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Talk:Bivalence and related laws

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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)[reply]

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)[reply]

Law of bivalence

[edit]

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.