ChiranjeevSingh I think in our discussions, one of us is making a mistake in understanding the term
sufficiency (most likely me, since you are an expert in this field).
I beleive sufficiency means the following: If there are two events A and B, and A is sufficient for B, then just by knowing the existence of a event A, I can tell the existence of event B with 100% guarantee. There will not exist an exceptional case where "A happens but B does not happen".
Qx: Similarly, with the satement
"Smoking causes cancer" how can I tell it is sufficient if I find one person who smokes but does not get cancer?
You said if
"you keep smoking you will eventually get cancer".
Here the event of
"Smoking" did occur then why should I be concerned about
"how long smoking lasts" if it is a sufficient to get cancer?
Qy: I would also like to know your perspective on this: Is there any difference between (a) "If you smoke you get cancer" and (b) "Smoking causes cancer"?
............................................................................................................................................................................................................................................
When I think about the question (Qy), I feel earlier I was trying to point out the sufficiency flaw in the statement
"Smoking causes cancer" by showing that there exists one person who smokes but does not get cancer. If that is the case, then wouldn't it make above both statements (a) and (b) wrong?
Qz: So what is really going wrong here? Is it that I am mixing universally true statements (
e.g. If you are a man then you are a human) with conditional Statements
(e.g. If you smoke you get cancer)?
Am I implicitly adding
"universally true" constraint on all conditional statements e.g. whenever I read
"If X then Y" , I assume no exception exist since it is universally true.
But in case of
"X causes Y", I don't apply the
"universallly true" constraint because in real life I can find exceptions where people smokes and do not get cancer.
Qa: So what does "Sufficient" really mean then? Does a condition is sufficient only if it is universally true?
Before reading this article on Correlation to Causation, I was of the beleif that statements like
"X causes Y", "X leads to Y" are different from
"X implies Y" which is equivalent to
"If X then Y" .
This belief was also supported by the fact that the negation of these statements are different:
"X does not cause Y", "X does not lead to Y" compared to
"Even if X, not Y".
Qb: If all these statements were the same, then why are their negation different?
............................................................................................................................................................................................................................................
To be honest, I am still confused and I cannot internalize
"X causes Y" means
"X is sufficient for Y" in the same way as I could do for
"X implies Y" or
"If X then Y".
ChiranjeevSingh
"Smoking causes cancer" means that if you keep smoking, you will eventually have cancer. So, yes, all smokers will eventually have cancer.