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Traditional Logic I- Contraposition

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    Traditional Logic I- Contraposition


    I've been teaching students in our co-op using Traditional Logic I. We will be beginning Chapter 9 next week on Obversion, Conversion, and Contraposition. As we walk through examples, I want to help the students see why all 4 types of statements can be obverted, but only certain types can be converted and contraposed. The text seems to explain why only E and I statements can be converted, and gives examples of how A & O statements are not equivalent when they are converted, but it doesn't explain why only A & O statements can be contraposed. Can anyone offer an explanation why E & I statements cannot be contraposed? I know that they will not produce logical equivalents, but I am looking for more than that. And I want the students to see it for themselves. One thought I had- since contraposition requires conversion as its second step and not all statements can be converted, then you cannot complete the contraposition. I am not sure if that is the right line of thinking, though.
    Thanks for any help or clarity you can offer!


    My DS took the TL1. Here is what he said in response to your post which I was reading when he walked by.

    Contraposition requires a series of obversion, conversion and obversion again. If one obverts an E or I statement, it becomes an A or O statement. And so when one tries to convert, it does not work because A or O statements cannot be converted.

    For instance, consider the following E statement: No cows are green chickens.
    Try to obvert that: All cows are not green chickens.
    The conversion of that would be: All non-green chickens are cows.
    This, of course, does not work because one is saying that all cows are not green chickens, not only cows are green chickens. Therefore, E & I statements cannot contraposed because after they are obverted, they cannot be converted because they are not A & O statements.

    I hope I reported his words correctly!
    DS16, mix of MP and other resources 2021-2022

    "[May] the peace of God, which passes all understanding, ... keep your hearts and your minds in Christ Jesus."


      This is all correct. Contraposition involves a simple conversion which cannot be performed on A and O statements. And the reason it cannot be performed on A and O statements is that A and O statements have subject and predicate terms with a different distribution status and you can only convert statements where the subject and predicate terms have the same distribution status. An A statement has a universal subject and a particular predicate, and an O statement has a particular subject and a universal predicate, so both are a no go. But in Es and Is, the subject and predicate terms are either both universal or both particular.

      You can switch two universal terms and two particular terms, but you can switch a universal with a particular. Which is just another way of saying you can switch two wholes or two parts, but you can't switch a whole with a part or vice-versa.

      This is easy to see if you do a Euler diagram. If you have to change the Euler diagram when you do a conversion, then you broke the rule. When you do a conversion with E and I statements, all you have to do is switch the labels for the subject and predicate terms between the circles. You can't do that with As and Os. With As and Os you have to change the diagram altogether.

      Hope that helps.