The Law of the Contrapositive

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  1. A Thousand Words profile image78
    A Thousand Wordsposted 4 years ago

    I argued with a professor today about why the example he gave of this law was insufficient. He is a religious Professor that likes to teach Western Civ as though it's Bible study at a secular institution, so I'm not a big fan, but he's not too bad of a guy otherwise it seems. Anyway, he gave this example.

    "If a man is drenched, then it is raining outside implies that if it is not raining outside, then the man is not drenched."

    Now to most Western thinking people, this may be just fine, I guess. But the only way that this law can be found true is if " a man that is standing outside without any kind of cover and has not been wet with any man made water/wetting devices or a natural disaster is drenched, then it is raining outside implies that if it is not raining outside, then a man that is standing outside without any kind of cover and has not been wet with any man made water/wetting devices or natural disasters is not drenched."

    Otherwise, if it isn't specific enough, there is room for other possibilities. Maybe the man was hit with a water balloon. Maybe there was a tsunami. Maybe a little kid with a super soaker caught him off guard. I think I'm venting, because the other students kind of snickered as though I was slow, but I have this tendency to fight things I think don't stand well, and I'm sure they thought it was "simple" logic.

    Would the original statement follow this law sufficiently?

    1. Dr Lamb profile image58
      Dr Lambposted 4 years agoin reply to this

      One can get drenched inside is a sprinkler system goes off or it one falls in a pool of water.

    2. kess profile image60
      kessposted 4 years agoin reply to this

      A law must be very specific for it to be effective as a law.
      Laws are effective only when it is conclusive.

      In this situation the specifics have been established thus the law can operate.

      A drenched man is equal to rain on the outside. This is the law.

      It matters not how many  different wetting agents there are.
      It matter not  how many "whats" or "Who"  that can be drenched.

      The laws merely looks for a man who is drenched. That  is it.

      A drenched man = rain outside
      No drenched man = no rain outside.

      You computer crashes because it operates laws like and  there is a clashing conclusion between two, For the computer to continue to work at least one clashing law must be nullified.

  2. profile image0
    Emile Rposted 4 years ago

    I may be slow, and i agree that there could be an infinite number of possibilities as to why a guy could be standing outside drenched. But, the first part of the statement appears to close other possibilities from discussion. I guess, that's the point. If you accept an if-then statement as being rock solid you can then make firm conclusions.

    I would think this would be his way of setting you up for further discussion as to the problems with accepting if-then statements at face value, without further thought.

    1. A Thousand Words profile image78
      A Thousand Wordsposted 4 years agoin reply to this

      His goal may have been quite the opposite. He was saying that secular scientists/individuals ignore this law and he gave this as an example of the principle.

  3. wilderness profile image97
    wildernessposted 4 years ago

    The professors original statement is logically correct and cannot be argued against from a logic standpoint.  And it has nothing to do with "western thinking".

    The premiss, however, is incorrect just as you pointed out and the old GIGO principle comes into effect.

    1. A Thousand Words profile image78
      A Thousand Wordsposted 4 years agoin reply to this

      I looked up the GIGI principle. Are you referring to GIGO? (Garbage In, Garbage Out)?

      1. wilderness profile image97
        wildernessposted 4 years agoin reply to this

        Yes.  And edited my post to reflect that.  Sorry.

        1. A Thousand Words profile image78
          A Thousand Wordsposted 4 years agoin reply to this

          That's ok. Thank you. smile I might bring this up after doing a little more research. He seems eager to have us not trust that evolution is sound science and that all secular scientists are purposeful liars, etc, and I intend to challenge him whenever possible.

          1. wilderness profile image97
            wildernessposted 4 years agoin reply to this

            Few theists seem to truly understand logic very well.  It is possible that your professor makes the statement thinking that the truth of the premise does not affect the truth of the conclusion as long as the logic is correct.  Or perhaps he simply ignores all the possibilities you mention, thinking everyone else will do the same.

            1. profile image0
              Beth37posted 4 years agoin reply to this

              It's funny to me, how you don't find this to be an insult... and if you do, that you feel it's an acceptable one. Well, you are covered, my God has told me to turn the other cheek.

              As a matter of fact, He has instructed me, quite illogically (or so it may seem to you) "Do not repay evil with evil or insult with insult. On the contrary, repay evil with blessing, because to this you were called so that you may inherit a blessing."

              Considering Christ is the son of God, fully indwelt with the power of God, and yet he submitted himself to death on a cross, in order to save those who would reject him, from their own sin... it kind of makes sense that Christians would appear to be illogical. Everything we believe is based on a kingdom turned upside down.

              1. wilderness profile image97
                wildernessposted 4 years agoin reply to this

                I'm sorry, Beth, but when the believer has faith, well, it just doesn't follow the rules of logic.  No real premise is needed, no evidence that the premise (if there is one) is true is needed and the "logic" is that if it fits what I think is right then it must be true.  Logic does not work that way, but faith and belief most emphatically do.

                It will forever be a bone of contention between the believer and the non-believer as neither can understand why the other doesn't agree with what is obviously true to the nth degree.  The reasoning process to a conclusion is not the same, but both find their own process to be right and correct.

                If you find that offensive, that logic is not used in faith based questions, I'm sorry, but it doesn't change the truth of the matter.  If, however, you took it to mean that the believer doesn't understand logic in ANY circumstance I do apologize.  I recognize that most believers can be logical and reason correctly as long as the topic has nothing to do with their faith.

                1. profile image0
                  Beth37posted 4 years agoin reply to this

                  I fully understand where you're coming from.
                  The thing is... if God is real... and I know this as an ABSOLUTE, it would be purely illogical for me not to believe. I understand you don't know how I got from point A to point B... and that there is nothing I can say to convince you. That changes nothing for me.

                  1. wilderness profile image97
                    wildernessposted 4 years agoin reply to this

                    You know NOTHING as an absolute (in the theology field).  You have no proof, you have no evidence and there isn't even the logical structure to support it.

                    Which is exactly what I said in the first place; logic has no place in the world of faith.  Faith produces belief (not knowledge despite your claim to the contrary), and that belief can and often does defy both logic and knowledge. 

                    And no, that should mean little to you.  You have chosen faith over logic and evidential proof and that's fine.  But you also shouldn't be offended when others recognize that you have done so.

                  2. EncephaloiDead profile image57
                    EncephaloiDeadposted 4 years agoin reply to this

                    Sorry, but you may believe in God, but to say you know He exists as an absolute is not honest at all. If God did exist as an absolute, everyone on the planet would know that. So obviously, that is not true.

  4. profile image0
    calculus-geometryposted 4 years ago

    A Thousand Words, under the assumption that the first statement is true, the contrapositive of the statement is always logically equivalent. 

    "Logically equivalent" is a technical term in logic/math that doesn't necessarily mean "true" in the normal sense of the word "true."  As you noticed, if the original statement is based on false assumptions (that there is only one way to get drenched) then the contrapositive statement is also based on the same false assumption. 

    If someone says "If a woman's name is Mary then she is a unicorn" then the contrapositive is "If a woman is not a unicorn then her name is not Mary."  The two statements express the same idea, namely that the set of people named Mary is a subset of the people who are unicorns.  But like the example of a drenched man, it may not be the best way to give students an intuitive understanding of the law of contraposition since its premise is fantastical. 

    Anyway, I hope my explanation was helpful.

    1. profile image0
      Beth37posted 4 years agoin reply to this

      Can you put that in the form of an equation please?

      1. profile image0
        calculus-geometryposted 4 years agoin reply to this

        http://img.sparknotes.com/figures/8/84ba14d565517459113594f30789b66a/tt4.gif

        1. profile image0
          Beth37posted 4 years agoin reply to this

          You're awesome.

 
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