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For a third facet, identify every mathematical predicate N with the set T(N) of objects, events, or statements for which N holds true; then asserting the necessity of N for S is equivalent to claiming that T(N) is a superset of T(S), while asserting the sufficiency of S for N is equivalent to claiming that T(S) is a subset of T(N).
Pages in category "Necessity and sufficiency" The following 5 pages are in this category, out of 5 total. This list may not reflect recent changes. ...
In propositional logic, affirming the consequent (also known as converse error, fallacy of the converse, or confusion of necessity and sufficiency) is a formal fallacy (or an invalid form of argument) that is committed when, in the context of an indicative conditional statement, it is stated that because the consequent is true, therefore the ...
The corresponding logical symbols are "", "", [6] and , [10] and sometimes "iff".These are usually treated as equivalent. However, some texts of mathematical logic (particularly those on first-order logic, rather than propositional logic) make a distinction between these, in which the first, ↔, is used as a symbol in logic formulas, while ⇔ is used in reasoning about those logic formulas ...
Modal fallacy – confusing necessity with sufficiency. A condition X is necessary for Y if X is required for even the possibility of Y. X does not bring about Y by itself, but if there is no X, there will be no Y. For example, oxygen is necessary for fire.
For this reason, or perhaps for their familiarity and simplicity, necessity and possibility are often casually treated as the subject matter of modal logic. Moreover, it is easier to make sense of relativizing necessity, e.g. to legal, physical, nomological , epistemic , and so on, than it is to make sense of relativizing other notions.
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