September 28th, 2016 (Permalink)

Logic Checking the First Debate, Part II

In this part, we will look closely at the he-said/she-said part of the exchange between the candidates concerning the murder rate in New York City (NYC). To refresh your memory, here's the relevant part, though you can see the larger context in Part I, below.

Clinton: Well, itís also fair to say, if weíre going to talk about mayors, that under the current mayor, crime has continued to drop, including murders. So there is…

Trump: No, youíre wrong. Youíre wrong.

Clinton: No, Iím not.

Trump: Murders are up. All right. You check it.

Now, the thing that started this back-and-forth was Clinton's claim that the number of murders continued to decline under the current mayor of NYC, Bill de Blasio. Putting aside the factual question for the moment, why is this logically an important enough point for the debaters to wrangle about? Because, according to Trump in the earlier part of this debate―see Part I, below―the so-called stop-and-frisk policy was discontinued by de Blasio.

Because if the number of murders continued to decline after S&F ceased, that would be evidence that S&F had little if anything to do with the decline. This, of course, is why Trump vehemently denied it, claiming that the number of murders increased.

If Trump is right, the increased murder rate is additional evidence that S&F was indeed contributing to the decrease in the number of murders. This is an application of Mill's method of difference―see Source 4, below―that is, if S&F were causally responsible for at least some of the decline in the murder rate, then when S&F is ended we should expect that the murder rate will at least slow its decline, stop completely, or even begin to climb again.

This is why the issue of who is right about the murder rate in NYC is not a trivial dispute about numbers, but is important to the larger issue of whether the S&F policy is effective in reducing crime. Unfortunately, the factual question is not a simple one, but here are the facts―see Sources 1 & 2, below. The number of murders for the last year of S&F, 2013, was 335. For 2014, De Blasio's first year as mayor, the number was 333. For 2015, it was 352. For the year to date, it's 246. The year-to-date figure, of course, can't be compared directly to the statistics for the previous full years, but the NYPD also provide the comparable figure for this time last year, which was 257.

So, who's right: Clinton or Trump? Is Clinton right because the murder rate in NYC declined slightly from 2013 to 2014 and is on track to decline from 2015 to this year? What about the increase from '14 to '15? Do we just ignore that? Is Trump right because of the '14-'15 increase? But then, what about the decreases from '13-'14 and '15 to the year-to-date? Perhaps when Trump claimed that "murders are up" he was thinking of the substantial '14-'15 increase; maybe he had seen that statistic, but not the incomplete numbers for the current year. When Clinton claimed that "under the current mayor, crime has continued to drop, including murders", perhaps she was only considering the "continued" decrease from last year to now.

So, who's right? Neither? Both? I'll let you decide.


  1. "CompStat, Volume 23, Number 37", New York City Police Department, 9/12/2016-9/18/2016 (PDF)
  2. "Seven Major Felony Offenses", New York City Police Department, Accessed: 9/28/2016 (PDF)
  3. "Debate Fact-Check: How Donald Trump and Hillary Clinton Stack Up", ABC News, 9/27/2016
  4. Michael K. Green, "Mill's Methods: Method of Difference", Logic Tutor, 1998

September 27th, 2016 (Permalink)

Logic Checking the First Debate, Part I

I mentioned in the previous entry that many critics of past presidential debates have complained about a lack of "clash" between the candidates; well, there was plenty of clash in the first presidential debate of this election year. In fact, at times the moderator, Lester Holt, appeared to have very little control over the proceedings, which descended into childish bickering.

One point on which the candidates clashed was the effect of past policing policies on the murder rate in New York City (NYC):

Clinton: …[W]e do always have to make sure we keep people safe. There are the right ways of doing it, and then there are ways that are ineffective. Stop-and-frisk was found to be unconstitutional…in part, because it was ineffective. It did not do what it needed to do. …

Trump: …[W]hen it comes to stop-and-frisk…. [I]n New York City, stop-and-frisk, we had 2,200 murders, and stop-and-frisk brought it down to 500 murders. Five hundred murders is a lot of murders. Itís hard to believe, 500 is…supposed to be good? But we went from 2,200 to 500. And it was continued on by Mayor Bloomberg. And it was terminated by current mayor. But stop-and-frisk had a tremendous impact on the safety of New York City. Tremendous beyond belief. So when you say it has no impact, it really did. It had a very, very big impact.

Clinton: Well, itís also fair to say, if weíre going to talk about mayors, that under the current mayor, crime has continued to drop, including murders. So there is…

Trump: No, youíre wrong. Youíre wrong.

Clinton: No, Iím not.

Trump: Murders are up. All right. You check it.

So who is wrong? The question is more complicated and harder to answer than you might at first think. There are two issues here that need to be untangled:

  1. The causal issue of whether the stop-and-frisk (S&F) policy was effective in reducing crime in NYC, with Clinton claiming that it wasn't and Trump claiming that it was.
  2. There is a difference of opinion over the statistics of murders in NYC, with Trump claiming that the number of murders has increased and Clinton claiming that it has decreased.

In this first part, I will examine only the first, causal issue, leaving the issue of NYC murder statistics until tomorrow. But first, how are these two issues related? The only evidence given by the candidates to support their positions on S&F are the alleged decreases and increases in the murder rate. Clinton initially claimed that: "Stop-and-frisk was found to be…ineffective. It did not do what it needed to do." However, she did not say who found this out, so we just have to take her word for it.

Trump, in contrast, vehemently insisted that S&F was effective: "…[S]top-and-frisk had a tremendous impact on the safety of New York City. Tremendous beyond belief. So when you say it has no impact, it really did. It had a very, very big impact." He also used causal language in saying that S&F "brought down" the number of murders.

The evidence that Trump provides for this causal claim is that the number of murders had gone from 2,200 to 500. There's much in this statement that is unclear. Presumably, these are annual numbers of murders for NYC, but Trump does not say which years. To support his claim that S&F caused the decline, 2,200 would have to be the murder rate in the year before S&F began, and 500 in the year following its end, or something similar. Clinton didn't actually challenge this part of Trump's claim, so let's accept for the sake of argument that it's correct.

So, assuming that the annual number of murders in NYC really did decline during the period of S&F to about a quarter of what it had been, how strong of evidence is this that S&F brought about that decline? Not very strong. The national murder rate has been declining until very recently, so how much, if any, of the decline in the number of murders in NYC is the result of S&F, and how much is the result of a general decline in murder? It would take a careful statistical study of the differences between NYC, and perhaps other cities that have had S&F policies, compared to similar cities in the same period who lacked such policies, to tease out just how much of the decline is due to S&F. Has such a study been done? Maybe, maybe not, but we don't hear a thing about it from either candidate.

So far, neither candidate's conclusion is warranted by the evidence provided; maybe S&F reduces murder rates, but maybe it doesn't. However, we still need to look at the he-said/she-said on NYC murder rates, which we will do in Part II.

To Be Continued…


Fallacy: Cum Hoc Ergo Propter Hoc

September 25th, 2016 (Permalink)

Debate Preparation

Sitting on a sofa on a Sunday afternoon,
Going to the candidates' debate,
Laugh about it, shout about it,
When you've got to choose,
Every way you look at it you lose.
―Paul Simon, "Mrs. Robinson"

The first of this election's presidential debates is scheduled to occur tomorrow. As in past election years, I expect to comment on each debate here shortly after they happen, though I won't promise to do so since I may not have anything worth saying.

This debate will have a single moderator: Lester Holt, the NBC Nightly News anchorman. Holt will ask the candidates questions, each candidate will have a couple of minutes in which to answer, and then additional time to respond to each other. Holt is also responsible for selecting the questions that he will ask.

Many people have criticized these "debates" in past years on the grounds that they're really joint press conferences. What's often been missing is what's called "clash" in debate jargon, that is, the debaters directly responding to each others' claims and arguments. However, earlier presidential debates often had panels of journalists who asked questions, and the formats sometimes discouraged follow-up questions or direct responses. The format of tomorrow's "debate" at least leaves open the possibility of clash, but much will depend upon the moderator and the candidates themselves.

Jill Lepore had a worthwhile article in The New Yorker about a week ago on the history of presidential debates and the role that debate plays in self-government:

How to argue is something people are taught. You learn it by watching other people, at the breakfast table, or in school, or on TV, or, lately, online. Itís something you can get better at, with practice, or worse at, by imitating people who do it badly. More formal debate follows established rules and standards of evidence. For centuries, learning how to argue was the centerpiece of a liberal-arts education. … Debating, like voting, is a way for people to disagree without hitting one another or going to war: itís the key to every institution that makes civic life possible, from courts to legislatures. Without debate, there can be no self-government. The United States is the product of debate.
Source: Jill Lepore, "The State of the Presidential Debate", The New Yorker, 9/19/2016

The presidential debates this year, assuming they take place, may be different than those of previous years. Donald Trump is a famously unpredictable candidate, and both candidates bring a lot of historical baggage to the debates. There's been much speculation in the media that one or the other of the candidates might back out: Clinton, because of her health problems; or Trump, because, well, he's Trump. However, Trump's also complained that the debates, like everything else, are "rigged", and that the schedule for a couple of the debates is "Unacceptable!" because they compete with football games. Nonetheless, tomorrow's debate appears to be go for launch.

I prefer to let a little time pass before commenting, so the earliest that an entry on a given debate is likely to appear here is the day after the debate, and some may take longer. This is because, in contrast to television pundits, I spend some time thinking about what was said before I comment on it. There's plenty of knee-jerk commentary around, so if that's what you're interested in, I'm sure you can find it elsewhere. Much of that, of course, is spin coming from partisan pundits attempting to influence your opinion in favor of their candidate. I will endeavor to keep my commentary to logical and related issues that are within my field of competence, since I doubt that you're interested in my political opinions, nor should you be.

Perhaps it should go without saying, but I won't attempt to comment on every logical topic raised in a given debate, or identify every single fallacy committed, because this simply wouldn't be possible. Rather, what I choose to comment on will be decided by what I happen to notice and what interests me. However, I will strive to be even-handed and non-partisan, but I won't attempt a kind of artificial balance between the two candidates. If you think I've missed a logical point or fallacy example in any of the debates, please let me know about it.


Resource: Pre-Debate Warm-Up, 10/3/2012. In this entry, I discuss some of the most common logical problems to be on the lookout for in political debates.

September 3rd, 2016 (Permalink)


Pope Francis looking into female clergy members

No comment.

September 2nd, 2016 (Permalink)

Hey, MoE!

It's been a while since I did a "Poll Watch" entry, but with the general election only a couple of months away, this is a good time to do so. Here's how The Washington Post reported the results of a recent survey:

As of today…Americans' views of [Hillary Clinton] just hit a record low. A new Washington Post-ABC News poll shows 41 percent of Americans have a favorable impression of Clinton, while 56 percent have an unfavorable one. … Her previous low favorable rating this year was in July, when it was 42 percent…. Her previous high for unfavorable views was in June, when 55 percent disliked Clinton.

In other words, the "change" in Clinton's favorability rating is a shift of just one percentage point from "favorable" to "unfavorable". As far as I know, no national political poll has a margin of error (MoE) so low that a one percentage point difference would be statistically significant. In fact, the margin of error for this particular poll is 3.5 points, so that one point is well within it.

Oddly enough, some reporters appear to have an intermittent ability to understand the margin of error. For instance, in ABC News' account of the same poll, we read the following:

[Trump] scored particularly low with blacks, 84 percent of whom view him unfavorably. Given the sample sizes, thatís not a significant difference from the 91 percent of this group who responded similarly in early August….

The report doesn't go into the details but, presumably, the subsample of blacks who took the survey was so small that even seven percentage points is "not a significant difference". It's nice to see that the reporters actually understand the effects of sample size on the margin of error, and the fact that sometimes a difference in numbers is not necessarily a difference in reality. But if they understand that for Trump's unfavorability with blacks, why can't they understand it for Clinton's unfavorability with all Americans?


  1. Aaron Blake, "A record number of Americans now dislike Hillary Clinton", The Washington Post, 8/31/2016
  2. Gregory Holyk & Gary Langer, "Poll: Clinton Unpopularity at New High, on Par With Trump ", ABC News, 8/31/2016

Resource: How to Read a Poll

August 29th, 2016 (Permalink)

Don't Check it Out, Too

I have a book review of Scrutinizing Argumentation in Practice, edited by Frans van Eemeren and Bart Garssen, in the latest issue of the journal Cogency. The book is a collection of scholarly conference papers, so probably not of interest to the casual or beginning student of argumentation. However, if you're interested in taking a deeper dive into the topic, do check it out.

Source: Gary N. Curtis, "Review of Scrutinizing Argumentation in Practice", Cogency, Vol. 8, No. 1 (111-121), Winter 2016 (PDF)

August 24th, 2016 (Permalink)

Don't Check it Out

Brian "Skeptoid" Dunning has a new podcast about the meme that says you shouldn't criticize something unless you've tried it. The title for this entry doesn't refer to the podcast: Do check it out!

The meme is quite obviously not generally good advice: I've never jumped out of an airplane without a parachute, but I'm rather critical of the idea. I'm sure that the first few seconds are thrilling; it's what comes after that concerns me.

I generally agree with Dunning, but would like to add my own take on this, relating the issue more explicitly to the three logical fallacies that Dunning alludes to:

  1. Post Hoc: The sort of things that people keep telling Dunning to shut up about unless he's tried them are "alternative" medical treatments and the like. The trouble with evaluating such treatments by trying them is that most medical problems will eventually improve on their own, so if you try some new "treatment" you may well improve for reasons having nothing to do with the treatment.

    The post hoc effect can even go the opposite direction: I recently began a course of treatment with a daily medication that I had never taken before. Shortly after beginning the new treatment, I experienced extreme back pain. This led me to wonder whether the pain was caused by the medication, though this was not a known side effect. Fortunately, the pain went away after a few hours and was probably due to raking the yard rather than the new medication. However, the coincidence of the pain occurring so soon after starting the medicine was compelling enough to cause me to temporarily stop taking it.

    One thing that Dunning says that I disagree with is the following: "Crediting something with efficacy because it appeared to work when you tried it is a perfectly rational conclusion for an intelligent person to make." If you substituted the word "normal" for "rational", I would agree. It's normal for people to think that way, just as I did when I hurt my back, but it ain't rational. That's why the post hoc fallacy is such a common one. Moreover, it's often just plain impossible for us to tell what caused what, especially when you're talking about health. Viruses and bacteria are too small to see, and you generally can't see inside your own body to tell what's going on in there. That's what you need science for.

  2. Hasty Generalization: You're only one data point. Even if you have experienced something, you shouldn't generalize from the experience of just one person, even if that person is you―that's as hasty a generalization as you can get. Just because something "worked" for you doesn't mean that it will "work" for anyone else, so you shouldn't generalize to other people. Not only that, but just because something worked in the past doesn't mean that it will work in the future, so you shouldn't even generalize for your future self on the basis of just one past experience.
  3. The Anecdotal Fallacy: The anecdotal fallacy is the tendency for a vivid anecdote―or story―to overwhelm other and better evidence, and what could be more vivid than your own experience?

Source: Brian Dunning, "Don't Try It Before You Knock It", Skeptoid, 8/23/2016

August 17th, 2016 (Permalink)

Lesson in Logic 13: Categorical Statements

A categorical statement is one that asserts something about a category, that is, a class or type of thing. Classes are talked about using class terms, which are common nouns or noun phrases.

Examples of class terms: "shoes", "ships", "cabbages", "kings", "pileated woodpeckers"

As mentioned in lesson 11―see the Previous Lessons, below―classes need not have members, and some class terms refer to such empty classes.

Examples of empty class terms: "unicorns", "vampires", "werewolves", "passenger pigeons"

Moreover, there also terms for classes about which we may not know whether they are empty or not.

Examples: "bigfeet", "Loch Ness monsters", "ivory-billed woodpeckers"

The simplest categorical statements are those that talk about a single class, and thus contain a single class term. The simplest thing that you can say about a single class is that it is non-empty or empty, that is, that something of that type exists or does not exist. You learned in a previous lesson how to represent on a class diagram that a single class is empty or non-empty by using shading to represent emptiness and an "X" to represent a non-empty class.

The type of categorical statements that you will learn about in this lesson contain two class terms, but representing them on a two-circle Venn diagram is a simple extension of what you've already learned. There are four types of such statements that are studied in traditional logic and designated by the letters: A, E, I, and O. The I and O type of statement say something about "some" member of the subject class, so an "X" is used to indicate that a subclass is non-empty. Venn Diagram for I Proposition

I: An I statement has the form: "Some A is a B".

Example: Some arguments are syllogisms.

There are many ways to express I statements in English, including: "some As are Bs", "there are As that are Bs", etc. This type of statement relates two classes by asserting that at least one member of the first class, A, is also a member of the second class, B. To use a Venn diagram to represent this information you need to show that there is something in A that is also in B, that is, that something is in the overlap of the two classes.

The A and E types of statement assert that a certain subclass is empty, so you will need to use shading instead of an "X". Venn Diagram for E Proposition

E: An E statement has the form: "No A is a B".

Example: No bats are birds.

There are many ways to express E statements in English, such as "no As are Bs", as in the Example. This type of statement relates two classes by asserting that no member of the first class, A, is a member of the second class, B. E statements are the opposite of I statements in that the I asserts that there is something in the overlap of the two classes, whereas the E asserts that there is nothing there. Thus, to represent this information on a Venn diagram we need to show that there is nothing in A that is in B, that is, that the overlap area is empty. So, instead of an "X", you shade in the overlap as shown.

Exercises: If you understand how to represent the I and E statements on Venn diagrams, you should be able to figure out how to represent the other two traditional categorical statements. For the following two exercises, draw the primary diagram and label the circles "A" and "B", then use either an "X" or shading to indicate that a subclass in the diagram is either non-empty or empty:

  1. "Some A is not a B."
  2. "All As are Bs."

Answers to the Exercises

In the next lesson, you'll learn how to use these diagrams to determine logical relationships between these four types of categorical statement.

Previous Lessons:

August 12th, 2016 (Permalink)

You May Need a Napkin

Check out this quote from the beginning of a New York Times editorial:

Global trade allows Americans to satisfy their appetites for strawberries in spring, apples in midsummer and asparagus in autumn. … But getting fresh produce year round also means that consumers are exposed to foreign food production systems that may not be well regulated. Although the vast majority of the 30 billion tons of food imported annually is wholesome, recent incidents of illness caused by tainted Guatemalan raspberries…have made food safety a public concern.
Source: "Safety Standards for Imported Food", International New York Times, 10/3/1997

Is there anything there that grabs your attention? Something that makes you feel a bit doubtful―a little skeptical? No?

How about the claim that "30 billion tons of food [is] imported annually". If you're like me, you have no idea how much food is imported into the United States on a yearly basis. In fact, you may have no notion of even a ballpark figure; is it millions or billions of tons? Do you have a sense of how much food a ton is? I wouldn't blame you if you just read over that claim with glazed eyes and didn't think about it at all. You probably would just accept it because it is the Times, after all, and surely they know what they're talking about.

Don't do that, because this is a claim that you can easily test yourself. I'm not talking about doing research on how much food is imported annually. No, I'm talking about doing a simple back-of-the-envelope calculation (BOTEC) to test the claim for sanity. Such calculations are called "back-of-the-envelope" because they are short and simple enough to be scribbled on an envelope or even a cocktail napkin.

How do you do such a test? Here's a hint: use elementary math together with what you already know―that's all you'll need. Try to transform a number that is too big to grasp into one that you can evaluate using common sense.

Give it a try, then click on the link below when you think you've figured it out.

Go to the Back of the Envelope

August 11th, 2016 (Permalink)

New Book: A Survival Guide to the Misinformation Age

I haven't read the new book with the above title, so this is not an endorsement―just a notice. The author is David J. Helfand, an astronomer, which presumably explains its subtitle: Scientific Habits of Mind. I could certainly use a survival guide to misinformation, and this one appears promising. Judging from the chapter titles, the book has sections on the following topics:

I'm especially excited to see a chapter on back-of-the-envelope calculations (BOTECs) (ch. 4), since I've complained for years that they are an important skill that books and courses on logic and critical thinking fail to teach. Some of the misinformation that inundates us every day can be debunked with a BOTEC, so that one doesn't need to do any research to show that it can't be true. This book may be worth getting for that chapter alone.

August 6th, 2016 (Permalink)

The Second Puzzle of the Sleeper Cells

The Agency for Counter-Terrorism (ACT) has again discovered the existence in a target country of a sleeper cell of agents of a second foreign power―see the Previous Puzzle, below, for the first case. Once again, I cannot here reveal the names of either the target country or the foreign power. In addition to discovering the cell, the ACT recovered a secret document outlining the strict rules used by this power in its sleeper cell operations in target countries. According to the secret document, this second power did not use the set of four rules that the first power used. Instead, it used the following two rules:

  1. "The membership rule": Every sleeper agent belongs to exactly two cells.
  2. "The overlap rule": Any two cells have exactly one sleeper in common.

These rules are rigidly adhered to, and the foreign power would shut down its entire sleeper operation rather than violate a rule. In addition, the secret document reveals that the power currently has exactly five cells in the target country. Of course, what ACT would most like to know is just how many sleeper agents they should look for. Can you help? Can you determine from the above information what is the exact number of sleeper agents there are in the target country?


Previous Puzzle: The Puzzle of the Sleeper Cells, 2/29/2016

August 1st, 2016 (Permalink)


McDonaldís Nixing Some Unpalatable Ingredients

Only "some"? That could explain a lot.

Previous Entry

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