Sorry I'm not clearer :-(

See... In classical logic (of the above variety) truth values are binary. Every proposition (assertorial statement in a language where logic and mathematics and computer languages count as languages too) is either T or F and not neither or both.

There are some problems with two valued logics however.

This has led to the development of a number of other logics...

See... In classical logic if something is not false then it logically follows that it is true. If something is not true then it logically follows that it is false.

There is a nifty little rule that some people find amusing.

not P means that P is false
not not P means that P is true (because there are two values a pair of negations cancel each other out)
not not not P means that P is true (because once the pair cancel each other out there is one left)
So the general rule is that if there is an even number of negations P is true whereas if there is an odd number of negations P is false.

So I am not not not not not not not sad means that I am not sad lol.

Anyway... Back to classical logic being two valued. In the face of some problems with two valued logic some people have proposed alternative logical systems with more than two truth values. E.g., there is a system with TRUE, FALSE, and NEITHER TRUE NOR FALSE. This is meant to deal with statements such as 'the present king of France is bald'. In a two valued logic we want to say that it is false that the present king of france is bald but that seems to logically entail that it is true that the present king of france is not bald (in two valued logic) but the problem is that there isn't a present king of france. So one can say that the statement is NEITHER TRUE NOR FALSE.

In this logical system not not P doesn't logically entail P becaue not not P could mean P or could mean IT IS NEITHER TRUE NOT FALSE that p.

One could say that it is neither true nor false that god could make a rock so big that god can't move it.

But if it is neither true nor false it would still follow that there is something that god can't do (ie can't make true).

But still... Thats okay, I think...