Back to the classic problem

This topic contains 10 replies, has 5 voices, and was last updated by  Simon Paynton 1 month ago.

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    It’s been a few years since we visited this question. Perhaps a few people’s “minds” have changed on the issue. I’ll frame the question slightly differently from last time.

    Someone is counting books on her bookshelf (from a distance) and counts 15 books. Little did she know one of the objects she thought was a book was a brick. Was she correct that there were 15 books on the shelf?

    As it turns out, there was a book behind that brick…so in reality there were 15 books on the shelf. However, even though there were 15 books on the shelf after all and she concluded there were 15 books (even though she included the brick in his count) … WAS SHE CORRECT?

    In answering this question try to explain why you think she was or wasn’t correct taking into account what “knowing” something means, what role subjective and objective information plays in “being correct” and try to consider all the variables in this scenario and the relationship between knowledge and being correct.



    I think that yes ultimately she was correct, but she was lucky that there was a book behind the brick. Had there not been then she would not have been correct. How is that so complicated?


    People “think” they “know” a lot of things that they really don’t.


    I’m not sure what the discussion was a couple of years ago, perhaps you could provide a link?

    I would say that the vast majority of things that we think we know we really don’t know “for sure.”

    And our perceptions are usually off about the way that we view the world. We are almost never right. But we make calculations and decisions in our head based on what we perceive reality to be. Most of the time we are foolish, stumbling blindly through the world.



    Thanks Unseen for answering the question. That’s an interesting explanation.

    Ivy, I wish you had have actually answered the question as I had posed it. For example: is being correct contingent on knowing something? Can you truly be correct if it is only out of luck? It is a little similar to the stopped clock effect (where a stopped clock is actually “correct” twice a day even though it isn’t working). If your premises and/or the structure of your argument are faulty and yet your conclusion turns out to be true…were you actually correct?

    I would argue Ivy that there is a different between being correct through sound premises and the structure of the argument (a sound argument with true premises) and, as you put it…simply “being lucky”.

    We often use the same term for both these cases “correct”, but I believe they are two different phenomena.

    Imagine Ivy if we replaced the word “correct” in that whole question with the word “know”. Would you still give the same answer?

    • This reply was modified 1 month, 1 week ago by  Davis.


    @davis I did answer your question.



    Sorry Ivy but answer the question as I posed it…you did not.



    I answered your question @davis. Whether you liked my answer is a separate question.



    Thinking the brick was a book was just an incorrect assumption. She didn’t know that she was only seeing 14 books, and neither did she know that one or more books were hidden.

    So she didn’t really know the correct book count (even though she knew how to count up to 15), she just accidentally and incorrectly perceived 15 books while one or more books were not even visually countable.

    Nice art, by the way.






    We run into a problem with the term ‘correct’. We need parameters for applying it. Correctness is relative to a number of variables such as desired outcome, acceptable margin of error, methodological limitations etc.

    What is it she needs to know in this example? Does she need to know specifically the number of books as accurately and individually counted? In that case, she is not correct in her count, regardless of the fact that the number she arrived at aligns with material reality. One book remained uncounted, and one object was counted erroneously as a book. She may be confident in her count, but she doesn’t know

    However, if all that was needed was an inventory of the number of books on the shelf, then she was correct even if accidentally. Perhaps her method of counting was faulty and that may create liabilities in the future, but even if by accident, she provided the correct answer. As to whether or not she knew the correct answer, that depends.

    If the definition of knowing is that each book is known to her as she counts it, then no, she doesn’t know how many books there are. While much more extreme, it would be akin to someone who said their dead relative spoke to them from beyond the grave and revealed the winning lotto numbers. As a matter of chance, it was always possible for them to win, but even if they do win, few would believe they actually knew the numbers beforehand. Their odds were the same as anyone randomly guessing the numbers. In the book counter’s case, it’s not quite as random as that, but it matters that the method for determining the number of books is flawed and has the potential to produce incorrect results.

    However, imagine instead of counting the books on a shelf, it was an entire library. For whatever reason, she was tasked with taking the count of how many books there are in the library. Perhaps there is a radical discrepancy between the number of books in physical card catalogues of old, and the number of books in the electronic catalogue, and a count is necessary to determine which is correct.

    When the books are counted, it is assumed that a certain number of ‘books’ on the shelves may actually be bricks or decorative bookends dressed up as books. It’s also assumed that a certain number of very thin books may go unseen pressed tightly between thicker volumes. These aren’t random assumptions, but rather variables which can be reasonably assumed. At the end of the count, she reaches a number of 15,678. Some of the ‘books’ in that figure are not actually books. Some books not in that figure were overlooked. But if the methodology for counting was soundly designed, it’s known there are that many books plus or minus a margin of error.

    That may seem like I’m changing too much in the original question or that it’s straying from the actual purpose of the question, but I think it speaks to a certain reality of what it means to be correct or to know things. We can know things as a matter of direct observation or interaction, or we can know them as a probability, or as a statistical reality, or as a computational model. What matters is we have reasonably assessed the limits and properties of our sensory inputs, we’ve constructed a sound model for processing that input, and we’re able to competently contextualize the data. In that sense we can say we know things, even if with varying degrees of confidence and accuracy.


    Simon Paynton

    I think it speaks to a certain reality of what it means to be correct or to know things.

    Someone said, there are at least two kinds of truth: 1) “correspondance”, where a proposition accurately captures reality; 2) “consistency”, where a proposition is logically consistent with other propositions that are known to have correspondance with reality.  Reality always makes sense and is logical.

    But like you say, the question remains, what does it mean to know something?  It depends on information transmitted by light, radio waves or some other medium, from reality, reaching our senses and our technological sensing instruments.


    Simon Paynton

    I’m told that the Buddha taught that the mind is also a sense organ.  I think that’s true, we can use the mind to know things – to join dots, distill data into knowledge.

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