If P is sufficient for Q, then knowing that P is true is reason enough to conclude that Q is true; However, knowing that P is false does not satisfy the minimum need to conclude that Q is false. Many people confuse a cause as a sufficient condition for something to happen (sometimes considered an “effective cause [edtechbooks.org/-CzX]” or a “causal agent”). But formally, we should consider a “cause” as “a necessary and sufficient condition for an effect.” The idea of a necessary condition is that something will not happen if the condition does not occur. For example, we could say that the car will not move forward if we have not cut the parking brake. Shutting down the brake is therefore a necessary prerequisite for the future journey of the vehicle. In general, if the explanation is directional, it may not seem surprising that when A explains B, it is generally not true that B or its negation is in turn an explanation of A (or its negation). Audrey`s victory explains our celebration, but our failure to celebrate is (usually) not a plausible explanation for her non-victory. Solange`s presence may explain why the seminar was such a great success, but a boring seminar is – under normal circumstances – no reason why Solange should not be there. This result seems to undermine the common understanding that if A is a sufficient condition of B, it will typically be the case that B is a necessary condition for A and the lie of B is a sufficient condition for the lie of A. You should also be wary of hidden and often changing assumptions about the necessary conditions implicitly contained in (often tacit) ceteris paribus clauses.

Like other basic concepts, the concepts of necessary and sufficient conditions cannot be easily specified in other words. This article shows how elusive the search for a definition of the terms “necessary” and “sufficient” is, indicating the existence of a systematic ambiguity in the concepts of necessary and sufficient conditions. It also describes the connection between puzzles on this topic and problems with the word “if” and its use in conditional sentences. To say that one thing is a condition for another is to say that one thing is involved in the realization of the second thing. One of the goals of twentieth-century philosophy was to analyze and refine definitions of meaningful concepts—and the concepts they expressed—in hopes of shedding light on the thorny problems of, say, truth, morality, knowledge, and existence that were beyond the reach of a scientific solution. The essence of this objective was to determine, at least in part, the conditions which must be fulfilled for the correct application of the concepts or in which certain phenomena can actually be described as existing. Even today, the unique contribution of philosophy to interdisciplinary studies of consciousness, the evolution of intelligence, the importance of altruism, the nature of moral obligation, the field of justice, the concept of pain, the theory of perception, etc. always relies on their ability to bring a high degree of conceptual rigour and rigour to discussions in these areas. The possibility of ambiguity in these concepts raises another problem for standard theory. Thus, as Georg Henrik von Wright (von Wright 1974, 7) points out, the concepts of necessary condition and sufficient condition are themselves definable: the discussion of “necessary and sufficient conditions” is well understood in philosophy, and so I sometimes make the mistake of assuming that it is generally understood in the wider community. This article addresses this by describing the concept and why it is important.

As mentioned at the beginning of the article, the specification of necessary and sufficient conditions is traditionally part of the philosophical activity of analyzing concepts, concepts and phenomena. Philosophical research on knowledge, truth, causality, consciousness, memory, justice, altruism, and a host of other questions is not intended to state evidence or explanatory relationships, but to identify and develop conceptual relationships (see Jackson 1998 for a detailed presentation of conceptual analysis and the additional entry on analytical concepts in analytic philosophy for an overview). But again, the temptation to look for reasons for this or reasons to think is not far away. While conceptual analysis, like dictionary definition, avoids conditions of proof and explanation, conditions of proof seem to be natural consequences of definition and analysis. That Nellie is an elephant may not be (or the) reason she is an animal, any more than a figure is a square, a reason why she has four sides. But some claims seem to make sense even in such contexts: being an elephant apparently gives reason to think that Nellie is an animal, and a particular character can be considered to have four sides because it is a square, in a conclusive sense of “because”. In the conditional statement “if S, then N”, the expression represented by S is called the antecedent, and the expression represented by N is called the consequent value. This conditional statement can be written in several equivalent ways, such as “N if S”, “S only if N”, “S implies N”, “N is implicit by S”, S → N, S ⇒ N, and “N whenever S”. [7] For example, in graph theory, a graph G is said to be bipartite if it is possible to assign the color black or white to each of its vertices so that each edge of G has an end point of each color. And for a graph to be bipartite, it is a necessary and sufficient condition that it does not contain cycles of odd length. Thus, the discovery of whether a graph has odd cycles indicates whether it is bipartite and vice versa.

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