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Cogito ergo sum

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When does proving one's truth claims come to an end?

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  • Originally posted by Stoic View Post
    It really appears that you have justified Suber's first sentence: "The Principle of Non-Contradiction (PNC) and Principle of Excluded Middle (PEM) are frequently mistaken for one another and for a third principle which asserts their conjunction."

    His description of the PNC and PEM matches what I find elsewhere. Your claim that they are the same thing does not.

    I would be more likely to take your claims seriously if you provided some links that back you up.
    I'm not mistaking PEM and PNC at all. They are conceptually distinct. I'm not sure where you thought I was mistaking them.

    Two propositions are contradictory iff they cannot both be true and they cannot both be false.
    Two propositions are contraries iff they cannot both be true but can both be false.
    Two propositions are subcontraries iff they cannot both be false but can both be true.
    A proposition is a subaltern of another iff it must be true if its superaltern is true, and the superaltern must be false if the subaltern is false.
    From: https://plato.stanford.edu/entries/square/

    PNC applies to the first. PEM applies to 1 always and to 2 and 3 when the disjunction is exclusive.
    Many and painful are the researches sometimes necessary to be made, for settling points of [this] kind. Pertness and ignorance may ask a question in three lines, which it will cost learning and ingenuity thirty pages to answer. When this is done, the same question shall be triumphantly asked again the next year, as if nothing had ever been written upon the subject.
    George Horne

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    • Originally posted by mattbballman31 View Post
      I'm not mistaking PEM and PNC at all. They are conceptually distinct. I'm not sure where you thought I was mistaking them.
      You stated that according to the PNC, a statement and its negation can't both be false. But that's the PEM. The PNC only implies the PEM in classical logic.

      From: https://plato.stanford.edu/entries/square/

      PNC applies to the first. PEM applies to 1 always and to 2 and 3 when the disjunction is exclusive.
      PNC and PEM both apply (and therefore PEDC applies) to contradictories in classical two-valued logic.

      Suber is mainly talking about other logics where the PNC or the PEM or both do not apply to contradictories. He doesn't mention contraries until the end.

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