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    Traditional Logic II

    Good afternoon!
    I am hoping that someone can help! I am working with two students to complete the Traditional Logic II program, and we encountered difficulty in Chapter 8, Hypothetical Syllogisms - Disjunctive Syllogisms. For #25 and #37, we feel unclear on the process for step 4, changing the invalid syllogism to a valid one.

    Is there a set process for knowing whether one should negate both elements in the major premise, a single element in the major premise and the minor premise, etc? I apologize if this has been covered in a different post and I missed it.

    Two specific examples in #25:

    Either Frodo destroys the Ring or evil will triumph
    Frodo destroys the Ring
    Therefore, evil will not triumph

    becomes

    Either Frodo does not destroy the Ring or evil will not triumph
    Frodo destroys the Ring
    Therefore, evil will not triumph

    whereas,

    Either Frodo destroys the Ring or evil will triumph
    Frodo does not destroy the Ring
    Therefore, evil will triumph

    becomes

    Either Frodo does not destroy the Ring or evil will triumph
    Evil will not triumph
    Therefore, Frodo does not destroy the Ring

    If the mood is Ponendo Tollens, Fallacy of Affirming the Second Alternant, do we always negate the first element of the major premise and the minor premise? If it is Ponendo Tollens, Fallacy of Affirming the First Alternant, would one consistently change both elements of the major premise from positive to negative?

    I appreciate any assistance you can offer on this!

    #2
    Hello!

    Thanks for the question. Glad to help. I think I'm reading the question correctly, so here goes:


    If the mood is Ponendo Tollens, Fallacy of Affirming the Second Alternant you would want to do something like this:


    Original Invalid Disjunctive

    Either God created us or aliens did
    Aliens created us
    Therefore God did not create us

    This is the fallacy of affirming the Second Alternant. In this case, to make it valid you would deny the Second Alternant:

    Either God created us or aliens did
    Aliens did not create us
    Therefore God created us


    Or, you could do it like this:

    Either God created us or aliens did not create us
    Aliens created us (this, see is then negation of the proposition in blue above)
    Therefore God did not create us

    That way you've negated the second compound proposition in the major premise and haven't changed the minor premise or the conclusion.

    Does this help? There are multiple ways you could accomplish this. Ultimately you want the argument you construct to be valid but also sound, with no third alternative.

    I hope this helps!

    Scott Piland
    Director
    Memoria Press Online Academy
    onlineacademy@memoriapress.com
    (877) 745-8866

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