The law of excluded middle (tertium non datur in Latin) states that for any proposition P, it is true that (P or ~P). (The tilde symbol, '~', reads 'not'.)
This is not quite the same as the principle of bivalence, which states that P must be either true or false. It also differs from the law of noncontradiction, which states that ~(P and ~P) is true. The law of excluded middle only says that the total (P or ~P) is true, but does not comment on what truth values P itself may take. In any case, the semantics of any bivalent logic will assign opposite truth values to P and ~P (i.e., if P is true, then ~P is false), so the law of excluded middle will be equivalent to the principle of bivalence in a bivalent logic. However, the same cannot be said about non-bivalent logics, or many-valued logics.
Certain systems of logic may reject bivalence by allowing more than two truth values (i.e., true, false, and indeterminate), but accept the law of excluded middle. In such logics, (P or ~P) may be true while P and ~P are not assigned opposite truth-values like true and false, respectively.
In logic, the law of excludedmiddle, or the principle of tertium non datur, is formulated in traditional logic as "A is B or A is not B ".
The law of excludedmiddle can be misapplied, leading to the logical fallacy of the excludedmiddle, also known as a false dilemma.
Take, for example, the law of excludedmiddle, in the form 'all propositions are true or false.' If from this law we argue that, because the law of excludedmiddle is a proposition, therefore the law of excludedmiddle is true or false, we incur a vicious circle fallacy” (p.
Anyway, as I understand the law of excludedmiddle, it simply means that something has to be either true or false; it can't be both, or partially-true, or whatever.
The law of the excludedmiddle implies that the square root of 2 cannot have the qualities of an integer and thus must be something other than a rational number.
Part of the confusion is that I'm still trying to determine whether the Law of excludedmiddle is in fact a disjunction or an exclusive disjunction, so I know whether Radical Middle thought disagrees with it.
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