P or -P

Anyone taking or who has taken a logic class should recognize the statement P or -P. It's called the law of excluded middle and is a simple truth of logic. For any proposition P, either P or -P (not P). Example from Wikipedia:

For example, if P is
Joe is bald
then the inclusive disjunction
Joe is bald, or Joe is not bald
is true.

I had people arguing that it would be false. They were saying that it could be true that P and -P and proceded to give confused statements to confuse the case. Here are a few;
Columbus is both a hero and villian.
You are both yourself and not yourself.
You are happy and sad.

There is really no arguing with them, if they believe that to be true then I simply can't talk sense into them. I see logical truths as simple truths in themselves. Truths of thinking. Anyone here in SMP believe that P and -P could be true. I believe Hegel was a believer in it.

[atrifix]

This is just not true. The law of excluded middle is not a basic law in logic and is not used in intuitionstic logics or certain n-valued logics where n>2. It is used in classical logic, which is probably what you are familiar with. Under classical logic, the law of excluded middle holds.

The whole point of logic is that it ISN'T simple truths. We define certain sets of statements and relations to be true, and then we use the given model to deduce (or induce) other conclusions.

For a better counterexample to the law of excluded middle, take the following:
Food X either tastes good or it does not.

Under classical logic, this is a truth, but it is fairly apparent that the statement need neither be true or false. There could be no fact of the matter about how the food tastes.

[Trantor]

[ QUOTE ]
Anyone taking or who has taken a logic class should recognize the statement P or -P. It's called the law of excluded middle and is a simple truth of logic. For any proposition P, either P or -P (not P). Example from Wikipedia:

For example, if P is
Joe is bald
then the inclusive disjunction
Joe is bald, or Joe is not bald
is true.


[/ QUOTE ]

This is true for bivalent logic systems, as I understand it ( and as expressed by the axiom that "For any proposition P, either P or -P (not P)" of your post) but not all logic systems.

I am not disagreeing with your conclusion (I have no view because I didn't understand the question)! I guess the question made it clear to you it was concerned with bivalent propositions.

[Cyrus]

[ QUOTE ]
if P is Joe is bald then the inclusive disjunction
Joe is bald, or Joe is not bald
is true.
Columbus is both a hero and villain.
You are both yourself and not yourself.

[/ QUOTE ] "Hero" and "villain" are not mutually exclusive, strictly speaking*.

"Being yourself" and "not being yourself" are not mutually exclusive, when the terms are used metaphorically. (If they are used literally, they most certainly are mutually exclusive!)

And, let is be said that with the advances in modern medicine, "Joe is bald" and "Joe is not bald" are NOT mutually exclusive!

_______________

* I say "strictly speaking" because, in most (but not all) moral systems, someone who is a villain cannot redeem himself out of villainy just by being also a hero. That person is considered a villain. In Christianity, for example, the individual who is a villain cannot be a generous donor to the Red Cross and be "saved" just like that; he must repent and be forgiven of his villainy.

[ QUOTE ]

I had people arguing that it would be false. They were saying that it could be true that P and -P

[/ QUOTE ]

Actually, if (P and -P) were true, then (P or -P) would, by logic, be true as well (in fact, *anything* follows from a contradiction). So if you wanted to show that (P or -P) is false, arguing that P and -P is true, or could be true, would not be the way to do it.