Two Strange Proofs

Mr. Nance,

Could you give real-world examples of the arguments to prove in Intermediate Logic Lesson 18, number 7) U / ∴ W ⊃ W, and number 8) X / ∴ Y ⊃ X, showing how they would be used, or explain them a bit? Thank you.

Thanks for the great question! These two arguments are unusual, so I am not surprised that you are asking about them.

A real-world example for #7 might be Esther 4:16, “I will go to the king which is against the law; if I perish, then I perish!” This argument form basically shows that any proposition implies a tautology.

An example for #8 could be, “God created all things. So even if evolution can be used to explain some fossils, it’s still true that God created all things.” The form of this argument shows that if a proposition is given, any other proposition implies it.

To be honest, my purposes for including those two problems were: 1) to show how very strange the conditional proof is, and 2) to show how this method can be used to simplify otherwise difficult proofs.


4 thoughts on “Two Strange Proofs

  1. The translation of each of these enthymemes is a little tricky.

    #2: “I will fear no evil, for you are with me.” The conclusion is “I will fear no evil.” This could be translated either as No evil will be a thing I fear, or No I will be an evil fearer (recognizing how we translate singular statements into universals). The given premise is also talking about persons, so we should use the second translation. But that means we must use one of the terms in the conclusion — “I” or “evil fearer” — in the translation of “You are with me.” Since this does not mention evil, it seems we must use the “I.” Thus we should translate the premise “You are with me” as All I am a person with you. That means the two terms in the assumed statement must be person with you and evil fearer. Since the conclusion is an E statement and the given premise an A statement, that means that the assumed statement must also be an E statement. Thus the complete syllogism is:

    (No person with you is an evil fearer.)
    All I am a person with you.
    .’. No I will be an evil fearer.

    They enthymeme in #3 is “You are worthy, our Lord and God, to receive glory . . . for you created all things.” The tricky thing here is that the statements are singular, but that the conclusion gives more detail in the subject. As singulars they must be translated into universals. Something like this (with the assumed statement in parentheses):

    (All the Creator of all things is a worthy glory receiver.)
    All God is the Creator of all things.
    .’. All God is a worthy glory receiver.

    The enthymeme for #5 is similar, because like #3 it uses slightly different words for the same term: “Here are my mother and my brothers! For whoever does the will of my Father in heaven is my brother and sister and mother.” When one of the statements uses an inclusive word like “whoever” then we should start the translation with that statement. “Whoever does the will of my Father in heaven is my brother and sister and mother” can be translated a little shorter as All people doing my heavenly Father’s will are my family members. Since the terms of this statement are people, we must use people to translate the other statements. “Here are my mother and brothers” would become All the people here are my family members. This would lead to this complete syllogism:

    All people doing my heavenly Father’s will are my family members.
    (All the people here are people doing my heavenly Father’s will.)
    .’. All the people here are my family members.


  2. struggling with chapter 14 and 16 intermediate logic. Any tips or suggestions to help clarify solving using steps and rules? We are getting tangled up a bit thanks!

  3. Not sure I can think of general tips or suggestions beyond what I have written in the text. Have you looked through my posts on this website?
    I would be happy to answer any specific questions from these lessons.

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