TITLE: Conditional Statements: "only if"
QUESTION [22 upvotes]: For some reason, be it some bad habit or something else, I can not understand why the statement "p only if q" would translate into p implies q. For instance, I have the statement "Samir will attend the party only if Kanti will be there." The way I interpret this is, "It is true that Samir will attend the party only if it is true that Kanti will be at the party;" which, in my mind, becomes "If Kanti will be at the party, then Samir will be there." 
Can someone convince me of the right way?
EDIT:
I have read them carefully, and probably have done so for over a year. I understand what sufficient conditions and necessary conditions are. I understand the conditional relationship in almost all of its forms, except the form "q only if p." What I do not understand is, why is p the necessary condition and q the sufficient condition. I am not asking, what are the sufficient and necessary conditions, rather, I am asking why.

REPLY [4 votes]: The mathematician R.L. Moore, who was very careful with his language, interpreted "only if" to mean "if and only if".  In his mind, "A only if B" was a stronger statement than "A if B".  In other words, "A only if B" tells us that "A if B", but also gives us a little extra information: "A only if B".  He would have insisted that any other interpretation of "only if" is inconsistent with the standard use of the English language.  
(However, Moore did frequently say "if and only if" for the sake of clarity.)
Therefore, if you think that "only if" should mean "if and only if", you are not alone.  But, mathematicians have established the convention that "A only if B" means "if A then B", and so now we must follow this convention.