Necessary versus Sufficient Conditions

Necessary Example

A NC for getting an A in 341 is that a student hand in a term paper. This means that if a student does not hand in a term paper, then a student will not get an A, equivalently, if a student gets an A, then a student hands in a term paper

Sufficient Example

A SC for getting an A in 341 is getting an A on every piece of graded work in the course. This means that if a student gets an A on every piece of graded work in the course, then the student gets an A.

Being a mammal is [sufficient] condition for being human

False -- being a mammal does not guarantee that one is a human.

If it is true that if P is not the case, then Q is not the case, then P is a sufficient condition for Q

False -- the truth of P does not guarantee the truth of Q. All we know is that the falsity of P guarantees the falsity of Q. -- Let P be "a student hands in his/her term paper" and Q be "this student gets an A in 341"

Being alive is sufficient condition for having a right to life

False -- there are lots of things that are alive that do not have a right to life. What about, for example, grass? this answer could be questioned by those who think that it is seriously wrong to kill anything that alive

SC Example

In her essay, Mary Anne Warren does not maintain that each of her five conditions is individually sufficient for being a person, though she thinks that some of them may be, and she thinks that the conjunction of the first three (consciousness, reasoning, and self-motivated activity) is probably sufficient for personhood. This means that she thinks it is probably true that if anything is conscious, able to reason, and engages in self-motivated activity, then that thing is a person. She maintains that satisfying all three of these conditions is sufficient for being a person.

Necessary Condition

Is for some state of affairs S is a condition that must be satisfied in order for S to obtain. A condition that is (required) to bring about another condition.

Sufficient Condition

Is for some state of affairs S is a condition that, if satisfied, guarantees that S obtains. "enough" to bring about another condition

Something is a brother if and only if it is a male sibling, this means that being male sibling is both necessary and sufficient for something to be a brother

True -- In general if it is the case that P is true if and only if Q is true, then Q is necessary and sufficient for P and P is N and S for Q.

Being human is a sufficient condition for being a mammal

True -- being a human guarantees that one is a mammal, as soon as we find out that something is not a mammal, we know that it cannot be a human

If it is true that if P then Q, then Q is necessary condition for P.

True -- if Q is not true, then P is not true. The falsity of Q rules out the truth of P. It is necessary for Q to be true in order for P to be true

If it is true that if P is not the case, then Q is not the case, then P is a necessary condition for Q.

True -- the truth of P is necessary in order for Q to be true. When P is not true, Q is not true

If it is true that if P then Q, then P is a sufficient condition for Q.

True -- the truth of P is sufficient for, guarantees the truth of Q

Being alive is a necessary condition for having a right to life

True, nothing that is not alive can have a right to life

NC example

Warren does not argue that any of her five conditions is individually necessary. But she does maintain that the disjunction of the five conditions is necessary. That is, she maintains that a necessary condition for personhood is that something satisfy at least one of these five conditions. In other words, she maintains that if none of these five conditions is true of something, then that thing is not a person.