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In logic, the law of non-contradiction (LNC) (also known as the law of contradiction, principle of non-contradiction (PNC), or the principle of contradiction) states that contradictory propositions cannot both be true in the same sense at the same time, e. g. the two propositions "the house is white" and "the house is not white" are mutually exclusive.
In logic, two propositions and are mutually exclusive if it is not logically possible for them to be true at the same time; that is, () is a tautology. To say that more than two propositions are mutually exclusive, depending on the context, means either 1. "() () is a tautology" (it is not logically possible for more than one proposition to be true) or 2. "() is a tautology" (it is not ...
The proverb's meaning is similar to the phrases "you can't have it both ways" and "you can't have the best of both worlds." For those unfamiliar with it, the proverb may sound confusing due to the ambiguity of the word 'have', which can mean 'keep' or 'to have in one's possession', but which can also be used as a synonym for 'eat' (e.g. 'to ...
A heterarchy may be orthogonal to a hierarchy, subsumed to a hierarchy, or it may contain hierarchies; the two kinds of structure are not mutually exclusive. In fact, each level in a hierarchical system is composed of a potentially heterarchical group which contains its constituent elements.
The events "even" (2,4 or 6) and "not-6" (1,2,3,4, or 5) are also collectively exhaustive but not mutually exclusive. In some forms of mutual exclusion only one event can ever occur, whether collectively exhaustive or not. For example, tossing a particular biscuit for a group of several dogs cannot be repeated, no matter which dog snaps it up.
In probability theory, the complement of any event A is the event [not A], i.e. the event that A does not occur. [1] The event A and its complement [not A] are mutually exclusive and exhaustive. Generally, there is only one event B such that A and B are both mutually exclusive and exhaustive; that event is the complement of A.
Fallacies of definition are the various ways in which definitions can fail to explain terms. The phrase is used to suggest an analogy with an informal fallacy. [1] Definitions may fail to have merit, because they are overly broad, [2] [3] [4] overly narrow, [3] [4] or incomprehensible; [4] or they use obscure or ambiguous language, [2] contain mutually exclusive parts, [3] or (perhaps most ...
While false dilemmas involving contraries, i.e. exclusive options, are a very common form, this is just a special case: there are also arguments with non-exclusive disjunctions that are false dilemmas. [1] For example, a choice between security and freedom does not involve contraries since these two terms are compatible with each other. [5]