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December 31st, 2019 (Permalink)

Richard Jewell and "The Voice of God"

* Ellipsis in the original.

December 25th, 2019 (Permalink)

What's in Santa's bag?

'Twas the night before Christmas and Santa Claus had arrived at the very last city block of buildings that he had to deliver presents to. His bag of presents was almost empty, and if he ran out before he finished, he would have to fly all the way back to the North Pole to fetch more. Would he have enough presents for everyone on the block?

There were six buildings on the block. The first was an apartment building with many apartments. It took one less than half of the presents in Santa's bag to deliver a present to each person in the building.

The next building on the block was also an apartment building, but about half the size of the first. It also took one less than half of the remaining presents in the bag to leave one present for each resident of the building.

The same process continued for the next three buildings as each time it took one less than half of the remaining presents in the bag to treat each resident of the building to a present.

Finally, Santa came to the last building on the block, which was a small house occupied by a married couple and their two children, a boy and a girl. Santa looked into his bag and there were exactly four presents left. A Christmas miracle! Santa would not have to make another trip to the North Pole for additional presents.

How many presents were in Santa's bag when he arrived at the last block?

December 22nd, 2019 (Permalink)

Rule of Argumentation 111: Make your arguments relevant to claims!

The previous rule invited you to focus your argumentation on claims, and not be distracted by irrelevancies. In this rule, I will discuss in more detail how to make your arguments relevant to the claims you are arguing about.

As discussed in rule 9, argumentation won't begin unless you and your partner think that you disagree about something, and that something can be stated as a claim―that is, a sentence that is true or false. Your argumentation should consist of a series of individual arguments relevant to that claim or to other claims that have arisen during the discussion.

Logically speaking, an argument is a series of claims, one of which is called "the conclusion" and the remainder are "premisses"2. There are two ways for an argument to be relevant to a claim:

  1. The premisses provide support for the claim, thereby making it more likely that it is true. This is what I called, in the previous rule, "defending" a claim.
  2. The premisses provide support for the negation of a claim, thereby making it more likely that the claim is false. This is what I called, in the previous rule, "attacking" a claim.

In addition, there are two degrees of support that an argument can give to its conclusion:

  1. The premisses provide conclusive support for the conclusion, thereby showing that the conclusion is true assuming that the premisses themselves are true. Such an argument is called "deductively valid".
  2. The premisses provide less than conclusive support for the conclusion, but make it more likely that the conclusion is true given that the premisses are true. Such an argument is called "inductively strong".

These two types of argument are important because what counts as relevant to a claim depends on which type of support the argument is supposed to provide. Deductive relevance is studied in formal logic and inductive relevance in probability theory. Unfortunately, there is no short cut to fully understanding relevance than to study logic3 and probability theory4. As a result, this isn't the place to go into detail about either deductive or inductive relevance.

However, short of learning logic or probability theory, here is an informal technique for evaluating the relevance of premisses to a conclusion:

  1. Deductive: Put aside for the moment the question of whether the argument's premisses are true or false and assume that they are true. Will the conclusion also be true? Can you imagine circumstances in which the conclusion would be false? If assuming that the premisses are true means that the conclusion would have to be true―or, in other words, in no circumstances would it be false―then the argument is deductively valid. In contrast, if you can imagine a possible situation in which the premisses are true and the conclusion false, then the argument is invalid. However, if it is invalid it still might be a strong inductive argument, so don't stop here but go to the next step:
  2. Inductive: Again, assume that the argument's premisses are true. Does that assumption make it more likely that the conclusion is true? If so, how much more likely does it make it? Deductive validity is an all-or-nothing affair, that is, either an argument is valid or it isn't. In contrast, inductive strength is a matter of degree. A set of premisses might make a certain conclusion no more likely, almost certain, or anywhere in between. Try to get a sense of just how strong the argument is.

The logical strength of an argument just described is a measure of how relevant its premisses are to its conclusion. However, strength is not enough to make an argument good. It is also necessary that the premisses be true or at least probable.

Just as claims are sometimes confused with their histories, effects, or motivations, arguments are sometimes confused with their sources. By "source" I mean to include both the person or group advancing an argument, and others who may defend it. Too often people confuse an argument with its source, and instead of evaluating or criticizing the argument itself, they evaluate its source. There are many different ways in which this is done, and many of them are named fallacies5, but what these mistakes have in common is that the argument targets the source of the argument instead of the argument itself. Good arguments can come from bad sources, and bad arguments can come from good ones. So, when you follow the steps above, ignore its source and concentrate on the argument itself as a series of claims.

Next Month: Rule 12


  1. Previous entries in this series:
    1. Rule of Argumentation 1: Appeal to reason!, 12/14/2018.
    2. Rule of Argumentation 2: Be ready to be wrong!, 1/26/2019.
    3. Rule of Argumentation 3: Focus on claims and arguments!, 2/13/2019.
    4. Rule of Argumentation 4: Be as definite as possible!, 3/8/2019.
    5. Rule of Argumentation 5: Be as precise as necessary!, 5/29/2019.
    6. Rule of Argumentation 6: Defend your position!, 7/7/2019.
    7. Rule of Argumentation 7: Aim at objectivity!, 8/9/2019.
    8. Rule of Argumentation 8: Consider all the evidence!, 9/19/2019.
    9. Rule of Argumentation 9: Agree about what you disagree about!, 10/20/2019.
    10. Rule of Argumentation 10: Attack or defend claims!, 11/12/2019.
  2. Often spelled "premises".
  3. You can begin studying logic by accessing the Lessons in Logic from the navigational pane to your left.
  4. You can begin studying probability by accessing the entry for Probabilistic Fallacy from the drop-down menu to your left.
  5. If you wish to pursue this issue further, see the fallacy of Red Herring and its subfallacies, which are available from the drop-down menu to your left.

Debate Watch
December 21st, 2019 (Permalink)

And Then There Were Seven

Ten little Democrats standing in a line;
One toddled home and then there were nine.
Nine little candidates having a debate;
One's polling dropped and then there were eight.
Eight little debaters is better than eleven;
One fell asleep and then there were seven.1

I don't have much to say about this month's Democratic presidential debate, which was held two nights ago, because it was mostly a rerun. However, here are a few passing observations:


  1. Based on the traditional nursery rhyme "Ten Little Indians".
  2. The Big Democratic "Debate", Part 1, 6/27/2019.
  3. Zach Montellaro & Steven Shepard, "DNC raises thresholds again for January debate; Booker will likely be excluded", Politico, 12/20/2019.
  4. Déjà Vu All Over Again, 9/16/2019.
  5. The Fix team, "Transcript: The December Democratic debate", The Washington Post, 12/20/2019.
  6. See:
    • Glenn Kessler & Salvador Rizzo, "Fact-checking the sixth Democratic debate", The Washington Post, 12/20/2019.
    • Ricardo Alonso-Zaldivar, "AP FACT CHECK: Examining claims from 2020 Democratic debate", The Gazette, 12/19/2019.
  7. Which is currently $2,800; see: "Contribution limits", Federal Election Commission, accessed: 12/21/2019.
  8. Philip Bump, "Bernie Sanders keeps saying his average donation is $27, but his own numbers contradict that", The Washington Post, 4/18/2016.
  9. Bernie Sanders campaign fundraising page, Bernie, accessed: 12/21/2019. The Biden campaign lacks such a curious donation structure; see: Biden campaign fundraising page, Joe Biden, accessed: 12/21/2019.
  10. Will Thorne, "Sixth Democratic Debate Draws 6 Million Viewers, Lowest Figure in Current Cycle", Variety, 12/20/2019.
  11. The State of the Debates, Scientific Graphs, Fact-Checking Books & Autism Profiteering, 11/30/2019.
  12. John Bowden, "Buttigieg campaign introduces contest for lowest donation", The Hill, 12/24/2019.
  13. Added, 1/17/2020: Sanders did not repeat the claim in the next debate, which was held on 1/14/2020―so much for my powers of prophecy. However, it's too soon to hope that he's learned his lesson and is dropping it permanently. I still think, based on his past record, that it will appear again before this election is over.

Bad Advice
December 14th, 2019 (Permalink)

Bad Advice

Title: Bad Advice

Subtitle: Why Celebrities, Politicians, and Activists Aren't Your Best Source of Health Information

Author: Paul A. Offit

Date: 2018

Quote: Science delivered us out of the Age of Darkness and into the Age of Enlightenment. Three hundred years ago, graveyards overflowed with small, white coffins. Children died from smallpox, meningitis, pneumonia, whooping cough, bloodstream infections, scarlet fever, diphtheria, hepatitis, measles, and food poisoning. Of every hundred children born, twenty would be dead before their fifth birthday. Mothers died from tuberculosis and childbed fever. Crop failures led to famines and starvation. Homes were infested with filth and vermin. The average life span was thirty-five years. Scientific advances have eliminated most of this suffering and death. Vaccines, antibiotics, sanitation programs, pest control, synthetic fertilizers, X-rays, air conditioning, recombinant DNA technology, refrigeration, and pasteurization―to name just a few―have allowed us to live longer, better, healthier lives. During the last hundred years alone, the life span of Americans has increased by thirty years.1

Comment: This book was published about a year ago, so it's not brand new, but it's new to me. I haven't read it yet, but I have read two of Offit's previous books: Deadly Choices2 and Do You Believe in Magic?3. I thought those were both good books, so I have similar expectations for this one.

The title does not refer to the contents of the book, I hope, but to its topic, which I guess is the bad advice coming to us from all those "celebrities, politicians, and activists". Where should we get advice if not from movie stars and talk show hosts? Here's a suggestion: try science. But what is science?

Stripped to its essence, science is simply a method to understand the natural world…. In a sense, everyone is a scientist. For example, if a car doesn't start, a mechanic considers several possibilities: the battery is dead; the starter is defective; the car is out of gas; the fuel system is clogged. Then, the mechanic tests each of these potential problems. This is exactly how scientists think….4

In other words, science is not magic; it's a logical method for finding out how things work. So, should we take advice from scientists? Not so fast:

It will probably come as a surprise to learn what science isn't―it isn't scientists or scientific textbooks or scientific papers or scientific advisory bodies. As once-cherished hypotheses are disproved, scientists throw away their textbooks without remorse.5 For some people, this is unnerving. We want certainty, especially when it comes to our health. And that's when we get into trouble….6

So, if we're not to take advice from Gwyneth Paltrow or Jenny McCarthy, where should we get it? Since I haven't read the whole book yet, but only those parts that Amazon lets me look at, I don't know what answer Offit provides. However, I'm encouraged that he makes the distinction between science and scientists, since I don't think the answer is to blindly follow scientists. One clue is suggested by the following remark:

By far the most important part of the scientific process is reproducibility. If a scientist's hypothesis is right, then other investigators will confirm that it's right. If it's wrong, they won't.4

Or, as I like to put it, replication is not optional. This is why you should not be impressed by the latest study in health, nutrition, or any other area of science until it's been replicated. Most studies turn out to be wrong, so if you're going to bet your life, health, or wealth on it, you should bet against an unreplicated study. Once a study has been replicated―ideally, multiple times by independent investigators―then you should provisionally rely upon it.

Coincidentally, tying in to my recent discussion of the problems with research into the relation between diet and health7, Offit gives the following as an example of how science can get things wrong:

In 1957, the American physiologist Ancel Keys published a paper claiming that people who consumed less fat had a lower incidence of heart disease, coining the term "heart-healthy diet." Keys was a well-respected scientist, a best-selling author, and a consultant to the World Health Organization and the United Nations. In 1961, he even appeared on the cover of Time magazine. When Ancel Keys gave advice, people listened. Because of Keys, margarine, which contained partially hydrogenated vegetable oils, became the "heart-healthy" alternative to butter, which contained animal fats. Although he didn't realize it at the time, Keys had driven Americans into the waiting arms of trans fats. Four decades later, the Harvard School of Public Health estimated that trans fats were causing about two hundred fifty thousand heart-related deaths every year.8

The lesson of all this is that science is hard. Unfortunately, there isn't any easier way to figure out how the world works, so get used to it.

I would think that most Fallacy Files readers already understand that you shouldn't take advice about health, or much of anything else, from celebrities, politicians, or activists. However, with the holidays rapidly approaching, maybe there's someone on your gift-giving list who could benefit from some good advice about bad advice. On the other hand, you can give a book as a gift but you can't make anyone read it, which raises the question of who the target audience is for this book. I suspect that those who read it probably won't really need it, and those who need it most probably would refuse to read it.

Oh well, teaching people about science is hard, too.


  1. P. 1.
  2. See: Book Review: Deadly Choices, 7/21/2013.
  3. See: New Book: Do You Believe in Magic?, 7/10/2013.
  4. P. 2.
  5. This is rather idealized. It's more in line with Offit's point, here, to emphasize that scientists are human―all too human―and can stubbornly cling to disproven theories, but science itself ruthlessly discards them.
  6. P. 3.
  7. See: Junk Food Research, 11/29/2019.
  8. P. 4.

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