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Raymond Smullyan on Ted Cruz, Al Sharpton, and those scary congressmembers

Palko shares this fun logic puzzle from the great Raymond Smullyan which also has obvious implications for modern politics:

Inspector Craig of Scotland Yard was called to Transylvania to solve some cases of vampirism. Arriving there, he found the country inhabited both by vampires and humans. Vampires always lie and humans always tell the truth. However, half the inhabitants, both human and vampire, are insane and totally deluded in their beliefs: all true propositions they believe false, and all false propositions they believe true. The other half of the inhabitants are completely sane: all true statements they know to be true, and all false statements they know to be false. Thus sane humans and insane vampires make only true statements; insane humans and sane vampires make only false statements. Inspector Craig met two sisters, Lucy and Minna. He knew that one was a vampire and one was a human, but knew nothing about the sanity of either. Here is the investigation: Craig (to Lucy): Tell me about yourselves. Lucy: We are both insane. Craig (to Minna): Is that true? Minna: Of course not! From this, Craig was able to prove which of the sisters was the vampire. Which one was it?

With all the conspiracy theories floating around, this distinction between “vampires” and “humans” keeps arising. I assume people such as Al Sharpton and Ted Cruz are “sane vampires” who know when they’re promoting lies, but then there are lots of others like those notorious q-anon congressmembers who are “insane humans” who actually believe what they’re saying.

A complicating factor is that these people help each other. The sane vampires make use of the insane humans in order to increase their political power, and, conversely, the insane humans get support for their false beliefs from the political power of the sane vampires.

So it’s not just Inspector Craig who’s playing the vampires and the humans against each other. The vamps and humans are getting into it directly. And then there are the false statements that get amplified by some mixture of sane vampires and insane humans in the news media.

I don’t think that this post adds anything to our understanding of politics or political science—lots of observers, academics and non-academics, have been talking for awhile about the interaction between political manipulators and sincere believers. And this doesn’t even get into issues such as internet trolls who are being paid expressly to spread disinformation and to attack debunkers. So, these concerns are out there, even if we don’t always know what to do about it. It’s just think it’s interesting to see how Smullyan anticipated all this.

16 Comments

  1. John Richters says:

    Note to Inspector Craig: Since the premise that all humans tell the truth is obviously false, there’s at least a 50% chance that your elegant math and logic will lead you to the wrong answer. Sure, if the premises and background assumptions were on all fours, your fancy shmancy formal tools would be reliable, indispensable guides to a the correct answer. In this case, though, they’re not, so you’ll be slicing spam with a laser beam; your solution strategy will be overkill— literally, in this case, because it may place you on the receiving end of an impromptu phlebotomy. My advice under the circumstances would be to step away from those flawed assumptions and rely instead on some common sense and the evidence of your own senses. The vampire sister is likely to be the one with the ruddy, purplish skin from drinking blood— probably also the one staring at your neck. It’s not my place to pass judgment on your logic and math prowess. I’m just sayin.

    • Michael Nelson says:

      I was going to say something about it being silly to allow for a country with vampires but not a country with truth-tellers. But then I remembered what Aristotle said about people being able to suspend their disbelief in the impossible for the sake of a good story, but unable to accept more realistic plot elements that are very implausible. I guess the same can apply to logic problems.

  2. jim says:

    “lots of observers, academics and non-academics, have been talking for awhile about the interaction between political manipulators and sincere believers. “

    If everyone believes something is true but it turns out to be false, was the belief sane or insane? When people have a belief that can’t be determined as true or false, which belief is sane?

    Everyone believed bacon and eggs were Good Food for a long time. Then, thanks to some (sane/insane) scientists, they were believed to be Bad Food. Now, much of the purported evidence that they are Bad Food is viewed as Bad Evidence, thus the scientists who advanced the claim that they are Bad Food must now be (sane/insane). Yet people persist in the belief that they are Bad Food. Just the same, I don’t know that it’s been demonstrated that they are Good Food. Thus it must be (sane/insane) to believe that they are Good Food, even now.

    I conclude that anyone who’s ever professed any belief about the degree to which bacon and eggs are good food has invested in a false belief – or at least one that can’t be proven true – and is thus insane.

  3. Dzhaughn says:

    The sane vampire almost always tells the truth.

  4. Steve says:

    I was confused by your post because you keep talking about sane Vampires using insane humans. But, Lucy is definitely a Vampire, but she could be either sane or insane. If Lucy is an insane Vampire and both she and Minan are insane, then Lucy will believe she is lying when she says they are both insane, and Minna being honest and insane will deny the truth believing she is honest. If Lucy is a sane Vampire, she will lie and claim that they are both insane, and if Minna is a insane human, she will deny that claim as she did. If Lucy is a sane human, she won’t make the claim, and if Lucy is an insane Vampire, she won’t make the claim.

    I know the point was not to solve the problem, but it was more fun than thinking about how some guy in Japan caused a mass insurrection but creating a fiction on 8chun, and how that will probably keep happening. But, I also think that the Smullyan’s puzzle is neat because you can tell Lucy is a liar without knowing whether she is sane or insane, and I think that is the same situation with Cruz and alot of other people spreading misinformation. They are definitely liars, but are they crazy. It doesn’t matter.

    • Steve says:

      No, I got it wrong. Lucy is an insane Vampire. If Lucy were a sane Vampire and made the false claim, “we are both insane,” then Minna has to be an insane human who will flip the truth value of the false claim to true and affirm the claim. She didn’t do that so Lucy is not a sane Vampire. If they are both sane, Lucy won’t make the claim if she is a sane human. If they are both insane , Lucy won’t make the claim as a insane human. Thus, she only makes the claim, and Minna only denies it, if they are both insane and Lucy is a vampire. SO, Ted Cruz is an insane vampire. All liars are crazy. QED

      • Eric says:

        I disagree with this logic: If Lucy were a sane Vampire and made the false claim, “we are both insane,” then Minna has to be an insane human…
        Minna could be a sane human and the claim is still false.

        • Andrew says:

          Yes, this is where I wanted the blog comments to be going on this post. I’m so glad nobody took the bait and started talking about Ted Cruz and Al Sharpton.

        • Steve says:

          Eric:

          You are right. I was right the first time. Lucy can be a sane Vampire and Minna a sane human and Minna will deny the claim. I went temporarily insane for a moment. I was right the first time Ted Cruz is a lying Vampire who is either sane or insane, but definitely a Vampire sane or insane doesn’t matter. Thus, the entire premise of this blog post is wrong.

  5. paul alper says:

    Is there not some conspiracy that emanated from the University of Minnesota back in the 1940s regarding the evils of salt that was put out secretly by the sugar industry in order to avoid the nutrition spotlight? Instead of the University of Minnesota, Harvard keeps popping up–sugar vs. fat instead.

  6. Rick G says:

    I always have to work these out by brute force (checking all 16 possible joint identities), but I concluded that either they are both sane or both insane, and Lucy is the vampire.

  7. BD says:

    For something along these lines that DOES add to our understanding of politics, try this…

    https://www.lesswrong.com/posts/qDmnyEMtJkE9Wrpau/simulacra-levels-and-their-interactions

  8. Phil says:

    I do appreciate the logic puzzles, and just recommended Smullyan to someone last week in fact.

    But, to rise to Andrew’s bait: the characteristic thing about Cruz and Sharpton (and many others) is not that they do or don’t ‘always’ lie or ‘always’ tell the truth, it’s that they are indifferent to what is or isn’t true. Or at least, what is or isn’t _factually_ true; I’ve heard people talk about propositions that are ’emotionally’ true, whatever that means, and the bullshitters might care about that. This is not a new thing: recall that “truthiness” was Merriam-Webster’s “word of the year” back in 2006 — fifteen years ago! where does the time go? — and it’s defined as “the quality of seeming or being felt to be true, even if not necessarily true.”

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