bad idea to build such subjective judgments into the ratings system, if that's what the fact checkers are doing. One of the criticisms made of them is that they are just pundits masquerading as objective reporters16, and to the extent that they are building such subjective judgments as "ridiculous" and "outright" into their ratings, the criticism is correct.

I'm also a little shocked that Boudin's claims went without challenge, that no follow-up was done, and that the show broadcast such falsehoods and never corrected them. This is one reason we have a pandemic of misinformation today. There's been so much of this in recent years that I should no longer be shocked and outraged by it, but I still am.

I mentioned in the entry, above, the need of fact checkers and reporters for a "skeptical immune system" that will raise the alarm when confronted with a claim that is "outrageous" or "ridiculous". Of course, any warning system will have false positives, but a well-calibrated skeptical immune system will prevent most misinformation from entering your brain and taking up permanent residence. Given the epidemic of misinformation, and the failures of those who are supposed to prevent it but instead spread it themselves, we all need such a system.


Notes:

  1. A happy exception is the Annenberg fact-checking project, which is one reason why I consider it the best fact checker; see: "Our Process", Fact Check, 8/12/2020.
  2. Angie Drobnic Holan, "How we determine Truth-O-Meter ratings", PolitiFact, 10/27/2020.
  3. "About the Fact Checker column", Glenn Kessler, accessed: 10/16/2021.
  4. This is the second entry in the fact-checking series on what is wrong with professional fact-checking as it is now practiced. For the previous entry, see: Fact-Checkers ≠ Lie-Detectors, 8/27/2021.
  5. Salvador Rizzo, "San Francisco DA claims 'vast majority' of Americans have had family behind bars", The Washington Post, 7/30/2021.
  6. For video of the interview, see: "San Francisco's Polarizing District Attorney: 'I Refuse to be Distracted'", Amanpour & Co., 7/28/2021. The quote comes at about 15:00. The transcription and punctuation are taken from the Fact Check; see the previous note.
  7. See the short biography included in the The Post's fact check; note 5, above.
  8. Rachael Bale, "What is Mark Zuckerberg's Fwd.us?", KQED, 4/11/2013.
  9. See: "Why People First?", FWD.us, accessed: 10/7/2021. Also, see: Close Encounters with Doublespeak of the Third Kind, 9/8/2019.
  10. Peter K. Enns, et al., "What Percentage of Americans Have Ever Had a Family Member Incarcerated?: Evidence from the Family History of Incarceration Survey (FamHIS)", Socius: Sociological Research for a Dynamic World, 3/4/2019, under "Measuring Family Incarceration". Paragraphing suppressed; all-capitals in the original.
  11. Ibid., under "Abstract".
  12. "CNN/Kaiser Family Foundation Survey of Americans on Race", Kaiser Family Foundation, 11/2015.
  13. Ibid., p. 33, question D12; all-capitals in the original.
  14. "Outright", Cambridge Dictionary, accessed: 10/16/2021.
  15. "Outrageously", Cambridge Dictionary, accessed: 10/18/2021.
  16. For an example, see: Mau-Mauing the Fact Checkers, 10/27/2008. I've changed my opinion since I wrote this.

October 12th, 2021 (Permalink)

True Lies

It's not just the news media that exaggerate the numbers of cases and of children hospitalized due to COVID-191. I suppose that it won't come as too much of a shock that politicians do it, too.

Case in point: Democrat Terry McAuliffe is running for Governor of Virginia. Strike one: In a debate on the 28th of last month, he claimed: "We had 8,000 cases yesterday in Virginia.2" Strike two: In a television interview the day after the debate, he said: "You know, we had 8,000 cases yesterday.3" Strike three: During a candidate roundtable on a local television station last Thursday, McAuliffe said: "Just this week, 8,000 cases on Monday in Virginia.4" He's out!

Obviously, this is memorized boilerplate from McAuliffe's stump speech. Even without doing any research, you can tell that there must be something wrong, since he attributes the same number of cases to three different days. The debate was held on the 28th of last month and the interview was the day after, so "yesterday" was the 27th and 28th, respectively. The roundtable was held last Thursday, so the Monday in question was the fourth of this month. How likely is it that there were 8,000 cases in Virginia on each of those days?

How many cases were there in Virginia on those three days? It's not hard to find out: the Virginia Department of Health (VDH) has an accessible website that's easy to use5. You can find out the answer in just a few minutes―I know, that's what I did―and I suggest checking them out for yourself. Here they are for the record:

DateConfirmed CasesProbable CasesTotal
9/27/20211,9141,1503,064
9/28/20211,8921,0222,914
10/4/20211,6289702,598

So, even including the merely probable cases, McAuliffe's number was between 2.5 and 3 times too many. These numbers may go up somewhat over the next week or two as backlogs come in, but they're unlikely to end up anywhere near 8,000.

In a meeting with a group of doctors in Charlottesville, McAuliffe was quoted as saying: "Today in Virginia, we have 1,542 children in emergency rooms, ICU beds.6" The next day, in the same roundtable interview quoted above, he said: "We in Virginia today, 1,142 children are in ICU [Intensive Care Unit] beds.4"

I haven't been able to find statistics specifically on child hospitalizations, but on the day of the meeting with the doctors there were a total of 468 ICU patients of all ages. Similarly, there were 460 occupied ICU beds a day later on the date of the candidate forum7. Given the typical age rates for serious cases of COVID-19, a tiny fraction of those totals will be for pediatric patients.

Why does McAuliffe keep repeating these wildly false numbers? He's campaigning on a platform of mandating vaccines and masks for students, teachers, and state workers among others8. So, it's obviously in his political interest to convince people that the disease is dangerous enough to justify such measures. Of course, one effective way of alarming people is to claim that their children are in danger.

Unfortunately, the people of Virginia cannot look to their state news media for a debunking of these falsehoods. As far as I've been able to find out, no news outlet in Virginia has done so. Of course, it would be difficult for reporters to check such claims in a live forum, such as a debate, an interview, or a roundtable, but the television stations that broadcast them have done no follow-up that I can find, nor have newspapers based in the state.

I'm hesitant to call anyone a liar9, but it's hard to see how this could be anything but lying. Surely McAuliffe must have realized that even if there had once been 8,000 cases "yesterday", it wouldn't still be true the next day or the next week. Why did he keep robotically repeating the same inflated number? Either he knew it was false, or he simply didn't care whether it was true or false as long as it helped to get him elected. I'm not sure which is worse.


Notes:

  1. I allude to: A Sign of The Times, 10/8/2021.
  2. "Virginia Gubernatorial Debate", C-SPAN, 9/28/2021. The quote is at about 8:00. My transcription and punctuation.
  3. Matt Pusatory, "Virginia gubernatorial candidates talk to Get Up DC following second debate", WUSA9, 9/29/2021. See the second video at about 1:30. My transcription and punctuation.
  4. "2021 Race for Governor: Virginia Roundtable Discussion", WAVY, 10/7/2021. The quote is at about 23:00. My transcription and punctuation.
  5. "Cases", Virginia Department of Health, accessed: 10/12/2021.
  6. Elizabeth Holmes, "McAuliffe meets with Charlottesville-area doctors", NBC29, 10/6/2021.
  7. "VHHA Hospitalizations", Virginia Department of Health, accessed: 10/12/2021.
  8. Eric Bradner, "Virginia governor's debate: McAuliffe and Youngkin battle over Covid-19 vaccine mandates", Cable News Network, 9/29/2021.
  9. See, for instance: Fact-Checkers ≠ Lie-Detectors, 8/27/2021.

October 8th, 2021 (Permalink)

A Sign of The Times

I've previously asked the question: why do mistakes in the news media about COVID-19 always seem to go one way1? Why do they always exaggerate, sometimes enormously, the risks and ill effects of the disease? Is it just me? Do I only hear about the mistakes that exaggerate? Are there just as many or more that downplay the disease that I don't hear about?

I don't think it's just me, though I can't prove it. I think the explanation for this effect is bad news bias; in other words, there is little incentive for news outlets to avoid errors that exaggerate the scariness of the disease. Alarming news gets people's attention, and the news media are in the attention-getting business.

All of which is by way of introduction to the latest horrid example of misreporting. On Wednesday, in an article about the trade-offs in vaccinating children against COVID-19, the Gray Lady herself told us: "Nearly 900,000 children have been hospitalized with Covid-19 since the pandemic began….2" Thankfully, that's not true, and the article has since been revised to read: "More than 63,000 children were hospitalized with Covid-19 from August 2020 to October 2021….3" So, according to the corrected article, the original exaggerated the number of hospitalized children by fourteen times.

How did this error occur? Unfortunately, the correction issued by the Gray Lady provides no explanation of where the extra 837,000 hospitalized children came from4.

What would have happened if this mistake had gone the other way, that is, if the statistic had underestimated the number of hospitalized children by a factor of fourteen? That would mean that the Gray Lady would have reported that only 4,500 children had been hospitalized since the epidemic began. Do you think that such a mistake would have gotten past the reporter and editor of the story? I don't.


Notes:

  1. Here We Go Again: Florida's New Record Number of Cases (Updated), 8/12/2021. See the first Update.
  2. Apoorva Mandavilli, "A New Vaccine Strategy for Children: Just One Dose, for Now", The New York Times, 10/6/2021. This is an archived copy of the uncorrected article.
  3. Apoorva Mandavilli, "A New Vaccine Strategy for Children: Just One Dose, for Now", The New York Times, 10/6/2021. This is the corrected article.
  4. "Corrections: Oct. 8, 2021", The New York Times, 10/8/2021. See under "National".

October 3rd, 2021 (Permalink)

The Case of the Disappearing Bat

The following headline introduces a mysterious and tragic tale:

Texas man chased down carjacker who allegedly dragged women to her death with baseball bat1

Before looking at the story beneath it, let's see if we can figure out what happened from the headline alone. There are two grammatical problems with the headline, both of which introduce mysteries into the tale. First of all, the singular pronoun "her" appears to refer back to the plural noun "women". So, the first mystery is: was it one woman or more than one?

Since it seems unlikely that even one woman would be dragged to her death, let alone more than one, I'm going to guess that it was just one and that "women" is simply a typographical error. So, as a first step, let's correct the headline:

Texas man chased down carjacker who allegedly dragged woman to her death with baseball bat

The second problem is also grammatical: what noun does the adjectival phrase "with baseball bat" modify? In other words, who had the baseball bat? The Texas man, the carjacker, or the woman? So, there's a triple ambiguity in the headline, or an amtriguity2. Even more specifically, it's a triple amphiboly, that is, it is triply grammatically ambiguous.

The phrase "with baseball bat" is closest to "woman", but it seems unlikely that a woman with a baseball bat would be dragged to her death. Wouldn't she drop the bat? Maybe it's the carjacker who had the bat, but how do you drag someone to death with a bat? A rope or chain would seem to be the sort of implement to use, though I have to admit to a lack of experience. So, by a process of elimination, it must be the Texas man who had the bat. It's rather more obvious how a Texas man―or one from any other state for that matter―could chase down a carjacker while carrying a bat. Personally, if I were going to chase a carjacker, I would like to have some sort of weapon, though again I speak from a dearth of experience. So, assuming that it was the Texas man carrying the bat, let's revise the headline:

Texas man with baseball bat chased down carjacker who allegedly dragged woman to her death

This revised headline tells a horrifying but less mysterious tale. So, now let's read the article beneath the headline and see if this hypothesis as to what happened is correct.

Surprisingly, there's no mention of a baseball bat in the story! Here are the relevant parts of the short article:

A Texas man helped to stop a suspected killer during a carjacker [sic] after surviving a similar incident months ago. … Months later, he was in the same area of Uvalde on Wednesday at 2:30 p.m. when he saw a man trying to force a woman, Jessica Garza, from her car, ABC 13 reported. "I jumped in my car, I didn't even think," Matos [the Texas man] said. "All I kept thinking was 'he's not getting away.'" Marcus Wayne Brock, identified by police, drove off with the vehicle while dragging Garza along the ground for four or five blocks as her seatbelt trapped her against the car. Matos followed for a time but was not able to stop the incident before Garza died. "I was mortified," Matos said. "When I picked up that piece of signage that was on top of her car, and I saw what he did to her, I was enraged." Brock eventually crashed into a carwash before fleeing on foot. Matos continued to pursue Brock until he found him in Ralston Liquors and kept him there until police arrived.…1

There's no bat but a mysterious "piece of signage" that was somehow on the top of the woman's car. Was the piece of signage mistaken for a bat? Did the Texas man wield that piece of signage as a weapon when chasing the carjacker? This story raises more questions than it answers.

The bizarre headline was subsequently revised to:

Texas man chased down carjacker who allegedly dragged woman to her death3

The grammar was corrected and the bat has now disappeared from the headline. The story itself appears to be unchanged, including the grammatical error in the first sentence.

However, the bat makes a surprise reappearance in a video accompanying a different article on the same crime by a local television station. According to the video, the heroic Texas man, Matos, had a bat while holding the suspect prisoner in the liquor store4. Also, in the same video you can see what may be a sign of some sort leaning against the driver's side of the carjacked vehicle. So, apparently there really was a bat and not a piece of signage. Where the bat came from is not explained.

There's one final mystery I can't solve: does Fox News employ copyeditors?


Notes:

  1. Peter Aitken, "Texas man chased down carjacker who allegedly dragged women to her death with baseball bat", Fox News, 10/2/2021. This is the Internet Archive Wayback Machine's archived copy of the original page, which has since been revised as explained above.
  2. Oddly enough, I can't take the blame for perpetrating this ugly neologism, as a websearch indicates that it's been committed a few times previously. However, I am to blame for perpetuating it. See: Perpetrate or Perpetuate, 7/2/2021. For an example of a previous occurrence of the word, see the following paper on explanation: Jonathan Waskan, "Intelligibility and the CAPE: Combatting Anti-psychologism About Explanation (Draft)", Academia, accessed: 10/3/2021.
  3. Peter Aitken, "Texas man chased down carjacker who allegedly dragged woman to her death", Fox News, 10/2/2021. This is the current page with revised headline; accessed: 10/3/2021.
  4. Stefania Okolie, "Witness to carjacking months ago helped to stop suspected killer on Uvalde", ABC 13, 10/1/2021. The article itself does not mention the bat.

Previous Month


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Recommended Reading
September 30th, 2021 (Permalink)

The Lab Leak Debate & Ideas Vs. Ideology

Censorship is again the theme of this month's recommended readings. I wish it didn't have to be. There are two fronts in the advance of censorship in our society: the media and academia. First, the media:

In June's "Recommended Reading"1, we saw how Chinese propaganda and censorship has infiltrated America's news media, and the following article discusses how it may have affected the most august American news organization of them all. It's by the author of The Gray Lady Winked, which I reviewed here last month2.


Notes:

  1. The Tank Man & Speaking Out Against Lockdowns, 6/30/2021
  2. Book Review: The Gray Lady Winked, 8/23/2021
  3. See: The editors of Lingua Franca, The Sokal Hoax: The Sham That Shook the Academy (2000)
  4. "What Exactly Is a 'Liberal'?", Merriam-Webster, accessed: 9/30/2021

Disclaimer: I don't necessarily agree with everything in these articles, but I think they're worth reading as a whole. In abridging them, I have sometimes changed the paragraphing and rearranged the order of the excerpts in order to emphasize points.


September 29th, 2021 (Permalink)

A trillion here, a trillion there, and pretty soon you're talking about real money.1

No number is big or small in itself. I'm not referring to the fact that "big" and "small" are vague concepts, though they are. Rather, I mean that whether a number is big, small, or in-between depends on what you're talking about. Seven may seem like a small number, but not if you're talking about human height in feet. Of course, some numbers are bigger than others: a million is definitely a larger number than seven. So, whenever you wonder whether a number is big or small, you should ask: relative to what? A million may seem like a large number, but not if you're dealing with dollars of federal spending. These days, even a billion dollars is peanuts to the federal government.

One of the uses of numbers is to compare the sizes of sets of things, but we can't do this well if we don't have a sense of the relative sizes of the numbers. Most of us don't have a good sense of the size of any number ending in "-illion", because we have little personal experience with numbers of such size. We suffer from "number numbness"2 when confronted by numbers in the millions, billions, and trillions, which is the paralyzing effect that very large or extremely small numbers have on our brains.

In particular, few of us have experience with amounts of money greater than a few thousand dollars, and thus no sense of the size of a million dollars, let alone a billion or a trillion. A trillion might as well be a gazillion for all it means to us. However, to put it in a bit of perspective, a trillion is a thousand billion, which is a thousand million; so a trillion is a million million. Also, it may help to at least write out $3.5 trillion dollars with all the zeros, rather than just use the number "trillion", so here it is: $3,500,000,000,000.

I mention the number 3.5 trillion, because that's the price tag in dollars of the federal "reconciliation" bill that has been so much in the news3. "Reconciliation" refers to the recondite legislative process whereby the House of Representatives and the Senate somehow manage to merge their separate bills into a single one4. No one knows exactly what is in the resulting bill, except that it is a grab-bag of taxing and spending. I mean that, literally, no one knows; the current bill is almost 2,500 pages long5, which is a big number for the length of a legislative bill. To put that number into perspective, if you could read the bill at the rate of a page per minute, which is fast, it would still take over forty hours to read. So, there's no way that any one person has read the whole thing carefully.

Even the president of the United States doesn't appreciate the size of a trillion dollars, for he recently made the following statement: "Trillionaires and billionaires are doing very, very well…6." But there are no trillionaires7. The current richest person on Earth is Jeff Bezos, who has a fortune of less than $200 billion, which may sound like a lot, but that's only a fifth of a trillion. So, he's still got a long way to go to become a trillionaire.

Part of numeracy is developing a "number sense" in place of number numbness, that is, developing a feel for the relative sizes of numbers. One way to do so is to learn how to "divide and conquer", that is, to divide a large number by some other number in order to produce a number small enough to "conquer". Of course, the divisor must make sense when dividing the large number. For instance, it's often helpful to divide a large number by the population of the world, a particular country, or some other geographical unit; the result is a ratio "per capita"―that is, "by the head" in Latin8. So, let's do this with the price tag on the reconciliation bill.

A "landmark" number is a statistic that is useful enough to remember. A geographical landmark helps us to find our way around the landscape, whereas a landmark number can help us navigate the statistical landscape. One such number is the current population of the United States, which is easy to remember: about a third of a billion people9. So, to figure the amount per capita of the reconciliation bill, divide 3.5 trillion by 330 million. You'll probably want to use a calculator.

If $3.5 trillion were distributed equally to every man, woman, and child in the United States, it would come to about $10,500 a head, or over $42,400 for a family of four. While $42K is sofa change to the federal government, it is a large sum for most American families. Wouldn't they rather have the government send them a check for their share, rather than spend it on whatever pork barrel projects are funded in the bill?

Any way you look at it, $3,500,000,000,000 is a lot of money. Could Congress get away with trying to spend so much if the American people really understood just how much it is?


Notes:

  1. The title is based on the statement: "A billion here, a billion there, and pretty soon you're talking about real money", which is usually falsely attributed to Senator Everett Dirksen, according to Ralph Keyes, and is here adjusted for inflation. See: The Quote Verifier: Who Said What, Where, and When (2006), pp. xix & 13-14. This entry is based, in part, on the following entries:
  2. Douglas R. Hofstadter, "On Number Numbness", Metamagical Themas (1985), pp. 115-135.
  3. See, for instance: Kristin Wilson, "House Budget Committee votes to pass the $3.5 trillion spending bill", CNN, 9/25/2021.
  4. Eric McDaniel & Kelsey Snell, "A $3.5 Trillion Question: What Is Budget Reconciliation? Here's An Explainer", National Public Radio, 9/14/2021.
  5. Andrew Solender, "Pelosi Says It's 'Self-Evident' Reconciliation Spending Will Be Less Than $3.5 Trillion", Forbes, 9/26/2021.
  6. "Remarks by President Biden on the COVID-19 Response and the Vaccination Program", The White House, 9/24/2021.
  7. Dan Evon, "Do Trillionaires Exist?", Snopes, 9/24/2021.
  8. Eugene Ehrlich, Amo, Amas, Amat and More: How to Use Latin to Your Own Advantage and to the Astonishment of Others (1985).
  9. "What is the current population of the United States of America?", Wolfram Alpha, accessed: 9/29/2021.

September 19th, 2021 (Permalink)

What's New? The Fallacy of the Sheep is!

While writing the previous entry I was somewhat surprised to discover that it was the fourth example over the last ten years of the fallacy of the sheep, yet I didn't have a separate entry for that fallacy. So, now I've filled that lacuna. You can access the new entry from either the Taxonomy on the Main Menu, or the drop-down menu of the alphabetized fallacy entries, both available in the navigational frame to your left. Check it out!


September 16th, 2021 (Updated)(Permalink)

"Breakthrough" Infections and the Fallacy of the Sheep

…[T]he operator of a diner…offered rabbit sandwiches at a remarkably low price. When questioned about it, he admitted that he used some horse meat to keep his costs down. "But I mix 'em fifty-fifty," he avowed. "One horse to one rabbit."1

In the last few months we've started hearing a lot about "breakthrough" infections. Google Trends shows that the number of searches for the phrase "breakthrough infection" was almost none before April of this year, then peaked in the first week of last month, has declined some since, but remains much higher than before April2. What exactly is a "breakthrough" infection?

A breakthrough infection is simply one in which a vaccinated person becomes infected with the virus the vaccine protects against; it does not mean that the person has any symptoms of the disease3. Since no vaccine is 100% effective in preventing infection, there will always be some breakthrough infections.

Nonetheless, recent events have led to some alarm about coronavirus breakthrough infections: in late June, it was reported that nearly half of new cases in Israel were in people who were vaccinated4, and 75% of those infected in Provincetown, Massachusetts a month later were also vaccinated5.

Some people have misinterpreted these statistics to mean that the vaccinated are just as likely, or even more likely, to become infected than the unvaccinated6. Doing so, however, commits the fallacy of the sheep7.

You may have heard the old riddle: Why do white sheep eat more than black sheep? Because there are more of them. It's not a very good riddle, but it illustrates an important point. When comparing two or more classes of things, you should take into consideration the size of the classes compared. Unless the two classes are the same size, comparing the absolute numbers of a characteristic, such as an infection, between the two classes will be misleading8.

In the case of Israel noted above, the fact that half of those infected were vaccinated and half were unvaccinated, does not mean that the former were just as likely to be infected as the latter. Israel has a high rate of vaccination, with about two-thirds of Israelis having received at least one dose of a vaccine, and about 90% of those being fully vaccinated, at the time of the report9. This means that there were at least twice as many vaccinated Israelis than unvaccinated, yet only half of the new cases were in those vaccinated. Similarly, close to 95% of the population of Provincetown was vaccinated, yet only three-quarters of those infected10. So, there were more white sheep than black ones.

It's likely that we will see more breakthrough infections in coming months as the rate of vaccination continues to increase. So, when you read reports about breakthrough infections in a particular area, always look for the rate of vaccination there. The higher that rate, the higher the percentage of all infections will be breakthrough ones.


Update (9/22/2021): The United States just passed another "grim milestone"; here's how Newsweek reports it:

Deaths related to COVID-19 in the U.S. have reached 676,000, surpassing the number that died during the Spanish Flu pandemic of 1918. Until now, the Centres for Disease Control and Prevention (CDC) had considered the influenza epidemic of 1918 to be the worst pandemic in modern history. … In the U.S. alone the 1918 influenza epidemic killed an estimated 675,000, around one in five people who contracted the virus. … The global spread of the 1918 flu is often referred to as "the forgotten pandemic" because it was overshadowed by the First World War…. Just as it was once overshadowed by WWI, the 1918 pandemic has now been eclipsed by COVID-19. According to The New York Times COVID map, the number of deaths in the U.S. during this current pandemic has topped the number reached by the Spanish Flu.11

As far as I can tell, the CDC still considers the Spanish Flu "the worst pandemic in modern history", specifically calling it "the most severe pandemic in recent history"12. The page from which I take that quote is from a few years ago, but it hasn't been updated due to the latest "grim milestone". Moreover, I doubt that it will be updated, at least not to claim that COVID-19 is worse than the Spanish Flu, and here's why.

I mentioned in the "Exposure" section of the new entry for the Fallacy of the Sheep, q.v., that you need to be wary of comparing statistics from the past and present that may be affected by the increase of population over time. This is what makes the above Newsweek report a perfect example of the fallacy, since it compares the absolute numbers of deaths from COVID-19 with those of the Spanish Flu from over a hundred years ago, without any mention of the difference in population.

The population of the United States in 1918 was 103 million13, whereas it is currently 331 million14. Thus, the 1918 population was less than a third of what it is today, which means that the death toll of COVID-19 would have to be three times as much as the current "grim milestone" to match the death rate of the Spanish Flu.

So, COVID-19 is not now the worst pandemic in modern history, as suggested by Newsweek. It's not even close.


Notes:

  1. Darrell Huff, The Complete How to Figure it: Using Math in Everyday Life (1996), p. 391.
  2. "breakthrough infection", Google Trends, accessed: 9/16/2021.
  3. See:
  4. Marianne Guenot, "Israel says the Delta variant is infecting vaccinated people, representing as many as 50% of new cases. But they're less severe.", Business Insider, 6/24/2021.
  5. Kristina Fiore, "No, Most COVID Infections Are Not Occurring in Vaccinated People", MedPage Today, 8/6/2021.
  6. Jessica McDonald, "Posts Misinterpret CDC's Provincetown COVID-19 Outbreak Report", Fact Check, 8/6/2021.
  7. Stephen K. Campbell, Flaws and Fallacies in Statistical Thinking (1974), pp. 101-104. For other examples of the fallacy, see:
  8. Katelyn Jetelina calls the mistake "base rate bias" or "the base rate fallacy"―see the entry for the latter from the drop-down menu to your left. I'm not sure what "base rate bias" refers to, but I don't think that this is an example of the fallacy of the same name. The base rate fallacy and the fallacy of the sheep are similar, but the latter is a better match for the mistake committed here. See: Katelyn Jetelina, "Israel, 50% of infected are vaccinated, and base rate bias", Your Local Epidemiologist, 6/27/2021.
  9. Edouard Mathieu & Hannah Ritchie, "Vaccinations and COVID-19―Data for Israel", Our World in Data, 2/8/2021. See the charts; accessed: 9/16/2021.
  10. Ellen Barry & Beth Treffeisen, "'It's Nowhere Near Over': A Beach Town's Gust of Freedom, Then a U-turn", The New York Times, 7/31/2021. The outbreak took place due to an influx of visitors to the town, and 80% of the infections due to the event were in such visitors, but I haven't been able to find out what percentage of those visitors were vaccinated. Presumably that percentage was less than 95%, so that the overall percentage of vaccination among those in the town at the time of the outbreak would also be less, but how much less I don't know.
  11. Robert Lea, "How Many Americans Died From Spanish Flu and How Did the Pandemic End?", Newsweek, 9/21/2021. Paragraphing suppressed.
  12. "History of 1918 Flu Pandemic", Centers for Disease Control and Prevention, 3/21/2018.
  13. "What was the population of the United States in 1918?", Wolfram Alpha, accessed: 9/22/2021.
  14. "What is the current population of the United States?", Wolfram Alpha, accessed: 9/22/2021. This is a useful landmark number―that is, a number that can help you navigate the statistical landscape―and it's easy to remember since it's about one-third of a billion.

The March Hare, the Dormouse, and the Mad Hatter
September 11th, 2021 (Permalink)

Play with Your Mind, Part 2

Note: Here's an example of the second of the two types of logic puzzle found in this month's new book, Games for Your Mind1, namely, a "knights and knaves" puzzle. Specifically, it's from the master of this type of puzzle, Raymond Smullyan:

…Alice [and] the Duchess…had the following remarkable conversation.

"The Cheshire Cat says that everyone here is mad," said Alice. "Is that really true?"

"Of course not," replied the Duchess. "If that were really true, then the Cat would also be mad, hence you could not rely on what it said."

This sounded perfectly logical to Alice.

"But I'll tell you a great secret, my dear," continued the Duchess. "Half the creatures around here are mad―totally mad!"

"That doesn't surprise me," said Alice, "many have seemed quite mad to me!"

"When I said totally mad," continued the Duchess, quite ignoring Alice's remark, "I meant exactly what I said: They are completely deluded! All their beliefs are wrong―not just some, but all. Everything true they believe to be false and everything false they believe to be true." …

"What about the sane people around here?… I guess most of their beliefs are right but some of them are wrong?"

"Oh, no, no!" said the Duchess most emphatically. "That may be true where you come from, but around here the sane people are one hundred percent accurate in their beliefs! Everything true they know to be true and everything false they know to be false."

Alice thought this over. "Which ones around here are sane and which ones are mad?" asked Alice. … "I've always wondered about the March Hare, the Hatter, and the Dormouse," said Alice. "The Hatter is called the Mad Hatter, but is he really mad? And what about the March Hare and the Dormouse?"

"Well," replied the Duchess, "the Hatter once expressed the belief that the March Hare does not believe that all three of them are sane. Also, the Dormouse believes that the March Hare is sane."2

Are the Mad Hatter, March Hare, and the Dormouse mad or sane?


Notes:

  1. Playing with Your Mind, 9/7/2021
  2. Raymond Smullyan, Alice in Puzzle-Land: A Carollian Tale for Children Under Eighty (1982), pp. 20-22 & 24-25
  3. Ibid., pp. 146-147

Puzzle
September 8th, 2021 (Permalink)

Play with Your Mind, Part 1

Here's an example of one of the two types of logic puzzle found in this month's new book, Games for Your Mind1. This one was created by Lewis Carroll of Alice in Wonderland fame2. Consider the following clues:

  1. Every one who is sane can do Logic.
  2. No lunatics are fit to serve on a jury.
  3. None of your sons can do Logic.

Based on the above clues, are any of your sons fit to serve on a jury?


Notes:

  1. Playing with Your Mind, 9/7/2021
  2. Lewis Carroll, Symbolic Logic and the Game of Logic (1958), pp. 112 & 132

New Book
September 7th, 2021 (Permalink)

Playing with Your Mind

Quote: "Among mathematical recreations generally, logic puzzles are the most ecumenical. All that is needed is a bit of patience and some clear thinking. No algebra, geometry, computational skill, or any other sort of specialized knowledge is required. The payoff for solving one, however, is the smile you wear on your face for the rest of the day."1

Title: Games for Your Mind

Subtitle: The History and Future of Logic Puzzles

Author: Jason Rosenhouse

Comment: Rosenhouse is a professor of mathematics who has written a previous book on the Monty Hall problem that I haven't read.

Date: 2020

Summary: Despite its subtitle, this book seems to be more an introduction to logic through puzzles than a discussion of their history or future. It's focused on two types of puzzle, rather than on all those that could be labelled "logic puzzles":

  1. Puzzles based on Aristotelian categorical logic. In particular, the book concentrates on puzzles created by Lewis Carroll, who is better known as the author of the Alice children's books than as a puzzle creator.
  2. What are traditionally called "knights and knaves" puzzles in which there are two types of character, "knights" that always tell the truth and "knaves" that always lie. The late Raymond Smullyan was the master of this type of puzzle, writing several books filled with them.

I've offered a number of puzzles of both types here on the weblog, including the recent "New Logicians' Club" puzzles, which are variations on the second type. Other common types of logic puzzle receive only passing mention in the book. You won't find much on Sudoku puzzles, despite the fact that they are currently the most popular type of logic puzzle. However, Rosenhouse has co-written an entire book on them2, so check that out if Sudoku seriously interests you.

Rather to my disappointment, another common type of puzzle that is largely missing is that which often goes by the name "logic puzzle"―there doesn't seem to be a more specific name for them. There are whole books and magazines devoted to this type of puzzle. Familiar examples are the Smith, Jones, and Robinson puzzle, and the Zebra puzzle―Rosenhouse does give a version of the latter as an example.

If you're interested in learning logic, but don't want to take a class or are daunted by the prospect of reading a text book, and if you enjoy puzzles, you might try this approach. You will, in fact, learn much more from working logic problems than just passively reading a book.

What little I've read of the book is clearly and accurately written, though perhaps aimed at a somewhat more sophisticated readership than I would have expected. For instance, there's a section of the first chapter on philosophy of logic3 that I would suggest skipping unless you're really interested in the topic. In fact, it wouldn't hurt to just skip the whole first chapter and get right to the puzzles in chapter 2.

Disclaimer: This book is from late last year, so it's not brand new, but I haven't read it in its entirety yet. My comments above are based on reading a short excerpt and studying its table of contents.


Notes:

  1. Section 2.2
  2. Jason Rosenhouse & Laura Taalman, Taking Sudoku Seriously: The Math Behind the World's Most Popular Pencil Puzzle (2012)
  3. Section 1.2

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