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?
Lv 7
? asked in Science & MathematicsMathematics · 1 decade ago

This week's paradox is (drum roll please)...?

Consider the following two statements:

1. If the second statement is true, then all numbers are even.

2. This statement is true.

why does this not prove all numbers are even?

Update:

now suppose i make this small modification:

if this statement is true, then all numbers are even.

is that better, or worse? :)

7 Answers

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  • 1 decade ago
    Favorite Answer

    You have implicitly assumed that if statement 2 holds then all numbers are even.

    Putting together what statement 1 and 2 have to tell us, you have just made an statement "All numbers are even!"

    So you just throw at the reader that "All numbers are even"

    No need to say it doesn't prove anything. I can say "10 is odd". Sure I can, but that's not a proof obviously.

    Regarding your Additional Details

    ========================

    You are assuming an unproven implication "If ( ) then ( )" without proving that this implication holds.

    Besides even if you can prove that this implication holds, it does not prove the "Then" proposition.

    For example,

    "If (A = 1) then (A > 0)"

    is obviously true. But it doesn't prove that (A > 0) is true

    In that sense you've made it worse by saying "if this statement is true, then all numbers are even."

  • 1 decade ago

    There is no indication that the first statement is true, so even though the second statement is true, it does not necessarily mean that all numbers are even because the first statement could have been lying about all numbers being even if the second statement it true.

  • Anonymous
    1 decade ago

    You ae assuming hat the first statement is true, and it is not.

  • JOS J
    Lv 7
    1 decade ago

    This is a If - Then statement

    Since If is not true it does not follow that Then is true

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  • Mark
    Lv 7
    1 decade ago

    Self-referential fallacy.

  • 1 decade ago

    Because the first statement may be false. You haven't proven the first statement, therefore you cannot use it to prove anything else.

  • ?
    Lv 4
    1 decade ago

    It is fallacious to assume that the first statement is true, as we are given no such indication that it is.

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