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Thread: McGee's counterexample to the Modus Ponens

  1. Top | #31
    Mazzie Daius fromderinside's Avatar
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    Quote Originally Posted by MxM111 View Post

    A statement "A Republican will win the election" must mean "we live in the word where the only possibility is a republican wining election", otherwise Modus ponens is not applicable. Then again "If it's not Reagan who wins, it will be Anderson" is completely valid statement.
    This ^^^^^

    captures real conditions in Hungary and US. So your example is bogus.

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    Contributor Speakpigeon's Avatar
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    Quote Originally Posted by MxM111 View Post
    Quote Originally Posted by Speakpigeon View Post
    Here is an interesting example to try your wits...
    McGee's counterexample


    If a Republican wins the election, then if it's not Reagan who wins it will be Anderson.
    A Republican will win the election
    .

    Yet they did not have reason to believe

    If it's not Reagan who wins, it will be Anderson.
    This example shows that modus ponens is not an entirely reliable rule of inference.
    I think the problem is the following. Modus ponens principle is a logic principle, not probability principle. If A, then B. Then A happens. 100% happens. No "probably happens". Then B

    Applying to the election example, it is misleading to say "A Republican will win the election", because it does not convey the 100% certainty, because we talk about future. Modus ponens does not have time dimention, it just says "this happen therefore that". Change "A Republican will win the election" to "A Republican won the election", then it is true that "If it's not Reagan who won, it is Anderson."

    A statement "A Republican will win the election" must mean "we live in the word where the only possibility is a republican wining election", otherwise Modus ponens is not applicable. Then again "If it's not Reagan who wins, it will be Anderson" is completely valid statement.
    This is a red herring. We can modify McGee's counterexample as follows, putting everything in the present:

    McGee's counterexample modified:
    If a Republican has won the election, then if it's not Reagan who has won it is Anderson.
    A Republican has won the election.
    Yet they did not have reason to believe

    If it's not Reagan who has won, it is Anderson.
    It is certainly better this way, but we should all be able to interpret McGee's original in this vein without requiring my assistance.
    EB

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