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May 31st, 2009 (Permalink)

The Puzzle of the Airtight Alibi

The prosecution has proven that the defendant on trial had both the means and motive to commit the crime, but what about opportunity? The only defense given is an alibi: multiple unimpeached witnesses last saw the defendant at 9:33 A.M., but the crime was committed at 9:52 A.M. It would have taken at least an hour for the defendant to have travelled from the alibi location to the crime scene. Nonetheless, the prosecutor convinced the jury that the defendant had plenty of time to make the trip and commit the crime. How did the prosecutor do this?


May 25th, 2009 (Permalink)

What's New?

Afirmación del Consecuente: this is the Spanish translation of the entry for Affirming the Consequent. Thanks to Jaime Vilarroig Martín for translating this entry! This should be the first of several more Spanish-language entries. Hopefully, the entire website will one day be available in Spanish, and this is the first small step towards that distant goal. Ideally, some day there will be French, Russian, Chinese, … and maybe even Klingon, translations (though I suppose that in Klingon logic the Argumentum ad Baculum is valid). After that, The Singularity will occur. As always, if you have any comments or criticisms, please let me know.

Update (10/9/2013): Unfortunately, the Spanish version of this entry no longer exists.

May 23rd, 2009 (Permalink)


Q: If I may ask a technical question: why should moral fallacies be considered necessarily fallacious in the first place? This is not a matter of me disagreeing that "two wrongs make a right", "tu quoque", the naturalistic fallacy, or the moralistic fallacy are indeed fallacious. It is rather a matter of how morality is defined. As far as I can tell, all moral systems are a matter of opinion or social construct. "Good" and "evil" are not concepts rooted in physical reality, and different people, ideologies, and societies have felt free to define them differently, often in terms of the opinions of a god, a sage, or their own consciences. Now, while most people (at least when cornered and forced to deal with the issue consciously) might agree that "two wrongs make a right" is morally invalid, what is to stop anyone from defining his/her personal moral system in such terms as to make "two wrongs make a right" morally valid?―Aaron Adelman

A: I assume that when you ask why moral fallacies should necessarily be considered fallacious you mean why should they be considered logically fallacious. Errors in moral thinking, even common ones, are not necessarily logically fallacious. The Fallacy Files is limited to logical fallacies, thus excluding purely moral mistakes. For this reason, the so-called naturalistic fallacy is not included in the files―except in the sense that it is an alias of the Appeal to Nature (see the Previous Q&As below for more on the naturalistic fallacy).

The moralistic fallacy, is defined as the inference from what ought to be to what is. It is not included in the Fallacy Files under that name, but appears to be either an alias or subfallacy of Wishful Thinking. Of course, Two Wrongs Make a Right and its subfallacy Tu Quoque are included under those names.

While you may be right about the nature of ethics, that does not mean that there are not logical principles that govern moral reasoning. First of all, the general rules of logic apply to arguments about ethics as much as they apply to arguments about anything else. Furthermore, there are logical principles that apply to specifically moral language. For instance, if you morally ought to do something, then it is morally permissible for you to do so. In contrast, the converse does not hold, that is, from the fact that something is permitted it does not follow that it is obligatory. To make the latter inference would be a logical blunder, and if doing so were common enough it would count as a logical fallacy, specifically a fallacy of deontic logic.

Why is this the case? In general, logical relations are the result of semantic relations between words; for instance, the fact that a conjunction entails each of its conjuncts is a consequence of the meaning of words such as "and". If "and" meant "or"―but of course it doesn't!―then this entailment wouldn't hold. Moreover, the converse inference from a conjunct to a conjunction is generally invalid, whereas the inference from a disjunct to a disjunction holds. Similarly, the meanings of the words "ought" and "may" are such that they have a logic of their own.

Of course, all that this shows is that it's possible to have logical fallacies of deontic reasoning, not that any specific pattern is such a fallacy. Why do I consider the specific moral fallacies that you mention also logical fallacies? Let's consider the case of the Appeal to Nature in its alias as the "naturalistic fallacy".

You'll notice that I classify the Appeal to Nature as a subfallacy of Vagueness, because the words "natural" and "unnatural" are vague. Moreover, "natural" sometimes means normal and "unnatural" abnormal, so that calling something "natural" or "unnatural" may already include an evaluation of it, thus begging the question. These are semantic features of the words, so no matter what moral theory you happen to subscribe to, it will remain possible to commit fallacies with them.

Similar stories could be told about the other fallacies you mention. As an example, let's look at a recent "two wrongs" argument taken from a letter to the editor:

From Paul M. Barrett’s review of Mark Rudd’s memoir, "Underground: My Life With SDS and the Weathermen"…, one might imagine that Rudd had written an unrepentant, unreflective, shallow defense of his activist days with "some mistakes" tossed in.

In his introduction, Rudd expresses the hope that his story will help young people "figure out what they can do to build a more just and peaceful world." The reviewer is indignant. How can this would-be terrorist claim that "his exploits" should "offer inspiration" to anyone? …

As an aging historian, I have been reading the declassified papers of other men of that period who made plans to set off bombs in the middle of cities. Some had their doubts, some were neutral, some were plainly excited and enthusiastic about the damage they could do. Unlike the Weathermen, whose elaborate schemes never materialized, these men carried out their plans, not once but thousands of times, with excruciating human consequences. None has ever apologized or been called to account. To this day, those who are still alive are described as statesmen, not "terrorists," and when they publish books they are treated respectfully.

In the last paragraph, the letter simply changes the subject from the question of whether Rudd was a terrorist or sufficiently contrite, to the question of whether some other unnamed, vaguely-described men are guilty of similar things but not blamed for them. Even if we suppose that the letter writer holds some bizarre moral theory according to which one wrong is excused by some other equal or worse wrong, the letter does not spell out such a theory or the reasoning that would connect up the last paragraph with the topic. It is the writer's responsibility to spell out such a connection, since it's far from obvious. So, even if the logical gap could be filled somehow, the letter itself does not fill it, and that is enough to convict it of a fallacy of irrelevance.

To sum up, general logical principles apply as much to reasoning about morality as to any other reasoning. Moreover, there are logical principles specific to moral terms, such that they apply to any moral theory. So, even if it is true that we create our moral theories, it's not the case that just anything goes.


Previous Q&As: 12/24/2003, 5/13/2004, 6/7/2005

May 16th, 2009 (Permalink)

Wikipedia Watch

After movie composer Maurice Jarre's death, a sociology student doing an experiment added a phony quote to Jarre's Wikipedia biography. Subsequently, the quote was picked up by some news media, including the Guardian newspaper, and used in Jarre's obituaries. The only thing that seems to have stopped it from ending up in an authorized biography of Jarre is that the student eventually confessed the hoax.

As published in Wikipedia, the quote was unsourced and eventually deleted for that reason, yet the obituary writers used it. Moreover, the writers' editors, and any fact-checkers the news outlets employ, failed to catch it. Given that the only source for it was Wikipedia itself, a quick web search should have at least raised a red flag. A subsequent check of Wikipedia might have revealed that the quote had since been removed. Perhaps it was just "too good to check".

Theoretically, after the Guardian and other newspapers used it, the Wikipedia quote could have been sourced to one or more of them, creating a circular trail of attribution. Given that the newspapers didn't cite Wikipedia as a source, the circularity wouldn't be obvious. Perhaps a sharp-eyed Wikipedian would have noticed that the time-stamp on the Wikipedia quote actually preceded the dates of publication of the obituaries, but I'm not sure that would even be a violation of Wikipedia's requirement of attribution. Suppose that someone adds something to Wikipedia without attributing it, then later adds a source; would that trigger a deletion simply because the source was added later? I would presume not, but would it be deleted if the source were published after the addition was made? In any case, it could have been worse if the hoaxer hadn't confessed, but how many such hoaxes have been played where the hoaxer didn't?

Of course, journalists should not use Wikipedia as the sole source for a fact, but should find other, more reliable sources. However, the name "Wikipedia" and the claim that it is an encyclopedia probably contributes to misleading them, since people expect an encyclopedia to be a reliable source of information. Perhaps in time this will change, due to hoaxes such as this.

However, because Wikipedia doesn't live up to its billing as an encyclopedia doesn't mean that it's useless. Rather, it should be viewed more like Google, that is, as a starting point for the search for information, and not as an end point. I trust that no one would cite Google as the source of a fact; similarly, one should not cite Wikipedia. It's often a better starting point than a search engine, because search engines return a jumble of relevant sources mixed in with irrelevant ones. A relevant Wikipedia article, in contrast, will be at least somewhat organized, and the sources cited and external links should be among the most reliable available. If journalists would learn to use it this way, future embarrassments should be avoidable.


  1. Patrick O'Connor, "Maurice Jarre", The Guardian, 3/31/2009
  2. Shawn Pogatchnik, "Irish student hoaxes world's media with fake quote", Associated Press, 5/12/2009

May 13th, 2009 (Permalink)

Fact Check it Out

It's nice of the Annenberg folks to fact check those political chain emails that people forward to you, but it would be even nicer if people would stop forwarding them. Getting information from them is worse than getting it from Wikipedia. The latest such email debunked concerns the supposed effects of gun control in Australia on the murder rate. After checking the facts, Annenberg checks its logic and finds it wanting:

We have no doubt that Stalin, Hitler and Pol Pot tried to keep guns out of the hands of ordinary citizens. But that doesn't mean that gun control necessarily leads to totalitarian dictatorships. This reasoning is a classic example of the fallacy known as "post hoc, ergo propter hoc"―"after this, therefore because of this." The fact that one thing happens after another does not mean that there's any causation involved. And that rule would apply to anyone making an argument completely counter to that of our e-mail author, as well. Simply saying "Australian law reform reduced gun fatalities," if all you know is that deaths dropped after 1996, would be post hoc ergo propter hoc, too.

Source: Jess Henig, "Q: Did gun control in Australia lead to more murders there last year?", Annenberg Political Fact Check, 5/10/2009

May 8th, 2009 (Permalink)

New Book: Voodoo Histories

David Aaronovitch has a book on conspiracy theories out titled Voodoo Histories: The Role of the Conspiracy Theory in Shaping Modern History, which sounds interesting. I've long wanted to think more about conspiracy theories and what sets them apart from genuine scientific theories, and perhaps this book would provide the occasion for that. It might make a good Book Club book, if someone would send me a review copy. I'm having some difficulty finding a suitable book for the club. I've read some prospects in the last few months, but none interested me enough to want to give it the full treatment. If you happen to know of a book that would make a good Fallacy Files Book Club subject, please let me know.


May 6th, 2009 (Permalink)

Silly Celebrities of the World, Unite!

Slate has a good article by Arthur Allen about Oprah joining forces with Jenny McCarthy. Read the whole thing, as they say, but I have a couple of comments to add:

What we really need is a vaccine against the cult of celebrity.



Update (5/10/2009): Here's a New York Times story from earlier this year on Offit's book. The article also mentions that Arthur Allen, the author of the Slate story, had previously written a story sympathetic to the anti-vaccinationists, but now regrets it. There's also an excellent excerpt from the book; read the whole thing, but here are a few choice excerpts from the excerpt:

At the time of Jenny McCarthy’s book tour, ten studies had examined the relationship between MMR vaccine and autism and five between thimerosal and autism. All showed exactly the same thing: vaccines didn’t cause autism. But with the help of television celebrities like Oprah Winfrey, Diane Sawyer, and Larry King, Jenny McCarthy was able to successfully counter these studies.
McCarthy trumped science with personal anecdote. ("My science is Evan, and he’s at home. That’s my science.") Had any of these television hosts chosen to have autism experts on their show, these experts would have had to argue against a mother’s personal, emotional story with statistics showing she was wrong―a nearly impossible task.

And yet that's how actual science is done, as opposed to using the anecdotal fallacy.

McCarthy also appealed to the strongly held societal notion that anyone can be an expert. … McCarthy had trumped her pediatrician’s four years of medical school, three years of residency training in pediatrics, and many years of experience practicing medicine by typing the word autism into Google. … By writing a popular book about her son’s autism, Jenny McCarthy had become a media expert on vaccines.

Also interesting to note is the Alar connection. This looks like a Book Club prospect; someone please send me a review copy!

Source: Donald G. McNeil, Jr., "Book Is Rallying Resistance to the Antivaccine Crusade", The New York Times, 1/12/2009

Update (5/12/2009): Here's further evidence that there really is a conspiracy of silly celebrities to advance each other's conspiracy theories: according to an article in the latest issue of Discover magazine, 9/11 conspiracist Charlie Sheen has joined the anti-vaccine crusaders. I think this goes to show that if you believe one conspiracy theory you'll believe them all. If you lower your standards of evidence so far that 9/11 conspiracy theories seem plausible, you might as well believe that vaccines cause autism, since the evidence is just as strong. Sorry, Charlie!

The notion that vaccines cause autism seems to have gotten started due to post hoc reasoning: childhood vaccines are administered when children are very young, and autism is usually diagnosed soon thereafter. Now, such reasoning isn't invariably fallacious; rather, it's only fallacious when people try to make it do what it cannot, namely, prove causation. Many causal hypotheses are based on post hoc reasoning, in that people notice that E follows C, and then hypothesize that C causes E. So far, so good; but to establish causation, it's necessary to test the hypothesis. However, as Chris Mooney writes, the hypothesis that vaccines cause autism has been tested and it failed the test:

Yet even as vaccine hysteria reached a fever pitch…, the scientific evidence was leaning strongly in the other direction. … It is a conclusion that has been "independently reached by scientific and professional committees around the world," as a recent science journal commentary noted. Either the scientific community has found a clear, reassuring answer to the questions raised about thimerosal in vaccines, or there is a global scientific conspiracy to bury the truth.

Who are you going to believe? Jenny McCarthy, Jim Carrey, Oprah Winfrey, and Charlie Sheen, or a bunch of scientists you've never heard of?

Source: Chris Mooney, "Why Does the Vaccine/Autism Controversy Live On?", Discover Magazine, 6/2009

Resource: Silly Celebrity, 3/25/2006

Pepsi Natural
May 3rd, 2009 (Permalink)

It's Only Natural!

Pepsico is introducing a version of Pepsi-Cola called "Pepsi Natural". What makes Pepsi Natural "natural"? Apparently, that it contains "natural" sugar instead of "artificial" corn syrup. Why is corn syrup―which is called that because it's made from corn―somehow less natural than sugar? Of course, corn syrup is the result of a long process, but so is sugar, whether it comes from cane or beets. Not only that, but sucrose―table sugar―is a pure chemical.

I'm not sure when corn syrup replaced sugar in Pepsi, but when I was a kid all soft drinks were sweetened with sugar. Little did we know, then, that we were drinking healthy, natural colas! It makes me feel like the Woody Allen character Miles Monroe in Sleeper who, like Rip van Winkle, wakes up many years in the future. When Monroe asks for various health foods to eat, a couple of scientists have the following conversation:

Dr. Melik: Wheat germ, organic honey, and Tiger's Milk.

Dr. Aragon: Oh, yes. Those are the charmed substances that some years ago were thought to contain life-preserving properties.

Dr. Melik: You mean there was no deep fat? No steak or cream pies or hot fudge?

Dr. Aragon: Those were thought to be unhealthy; precisely the opposite of what we now know to be true.

Dr. Melik: Incredible!

Resource: "Naturally Sweetened with Sugar", 8/17/2008

May 1st, 2009 (Permalink)


Q: I've been reading over the fallacies and trying to organize them in a hierarchy that makes sense to me. I believe that some of them are related by a fundamental principle―omitting relevant information, essentially, not telling the "whole truth"― but, I'm not sure if I'm missing something relevant (no pun intended). Below is the list of these fallacies and how I understand them:

This is in a similar line of thought as the "Red Herring" category, except in the opposite direction, where instead of adding irrelevant information the arguer omits relevant information.

Expanding on the idea of omitting relevant information I use the following example:

Dean: Our university provides superior employment opportunities for its graduates since 94% of the graduates start jobs within 1 month after graduation. Analysis:

  1. While 94% sounds impressive, this would be misleading if it is omitted that the average for all universities is 99% or that all the other universities have employment of over 94%.
  2. However, let's assume that readers know that the average is 92%. This still would be misleading if it is omitted that the standard deviation of the average is 3%; even though "superior" is a vague concept, we can all agree that anything not over one standard deviation can hardly be called "superior." (I think these scenarios are closer to what you categorize as False Precision.)

What are your thoughts on these scenarios and how would you categorize them?―Henri M.

A: You may be happy to hear that you're not the first to make this distinction; or, you may be sad to hear it! For instance, Edward Damer in his book Attacking Faulty Reasoning has a category for "fallacies of missing evidence". Eight fallacies fall under this category, including the "fallacy of fake precision". Quoting out of context is not included, but is not mentioned at all in the book, as far as I can tell. Other logicians include a general fallacy of "suppressed evidence", "ignoring counter-evidence", or the like. In my own classification, One-Sidedness is the most general fallacy for the omission of relevant evidence. For this reason, any more specific fallacies of this type should be subfallacies of One-Sidedness.

I agree with you that Quoting Out of Context is a fallacy of this type and, therefore, should be a subfallacy of One-Sidedness, though it is not so currently. However, I'm not convinced that Fake Precision is also a type of One-Sidedness, though you have Damer on your side. Here's how he justifies including it:

The use of fake precision…is a way of reasoning that fails to satisfy the sufficient grounds condition of a good argument. When the claim at issue cannot be backed up by data that support the degree of precision claimed, the argument must be regarded as a faulty one. (P. 121)

Since the fallacy of fake precision occurs when overly-precise information is included in a premiss, Damer seems to be classifying not the argument with that premiss, but a different argument that has the premiss as a conclusion. This hypothetical argument supporting the premiss may indeed commit a fallacy of One-Sidedness, but I don't see that as a reason to classify Fake Precision itself as a case of missing evidence. For this reason, I don't think that Fake Precision is a subfallacy of One-Sidedness.

Another reason why I'm reluctant to include Fake Precision is that many occurrences of it, as I've frequently documented here, involve public opinion polls. Based on the example you give, the relevant information that is missing in such a case would be information about the poll's margin of error. However, in most such cases the margin of error information is included! So, it's not missing evidence at all.

The problem with such examples is that, though news sources have adopted policies of always reporting a poll's margin of error, their reporters do not use that information when analyzing it, perhaps because they don't understand it. While one might justify including such examples as instances of "ignoring counter-evidence", it seems to me that the problem with Fake Precision is often just not a lack of information, but a misunderstanding or misuse of it.

At any rate, you're right about the importance of including all relevant information in an argument. This is especially true of inductive reasoning, where it is called "the requirement of total evidence". Unlike deduction, inductive arguments may be weakened by the addition of new information. Thus, it's vital that all available relevant information be included when reasoning inductively.

Source: T. Edward Damer, Attacking Faulty Reasoning: A Practical Guide to Fallacy-Free Arguments (Third Edition) (1995), pp. 109-128.

Solution to the Puzzle of the Airtight Alibi: The prosecutor pointed out that the location of the alibi and the scene of the crime were in different time zones. The defendant was seen by the witnesses at 9:33 eastern daylight time (EDT), but the crime took place at 9:52 central daylight time (CDT), which is 10:52 EDT. Thus, the defendant had an hour and nineteen minutes to leave the alibi location in the eastern time zone, travel to the scene of the crime in the central time zone, then commit the crime.

The puzzle is based on a real-life case: some 9/11 conspiracy theorists claim that the U.S. Air Force must have been ordered not to intercept the hijacked airliners on the 11th of September, 2001. If true, this would suggest that the government was somehow complicit in the attacks. Allegedly, Air Force jets should have been able to intercept the hijacked planes within minutes, and since they did not do so, there must have been a "stand down" order.

One piece of evidence for this claim is the case of professional golfer Payne Stewart: in 1999, Stewart's private jet lost cabin pressure, and air traffic controllers lost contact with it at 9:33 A.M. According to news reports, an Air Force jet intercepted it at 9:52 A.M., seemingly only nineteen minutes later. However, the first time given was EDT and the second CDT, so that it actually took an hour and nineteen minutes for the interception. On 9/11, each of the hijacked airliners was in the air for less than an hour from the time they were hijacked until they crashed. Thus, the Payne Stewart incident does not support the conspiracy theory; rather, it undermines it.


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