Talk:Logical biconditional

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

message: 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)
thread_title:  Equivalence sign? 

message: 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)
thread_title:  Proposed project 

message: 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)
thread_title:  Biconditional Elimination 

message: Please see Talk:If and only if. Melchoir (talk) 23:48, 21 February 2010 (UTC)
thread_title:  On the need for expert maintenance 

message: 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)
thread_title:  Like all connectives in first-order logic ... ? 

message: 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)
replies: text: 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  tag, but I don't think it's completely justified.  — Arthur Rubin  (talk) 10:34, 5 July 2012 (UTC)

text: 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)
replies: text: 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)
replies: text: Do you have a definition?  — Arthur Rubin  (talk) 17:55, 5 July 2012 (UTC)
replies: text: 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)
replies: text: That's not the definition of "material biconditional", which is the usual definition of biconditional.  — Arthur Rubin  (talk) 10:11, 9 July 2012 (UTC)
replies: text: 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)
replies: text: "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)
replies: text: 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)
replies: text: In fact, I still don't believe it! -Hanlon1755 (talk) 02:12, 15 July 2012 (UTC)
thread_title:  Both p and q, or neither? What!