TITLE: Understanding how contrapositive work
QUESTION [5 upvotes]: I want to understand contrapositive clearly. I'll start by saying: "If it is sunny, then there is light". The statement is true. But now consider the contrapositive: " If there is no light then it is not sunny".  The contrapositive is false because you could create light with a flashlight.
What is wrong here?

REPLY [7 votes]: A usefull distinction to be made here is the distinction between : sufficient condition and necessary condition. 
The sentence  "Sunny --> Light" says that 
the fact "it is sunny" is a SUFFICIENT condition in order " there is light" to be true. ( Saying that "X is sufficient for Y" does not exclude the possibility of obtaining Y without X. If I am a pianist, I am a musician. This is perfectily true, and it does not deny the possibility of being a musician without being a pianist). 
One cannot object to this that " one can make light with a flashlight". 
Such an objection amounts to saying " the sun is not a necessary condition in order " there is light" to be true". 
Such an objection is directed at an assertion that was NOT contained in the original sentence.
Both the original sentence and its contrapositive say exactly the same thing under various points of view, namely 
(1) sun is sufficient for light 
(2) light is necessary for sun 
(3) absence of light is sufficient for absence of sun
(4) absence of sun is necessary for absence of light. 
NOTE : Saying  " X --> Y " is equivalent to 
(1) X is sufficient for Y 
or, equivalently 
(2) Y is necessary for X