I think you're wrong. Can you provide a link or give me a source that says the law of excluded middle requires that the truth value's have to be known?
"The law of excluded middle only says that the total ( P v ~P) is true, but does not comment on what truth values P itself may take" ( Link )
"The false dilemma fallacy refers to misuse of the or operator" ( Link ). In Bush's statement, the false dilemma is created because there are more than two options than either being with us or being with the terrorists.
The difference between love and mathematics is the concepts themselves. Without something around that is capable of love, then love cannot exist. As I said, the concept of love deals with the relationship between two entities. Theoretically, love could still exist without humans if other animals also had the capacity to love. However, if nothing exists that can love, then love does not exist. Math is different. If you take a group of something ( say two ), and you put it together with another group of something ( say six ), it will always equal the same amount ( in this case, eight ). The concept itself exists independent of any thing else. The only way it wouldn't exist is if nothing existed.
Decessus
"In classical logic, the only possible truth values are true and false." http://en.wikipedia.org/wiki/Truth_value
You cannot deduce (Pv-P) is true without P. Given that theism and atheism take a dualistic approach as even you stated, one is either a theist or atheist, it requires that P be either true or false. In our case we use G as the God statement:
(G v -G) is true.
In the Bush statement the flaw lies in the assumption that -A is B. Your original statement is actually an if A then B, not an A v -A (You are with us or you are not with us) which is where the misunderstanding of the case lies.
(A ->B) != (Av-A) because (Av-A) is true in all cases while (A->B) is false when A is true and B is false.
Without an observer one cannot take a group of quantities and incorporate it in a relation. The universe doesn't actually work in mathmatical relations, it is just a system that can be defined by it. Math and physics are simply abstractions that allow us to define aspects of the universe based upon our perceptions. In fact, there are abstractions in math and physics that aren't even observable or proven to exist but are said to exist as a result of explaining universal structure.
These properties exist without human existence as that is how universe fundamentally operates, but it technically doesn't exist until there is an observer since math and physics are abstract definitions for human interpretation. After all what is 2? There is no definite meaning as to what a number is and our number systems themselves are one of perhaps many number systems to define the universe with. For instance, Complex Numbers use i, but where in the Universe do you count i except for mathmatical equations?
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