To Your Health!
Here's an instructive example of how difficult it can be to establish causation:
All those health benefits of moderate drinking may be based on nothing but a common methodological error in the studies, a meta-analysis suggested. Of 54 studies reviewed, 47 included in the "abstainer" category individuals who were not long-term abstainers but had only recently stopped drinking or cut down to once per month or less….
Because many older people abstain from or cut down on drinking for health reasons such as disability, frailty, or medication use, the abstemious group in these studies likely included many people in poorer health than those who continued to drink moderately….
"In other words, regular light drinking may be a marker for good health among middle aged and older people, not a cause of it,"…. And clinicians who have been recommending moderate drinking for its health benefits should rethink their position….
Source: Jeff Minerd, "Health Benefits of Moderate Drinking May Be Statistical Haze", MedPage Today, 3/30/2006
Puzzle: Billions and Billions
A very rich American went to Geneva to withdraw a fortune from his Swiss bank account. "I wish to withdraw one billion Swiss francs from my account," he told the banker, who checked his computer and then replied: "I'm sorry, M'sieur, but you have insufficient funds in your account to cover such a large withdrawal." "What?" shouted the American, "according to my bank book, I should have several billion in my account! This is an outrage! What happened to my money?" Both the American and the banker were correct. How is this possible?
Here's a quote from an ad for a new vitamin supplement:
Vitamin X is a powerful antioxidant found in celery that helps neutralize free radicals which can cause cell damage. Emerging science suggests that this remarkable ingredient may help maintain pineal gland health.
This is, of course, made up, but it's based on an actual ad which is just one example of recent ads that appeal to "emerging science". What in the world is "emerging" science? The only meaning of "emerging" that seems to make sense when applied to the word "science" is "coming into existence" or "developing". Thus, "emerging science" is science that is coming into existence―in other words, it is not yet science! However, the word "emerging" suggests that it will have at some future time emerged, but then again it may not.
This is a remarkable piece of advertising doubletalk. It gives the illusion of scientific support for the health benefits of vitamin X, while actually denying that such benefits have been scientifically established. Also, note how carefully hedged the claim is: emerging science suggests that vitamin X may help maintain pineal gland health. For the ad's claim to be true, there has to have been some less than conclusive research suggesting some benefit to the pineal gland, but if the evidence were strong then the science would have already emerged.
I suggest waiting until the science has emerged before spending your money on vitamin X.
Did you know that TV sitcom actor Charlie Sheen is a "highly credible public figure", a structural engineer, a demolition expert, and an expert on aviation? At least, in his own mind he is. Thanks to Robert Todd Carroll of "Skeptic's Dictionary" fame for debunking Charlie's silly 9/11 conspiracy theories. Check it out. Also, thanks to Charlie, as this is much funnier than that sitcom he's in! He's performing a public service by reminding us why we should be skeptical when a celebrity tries to sell us something, whether it's a cigarette or a conspiracy theory.
Source: Robert Todd Carroll, "9/11 Conspiracies and the War on Truth", Mass Media Bunk 27, 3/23/2006
Update (3/28/2006): John Congdon sent in the following response to Carroll's article criticizing Sheen:
I read the article you linked to, regarding Charlie Sheen's pronouncements about 9-11. Like both you and Mr Carroll, I find his assertions ridiculous and any attention paid to them, a classic example of Appeal to Celebrity. On the other hand, I wonder if Mr Carroll perhaps goes a little too far in his rhetoric? Certainly, Mr Sheen is far exceeding his expertise in his assessments of 9-11. However, Mr Carroll himself indulges in a little argument ad hominem, from his "who cares what Sheen says about anything except acting or prostitution?" in the opening paragraph (with the nice link to a not-so-nice article about Mr Sheen's fondness for prostitutes) to his rhetorical headline "Eminent Actor and Whoremonger Accuses President of Murder and Treason". To begin with poisoning the well and ending with loaded language is ironic, given that Mr Carroll (accurately) characterizes conspiracy theories as "insulting and demeaning". After all, what does a fondness for prostitutes have to do with scientific illiteracy?
All the President's Straw Men
The Associated Press has done something I've never seen a major press institution do before, namely, report on the President's use of straw man arguments. It's a "dog bites man" story, since it's not news that politicians attack straw men, as one of the experts the AP interviewed pointed out. However, it's a welcome development when the mainstream press begins to pay attention to fallacies. If politicians were publicly called more often on their fallacious arguments, perhaps they would be forced to argue better.
Source: Jennifer Loven, "Bush Using Straw-Man Arguments in Speeches", Associated Press, 3/18/2007
Via: "Straw Men", The NonSequitur, 3/18/2007
Update (4/23/2006): Actually, there was a precedent to this article in one by reporter Dana Milbank almost two years ago, which I linked to and commented on at the time, but completely forgot about until I stumbled upon the entry in the archives.
Source: Check it Out, 6/1/2004
Poll Watch: A New Low?
Here's USA Today on its latest poll results:
President Bush's "approval rating" has sunk to a new low according to a USA TODAY/CNN/Gallup poll released Monday. The latest results show only 36% of those polled saying they "approve" of the way Bush is handling his job. Bush's previous low was 37%, set last November. Sixty percent of those polled said they "disapprove" of Bush's performance. That matches an all-time worst rating hit last November and again two weeks ago. … The public's approval rating of Bush, according to the poll, slipped below 50% last May and has been hovering just above or below 40% since October. Two weeks ago, Bush's approval rating was 38%.
The logical trouble with this claim is that the poll―as most national public opinion polls―has a margin of error of ± 3 percentage points, so that the one-point difference with the previous record is statistically insignificant. Note that there's an odd contradiction in the article which first claims that the approval rating in the previous poll "match"ed the previous record of 37%, then later says that the previous poll had it at 38%. The complete results of the poll indicate that 38% is correct, but this is also within the margin of error.
The Mystery Pollster concludes from examining the results of all the recent national political polls that the approval rating has dropped since late February, but that there is no statistically significant change in the rating over the last three weeks. This leads M.P. to ask the question:
Why does each intra-pollster comparison herald a new "new low" headline, when the more accurate read (for now) would be to treat each new survey as confirming the same drop since February recorded by all? … It could be done in a sentence: "Our results are consistent with those last week by…"
He, then, answers his own question:
[T]he "new low" headline or lead is a lot more dramatic and easier to write. Most pollsters are guilty of this habit―I know I have done it in internal memos to clients―even when we hasten to add in the next sentence that, well, the new low is only a point or so lower than the old low measured last week, and therefore isn't statistically significant. But still, it is a new low! This bad habit is a matter of human nature. No pollster wants to report that the latest survey reveals "no significant change."
Unfortunately, reporters have the same motive as pollsters to hype the latest results of the poll paid for by their organization, and they're less scrupulous about adding in the next sentence that they don't really mean anything.
- Mark Blumenthal, "Another 'New Low'?", Mystery Pollster, 3/15/2006
- Mark Memmott, "Poll: Bush Approval Rating Hits New Low", USA Today, 3/14/2006
- "USA Today/CNN/Gallup Poll Results", USA Today, 3/16/2006
Update (3/20/2006): The latest Gallup poll since the one discussed above shows the approval rating back at 37%. This does not mean that Bush's public approval is improving! Rather, it shows no significant change since the previous poll, though no longer at the meaningless "record low". It supports the Mystery Pollster's analysis that Bush's popularity has remained roughly constant for the last month or so.
Source: Mark Blumenthal, "Gallup: 'Bush Approval Steady at 37%'", Mystery Pollster, 3/20/2006
According to ABC News: "Some experts think that" this satellite photograph "may be of Noah's Ark." Who are these experts? It just looks like a blob to me, but then I'm no expert! Only one "expert" is mentioned: an assistant professor at the University of Richmond. Is he an expert photographic analyst? An archaeologist, perhaps? A geologist, even? Or, maybe an expert on ships? No, he's an expert on national security law! Maybe it is just a blob, after all.
Source: "Satellite May Have Found Noah's Ark", ABC News, 3/15/2006
Logic Check: Dobson and Gambling
Annenberg Fact Check has sent out a report on a new political ad which uses guilt by association to try to link Focus on the Family founder James Dobson with the Abramoff political scandal. Of course, Dobson has used fallacies himself, as I've pointed out on more than one occasion; however, that's no excuse for a McCarthy-style attack on him. The Fact Check report does not seem to be available yet on their website, so here is an extended excerpt of the relevant portions:
An ad released by a liberal group calling themselves DefCon accuses three well-known Christian conservatives of being "knee deep" in the Jack Abramoff lobbying scandal. The ad is partly true: there is well-publicized evidence supporting the claims about political operative Ralph Reed and evangelist Lou Sheldon. However, James Dobson denies ever having met Abramoff, saying "I probably couldn't pick him out of a line-up." And one of DefCon's advisers concedes "There is no proof and I doubt there will ever be any proof that Dobson consciously colluded with Abramoff."
Their ad's claim about Dobson rests on Dobson taking anti-gambling positions that stood to benefit Abramoff clients. That's an attempt to prove guilt through mere association, a classic example of false logic. …
DefCon is accusing Dobson based on two incidents in which Abramoff's clients benefited from Dobson's actions―which were in both cases anti-gambling efforts consistent with Dobson's long crusade against legalized gambling. …Abramoff's casino-operating clients took the same position as Dobson, hoping to hold down potential competition. But there's no evidence Dobson knew that he was indirectly helping those clients. There is no record of correspondence between Abramoff and Dobson, and no evidence of any payments by Abramoff to Dobson.
Source: Justin Bank & Emi Kolawole, "Guilt by Association", Annenberg Political Fact Check, 3/13/2006 (Added: 4/22/2006)
Resources: Here are two examples of Dobson's use of fallacies:
Check 'Em Out
- John Allen Paulos' latest Who's Counting? column deals with what might be called "the bandwagon effect", namely, the tendency for already popular things to become more popular as people "jump on the bandwagon". This is no doubt one psychological source of the appeal of bandwagon arguments, in which a conclusion is argued for on the basis of its popularity, that is, the fact that many other people already believe it. (3/8/2006)
Source: John Allen Paulos, "New Blogs, New Songs and News Stories", Who's Counting?, 3/5/2006
- STATS' Rebecca Goldin has an interesting look at a study of violent abuse between siblings and how it was reported in the New York Times. She points to three problems:
- A common difficulty of studies of social problems is how to define the vague problem in precise enough terms to measure it. The vagueness of a concept such as sibling abuse is a boobytrap that can lead to serious over- or under-estimation of the extent of the problem, if the concept is defined too broadly or too narrowly.
- In this case, the overly-broad definition is defended by a weak analogy drawn by one of the researchers between violence among siblings and spouse abuse. As Goldin points out, children are less responsible and physically weaker than adults, so that actions which are serious and even criminal when committed by adults may be minor offenses when done by children.
- Journalists typically dramatize their reports of statistical studies of social problems by illustrating them with vivid examples. Such dramatic anecdotes can lead the reader to over-estimate the extent of the problem due to their vividness, which is to commit the anecdotal fallacy―also known as the "Volvo fallacy".
- Katy Butler, "Beyond Rivalry, a Hidden World of Sibling Violence", New York Times, 2/28/2006
- Rebecca Goldin, "Nasty, Brutish and Short: For The New York Times Childhood is a Battlefield", Statistical Assessment Service, 3/2/2006
A reader who wishes to remain anonymous asks the following question:
Q: I'm interested in your thoughts about what makes an argument trivial. The term "trivial" sometimes applies to circular arguments and sometimes to non-circular yet uninteresting arguments. Is there a more precise specification of triviality or does the sentence above provide the best description of this (possibly) ambiguous term?
A: This is a difficult question to answer because the word "trivial" is seldom, if ever, explicitly defined, especially as applied to arguments, proofs, or theorems. My sense is that "trivial" is a stronger version of "obvious", so that a trivial proof or theorem is one that is very obvious. However, a further meaning, as you indicate, is that a trivial argument is one that is so obvious that it is uninteresting, or uninformative. Circular arguments, as you say, are trivial because they are both very obvious and very uninformative. However, what is obvious or uninteresting is a subjective matter, which reminds me of one of Raymond Smullyan's anecdotes:
When I was a graduate student at Princeton, there was circulating the following explanation of the meaning of the word "obvious" when used by different members of the mathematics department. I shall not use names, but letters.
- When Professor A. says something is obvious, it means that if you go home and think about it for a couple of weeks, you will realize that it is true.
- When Professor L. says something is obvious, it means that if you go home and think about it for the rest of your life, the day might come when you will see it.
- When Professor C. says something is obvious, it means that the class has already known it for the last two weeks.
- When Professor F. says something is obvious, it means that it is probably false.
In researching your question, I came across the following definition: A proof is trivial in which a conditional statement is proven by proving the consequent of the conditional. Such a proof is both very obvious―given the standard truth-table for conditionals, in which a conditional is always true when its consequent is true―and uninteresting in that no logical connection is established between the antecedent and the consequent of the theorem. I had never heard this definition before, so that I don't think that it is a common one, but I do think that the distinction it draws is useful.
- "Mathematical Reasoning", from online materials for a computer science course on discrete mathematics.
- Raymond Smullyan, What is the Name of this Book? (Prentice-Hall, 1978), pp. 194-195.
Book Review: Humbug!
Title: Humbug! The Skeptic's Field Guide to Spotting Fallacies in Thinking
Authors: Jef & Theo Clark
Publisher: Nifty Books
Date of Publication: 2005
Quote: "From our perspective, the elimination of fallacious reasoning is the most important foundation of a sound argument. This book is therefore analogous to a scalpel. A surgeon uses a scalpel to remove diseased tissue―the skeptical enquirer can use this book to remove diseased arguments. … In the same way Humbug! may be used to identify and remove poor reasoning from the reader's own arguments, and to allow the reader to examine and expose poor reasoning in the arguments of others." (pp. 4-5)
Review: The authors of Humbug! are father and son Australian educators. The book is similar to Madsen Pirie's Book of the Fallacy in its alphabetical arrangement, its use of cartoons, and its witty writing style; it differs in that it is easier to acquire than Pirie's, which is out of print and hard to find. The thirty-five fallacies are by no means all logical errors, but they are certainly "bad moves" as Julian Baggini calls them.
The authors' intended audience is the undergraduate student not specializing in logic, but it presumably may be useful to those who don't know much about logic or critical thinking, and would like to learn a little. As in Pirie's book, the writing style is light and amusing. The examples are all humorously contrived, and populated by characters such as Harry Cackleberry and Orson Pecksniff. The authors occasionally engage in the "breathtaking hypocrisy"―their words, not mine! (p. 7)―of committing the very fallacy they are describing. For instance, take the following from the entry for "slippery slope":
[W]hen people who lack the mature judgement of the authors venture onto a slippery slope, they will inevitably wallow in ever-more bizarre misconceptions and fallacious reasoning until we end up with nothing but gibberish…―and finally, the complete destruction of civilization as we know it.
Physically, the book is about the size of a nature guidebook and would fit conveniently in a jacket pocket, which may explain its being called a "field guide" in the subtitle. Take it with you the next time you are called for jury service or hear a political speech. Many books on fallacies are more scholarly, but few are as entertaining as Humbug!.
Source: Humbug! is available from the Australian Skeptics.
Resource: Humbug! Online
The weblog companion to the book; it is more satirical than scholarly, with a heavy dose of Australian politics and an irreverent sense of humor.
Solution to the Puzzle: The amount that the rich American attempted to withdraw from his account was 1,000,000,000 Swiss francs, which is called a "billion" in the United States. However, in Europe, a "billion" refers to what is called a "trillion" in the U.S., namely: 1,000,000,000,000. Though the American had several "billion" in his account, he did not have a "trillion", which is what the banker took him to be requesting.
Source: Carl Bialik, "When a Billion Isn't a Billion", The Numbers Guy, 3/30/2006