Miles Neale (12/19/2014)
Tom I agree with you on this, but please correct me if I am wrong in the way I think of it. Logically I have thought that the boolean is a result or state either before or after a test. The result of a test being true or false. Logically then if the test has not been performed there is no result therefore null. The state of the boolean operator then tells three things, a true test result, a false test result, and that the test has not yet been performed.
Yes, I agree that that's one way of looking it, and perfectly valid (if sometimes not the most convenient way of looking at it): it has 3 states, and in two of those states it has a value(true in one of those two states, false in the other); in the other state it doesn't have a value. Another way of looking at it is that it has two states, in one of which it has one of two possible values and another in which it doesn't have a value (that's my usual way of thinking of it, because it means that all variables in a logical calculus always have two sates, regardless of how many values the can have when they have values, and it's useful to have commonalities across the logics because techniques of manipulation can then be shared and some things become much simpler).
That extra commonality between different logics is especially useful because using two valued logic (whether with three states or with two) is sometimes not useful, and mathematicians tend to be fairly well accustomed to logics with an infinte collection of values, especially mathematicians of the constructivist school or the intuitionist school (which have a lot of overlap) but even what you might call "classical" mathematicians (those who avoid anything that smells of philosophical difficulties) tend to be familiar with logics with more than 2 values.