Talk:Logical biconditional

0 and 1 instead of true and false, or was it the other way around...?

The text is not coherent in that it assumes that the reader knows that 0 means false and the 1 means true. This is not universal knowledge. What is confusing is that while the text describes functions as true or false, the truth table does not. — Preceding unsigned comment added by 213.113.4.17 (talk) 14:02, 23 March 2017 (UTC)

Equivalence sign?

According to the sources I've checked, the logical equivalence sign is not technically a connective -- this conflicts with what the page currently implies when it says "≡" can be used synonymously with "↔".

Source "Discrete Mathematics and its Applications" by Kenneth Rosen. Quote: "The symbol ≡ is not a logical connective and p ≡ q is not a compound proposition but rather is the statement that p ↔ q is a tautology."

Unfortunately there seems to be complete confusion in the Wikipedia about all the logic topics connected with arrows. But this confusion seems to come from the logicans themselves. We also have the articles If and only if, Logical equivalence and Logical equality.

I'd also say that "p ≡ q is not a compound proposition but rather is the statement that p ↔ q is a tautology", but for sure there's some logic author somewhere, who uses "≡" to express this operation (the negation of the exclusive or). Seems, that no logic sign beyond $\land$ and $\lor$ is generally accepted. Lipedia (talk) 10:35, 3 September 2010 (UTC)

Is this page what you call "readible"?

I am not joking, after reading this wikipedia article, I feel like I understand less about biconditionals than before. Sadly, this is true for so many other math related wikipedia articles.

Don't misunderstand, I'm quite familiar and comfortable with working with logic/math, but this page seems to be nothing more than a random collection of grammatically and information-ally correct but contextually and stylistically bankrupt sentences.

I suppose this is just the result of multiple authors though. Oh well.

unambiguous

In the section on colloquial usage it says that the only unambiguous way of putting the biconditional in English is to say, "b if a and a if b". Should a if and only if b not be included here?Davkal 22:31, 8 June 2006 (UTC)

I would also like to put in a brief note to include the formulation "just in case" which is commonly used in philosophy as th biconditional even though the usual English meaning of "just in case" is "as a precaution against...", as in, e.g., "I took my umbrella just in case it started raining". Davkal 22:33, 8 June 2006 (UTC)

The misleading and confusing expression "just in case", should never replace its correct, and easily understood equivalent, "if, and only if" (also, in more technical writing, "if and only if"). The following explains the error:

• Language Log: "Just in Case"
• Southern California Philosophy for philosophy graduate students: "Just in Case".Dr Lindsay B Yeates (talk) 22:10, 9 April 2014 (UTC)

Proposed project

I have been working on all of the logical operators recently. I would like to see a consistent format for them. There is a wikiproject proposal for this at: Wikipedia:WikiProject_Council/Proposals#Logical_Operators. Also see Talk:Logical connective.

I would like to see the logical, grammatical, mathematical, and computer science applications of all of the operators on the single page for each of those concepts.

Gregbard 08:56, 28 June 2007 (UTC)

merge from Logical equality

Not quite the same, as A = B = C may mean they all have the same truth value, while A iff B iff C may mean A iff (B iff C). — Arthur Rubin | (talk) 20:06, 28 June 2007 (UTC)

...which also means they have the same truth value. The convention that I have seen, and believe is convenient is the the equal with two bars (=) means "same numerical value as," the one with three bars $\equiv$ means "has the same truth value as," and one with four bars (which I don't think we can make yet) means "is the same set as."

I would like to see this article deal with this one: $\equiv$. I think that would include as least some of the material from logical equality, but not so much (if any) from logical equivalence. Gregbard 20:36, 28 June 2007 (UTC)

Just thought I should point out that the merger with if and only if has already been proposed, discussed, opposed and rejected -- see Talk:If_and_only_if#Merge. Also, I'm not an expert on logic, but it seems as if if and only if, logical biconditional and logical equality are related but distinct ideas, being from mathematical logic, propositional calculus, and electronic engineering (I think), respectively. Even if they're the same thing, that doesn't necessarily make a merger the right option; they seem to be written with different target audiences in mind, and it's often worth including different treatments of the same idea, for people from different backgrounds, such as with quantum mechanics and introduction to quantum mechanics. James pic (talk) 17:46, 1 April 2008 (UTC)

I have removed the templates regarding the merger with if and only if, there seems to be little support for that one. --_{tiny plastic} Grey Knight ⊖ 07:59, 18 June 2008 (UTC)

Biconditional Elimination

In section Biconditional Elimination there is the same text than in page Biconditional elimination. please do something Snushka (talk) 10:28, 19 June 2009 (UTC)

On the need for expert maintenance

Please see Talk:If and only if. Melchoir (talk) 23:48, 21 February 2010 (UTC)

Like all connectives in first-order logic ... ?

At the moment in the Rules of Inference section it is told, that this is a connective in first-order logic, which is predicate logic. Shouldn't it read "zeroth-order logic", or simply "propositional calculus"? Lipedia (talk) 00:17, 1 August 2010 (UTC)

all or nothing versus all xor nothing

EQV( ) should be true, not false. — Arthur Rubin (talk) 05:44, 1 August 2010 (UTC)

Well, I replaced for , which I don't like.

Operations are not usually done without arguments, so I don't know if we can ask, which one is more common. I used the xor version, because I felt it's inacceptable that adding an argument to EQV( ) shouldnt change the result.

And because I've seen the all XOR nothing matrix before:

Relations like the subset relation are nonexistential quantifications combined by AND, and thus their negations are existential quantifications combined by OR. Just for fun I replaced this OR by a XOR, and there you can see this matrix with the zero line. (Compare this overview.) So the xor version seemed more legitimate to me. Watchduck (talk) 13:35, 1 August 2010 (UTC)

In spite of the fact that someone changed my skin on this site....

I look at this as logical equality, rather than logical biconditional. To be precise, I look at the alternative form of EQV(X) as:

$\bigwedge _{A\in X}\bigwedge _{B\in X}\left(A\leftrightarrow B\right),$

making in clearly a generalization of the two-element logical biconditional, given that $A\leftrightarrow A$ is always true. — Arthur Rubin (talk) 16:40, 1 August 2010 (UTC)

Both p and q, or neither? What!

I think that saying "p if and only if q" just because p and q have the same truth value is a rather absurd definiton. That would mean, since it is both currently true that I am on a laptop and I am on Wikipedia, that it is currently true that I am on a laptop if and only if I am on Wikipedia! That just isn't what "if and only if" means! It's NEVER true that I am on a laptop if and only if I am on Wikipedia! A counterexample exists: I could be on a laptop, BUT NOT on Wikipedia. Another counterexample would be that I could be on Wikipedia, but on an iPhone and hence NOT on a laptop!

"p if and only if q" is supposed to be true when IT IS ALWAYS THE CASE that p and q have the same truth value! That is, when IT IS IMPOSSIBLE that p and q have different truth values!

I'm afraid NOBODY reading this page has ANY IDEA what it means for a logical biconditonal to be true! I don't care how many "respected publications" this bogus definition can be found in!

Rewrite this page, and rewrite the books! This Wikipedia article is an embarrassment for the whole human race! - Hanlon1755 (talk) 18:30, 4 July 2012 (UTC)

This article accurately describes the material biconditional (see material conditional). There are also biconditionals corresponding to the strict conditional and logical implication. I won't remove the {{disputed}} tag, but I don't think it's completely justified. — Arthur Rubin (talk) 10:34, 5 July 2012 (UTC)

And we are supposed to report what "the books" call it (see WP:OR), although I'm sure there are some which use the strict biconditional. — Arthur Rubin (talk) 10:35, 5 July 2012 (UTC)

Nonsense. We only need one definition of logical biconditional, and I can tell you right now this sad, sad page does not have it. -Hanlon1755 (talk) 17:40, 5 July 2012 (UTC)

Do you have a definition? — Arthur Rubin (talk) 17:55, 5 July 2012 (UTC)

Of course! "p if and only if q" means p and q ALWAYS have the same truth value. -Hanlon1755 (talk) 20:22, 5 July 2012 (UTC)

That's not the definition of "material biconditional", which is the usual definition of biconditional. — Arthur Rubin (talk) 10:11, 9 July 2012 (UTC)

Well, if that's true and a biconditional means simply both p and q, or neither, that certainly isn't self-evident at all. Look at the mess I'm in! I think in this case this definition should be justified. It should be a theorem rather than a definition. This definition seems very synthetic and arbitrary. -Hanlon1755 (talk) 00:55, 10 July 2012 (UTC)

"p ↔ q" means "p → q" and "p ← q" ("q → p"), for any definition of the conditional "→". Seems the appropriate definition of biconditional. — Arthur Rubin (talk) 03:00, 10 July 2012 (UTC)

That's not the definition I was disputing, Arthur. I agree that p ↔ q means p → q and q → p. I just dispute the definiton where p ↔ q means both p and q, or neither. I don't care that this is "equivalent" to p → q and q → p; I would also have disputed the definition of material conditional, as this weird definition is implied by it. -Hanlon1755 (talk) 02:28, 11 July 2012 (UTC)

In fact, I still don't believe it! -Hanlon1755 (talk) 02:12, 15 July 2012 (UTC)