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I've read from LR bible that "Cannot make A unless B" means "A - B" (sorry I cannot type an arrow here)

But if we directly understand from the sentence, the meaning will be: we cannot make A, except under the situation of B, meaning although we cannot make A under any other situation, when B happens, it works. Does that sound like making B a sufficient condition, not necessary one?

Thanks very much for your help!

A only if B.

or

If A then B


A is sufficient for B.


B is necessary for A.

It might be helpful to think of these things in terms of what we "know" is true.

For example, it cannot be a carrot unless it is orange. As you correctly pointed out, that would be symbolized as C -> O.

Here, "carrot" is the sufficient condition and "orange" is the necessary condition. This is because if we know something is a "carrot," that is sufficient information to conclude that it is also orange. However, "orange" is the necessary condition, because although it if something is a "carrot" it is necessarily "orange," knowing something is "orange" ISN'T sufficient to conclude that it's a carrot. It could be a pumpkin!

This statement:

although we cannot make A under any other situation, when B happens, it works

does not actually follow from A -> B. The ONLY thing this means is that "we cannot make A under any other situation" -- we cannot have a carrot unless it's orange. It doesn't mean that "when B happens, it works," because when "orange" happens, that doesn't make it a carrot.

"when B happens, it works" is indeed a sufficient condition, and would be represented as B -> A.

Thanks so much for your explanation.

So I guess maybe here we can understand in this way:

We cannot make A under any this situation, but if B happens, there's a chance that we can make A.

So my mistake just now was there no guarantee in the original sentence that "when B happens, it works". Then it does not make B a sufficient condition.

But so far, how does it make B a necessary situation? I mean B could be part of the sufficient condition, although may not be sufficient enough for A to happen, but why does it have to be "necessary"?

Correct me if I make any new mistake. Many thanks!

cc.celina wrote:It might be helpful to think of these things in terms of what we "know" is true.

For example, it cannot be a carrot unless it is orange. As you correctly pointed out, that would be symbolized as C -> O.

Here, "carrot" is the sufficient condition and "orange" is the necessary condition. This is because if we know something is a "carrot," that is sufficient information to conclude that it is also orange. However, "orange" is the necessary condition, because although it if something is a "carrot" it is necessarily "orange," knowing something is "orange" ISN'T sufficient to conclude that it's a carrot. It could be a pumpkin!

This statement:

although we cannot make A under any other situation, when B happens, it works

does not actually follow from A -> B. The ONLY thing this means is that "we cannot make A under any other situation" -- we cannot have a carrot unless it's orange. It doesn't mean that "when B happens, it works," because when "orange" happens, that doesn't make it a carrot.

"when B happens, it works" is indeed a sufficient condition, and would be represented as B -> A.

superhedy2011 wrote: But so far, how does it make B a necessary situation? I mean B could be part of the sufficient condition, although may not be sufficient enough for A to happen, but why does it have to be "necessary"? If A happens, then B happens. If A happens, it is necessary that B happens.

necessary = required

sufficient = enough

B is necessary in that if A happens, B HAS to happen. There's no other way. Let's say you're playing a sudden death game of air hockey, and the first one to score wins.

Score -> Win

Scoring is sufficient for winning.

Winning is "necessary" because there's no way you can score without winning. Resist the temptation to think that B "causes" A. It doesn't always. It's just that if A happens, B necessarily also has to happen.

Back to the carrot/orange example, orange is a necessary condition to being a carrot because if a vegetable is any other color, it's not a carrot. So being orange, while it doesn't cause carrotness, is nonetheless necessary to the condition of being a carrot.

I think I may get your point, cause I'm also thinking that whether I have made the mistake of thinking "sufficient makes necessary to happen".

Thanks very much.

cc.celina wrote:B is necessary in that if A happens, B HAS to happen. There's no other way. Let's say you're playing a sudden death game of air hockey, and the first one to score wins.

Score -> Win

Scoring is sufficient for winning.

Winning is "necessary" because there's no way you can score without winning. Resist the temptation to think that B "causes" A. It doesn't always. It's just that if A happens, B necessarily also has to happen.

Back to the carrot/orange example, orange is a necessary condition to being a carrot because if a vegetable is any other color, it's not a carrot. So being orange, while it doesn't cause carrotness, is nonetheless necessary to the condition of being a carrot.