1. SubscriberPianoman1
    Nil desperandum
    Seedy piano bar
    Joined
    09 May '08
    Moves
    188816
    14 Jun '12 06:281 edit
    Here are 10 numbered statements. How many of them are true?

    1. Exactly one of these statements is false.
    2. Exactly two of these statements are false.
    3. Exactly three of these statements are false.
    4. Exactly four of these statements are false.
    5. Exactly five of these statements are false.
    6. Exactly six of these statements are false.
    7. Exactly seven of these statements are false.
    8. Exactly eight of these statements are false.
    9. Exactly nine of these statements are false.
    10. Exactly ten of these statements are false.
  2. Joined
    18 Jan '07
    Moves
    6976
    14 Jun '12 12:13
    Originally posted by Pianoman1
    Here are 10 numbered statements. How many of them are true?

    1. Exactly one of these statements is false.
    2. Exactly two of these statements are false.
    3. Exactly three of these statements are false.
    4. Exactly four of these statements are false.
    5. Exactly five of these statements are false.
    6. Exactly six of these statements are false.
    7. Exactl ...[text shortened]...
    9. Exactly nine of these statements are false.
    10. Exactly ten of these statements are false.
    Of necessity (they contradict one another) at most one. And therefore, Reveal Hidden Content
    exactly one, since if it were zero, #10 would contradict itself. Hence number 9 is the only true ststement.


    Richard
  3. SubscriberPianoman1
    Nil desperandum
    Seedy piano bar
    Joined
    09 May '08
    Moves
    188816
    14 Jun '12 12:59
    Originally posted by Shallow Blue
    Of necessity (they contradict one another) at most one. And therefore, [hidden]exactly one, since if it were zero, #10 would contradict itself. Hence number 9 is the only true ststement.[/hidden]

    Richard
    Correct!
  4. Joined
    24 Apr '05
    Moves
    3061
    15 Jun '12 00:12
    Originally posted by Pianoman1
    Here are 10 numbered statements. How many of them are true?

    1. Exactly one of these statements is false.
    2. Exactly two of these statements are false.
    3. Exactly three of these statements are false.
    4. Exactly four of these statements are false.
    5. Exactly five of these statements are false.
    6. Exactly six of these statements are false.
    7. Exactl ...[text shortened]...
    9. Exactly nine of these statements are false.
    10. Exactly ten of these statements are false.
    None of the statements are truth-apt.
  5. Joined
    18 Jan '07
    Moves
    6976
    15 Jun '12 11:25
    Originally posted by LemonJello
    None of the statements are truth-apt.
    That doesn't work. If none of them are true, all of them are false, which makes #10 true, which contradicts your assumption.

    Richard
  6. Subscribertalzamir
    Art, not a Toil
    60.13N / 25.01E
    Joined
    19 Sep '11
    Moves
    45045
    15 Jun '12 13:211 edit
    Nice! ^_^
  7. Standard memberSwissGambit
    Caninus Interruptus
    2014.05.01
    Joined
    11 Apr '07
    Moves
    92274
    16 Jun '12 02:49
    Originally posted by Shallow Blue
    That doesn't work. If none of them are true, all of them are false, which makes #10 true, which contradicts your assumption.

    Richard
    A sentence is truth-apt if there is some context in which it could be uttered (with its present meaning) and express a true or false proposition. Sentences that are not apt for truth include questions and commands, and, more controversially, paradoxical sentences of the form of the Liar (‘this sentence is false&rsquo😉; or sentences (‘you will not smoke&rsquo😉 whose apparent function is to make an assertion, but which may instead be regarded as expressing prescriptions or attitudes, rather than being in the business of aiming at truth or falsehood. See expressivism, prescriptivism.

    Read more: http://www.answers.com/topic/truth-apt#ixzz1xv9NWjfw
  8. Subscribertalzamir
    Art, not a Toil
    60.13N / 25.01E
    Joined
    19 Sep '11
    Moves
    45045
    16 Jun '12 11:02
    Reminds me of the old dilemma of having a piece of paper with the text "the statement on the other side of this paper is false" printed on both sides. =)
  9. Joined
    29 Dec '08
    Moves
    6788
    16 Jun '12 12:57
    Originally posted by Pianoman1
    Here are 10 numbered statements. How many of them are true?

    1. Exactly one of these statements is false.
    2. Exactly two of these statements are false.
    3. Exactly three of these statements are false.
    4. Exactly four of these statements are false.
    5. Exactly five of these statements are false.
    6. Exactly six of these statements are false.
    7. Exactl ...[text shortened]...
    9. Exactly nine of these statements are false.
    10. Exactly ten of these statements are false.
    What would be the case as i -> infinity, that is, as the number of statements approaches infinity, each statement saying "Exactly i of these statements is/are true"?
  10. Subscribertalzamir
    Art, not a Toil
    60.13N / 25.01E
    Joined
    19 Sep '11
    Moves
    45045
    16 Jun '12 21:39
    n statements, n-1 'th is true, where n = 2, 3, 4, ... so we'd get

    lim n-1 as n-> oo as the ordinal of the statement that is true, and the ordinal approaches infinity as the number of statements increases without limit?
  11. Joined
    24 Apr '05
    Moves
    3061
    17 Jun '12 07:191 edit
    Originally posted by Shallow Blue
    That doesn't work. If none of them are true, all of them are false, which makes #10 true, which contradicts your assumption.

    Richard
    It works fine. If they are not truth-apt to begin with, then they are all neither true nor false.

    At any rate, the OP presumes that such statements are truth-apt (not explicitly, but in the spirit of the exercise as it was given). I rather doubt that. (But this is debatable.)

    If I am wrong and indeed such statements are truth-apt, then I would agree with the solution you gave.
  12. Joined
    18 Jan '07
    Moves
    6976
    17 Jun '12 11:04
    Originally posted by LemonJello
    It works fine. If they are not truth-apt to begin with, then they are all neither true nor false.
    That is only true (and the term "truth-apt" only meaningful) in one specific branch of logic. Real life is not that branch, and neither are logical puzzles unless explicitly stated.

    Richard
  13. Wat?
    Joined
    16 Aug '05
    Moves
    76863
    17 Jun '12 14:52
    Originally posted by SwissGambit
    A sentence is truth-apt if there is some context in which it could be uttered (with its present meaning) and express a true or false proposition. Sentences that are not apt for truth include questions and commands, and, more controversially, paradoxical sentences of the form of the Liar (‘this sentence is false&rsquo😉; or sentences (‘you will not smoke&rsquo😉 whos ...[text shortened]... expressivism, prescriptivism.

    Read more: http://www.answers.com/topic/truth-apt#ixzz1xv9NWjfw
    PERFECTLY asserted.

    I guess you are a language teacher, per chance?

    -m.
  14. Standard memberSwissGambit
    Caninus Interruptus
    2014.05.01
    Joined
    11 Apr '07
    Moves
    92274
    17 Jun '12 15:08
    Originally posted by mikelom
    PERFECTLY asserted.

    I guess you are a language teacher, per chance?

    -m.
    Thanks, but it was a quote from answers.com - see the link below the quote for more info. Sorry if I did not make this clear enough.
  15. Joined
    24 Apr '05
    Moves
    3061
    18 Jun '12 05:49
    Originally posted by Shallow Blue
    That is only true (and the term "truth-apt" only meaningful) in one specific branch of logic. Real life is not that branch, and neither are logical puzzles unless explicitly stated.

    Richard
    FAIL.
Back to Top