On page 124, in chapter 6, necessary and sufficient conditions are explained. It is for when two claims are equivalent to each other.
For a contrapositive argument, the following has to happen:
1.) If A is necessary for B that means If not A, the not B is true.
2.) If A is sufficient for B that means If A then B is true.
This confused me at first but I by looking at examples like the following it is more comprehensible.
1.) If you do not pass the driver’s test, you do not have a license.
2.) If you are 21, you can legally drink alcohol.
This type of condition depends solely on whether or not the first part of the argument is true or false. If the first part is true therefore the second part is true. If the first part is false therefore the second part is false.
Hey there Catherine. I had a tough time going through this as well. I looked at the same examples, but still had some questions. Your conclusion quite certainly helped me answer a couple of those questions I had. It was really confusing to follow the whole "necessary" and the "sufficient" concept. The license example caught me by surprise. I never analyzed that statement as such a claim. Its not just that sentence, there are so many other sentences that we claim, and do not realize its structure. { Strange! lol }. Anyway, your explanation to differentiate between the two was really helpful. :)
ReplyDeleteHey Catalina! I was slightly confused at first as well. I think it was mainly because of the terms “contrapositive” and “conditionals” but I feel like I have a better understanding now. Your example is good as well. If you do not pass the driver’s test, you do not have a license. This is true. There is no way for you to fail your test and still get a license. Therefore, the argument is valid because the premises and conclusion are both true. The second example is true for the most part. However, there could be some rare situation where an individual is 21 yet they are on probation and the court has taken away their privilege to drink alcohol. But that is rare and it was a good example. If A is true, then B is true. Great post keep it up!
ReplyDeleteHey Catalina, I agree with you that it definitely was a bit confusing at first. The use of "A" and "B" really gave it some math-like qualities, which I am pretty bad at! The example given in the book as well as your example helped a lot in clearing my initial confusion. I can now see how simple it is structually. There are literally many argument that are structure this way that we run into everyday. Take an amusement park for example. If you aren't this height then you can't ride the ride. A very simple concept overall after you get the "A" and "B" out of the way!
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