Hammster
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I've unashamedly stole this from a friend, but it's based on discussions we've had, so it's okay. 
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The concept of Necessity vs Sufficiency is a logical (ie, pertaining to logic) discussion that asks questions about the implicational relationships between two things.
Necessity:
If something is necessary, that is the same as saying that the consequence cannot be true unless the premise is true. That is, the premise is necessary for the consequence in question to become a reality.
Sufficiency:
If something is sufficient, that means the consequence will, without fail, be true. In other words, that one thing, all by itself, fulfils all the conditions for the consequence to be realized.
I like to use fire as an example to teach this concept.
Fire (the consequence) needs three things to be true:
A) heat
B) fuel
C) oxygen
Each of these things individually are not sufficient for a fire. If you take only A, B, or C, or any combination of two (2) of them, it is impossible to create a fire. That means that all three of those things are necessary for a fire, but none of them alone is sufficient for a fire.
In other words, heat is necessary for a fire, but heat (by itself) is not sufficient for a fire. Heat, by itself, will not cause a fire (the consequence) to form. (a fire also needs oxygen, and something to burn, aka fuel!)
The same is true of fuel and oxygen.
So what is an example of sufficiency?
Being a father is sufficient for being a male.
If a person is a father, it is automatically true that the person is a male. (If they were female,and had children, they'd be a mother instead)
So being a father (P) is sufficient for being a male (C)
However, the flipside of this is not the same. Observe:
Being a male is not sufficient for the person being a father. However, being male is necessary to be a father.
In this case, you can be a male without being a father. However, to be a father, the condition of "being male" must be true, which makes being male necessary, but not sufficient, for being a father.
Now that you know the difference between necessary and sufficient, let's talk theology.
In theology, we monergists like to say that Christ's atonement was sufficient to save people. That is, his death secured everything those people need to be ultimately saved: their regeneration, their faith, their repentance, etc. Everything a person needs to be saved is secured by Christ's life and death for them. That means that Christ's life and death (in monergism) is sufficient to result in salvation. Another way to say this is that if Christ died for a person, that person will, without fail, be saved. Thus, Christ is sufficient for salvation.
However, in synergism, this is not true. Christ can die for a person (in synergism), but yet that person might not be saved. However, the person does need Christ to be saved. That means in synergism, Christ is necessary, but not sufficient. He is necessary because salvation is impossible without him (the way fire is impossible without oxygen), but he is not sufficient for salvatoin (his work alone is not enough for the salvation of a person)
That is because in synergism, something else is necessary: man's cooperation, man's input, man's choice, man's decision, man's free will. Call it whatever you want, word it however you want, but in synergism, there is this other thing that is a necessary condition for his salvation.
So, in synergism, both (grace + man's free will) are necessary for salvation, but neither by itself is sufficient for salvation. Only the combination of both is sufficient for salvation.
Fire:
Fire
Oxygen
Fuel
Synergistic Salvation:
Man's Free Will
Grace
In these two, you can't create the consequence (fire/salvation) with any of the premises or conditions by themselves. It takes all of them together to produce the consequence.
Monergistic Salvation:
Grace/Christ's death
However, in monergism, Grace is sufficient for salvation. It is not merely necessary, but it is also sufficient. Whereas in synergism, Christ is necessary, but not sufficient, in monergism, Christ alone/grace alone is actually suffiicent. It always produces the end result (the consequence) of man's salvation. Every. Single. Time. Without fail. It does not need or rely on anything else. It does not rely on other necessary conditions the way fire or synergistic salvation do. It, all by itself, is the sufficient condition for its consequence.
This is why the reformers said "Sola Gratia" or "Grace alone!". This is what they had in mind when they coined the phrase. They understood the difference between something being necessary vs something being sufficient.
Luther understood it
Calvin understood it
Even Erasmus, Luther's opponent, understood it.
Hope this helped! And I hope you understand it now too!
[
The concept of Necessity vs Sufficiency is a logical (ie, pertaining to logic) discussion that asks questions about the implicational relationships between two things.
Necessity:
If something is necessary, that is the same as saying that the consequence cannot be true unless the premise is true. That is, the premise is necessary for the consequence in question to become a reality.
Sufficiency:
If something is sufficient, that means the consequence will, without fail, be true. In other words, that one thing, all by itself, fulfils all the conditions for the consequence to be realized.
I like to use fire as an example to teach this concept.
Fire (the consequence) needs three things to be true:
A) heat
B) fuel
C) oxygen
Each of these things individually are not sufficient for a fire. If you take only A, B, or C, or any combination of two (2) of them, it is impossible to create a fire. That means that all three of those things are necessary for a fire, but none of them alone is sufficient for a fire.
In other words, heat is necessary for a fire, but heat (by itself) is not sufficient for a fire. Heat, by itself, will not cause a fire (the consequence) to form. (a fire also needs oxygen, and something to burn, aka fuel!)
The same is true of fuel and oxygen.
So what is an example of sufficiency?
Being a father is sufficient for being a male.
If a person is a father, it is automatically true that the person is a male. (If they were female,and had children, they'd be a mother instead)
So being a father (P) is sufficient for being a male (C)
However, the flipside of this is not the same. Observe:
Being a male is not sufficient for the person being a father. However, being male is necessary to be a father.
In this case, you can be a male without being a father. However, to be a father, the condition of "being male" must be true, which makes being male necessary, but not sufficient, for being a father.
Now that you know the difference between necessary and sufficient, let's talk theology.
In theology, we monergists like to say that Christ's atonement was sufficient to save people. That is, his death secured everything those people need to be ultimately saved: their regeneration, their faith, their repentance, etc. Everything a person needs to be saved is secured by Christ's life and death for them. That means that Christ's life and death (in monergism) is sufficient to result in salvation. Another way to say this is that if Christ died for a person, that person will, without fail, be saved. Thus, Christ is sufficient for salvation.
However, in synergism, this is not true. Christ can die for a person (in synergism), but yet that person might not be saved. However, the person does need Christ to be saved. That means in synergism, Christ is necessary, but not sufficient. He is necessary because salvation is impossible without him (the way fire is impossible without oxygen), but he is not sufficient for salvatoin (his work alone is not enough for the salvation of a person)
That is because in synergism, something else is necessary: man's cooperation, man's input, man's choice, man's decision, man's free will. Call it whatever you want, word it however you want, but in synergism, there is this other thing that is a necessary condition for his salvation.
So, in synergism, both (grace + man's free will) are necessary for salvation, but neither by itself is sufficient for salvation. Only the combination of both is sufficient for salvation.
Fire:
Fire
Oxygen
Fuel
Synergistic Salvation:
Man's Free Will
Grace
In these two, you can't create the consequence (fire/salvation) with any of the premises or conditions by themselves. It takes all of them together to produce the consequence.
Monergistic Salvation:
Grace/Christ's death
However, in monergism, Grace is sufficient for salvation. It is not merely necessary, but it is also sufficient. Whereas in synergism, Christ is necessary, but not sufficient, in monergism, Christ alone/grace alone is actually suffiicent. It always produces the end result (the consequence) of man's salvation. Every. Single. Time. Without fail. It does not need or rely on anything else. It does not rely on other necessary conditions the way fire or synergistic salvation do. It, all by itself, is the sufficient condition for its consequence.
This is why the reformers said "Sola Gratia" or "Grace alone!". This is what they had in mind when they coined the phrase. They understood the difference between something being necessary vs something being sufficient.
Luther understood it
Calvin understood it
Even Erasmus, Luther's opponent, understood it.
Hope this helped! And I hope you understand it now too!
