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April 22nd, 2017 (Permalink)

The ABC Murder

Detective David Davidson was assigned to investigate the murder of notorious racketeer Victor Timm. It should have been an open-and-shut case since there were four eyewitnesses to the crime. Unfortunately for Davidson, the witnesses all disagreed.

The ABC Gang was so called because it consisted of three criminals: Adam Adamson, Brad Bradford, and Curt Curtis. It was known that the ABC Gang and Timm had had a falling out, but who was the triggerman? He had no doubt that the shooter was one of the ABC gangsters, but which one?

Davidson set up a line-up for the witnesses that included all three of the ABC gangmembers, together with a few fellow cops as ringers. Thankfully, none of the witnesses fingered any of the cops as the killer. Here's the gist of what each witness said:

  1. Adamson was the shooter.
  2. This witness wouldn't identify a shooter, but insisted that it wasn't Curtis.
  3. This one wasn't sure whether Adamson or Bradford was the shooter, but claimed that it was one of the two.
  4. The last witness refused to finger the shooter as Bradford but did rule out both Adamson and Curtis.

Davidson was disgusted. That didn't help at all! In fact, at least one of the witnesses had to be wrong since they contradicted each other. Luckily, Davidson received a call from a stoolie named Eddie "The Snitch" Edwards who informed him that one or more of the witnesses had been bribed or intimidated by the ABC Gang to lie to the police. At first, Davidson was still disgusted, since he already knew that at least one of the witnesses had not told the truth, but he didn't know which. However, when Eddie told him the exact number of witnesses who weren't telling the truth, Davidson smiled. Davidson now knew who the shooter was.

Assuming that one of the ABC gangsters was the shooter and that Eddie's information was correct, who shot Vic Timm?

Solution


April 9th, 2016 (Permalink)

Check it Out, Too

If you can tear yourself away from the tax forms long enough, philosopher Alan Hájek offers you a "philosophy tool kit" for thinking:

Philosophers pride themselves on thinking clearly by seeing what follows from what, exposing sophisms, spotting fallacies, and generally policing our reasoning. … But these skills are not the exclusive property of rarefied sages, accessed only with a secret handshake and insider training, as much as some philosophers wish this were so. Instead, some of these skills can be captured by generalisable, all-purpose techniques for the proper conduct of thought, whatever the topic. Many of these are easily taught and learned. As such, they can be utilised by non-philosophers too. At a time when we are bombarded more than ever with specious claims and spurious inferences, clear thinking provides a much-needed safeguard that we should all strive towards.1

It's not a full philosophical "tool kit", as it contains only a few tools. Rather, it's like the kind of small kit you might keep in your car in case of a breakdown on the road, so you might think of it as a tool kit in case of a philosophical emergency.

Hájek shows how to use the tools by applying them to some traditional philosophical problems but, as he mentions, they can be applied to many other types of intellectual, conceptual, and logical problems.

The tools in the kit are philosophical heuristics, but what is a philosophical heuristic? Well, wait: what is a heuristic? It's a rule of thumb2. Hájek gives the following example: "Here’s a good one for mathematics: if you are not making headway on a problem, modify it slightly to make it easier, and solve that one." I think this is a good rule of thumb for problem-solving in general, not just mathematics. The point of using heuristics is that, while they don't always work, they work often enough to be useful; also, even when they don't solve the problem, they may help point the way to a solution.

One reason I point you to this article is that many of the topics that Hájek discusses have been discussed here in The Fallacy Files, so you can compare his treatment of the issues to mine3:

This should keep you busy until I can get around to posting something new.

Notes:

  1. Alan Hájek, "Philosophy Took Kit", Aeon, 4/3/2017
  2. And, no, the phrase "rule of thumb" does not come from a law allowing a man to beat his wife with any stick no thicker than his thumb. See: Cecil Adams, "Does 'rule of thumb' refer to an old law permitting wife beating?", The Straight Dope, 5/12/2000
  3. A useful tool that Hájek doesn't mention is "the second opinion".
  4. "A" v. "The", 7/19/2008
  5. "False Dichotomy"
  6. Puzzle it Out, 7/3/2015
  7. Q&A, 5/21/2013
  8. The Logical Problem of Evil, 4/6/2015

April 5th, 2017 (Permalink)

Check it Out

April is the cruelest month….1

…And April 15th the cruelest day. It's that time of year again, and I'm going to be rather busy for the next couple of weeks trying to figure out what the IRS wants from me. In the meantime, if you can find some time to read something other than tax instructions, here's something worth checking out2.

Notes:

  1. T. S. Eliot, "The Waste Land", Poetry Foundation
  2. Eugene Volokh, "“Amid ‘Trump Effect’ fear, 40% of colleges see dip in foreign applicants”―but…", The Volokh Conspiracy, 3/28/2017

Solution to the ABC Murder: Curt Curtis (no relation) was the shooter.

In case you got the wrong answer, here's how to solve this puzzle: We know that at least one of the witnesses is not telling the truth, since the first witness accused Adamson but the last one claimed that Adamson was not the shooter. However, it may be that one or more of the other witnesses is not telling the truth.

Given that one of the ABC gang shot Timm, there are only three possible shooters to consider:

  1. Adamson: In this case, only the last witness did not tell the truth, since he or she claimed that Adamson was not the shooter.
  2. Bradford: Only the first witness did not tell the truth, since he or she claimed that Adamson was the shooter.
  3. Curtis: In this case, all four of the witnesses would have failed to tell the truth, since the identifications made by each are inconsistent with Curtis being the shooter.

When Eddie the Snitch informed Detective Davidson that at least one of the witnesses was not telling the truth, this fact did not help Davidson since that meant that each of the three gangsters might have been the shooter. However, when Eddie went on to tell Davidson the exact number of witnesses who were not telling the truth, Davidson was able to solve the case. How was he able to do so?

If Eddie had said that only one of the witnesses was not telling the truth, then all this would have done is rule out Curtis as the shooter. If Eddie had said that two or three of the witnesses were not telling the truth, then Davidson would have concluded that Eddie was the one who was wrong. The only way in which Eddie's information would have helped Davidson solve the case is if Eddie had said that all four of the witnesses were not telling the truth. Therefore, Curtis was the shooter.

Disclosure: The story you have just read is false. The names have been changed to protect the guilty.

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