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All statements are either true or false.
Now, we know that \(P\) is either true or false.
It means that a statement is either true or false.
Numbers don't have to be either true or false.
Must every statement be either true or false?
Propositions have truth value -- that is to say, they are either true or false.
There's a predicate, which is a thing that is either true or false.
"A thing is not necessarily either true or false; it can be both true and false".
So the law of excluded middle tells us that every statement whatsoever must be either true or false.
According to this principle, every mathematical statement is either true or false; no other possibility is allowed.
"Either p or not-p" ( p ∨ ∼p) is always true because p is either true or false.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com