principle of bivalence the principle that any (significant) statement is either true or false. It is often confused with the principle of excluded middle. Letting ‘Tp’ stand for ‘p is true’ and ‘T- p’ for ‘p is false’ and otherwise using standard logical notation, bivalence is ‘Tp 7 T-p’ and excluded middle is ‘T (p 7 -p)’. That they are different principles is shown by the fact that in probability theory, where ‘Tp’ can be expressed as ‘Pr(p) % 1’, bivalence ‘(Pr (p) % 1) 7 (Pr (~p) % 1)’ is not true for all values of p – e.g. it is not true where ‘p’ stands for ‘given a fair toss of a fair die, the result will be a six’ (a statement with a probability of 1/6, where -p has a probability of guish bivalence and excluded middle from the principle of non-contradiction, namely, ‘-(Tp • T-p)’, which is equivalent to ‘-Tp 7 -T-p’. Standard truth-functional logic sees no difference between ‘p’ and ‘Tp’, or ‘-Tp’ and ‘T-p’, and thus is unable to distinguish the three principles. Some philosophers of logic deny there is such a difference. See also MANY-VALUED LOGIC , PHILOSOPHY OF LOGIC , VAGUENES. R.P.