Talk:Material conditional/Archive 1

message: Is the material conditional synonymous with the subset relation? If it is we should strongly note it or even consider merging the articles. Fresheneesz 21:44, 7 January 2007 (UTC)
replies: text: Although it may be expressed in terms of sets, it is not synonymous. Gregbard 08:55, 28 June 2007 (UTC)
thread_title:  Subset? 

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 08:55, 28 June 2007 (UTC)
thread_title:  Proposed project 

message: I reverted a change because despite the assertion in the edit summary that the change is correct, it's not.  This portion of the article is describing how implication differs between natural language and logic.  --Doradus (talk) 19:45, 21 December 2008 (UTC)
replies: text: I've reverted it again to its original state.  We need to resolve this issue before changing the article. --Doradus (talk) 00:22, 25 January 2009 (UTC)
thread_title:  Implication in natural language 

message: Uhm, the commutativity stated in this article confuses me, despite knowing a little math. I only know commutativity as "being allowed to swap arguments", that is, A -> B = B -> A (in this particular case. This is obviously wrong, of course, consider A=1, B=0). However, even with some calculations on paper, I cannot see how this statement helps with commutativity. Can someone explain this to me?
--Tetha (talk) 10:56, 8 April 2009 (UTC)
replies: text: Thanks for spotting this. This is definitely a problem, and I don't know how to fix it because I don't know a name for this property. Calling it commutativity only makes sense if you think about it as follows: Define x \circ_C y as (x \rightarrow (y \rightarrow C)). Then x \circ_C y \equiv y \circ_C x. This is clearly too far-fetched. --Hans Adler (talk) 13:04, 8 April 2009 (UTC)
replies: text: Ah. After some thinking, your post, a bit of implementation and such, I think I understand what this formula wants to say: If both A and B are antecedents for a consequence C, then it does not matter in what order the set of antecedents (in this case, A and B) are investigated. I think, calling it "commutative antecedents" or "order-invariance of multiple antecedents" would help. --Tetha (talk) 13:51, 8 April 2009 (UTC)
thread_title:  Commutativity? 

message: Please see Talk:Entailment#Duplication of content. - dcljr (talk) 19:51, 15 January 2011 (UTC)
thread_title:  Duplication of content 

message: The explanation here is really confused.  In contrast, here is a very simple explanation. Could someone explain how the "example" is supposed to help in understanding this distinction? Vesal (talk) 21:36, 15 January 2011 (UTC)
replies: text: A \subseteq B  \Leftrightarrow (x \in A \Rightarrow x \in B) \Leftrightarrow \forall{x} (x \in A \rightarrow x \in B)
Is this a joke? What is the meaning of the unbound "x"??  Somewhere else I just eliminated this line, but now I see that example is supposed to show that "The relation \Rightarrow  can be expressed by \rightarrow  and the universal quantifier \forall."  I consider this such pure and blatant nonsense that I do not want to see this back anywhere on Wikipedia unless it can be attributed to a reliable source. Vesal (talk) 21:45, 19 January 2011 (UTC)
thread_title:  Connective versus implication 

message: I have made clear from the start there are fundamental differences between the material conditional and the strict conditional. I have also included detailed information on this difference in a new section. I have cited respectable references, with page numbers. Hopefully this addition should make the distinction clearer and easier for people new to the topic to understand. Considering the article lacked this helpful information, the addition should be greatly welcomed. Hanlon1755 (talk) 07:55, 19 December 2011 (UTC)
replies: text: Reverted per WP:BRD; see Talk:Strict conditional for ongoing discussion (also Talk:Conditional statement (logic)… WP:V/WP:SYNTH/WP:NPOV).—Machine Elf 1735 16:33, 20 December 2011 (UTC)
thread_title:  Made clearer the differences between material implication and strict implication 

message: Editors here may be interested in the related AfD discussion occurring at Wikipedia:Articles for deletion/Conditional statement (logic).—Machine Elf 1735 12:01, 15 January 2012 (UTC)
thread_title:  Afd: Nominated for deletion; see Wikipedia:Articles for deletion/Conditional statement (logic) 

message: Would someone object if I throw truth function away and replace it with logical connective? Truth functions are a matter of interpretation (for example, in model theory), but if I want to prove something like p→((p→q)→q), then I can do it just formally and have not to know anything about models and propositional values. Incnis Mrsi (talk) 09:51, 20 February 2012 (UTC)
replies: text: There are quite a number of articles on logical connectives which are either math-centric or logic-oriented. Many are stubs, so which are which is up to editors, maybe. This article has some development to it, so if user:Incnis Mrsi can see where to add in here, that would be good. I dont think I can help much, sorry. If there are any additional citations to be found, or new sourced material, etc. It does seem like you will be doing good here. When/if the cite tag no longer applies, it can come off. /* Truth function or logical connective? */  It's a good question / seems like a math-approach is justified as you suggest / Perhaps others will offer comment here. HTH.  NewbyG  ( talk) 20:25, 20 February 2012 (UTC)
replies: text: I already changed it. It's just an opening paragraph. Now both "connective" and "truth-functional" are mentioned and wikilinked, and redundancy has been reduced. But sections of the article are what really need work. The Tetrast (talk) 20:44, 20 February 2012 (UTC)

text: I don't know what got into me when I edited to the article to say that the material conditional "is" a logical connective. "Material conditional" usually refers to a whole compound "p→q", while "connective" refers to a compounding relationship such as "→" or "and", etc. - even if there isn't always a big practical difference between connective and compound. The Tetrast (talk) 22:05, 20 February 2012 (UTC)
thread_title:  Truth function or logical connective? 

message: This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. (April 2010) - stale, but article still needs more sources -
* I have removed the  [] []  tags. (5) inline cites already, all seem to be from 1 source though', so the article does need more and better references as it goes on. 
# -
# -
# -
Any editor who is able to help with citations that would be helpful.  NewbyG  ( talk) 20:52, 20 February 2012 (UTC)
thread_title:  Additional citations 

message: *"transitivity: (a \rightarrow b) \rightarrow ((b \rightarrow c) \rightarrow (a \rightarrow c))"
Is that correct ? Should'nt this be (A -> B & b -> C) -> (A->C)
TomT0m (talk) 22:01, 15 July 2012 (UTC)
replies: text: Per exportation, those are the same.  — Arthur Rubin  (talk) 00:20, 16 July 2012 (UTC)
replies: text:  Yeah, I figured that out myself later /o\. We are discussing a little bit on this article on french wikipedia, and the real concern was that transitivity is not really a property of material implication, but rather of the deduction relation, the naming seems confusing. TomT0m (talk) 13:54, 19 July 2012 (UTC)
thread_title:  Article inaccurate, proposal to change several parts 

message: I think that what it is said about monotonicity (under "Formal properties") is confusing. It is simple to see that material conditional is anti-monotonic in the first argument and monotonic in the second argument. Still, if we lift the reasoning from truth values to the inference process, then it is true that "if we know more, we cannot derive less" (in classical logic). Saying, as it is in the article, that if a→b then ∀c.(a∧c)→b doesn't mean that → is monotonic: the property is indeed true due to the anti-monotonicity of → in the first argument! (Adding "and c" to the premise can only decrease its truth value and thus increase the truth value of the whole implication, where "decrease" and "increase" refer to the total ordering of the boolean lattice ⊥ < ⊤).
Is there anyone who thinks that these two levels should be clarified and kept distinct? Grace.malibran (talk) 13:55, 9 January 2014 (UTC)
thread_title:  Monotonicity