A sufficient assumption is an unstated premise that, if true, guarantees that the conclusion is correct. It bridges the gap between the evidence and the conclusion completely. Where a necessary assumption only keeps the argument from collapsing, a sufficient assumption walks the argument all the way to the end.
Sufficient assumptions tend to speak in strong, absolute language. You will hear them say "always," or "all," or "every," or "in every case without exception." That strength is what makes them do the job. It is also what should make you cautious. An assumption broad enough to guarantee any conclusion is an assumption broad enough to be wrong in ways the narrower version would not have been.
The way you find one is with the Affirmation Test. Take the candidate assumption, state it plainly, and affirm it. If affirming it makes the conclusion undeniable, the assumption was sufficient. If affirming it still leaves wiggle room for the conclusion to fail, then whatever role the assumption played, it was not sufficient.
Arguments often fail by confusing a necessary condition with a sufficient one, leading to flaws such as mistaken reversal or mistaken negation. Q. Can an assumption be both necessary and sufficient at once? Yes, and when it is, the argument is tight: the assumption has to be true for the conclusion to follow, and its truth alone is enough to deliver it. But this is the rarer case. Most real arguments rest on a mix of necessary assumptions keeping the structure upright and weaker evidence doing the rest of the work. Knowing which is which is how you learn to trust, or not trust, the conclusion.
Question
Suppose an argument concludes that because a liquid boiled at one hundred degrees Celsius at sea level, it must be pure water. What sufficient assumption would make that conclusion undeniable, and why should the strength of that assumption make you suspicious?
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The sufficient assumption is something like: every liquid that boils at one hundred degrees Celsius at sea level is pure water. Apply the Affirmation Test. If that statement is true, the conclusion follows with no gap. That is the mark of a sufficient assumption. But notice how strong the statement had to be to do the job. "Every," with no exceptions. That strength is exactly what should make you check the assumption against reality before resting the argument on it.