What is the difference between "necessary" and "sufficient"?
What is the logical difference between something being necessary in order for something else to be true; as opposed to something being sufficient to make something else true. i.e.
Fuel is sufficient to make an internal combustion engine run.
Fuel is necessary to make an internal combustion engine run.
and what are some subtle examples of how the difference between these two things can greatly impact the meaning of a sentence, discussion, or conclusion.
The difference between these concepts is important to logical thinking; it would be good if someone could offer a nice clear answer to this.
@eMansipater The difference between these concepts is large and immediately apparent to anyone who knows the definitions. I think even English.SE would reject it as general reference.
In my experience of people learning about philosophy, this topic invariably comes up; and it is necessary to have a clear and concise answer to it which seemed precisely like the *What is a "straw man" argument?* example question from the commitment phase. The vast majority of people do not understand the **logical** difference between these two concepts at all.
I surprised to find this closed as "off-topic". It's a fairly fundamental question to the philosophy of science. Perhaps it would be a better question if it explored some of the edge case. The question that inspired this one (http://philosophy.stackexchange.com/questions/3/if-you-kill-someone-who-is-committing-suicide-are-you-culpable-for-his-death), for instance, does explore the question of what count for a scientific explanation.
@eMansipater: I think Bob has a valid point about the usage of the word "Killing" otherwise it's IMHO an important question for logicians..
The question is fairly basic and the example for necessary conditions is poor. But, the distinction between necessary and sufficient conditions is one that most philosophy students get exposed to early on and with good reason. It is clearly on topic; I voted to reopen.
This is a legitimate question, and a very important one at that. One can't do epistemology without an understanding of necessary/sufficient. Vote to re-open.
Ugh. Now all the answers are nonsensical. I think it would have been better to leave the original example and add your similar example as an update.
The question is not posed as a practical question about philosophy. I am with @Lennart, it seems to be for english.se
@boehj are you kidding? The logic tag is one of the most popular here. The problem as I see it is that there just doesn't seem to be much philosophical value here; it's a terribly basic question which as formulated can be answered with a definition
0 Degrees celsius is necessary to freeze water -20 degrees celsius is sufficient to freeze water
Someone should point out that fuel is necessary, AND NOT SUFFICIENT to make an internal combustion engine run. You also need electricity or mechanical force to start the thing.
Quite so. You also need oxygen, the laws of physics, time and space and other things. It seems an important question but a dictionary should answer it.
The difference between "necessary" and "sufficient" is the direction of the logical arrow.
If you have
A is sufficient for Bit means that every time you have A you will have B, without exception:
A ⇒ B
If you have
A is necessary for Bit means that every time you have B you will have A, without exception
A ⇐ B
So as an example of A being sufficient for B, it is correct to say that every time you (successfully) kill someone, they will be dead, and the assertion that "Person X being killed is sufficient for Person X being dead" would be true. By contrast, it is not correct to say that every time someone is dead, it is because they have been killed. They could have died of natural causes, or there could have been some sort of accident. So the assertion "Person X being killed is necessary for Person X being dead" would be false.
This page has an excellent example of how the difference between these two concepts can change your conclusion. In his answer to the famous Seven Bridges of Königsberg problem, Euler demonstrated that in order to walk across each bridge exactly once it is necessary that the number of places with an odd number of bridges is either 0 or 2. Or put another way, it is necessary that a graph have either 0 or 2 nodes with an odd number of edges for you to be able to draw it without lifting your pen from the paper. However, this is not sufficient to ensure that such a walk or drawing is possible:
Either 0 or 2 places have an odd # of bridges ⇐ You can walk across each bridge once is true
Either 0 or 2 places have an odd # of bridges ⇒ You can walk across each bridge once is NOT!
So the difference between the two matters very much. Can you think why? Hint.
"So in the first example, it is correct to say that every time you kill someone, they will be dead, and the assertion is true" - This is not true for Jesus.
yes it is true for Jesus - he was dead after having been killed. Being dead is necessery for resurrection.
Perhaps in math you can reverse the arrow. This is not standard in philosophy. Your answer does not address what propositions are and you only take a practical approach which does not hold 100 percent.
To conceive a child (B), a man (A) and a woman (X) are needed. "if you have A is necessary for B it means that every time you have B you will have A, without exception" is FALSE. It is not "you will have A...without exception" (because A depends not only on B but on X as well). It is "one of the requisites for B is fulfilled".