Talk:Bivalence and related laws

I felt the pages dealing with the differences between these 3 laws were confusing, so I've been bold and tried to improve them. However, I'm not quite an expert in these areas, so I acknowledge a (small, I hope) possibility that my understanding is totally flawed and my every edit on this matter needs to be reverted. If so, you would need to do the following:

Law of non-contradiction would need to be reverted to:


 * this edit

Principle of bivalence would need to be reverted to:


 * this edit

Law of excluded middle would need to be reverted to:


 * this edit

Having said that, I'm about 90% sure that my understanding is correct, so I will be disappointed if this is actually done. :-)

The crucial difference seems to be between bivalence and the excluded middle. The former says that P is either true or false, but the latter only applies to statements of the form (P or not-P), and says that all such statements are true. This is a different claim, and some people have rejected bivalence but not the excluded middle.

Evercat 19:20 1 Jul 2003 (UTC)


 * There are many systems that reject bivalence but not the law of excluded middle, and they include really any many-valued system. I suppose Russell's "truth-gap" semantics for certain modal systems does this as well, since there are statements that may not have any truth-value whatever (i.e. "Pegasus flies").


 * Intuitionistic logic, on the other hand, rejects the law of excluded middle but retains bivalence.


 * I'm not entirely sure how clear this page is on the differences between the 3 principles, but at first glance, it doesn't seem too clear and perhaps introduces superfluousness to it (i.e. with the "Vagueness" section). Nortexoid 06:08, 4 Nov 2004 (UTC)

I don't see how bivalence and excluded middle are distinct. (P or ~P) seems to me to be nothing more or less than the formalization of "either P is true or P is false". A statement can't be either true or false if it doesn't have a truth-value. Bivalence neither implies nor is implied by non-contradiction, unless you're understanding the "either ... or ..." construction to be an exclusive disjunction, which I don't think is the common usage of the term. A paraconsistent logic could deny non-contradiction but still accept bivalency or the excluded middle. Unnamed525 21:37, 26 August 2005 (UTC)

Bivalence and excluded middle are distinct because some logics might allow (P or -P) to be true even though neither P or -P have a determinate truth value. Evercat 22:13, 26 August 2005 (UTC)

Law of bivalence
Surely the law of Law of bivalence can be written:

(~(P and ~P)) and (P or ~P)


 * Surely that does not capture what the law of bivalence is.