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It may be the case that several sufficient conditions, when taken together, constitute a single necessary condition (i.e., individually sufficient and jointly necessary), as illustrated in example 5. Example 1 "John is a king" implies that John is male. So knowing that John is a king is sufficient to knowing that he is a male. Example 2
The principle of sufficient reason states that everything must have a reason or a cause. The principle was articulated and made prominent by Gottfried Wilhelm Leibniz , with many antecedents, and was further used and developed by Arthur Schopenhauer and William Hamilton .
Logical sufficiency; see necessary and sufficient conditions sufficiency (statistics) , sufficiency in statistical inference The sufficiency of Scripture , a Christian doctrine
It [the principle of sufficient reason] explains things in reference to one another, but it always leaves unexplained something that it presupposes,” and the two things that are absolutely inexplicable are the principle itself and the “thing in itself”, [7] which Schopenhauer connects with the will to live. The principle, in another point ...
X would instead be a sufficient cause of y when the occurrence of x implies that y must then occur. [2] in other words, when some factor is sufficient to cause an effect, the presence of the cause guarantees the occurrence of the effect. [3] However, a different cause z may also cause y, meaning that y may occur without x occurring.
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Wherever logic is applied, especially in mathematical discussions, it has the same meaning as above: it is an abbreviation for if and only if, indicating that one statement is both necessary and sufficient for the other. This is an example of mathematical jargon (although, as noted above, if is more often used than iff in statements of definition).
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