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  • daily puzzle: the rational reasoner

    From Rich D@21:1/5 to All on Wed Nov 15 17:28:51 2023
    A rational person believes a finite number of propositions;
    that is, he believes all of them they are true. (if he thought
    any one was false, he'd disbelieve it)

    A rational person also disbelieves in his own perfection.
    He expects to be wrong occasionally.

    This implies that one of the list of the propositions
    referenced above, must be false. And he's aware of this
    implication. Which means he believes he believes
    something false.

    Is this inconsistent? Is he rational? Explain.

    --
    Rich

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  • From Jeff Barnett@21:1/5 to Rich D on Thu Nov 16 00:43:33 2023
    On 11/15/2023 6:28 PM, Rich D wrote:
    A rational person believes a finite number of propositions;
    that is, he believes all of them they are true. (if he thought
    any one was false, he'd disbelieve it)

    A rational person also disbelieves in his own perfection.
    He expects to be wrong occasionally.

    This implies that one of the list of the propositions
    referenced above, must be false. And he's aware of this
    implication. Which means he believes he believes
    something false.

    Is this inconsistent? Is he rational? Explain.
    Rational does not imply perfection in thought. For a being to achieve
    that perfection, it must already be able to answer all questions and
    solve all well formed problems that it might encounter in the future
    whether relevant knowledge has been acquired/considered in the past or
    not. The fact the we often anthropomorphize logic problems by putting propositions in the mouth of humans is merely a literary device. There
    do not exist a Foo tribe whose members always tell the truth and a Snafu
    tribe whose members always lie so questions about interactions among
    such entities and them and one of us are just abstractions of logic
    issues, i.e., of lifeless communications that having little to do with us.

    You seem, above, to float a definition of a rational person (or a
    paranoid or etc.) then move on to ask a question given your definition.
    If the definition was of a abstract system (e.g., something in the class
    of Turing machines) you could ask if such a system could be defined, not whether it is consistent.
    --
    Jeff Barnett

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  • From Rich D@21:1/5 to All on Sat Nov 18 16:13:46 2023
    On November 15,  Jeff Barnett wrote:
    A rational person believes a finite number of propositions;
    that is, he believes all of them they are true. (if he thought
    any one was false, he'd disbelieve it)
    A rational person also disbelieves in his own perfection.
    He expects to be wrong occasionally.
    This implies that one of the list of the propositions
    referenced above, must be false. And he's aware of this
    implication. Which means he believes he believes
    something false.
    Is this inconsistent? Is he rational? Explain.

    Rational does not imply perfection in thought.

    I would not define rational as equivalent to perfection.
    In order to discuss the concept, one must first define the concept.

    You seem, above, to float a definition of a rational person then
    move on to ask a question given your definition.

    Define rational person: he attempts to avoid contradiction,
    he doesn't knowingly accept any contradiction. He utilizes
    the precepts of first order logic. He attempts to recognize
    facts and reality, assuming his perceptions of reality are accurate.

    He notices that no one is perfect. By induction, he presumes
    himself to be imperfect; that is, he's occasionally wrong. Which
    means one of his accepted propositions must be false.

    Therefore, he is aware that he believes a false proposition.
    Hence is inconsistent. Knowingly.

    A modest man must therefore be inconsistent, unavoidably.

    If the definition was of a abstract system (e.g., something in the class
    of Turing machines) you could ask if such a system could be defined, not whether it is consistent.

    You could frame the original question in regard to an abstract
    system, it wouldn't change anything pertinent.

    Here's a workaround: call on information theory. Assign b bits
    of information to each correct proposition. Then recognize that
    some of those are false, and strive to maximize the total
    information. Don't sweat the small stuff, I always say -

    --
    Rich

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