logic 101

i planned to write about logic for public long time ago. coz i saw many people made logic mistake during debates and arguments, especially more and more people joined discussions on public issues. And never the less, the new HK chief executive always using "double negation" statement, or logic, to fool people around.

here i will give a fundamental logic with minimum mathematical jargon, hope people from any background will understand it easily.

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first rule of logic is, we only talk about something that can be proved to be right or wrong. Expressing a feeling is not part of logic.

   Eunice is beautiful. <-- this is not a logical statement, since it cannot be right or wrong.

   Bill Gate is rich. <--- this is a logical statement, since we can prove Bill Gate is rich or not. of course this can also be an expression of feeling.


Most people understand the  conclusive logic.

    if A has property B  and C is part of A, then C has property B.

an example is : All human will die, John is a human, then John will die. a little explanation is, C is part of A. if C is not part of A, then the logic fail. an example is, i like apple, i am human, then human likes apple. obviously, we know that NOT all human likes apple!

we can generalized the logic as

   if A then B

which mean, A will cause B, expressing a relationship/consequence. for example, if my cell phone run out of battery, then i could not use the phone.


Most people can use associative law very easily:

     if A then B and B then C, then A then C.

an example is, if i work hard, then high score in exam, and if high score in exam, my parent happy. then, if i work hard, then my parent happy.

Now, a common mistake made by people is

  if A then B = if B then A

let me give an example of this mistake. if it is raining, Mary will bring an umbrella. OK, when we saw Mary bring an umbrella, some people will say, "oh, it must be raining." or, if it is not raining, then people will ask Mary, "why do you bring umbrella?"

i see this mistake happen very common. another example is. If i respect a teacher, he is a good teacher. and what if i don't respect a teacher? is it mean he is a bad teacher? NO, i simple Didn't Say anything when i not respect a teacher!

take the example of raining. we now know that if it is raining, Mary will bring an umbrella. But how about it is sunny, what Mary will bring? WE DON"T KNOW! Mary can bring anything or nothing, we just don't know.

let make a clear illustration here. we have 4 possible combination of A, B, not A , not B.

   a) if A then B
   1) if not A then not B
   2) if not B then not A
   3) if B then A

we now should be clear that, a) is not equal to 3). and 1) is simple wrong, or we cannot know by just given a). How about 2)???

Now, this is what i want to let everyone know.

    a) = 2) | if A then B = if not B then A

using if it is raining, Mary will bring an umbrella as an example. we now sure that, if Mary does not bring an umbrella, then it is not raining. we see here a double negation statement, which make many people confused.

so, to clear things, here is a conclusion.

if we given a statement, we can only know 1 extra things. and ask 2 questions to make sure we understood.

    if A then B  =  if  not B then not A
    1) what if not A ??
    2) what if B ??