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Question about contraposition in Traditional Logic Book I.

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    Question about contraposition in Traditional Logic Book I.

    I'm working through Traditional Logic Book I and have a question about contraposition. Specifically, in the daily exercises for Chapter 9, question 30 asks the student to contrapose a number of statements, including "Some soldiers are not brave."

    I'm having a difficult time understanding how contraposing O statements leads to a logically equivalent statement. Take the above example: Some soldiers are not brave. To contrapose, one must obvert, convert and obvert again. Here's what I'm doing:

    Step 1: Some soldiers are not brave (it stays the same, since to obvert you have to change the quality, and negate the predicate).
    Step 2: Some non-brave people are soldiers (interchange the predicate with the subject to convert).
    Step 3: Some non-brave people are non-soldiers (change the quality again, and negate the predicate).

    I'm left with "Some non-brave people are non-soldiers." That doesn't seem equivalent to "Some soldiers are not brave."

    Further in the exercises - question 33 - you get to create your own. I used "Some dogs are not friendly," with similar, confusing results. I ended up with "Some non-friendly things are non-dogs."

    A can see how it works with A statements like, "All men are mortal." That statement would contrapose as, "All immortals are non-men."

    However, the O statements are leaving me a little confused. Can anyone help?


    I think I just answered my own question. On the third step, you first change the quality, which gives you, "Some non-brave people are non-soldiers," and then you negate the predicate, leaving you with, "Some non-brave people are non-non-soldiers," or just, "Some non-brave people are soldiers."

    That is logically equivalent to "Some soldiers are not brave."

    So many negations of which to keep track!
    Last edited by John; 01-04-2014, 06:57 AM.