God Belief as a Logic Puzzle

God Belief as a Logic Puzzle July 27, 2018

When I was a kid, I liked to read puzzle books and try to figure out the answers without looking in the back. I do remember one puzzle, though, that I couldn’t understand even after I read the answer.

Here’s a variant of that puzzle. See if you do any better.

The puzzle of the hidden dots

The abbot at the Logical Monastery was retiring. He had submitted logical tests and puzzles to the monks to find the most worthy successor. With three candidates remaining, he presented his final problem.

He arranged them in a circle facing each other. “Close your eyes,” the abbot said. “I will put on your forehead a dot of paint, either red or blue.”

The abbot put a red dot on each monk’s forehead. “Now open your eyes, and raise your hand if you see at least one red dot.”

Each monk raised his hand.

“The first one to identify the color of his dot, with the correct reasoning, will take my place as head of this monastery.”

Finally, one monk said, “My dot is red, and I know why.”

What was his reasoning?

If this puzzle is new to you, you may want to work on it before reading the answer below.

God belief as a logic puzzle

Some Christians have little use for evidence and arguments and are content to accept a remarkable claim from an authority such as a parent or a priest. But for those who need reasons to support their beliefs, however, this logic puzzle is analogous to what some apologists say God has set before us. You must read books. You must study philosophy. You must listen to lectures and watch debates. You must wrestle with and overcome your doubts. You must learn obtuse arguments like the Transcendental Argument or the Ontological Argument, and you must defeat challenges like the Problem of Evil or the Problem of Divine Hiddenness.

Apologists imagine God belief as this kind of obtuse puzzle, not because the evidence points that way but because they’re forced to. They have no choice, since the simpler and more desirable option—that God’s existence is as obvious as the existence of the next person you walk past on the sidewalk—is clearly not available to them. Unwilling to give up their beliefs or to admit that they’ve been wrong, they assume God, double down on faith, and invent these bizarre rationalizations.

Find the simpler explanation. A loving creator god who desired a relationship with his creation would just make himself known. We have insufficient evidence to overcome the default hypothesis, that God is yet another made-up supernatural being.

If you’re just going to go with “well, his ideas lived on,”
I’ll put Jesus behind Archimedes, Socrates, Euclid, Galileo, Newton,
Darwin, Pasteur, Einstein, Fleming, and Bohr in that regard.
All of their ideas are current today
and of great value in modern society,
whereas Jesus espoused monarchy, slavery,
and 2nd-class status for women.
— commenter Richard S. Russell

.

(This is an update of a post that originally appeared 10/22/14.)

Image via David Singleton, CC license

Appendix: The reasoning of the logical monk

I suppose the test should be equally hard for each participant. I see two red dots, and for us to have the same puzzle, symmetry would demand that we all see two red dots. But I can’t be sure that we were each given the same puzzle, so that assumption may be a trap.

Let me start with the facts: I see two red dots, and the options are (1) I have a blue dot and (2) I have a red dot.

Consider option 1 first. How would the other monks reason if I had blue? Since they each have red, they would see Red Guy and Blue Guy. They would think, “Suppose I had blue. Red Guy would see two blues—me and Blue Guy. He wouldn’t have raised his hand to say that he saw at least one red. But he did! So therefore the hypothesis ‘I have blue’ is false. So therefore I must have red!”

This is simple reasoning, and they would have given the answer within seconds. But that didn’t happen. Therefore option 1—that I have a blue dot—must be false.

Therefore, option 2 is true, and I have a red dot.

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  • Doubting Thomas

    If we need logical proofs for god, did people who believed before the proofs were developed believe for illogical reasons? If so, why did god wait a millennium for those people to come along? God seems illogical.

    • eric

      Yes, the need seems counter to the general idea that God is accessible to everyone, regardless of intellect. And didn’t the early church attempt (fairly successfully) to stamp out gnosticism? Yet here we have the theological descendants of those gnosticism-destroyers developing proof after complex proof in an attempt to defend their belief as rational.

    • Michael Neville

      A couple of thousand years ago it was obvious that gods existed. The Japanese volcanoes exist because the fire kami Kagutsuchi was chopped into eight pieces by his father Izanagi. Mediterranean tsunamis were caused by Poseidon having a temper-tantrum. Thunder was caused by Thor beating on mountains with Mjölnir. Since then we’ve discovered non-supernatural causes for these things but back in the day there were logical proofs for gods.

      • Greg G.

        Osiris was chopped up into thirteen pieces which were hidden. Twelve of the pieces were recovered by Isis but his penis was thrown into the Nile and eaten by a fish. Horus resurrected the rest of him. Now he judges people when they enter the afterlife. He was more lenient on those who had no foreskins. Why don’t we have any scientific, non-supernatural reasons for circumcisions these days?

  • JustinL

    I am riding high that I figured that puzzle out on my own the exact way the monk in the story did! It’s a lot like that puzzle with the angel and the demon guarding the doors to Heaven and Hell where one always tells the truth and one always lies.

    • Grimlock

      I like xkcd’s version of that riddle: https://xkcd.com/246/

      (The link is to a webcomic.)

      • disciple_of_sithrak

        Or OoTS’s version:
        http://www.giantitp.com/comics/oots0327.html

        This comic shows why I’ve never been impressed by that riddle; a simple solution is very easy to find. People just tend to over think it by coming up with a complex question. Instead, go with “Am I wearing a shirt?”

        • Greg G.

          Usually the set up is that you only get to ask one question.

        • Otto

          “Whaaat…is your favorite color?”

          “Blue…no…arghhhhhhhhh”

        • Greg G.

          What is the airspeed velocity of an unladen swallow?

        • Pofarmer

          An English swallow or……..

        • I like such puzzles occasionally, and that comic response, but it also shows a couple of issues with the premise. Firstly, the idea of someone “always lying” or “always telling the truth” makes it much too easy – in everday English, that would typically mean that someone mostly tells the truth or mostly lies. Secondly, while they can’t trust the guards, the puzzle requires them to unconditionally trust the sign saying what they can expect of the guards. What reason do they have to trust that sign? And finally (similar to the first point), the sign has to be interpreted in context. It has only talked about asking the guards about which path is safe, so maybe the truth and falsehood statement is just about asking which path is safe. Maybe they swap roles in more mundane matters like an arrow in the foot?

          Possibly I overthink this, but it seems to me to be similar to the “self-refuting arguments” loved by some Christian apologists. They conclude that some part of a worldview stated in absolute terms contradicts itself, so therefore everyone should immediately abandon their worldview and accept Christianity (if you have faith you won’t question that last step too closely…) Whereas in my opinion the much simpler response is to say “OK, drop the absolute and say ‘As a generalisation, these statements are true’. No room for self-refuting arguments, and still way more rational than Christianity”.

        • Grimlock

          Heh, yeah, that one was funny.

          I’ve always seen the riddle posed in such a way as to only allow one question, though.

        • Zeropoint

          Always upvote Order of the Stick! I loved that strip!

        • Tommy

          Or hold up four fingers and say, “How many fingers am I holding up?”

  • RichardSRussell

    A good rule of thumb for puzzles like this (as well as scientific inquiry in general) is to come up with a hypothesis to be falsified. All too many theists only consider things that can be demonstrated to be true.

    • eric

      Another rule of thumb is not to try and solve it all at once; break it down in to bits, consider the possible states, and see if all such states lead to the same outcome (as they did here).

      • John MacDonald

        Yes. When it comes to Logic Games, I always ask myself: “What am I assuming that is preventing me from happening upon a resolution (or many resolutions) to the puzzle?”

  • John MacDonald

    Puzzles like this tend to be open-ended. One possible solution is that the abbot gave the solution to the monk who won beforehand because that monk was the abbot’s favorite, and he just conducted an unfair test on the rest of the monks because he wanted to avoid accusations of nepotism.

  • epicurus

    “They have no choice, since the simpler and more desirable option—that God’s existence is as obvious as the existence of the next person you walk past on the sidewalk—is clearly not available to them.”

    It is available to the self authenticating type like William Lane Craig who says the average person can’t do all the book learnin’ and abstract thinkin’ stuff so God/HS must be revealed through the heart. But that just opens up a can of double standard worms that has been discussed many times here.

  • Grimlock

    Writing my answer here before reading any other comments…

    Since all three monks can see at least one red dot, there is at least two red dots. All of them can deduce as much. So we have two possible scenarios:
    1) Two red, one black
    2) Three red

    All monks deduce that these are the options. If any of the monks had seen a black dot, they would’ve known their dot was red. But since none of the monks do so quickly, and we assume they’re reasonably intelligent, they can conclude that all dots are red. Including their own.

  • skl

    Next, we need the explanation of how the red dot puzzle relates to belief in Christianity.

    • Greg G.

      If you understand the red dot puzzle, no explanation is necessary for the relationship to Christianity.

      • skl

        I understand the red dot puzzle and its solution.
        Maybe someone else will be kind enough to explain its relationship to belief in Christianity. I thought the authors and commenters here were interested in educating the less informed.

        • Greg G.

          Read the article, particularly where it says:

          But for those who need reasons to support their beliefs, however, this logic puzzle is analogous to what some apologists say God has set before us. You must read books. You must study philosophy. You must listen to lectures and watch debates. You must wrestle with and overcome your doubts. You must learn obtuse arguments like the Transcendental Argument or the Ontological Argument, and you must defeat challenges like the Problem of Evil or the Problem of Divine Hiddenness.

        • skl

          The three people in the red dot puzzle were perplexed initially, but over a few minutes at least one of them solved it. Using observation and logic, one of them was convinced with near certainty of the unseen truth of what was on his forehead. The others were
          still in the dark.

          And using observation and logic over a few thousand years, many more than one person has become convinced with near certainty of the unseen truth of a godhead. And others are still in the dark.

          Maybe that’s it.

        • Greg G.

          Each one raised their hand to indicate that they saw a red dot, which means nobody saw two black dots. If one person had a black dot, one of the two others could quickly reason out that their own dot was red because there could not be a second black dot. Since nobody quickly reasoned that out, it was obvious that all three had red dots, so the first one to that conclusion won. The time delay was the final clue. The others may not have been in the dark but only mistimed the logic abilities of the others.

          And using careless, unsystematic observation and logic fallacies over a few thousand years, many more than one person has become convinced with near certainty of the unseen truth of a godhead.

          FTFY. If you disagree with my fixes, name one person who used careful, systematic observation and actual logic to prove a supernatural anything.

        • skl

          I don’t know where you’re getting the idea of black dots.

        • Len

          Colourblind.

        • Adam “Giauz” Birkholtz

          Using bald assertions they came up with “classical theology” and the four humors. Their observations were shallow.

    • Otto

      Oh grasshopper…clarity will come with understanding.

    • You and your incisive atheist critiques! Love it.

  • Herald Newman

    While I like the analogy it ultimately breaks down in one very critical place: We can verify what color of dot is on our forehead! Our reasoning has made an empirical prediction and we can see how well that prediction holds up. Not so much when applied to the existence of God. If your reasoning says one thing, but empirical observation says another, then clearly your reasoning is bad, or you started with bad assumptions.

    The idea that pure reason alone should be enough to convince us that God (and not just any god, but the Christian God Yahweh) exists only demonstrates that religious apologists are trying to pull the wool over the eyes of believers.

    • Adam “Giauz” Birkholtz

      Oh, yes. I called in to Catholic Answers Live on the radio a while back, and even though I pointed out that Jesus God could just as easily give whatever argument for his existence as Trent Horn could, meaning there is no necessity to rely on apologetics and the words of holy men and theistic texts, he just went right back to arguing Jesus could be logically reasoned for (predictably, no God entered into the conversation to talk about its existence- not a flaw for a huckster so long as they can get you to believe!).

      • Max Doubt

        “… he just went right back to arguing Jesus could be logically reasoned for (predictably, no God entered into the conversation to talk about its existence- not a flaw for a huckster so long as they can get you to believe!).”

        And let’s say we follow the alleged logic to the supposed conclusion that a god exists. Why would we have to do that? Because the gods simply do not manifest in any measurable, tangible way, that’s why. They don’t move anything, make anything appear or disappear, change the color, size, or shape of anything. They have no weight and take up no space. They don’t absorb or reflect light, sound, or radiation of any sort. They cannot be objectively distinguished from any other figments of the imaginations of those who claim gods exist. A god that can’t do anything at all, well, other than simply exist as the conclusion of a logical construct, is a pretty fucking useless god indeed.

        • Herald Newman

          Why would anyone want to believe in a god that cannot be distinguished from a god that doesn’t exist?

  • dala

    That logic puzzle is bad. It assumes facts not in evidence – specifically, that the head monk is being fair to the candidates, and that the candidates are actually supposed to figure out what color their dot is, rather than this being a more complicated test with rules they weren’t given. I’m glad I didn’t waste much time on it.

    Basically, what he’s really testing whether or not the other monks think he’s an asshole. Only someone who thinks well enough of him to take the test at face value AND assume his own fairness will pass.

    • Greg G.

      It assumes facts not in evidence – specifically, that the head monk is being fair to the candidates,

      No, it doesn’t. Since each of them indicated that they saw a red dot, it was obvious that there were not two blue dots as one of them would not have seen a red dot. The other two would then know they had a blue dot while the other would know he had a red dot since the other two indicated that there was a red dot. So that takes the fairness of the test administrator out of the matter. If there was one blue dot, the other two would see it and know that the blue dot was not on them. The time delay in the others not responding was the final clue which meant that each had a red dot.

      • Rational Human

        I disagree. 2 reds and one blue would get the same response – all three monks see “at least one” red dot. Even if you are red, you see one red and one blue, and blue man sees 2 reds. if you are blue, the others still see at least one red. So both 3 red and 2 red would elicit same affirmative response to “do you see at least one red”.

        • Rational Human

          Nevermind, read some more replies and now see my error.

    • We know he’s the head of the Logical Monastery, so that suggests that he’s trustworthy.

      • martin_exp(pi*sqrt(163))

        when one of those logic puzzles “goes viral” there is often at least one person who will reinterpret the story or setup of the logic puzzle or extend it in some way (like “this being a more complicated test with rules they weren’t given”) to favor their solution or discredit the the puzzle altogether, completely missing the point of those puzzles, solving the underlying logical or mathematical problem. the story is just garnish.

  • JustAnotherAtheist2

    Interesting comparison, Bob, it certainly seems reasonable. IMO, the defining similarity is the presumption that “how did it happen” has a logical explanation. For puzzles it makes sense; they are contrived specifically to have one. For god, however, the presumption allows believers to skip last the more fundamental question, “did it happen?”

    What I also find interesting is the it isn’t just god himself that is a puzzle, pretty much every characteristic reduces down to it’s own puzzle.

    For instance, I recently asked someone whether god can know that he is good. If god’s nature is what grounds goodness, wouldn’t that evaluation mean he is just comparing himself himself to see if they are equal? Wouldn’t that generate a positive result regardless of whether he is good or not?

    The responses were predictable: yes, god knows he is good and his knowledge requires no evaluation.

    This is a dodge, not an answer. Without any evaluation, how can god know he isn’t a morally flawed being with a deeply-held-yet-mistaken conviction that he is good and his nature grounds goodness? If god and this being encountered one another, could one change the other’s mind?

    And here’s where we see the biggest difference between god and logic puzzles. No one would find a response of, “he just does” to be a satisfying resolution to the monk example above. At their core, that’s all good puzzle responses have to offer.

    • Susan

      yes, god knows he is good and his knowledge requires no evaluation.

      Not only that, but “who are you to judge god?”

      All while judging him good because…

      Well, you know.

      • JustAnotherAtheist2

        The funny thing about objective morality is that, rather than giving it sturdier grounding, it makes it necessarily unknowable.

        f we find ourselves in a universe created by a Being where morality is grounded in its nature, we have no way of knowing whether this originator was perfect or flawed. Determining that something aligns with the creator only demonstrates <iIconsistency, it’s still unknown whether our creator was perfect Being A or flawed Being B. Furthermore, even if Being A was out there, steering us away from Being B, we could never know whether it was really perfect or just a differently flawed Being C.

        Worst of all, in this paradigm even our innate moral feelings would offer no insight because they also only demonstrate consistency. Actual goodness remains a bridge too far.

        So theists are right that we can’t judge god. But this is a bug, not a feature… and it’s anything but an asset.

  • martin_exp(pi*sqrt(163))

    three logicians walk into a bar …

    bartender: “does everyone want beer?”
    1st logician: “i don’t know.”
    2nd logician: “i don’t know.”
    3rd logician: “yes.”

    • Three logicians are on a train, and they see a hillside full of sheep. The youngest logician, a city boy, said, “Wow–I didn’t know that all sheep are white.”

      The next logician corrected him: “No, you can only say that all sheep on that hill are white.”

      And the eldest said, “No, you can only say that all sheep on that hill are white on one side.”

      • Greg G.

        No, you can only say that all sheep on that hill are white on one side on Mondays.

        • Damn you and your logic!

        • martin_exp(pi*sqrt(163))

          “logic, logic, logic. logic is the beginning of wisdom, valeris, not the end.” – captain spock in “star trek VI: the undiscovered country”

        • Then, we cannot be certain that these sheep retain that white hue after sundown on a moonless night.

        • Greg G.

          But they can only say that the visible sheep are white until sundown. We know the invisible sheep are invisible because we cannot see them and we know they are pink by faith.

        • Greg G.

          Apologies to the IPU.

      • martin_exp(pi*sqrt(163))

        a version of this joke only talks about the color of one sheep, not a hillside full of sheep (it simplifies the interpretation of on one side), and its (visible) color is often said to be black, not white.

  • Greg G.

    Never give in! Never give in! Never, never, never, never… In nothing great or small, large or petty, never give in except to convictions or honor and good sense! –Winston Churchill

  • Greg G.

    If there is a sin against life, it lies in hoping for another life and evading the implacable grandeur of the one we have. –Albert Camus