Posers and Puzzles

Posers and Puzzles

  1. DonationAcolyte
    Now With Added BA
    Loughborough
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    04 Jul '02
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    3790
    30 Mar '03 19:50
    True or false:

    1. If a is a real number such that a^2 = 2 and a^3 = 5, then a = 2.

    2. If Hitler had been assassinated in 1932, the Moon would never have existed.

    3. If Hitler was assassinated in 1932, then the Moon has never existed.
  2. Donationbbarr
    Chief Justice
    Center of Contention
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    14 Jun '02
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    17381
    30 Mar '03 22:37
    Originally posted by Acolyte
    True or false:

    1. If a is a real number such that a^2 = 2 and a^3 = 5, then a = 2.

    2. If Hitler had been assassinated in 1932, the Moon would never have existed.

    3. If Hitler was assassinated in 1932, then the Moon has never existed.
    Those pesky conditionals....

    All of those sentences are true, but trivially so. Whenever the antecedent of a conditional is false, the conditional itself is true. Whenever the consequent of a conditional is true, the conditional is itself true. The only way a conditional of that sort comes out false is if the antecedent is true and the conditional is false. Goes to show that using first-order logic to formalize natural languages may have some counter-intuitive consequences.
  3. Steelers Country
    Joined
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    32833
    30 Mar '03 23:19
    Originally posted by Acolyte
    True or false:

    1. If a is a real number such that a^2 = 2 and a^3 = 5, then a = 2.

    2. If Hitler had been assassinated in 1932, the Moon would never have existed.

    3. If Hitler was assassinated in 1932, then the Moon has never existed.
    I'm comfused😕, what do you mean by #2 and #3?
  4. DonationAcolyte
    Now With Added BA
    Loughborough
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    01 Apr '03 20:22
    Originally posted by bbarr
    Those pesky conditionals....

    All of those sentences are true, but trivially so. Whenever the antecedent of a conditional is false, the conditional itself is true. Whenever the consequent of a conditional is true, the conditional is itself true. The only way a conditional of that sort comes out false is if the antecedent is true and the conditional is fal ...[text shortened]... g first-order logic to formalize natural languages may have some counter-intuitive consequences.
    Oops, I should have said "one for the non-philosphers" 😉. The convention you explain is the one used in mathematics, but I was curious as to whether this was agreed upon by philosophers as well. Interestingly, we do use such constructions in evveryday conversation, but only as exclamations, eg "If those shoes are worth £100, then I'm the Queen of Sheba!" Perhaps the convention isn't as counter-intuitive as it might seem.

    On a similar note, my father, who has a contract to teach people to use a sophisicated search engine, informs me that many people find the formal definition(s) of 'AND' or 'OR' confusing. (That's an inclusive or 😛)
  5. Standard memberroyalchicken
    CHAOS GHOST!!!
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    01 Apr '03 21:36
    Actually, out of interest, I posed something like these at school. The ensuing shouting match among the listeners was very amusing. When I told them roughly what bbar has just said, they refused to believe it. I wonder why...
  6. Joined
    11 Jan '03
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    90
    07 Apr '03 22:53
    true
    false
    and...
    erm...i`m not sure.
    could the moon not exist?
  7. Joined
    12 Apr '03
    Moves
    31
    12 Apr '03 09:23
    Originally posted by Acolyte
    True or false:

    1. If a is a real number such that a^2 = 2 and a^3 = 5, then a = 2.

    2. If Hitler had been assassinated in 1932, the Moon would never have existed.

    3. If Hitler was assassinated in 1932, then the Moon has never existed.
    Hitler was not assassinated in 1932
  8. Standard membergenius
    Wayward Soul
    Your Blackened Sky
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    12 Apr '03 10:10
    Originally posted by waldorf
    Hitler was not assassinated in 1932
    "IF hitler was assasinated in 1932..."
  9. Joined
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    12 Apr '03 12:07
    Originally posted by genius
    "[b]IF hitler was assasinated in 1932..."[/b]
    He wasn't though, so why suppose otherwise?
  10. Standard membergenius
    Wayward Soul
    Your Blackened Sky
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    12 Apr '03 13:28
    Originally posted by waldorf
    He wasn't though, so why suppose otherwise?
    it's a situation that the question is based around! same with all these questions-look at the thread coins; there never was a blind man!...😛
  11. Standard memberroyalchicken
    CHAOS GHOST!!!
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    12 Apr '03 15:42
    Originally posted by waldorf
    He wasn't though, so why suppose otherwise?
    I think someone needs to be saddled with explaining the always-tricky assumption-versus-statement, literal-versus-figurative thing. Not me.
  12. Joined
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    12 Apr '03 21:22
    Originally posted by royalchicken
    I think someone needs to be saddled with explaining the always-tricky assumption-versus-statement, literal-versus-figurative thing. Not me.
    Oh, is that it? Now I understand 😕
  13. Standard memberroyalchicken
    CHAOS GHOST!!!
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    12 Apr '03 21:59
    Originally posted by waldorf
    Oh, is that it? Now I understand 😕
    Sorry...I should have used the facetious smiley. Read the first few posts in this thread to undertstand the "Hitler assassinated" business. You don't seem to be playing much chess...I can challenge you soon if you like.
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