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In biological research, experiments or tests are often used to study predicted causal relationships between two phenomena. [1] These causal relationships may be described in terms of the logical concepts of necessity and sufficiency. Consider the statement that a phenomenon x causes a phenomenon y.
For example, at present, "today is the Fourth of July" is a necessary and sufficient condition for "today is Independence Day in the United States". Similarly, a necessary and sufficient condition for invertibility of a matrix M is that M has a nonzero determinant. Mathematically speaking, necessity and sufficiency are dual to one another.
Necessary condition analysis (NCA) is a research approach and tool employed to discern "necessary conditions" within datasets. [1] These indispensable conditions stand as pivotal determinants of particular outcomes, wherein the absence of such conditions ensures the absence of the intended result.
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 ...
Necessity and sufficiency (5 P) Pages in category "Necessity" The following 10 pages are in this category, out of 10 total. This list may not reflect recent changes ...
The majority of textbooks, research papers and articles (including English Wikipedia articles) follow the linguistic convention of interpreting "if" as "if and only if" whenever a mathematical definition is involved (as in "a topological space is compact if every open cover has a finite subcover"). [17]
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.