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A logical question

  1. Aug 14, 2008 #1

    A.each sentence which ends with exclamation mark is lying!
    B.sentence A is lying!
    C.sentence B is lying.

    which claim is wright regarding these sentences?
    1.A and C are truthful and B is lying
    2.C is truthful while A and B are lying
    3. B is truthful while A and C are lying
    4.C is lying while A and B are truthful

    that exclamation mark thing makes me confused
    sentence A contradicts itself
  2. jcsd
  3. Aug 14, 2008 #2


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    A and B can both be truthful if it is really sentences that end in period that are lying.
  4. Aug 14, 2008 #3
    3. B is truthful while A and C are lying

    A contradicts itself if assumed to be true. The only way to avoid the contradiction is to assume it is false. Therefore, B is true, and C is false.
  5. Aug 14, 2008 #4
    a period meens nothing

    how did come to this answer
    how did you solve this exclamation mark thing??
  6. Aug 14, 2008 #5
    A proposition is either true or false, bot nut both (law of excluded middle + law of non-contradiction). The question clearly suggests that there is a way to assign truth values to the propositions without creating any inconsistency. Proposition A is either true or false. If we assume it is true, we obtain the following:

    a. Sentence A is true.
    b. Sentence A is a sentence which ends with an exclamation mark.

    c. Therefore sentence A is false.

    This is inconsistent; we have obtained both the statements "sentence A is true" and "sentence A is false" from the assumption that A is true. Therefore sentence A is not true. Therefore, it must be false. That said, we are forced to accept that B is true, and then that C is false.

    To be noted: some propositions are not classifiable as either true or false, this being perhaps the biggest failure of classic Aristotelian logic. For example, the sentence "This sentence is false." leads to a contradiction whether we assume it is true or false. However, like I said, the question suggests that there is a way to assign truth values without contradictions, and so you may assume the laws of classical logic can be applied.
  7. Aug 14, 2008 #6


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    There are 3 possibilities:

    1. All sentences that end in an exclamation mark are lying.
    2. All sentences that end in an exclamation mark are truthful.
    3. Some sentences that end in a "!" are lying, and some are truthful.

    The trick here is that many people do not think of or consider possibility #3.
  8. Aug 14, 2008 #7


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    You're right, I meant to say that A was internally consistent with a lie if such was the case, because in saying that exclamation marks are lies - that is a lie. It doesn't mean all exclamation mark sentences are lies however.

    B in calling A a lie is merely making a correct observation.

    And C of course is a lie because B is True.
  9. Aug 14, 2008 #8
    thanks i understand this question now
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