In Chapter 6 of his book on critical thinking, Epstein (2006) reminded me strongly of my geometry class. It was based on postulates and the proving or disproving of mathematical (geometrical) arguments. The real basics, If A then B/ If not A then B / If not A then not B etc, etc. I found the class very interesting. It was probably the first math class that really made sense to me. I've heard the saying "Mathematics doesn't involve understanding, just memorization". I don't work well in that mode. It probably why I didn't do too well at memorizing the times tables but did do well in statistics.
The concept that was interesting to me was called "Necessary and sufficient conditions" by Epstein. This is slightly different from the basis If "A then B". If A then B doesn't necessarily mean that for every B an A has to occur; only that for every A, a B has to occur.
For both A and B to be totally linked (can't have one without the other), then the statement is If A then B and if not A then not B - a compound conditional. sort of like - The first bit "If I buy oranges then I will have oranges to eat " yes, but I may be able to eat orages anyway because I have some in my fruitbowl. "If I buy oranges then I will have oranges to eat and if I don't buy oranges I will not have oranges to eat." This make it necessary for me to buy the oranges in order to eat them. I have no other source.
I liked how you compared your topic to geometry. This textbook uses letters of the alphabets a lot to explain the topic. This is a really important concept to know and good example.
ReplyDeleteHere are some examples I got:
-Is earning a final grade of C a necessary or sufficient condition for passing the course?
Earning a final grade of C is a sufficient condition for passing this course because earning a C guarantees passing it. It is not a necessary condition because there are other ways to pass the course other than earning final grade of C.
-Is being 20 years old a necessary or sufficient condition for being a college student?
Being 20 years old is neither necessary nor sufficient for being a college student. One can be a college students without being 20 years old, and there are other ways to be a college student than being 20 years old.