What is the difference between a sufficient condition and a necessary condition?

Technically:

1. Philosophy and Conditions

An ambition of twentieth-century philosophy was to analyse and refine the definitions of significant terms — and the concepts expressed by them — in the hope of casting light on the tricky problems of, for example, truth, morality knowledge and existence that lay beyond the reach of scientific resolution. Central to this goal was specifying at least in part the conditions to be met for correct application of terms, or under which certain phenomena could truly be said to be present. Even now, philosophy's unique contribution to interdisciplinary studies of consciousness, the evolution of intelligence, the meaning of altruism, the nature of moral obligation, the scope of justice, the concept of pain, the theory of perception and so on still relies on its capacity to bring high degrees of conceptual exactness and rigour to arguments in these areas.

If memory is a capacity for tracking our own past experiences and witnessings then a necessary condition for Penelope remembering giving a lecture is that it occurred in the past. Contrariwise, that Penelope now remembers the lecture is sufficient for inferring that it was given in the past. What, then, is a necessary (or a sufficient) condition? This article shows that complete precision in answering this question is itself elusive. Although we can use the notion of necessary condition in defining what it is for something to be a sufficient condition (and vice versa), there is no straightforward way to give a precise and comprehensive account of the meaning of the term "necessary (or sufficient) condition" itself. Wittgenstein's warnings against premature theorising and overgeneralising, and his insight that many everyday terms pick out families, should mandate caution over expecting a complete and unambiguous specification of what constitutes a necessary, or a sufficient, condition.

Specifically:

1.) If I opened the door, I used the key.

2.) If you touch me, I'll scream

While in the case of the door, using the key was necessary for opening it, no parallel claim seems to work for (2): in the natural reading of this statement, my screaming is not necessary for your touching me. McCawley claims that the "if"-clause in a standard English statement gives the condition — whether epistemic, temporal or causal — for the truth of the "then"-clause. The natural interpretation of (2) is that my screaming depends on your touching me. To take my screaming as a necessary condition for your touching me seems to get the dependencies back to front.

Confused? Good. My work here is done....

I linked the complete article from Stanford on the subject below....

A mathematician encounters this on a daily basis. Suppose

you have a hypothesis H and you get a conclusion C.

Restating this we have H implies C which means that

whenever you have H, then C necessarily follows. Then C

is called a necessary condition for H. This is clear enough

but mathematicians always want more. They ask: Is the

conclusion C actually a sufficiently strong image of H so

that C in some sense contains the complete H and not

just part of H? In other words, is C sufficient to get a

conclusion H? If so, then C is a sufficient condition for H.

To recap: If H implies C then C is necessary for H and H is sufficient for C. It's just an english language description of

what's going on. Another way is " H is strong enough "

to get C. I'll give you an example after this idea: It's quite

possible and advantageous for C to be both a necessary and sufficient condition for H. This makes C and H equal

strength or in some sense logically equivalent. Thus if

C is both necessary and sufficient for H then H is both necessary and sufficient for C, they "contain" each other.

Example: If a number is divisible by 4(call this H), then it is divisible by 2 (call this C). H implies C but C is not strong enough to imply H for example 6 is divisible by 2 but not by 4

Therefore C is necessary for H but not sufficient for H.

Example: In Euclidean geometry, a triangle has equal sides (call this H) if and only if the triangle has equal angles (call this C). This means

H if C: H is necessary for C since C implies H

H only if C: C is necessary for H since H implies C

H if and only if C: H and C imply each other and are both

necessary and sufficient conditions for each other

Necessary And Sufficient Conditions Math

I think it is not justified to assume that all life must require the conditions that support OUR life here on earth. We just don't know enough about it, or have looked in enough places. Like, virtually none other. Further we don't know whether the big bang was necessary. Perhaps a Lesser Bang would have done the trick - or a Big Squeeze - or something else altogether. This is all so above our pay grade, we look silly even talking about it, imho. But I always appreciate when someone contrasts necessary with sufficient. Those are two great concepts and the ability to differentiate bteween them is sharp.

this link also covers necessary conditions and gives a few examples

http://en.wikipedia.org/wiki/Sufficient_condition

very interesting question

thanks for all the answers!