Talk:Material conditional/Archive 1

Problems with material implication

I was thinking that there should be a section about the "problems with material implication". Here's some text that I propose could be part of it:

There are several known issues concerning the standard truth-functional interpretaion of the material conditional. Such problems are sometimes referred to as the "paradoxes of material implication", though they are not quite paradoxes in the strict sense.

One such issue concerning material implication involves the truth-functional interpretation of the falsity of a conditional statement. Take, for example, the following conditional: If God exists, then the Earth is flat. If one were to think that this proposition is false (which seems reasonable), then, interpreted as a material conditional, the antecedent must be true and the consequent false—for that is the only case in which the conditional is false, according to the standard truth-functional interpretation of the material conditional. However, the antecedent is God exists. So, the standard interpretation seems to establish the existence of God from a simple false conditional in which the antecedent and the consequent are fairly unrelated. Of course, one way to respond to this would be to argue that the conditional in question is not a material conditional after all, but some other kind of conditional statement.

However, I don't know a great deal about this stuff. I thought some logic buffs might be able to create the section or help out. Any ideas? - Jaymay 18:43, 14 August 2006 (UTC)

This article is about the material conditional, as it is used in math and computer science. Some discussion of its relation to other types of conditionals is useful, but long digressions belong in the more philosophistical articles, of which there are many, as I'm sure you know. That can be handled via the requisite links in the <see also> section. Jon Awbrey 18:54, 14 August 2006 (UTC)

Jon, first, I apologize for changing the references format without discussion. I only figured that since there was no discussion going on already here that no one was really watching this article much anymore. However, by putting in the full URL to the reference that I added, I was not changing the references format, since there was no style on the article according to which "Eprint" was used. Thus, I believe you just changed the references style without discussion.

Second, I wasn't trying to be territorial by tagging this article with Wikiproject philosophy. I submit that you are being the more territorial by verbally tagging this article as restricted to math and computer science. I was trying to be pluralistic by adding philosophy-related stuff to this article, not by replacing anything with philosophy-related stuff.

Third, this article does not specify that it is about the material conditional only as it relates to math and computer science. If it is supposed to, then it should be titled "Material conditional (math and computer science)" and there should be a diambiguation article where we can distinguish a "Material conditional (philosophy)" article. There is a disambiguation article for Conditional, in which it says "Material conditional, in propositional calculus, or logical calculus in mathematics". The propositional calculus fits squarely into logic/philosophy. So, why would you say that it is restricted to "math and computer science"?

However, I think that it's a poor option anyway to create two separate articles. It's not a long article as it is. And, there is no reason that issues with the material conditional (philosophical or otherwise) should not be in this article. It need not be a "long digression" either, unless you think that any philosophically-related discussion is too long and a digression. Furthermore, while it's true that there are many philosophy articles on Wikipedia, there are none on the material conditional, except this one.

Fourth, cooperation is fun; hostility is lame. - Jaymay 22:03, 14 August 2006 (UTC)

I realize it's totally uncool to talk about one's expertise in WP, but my "commitment" here is shorter than it used to be, so maybe it will save some wasted breath to mention that I've been a student of logic in both mathematical veins and philosophical vains for 40 very odd years now, and so I'm quite familiar with all of the basic issues you mention here. But the article is titled what it is, and that is the kind of truth-functional implication that is used by mathematicians everywhere in almost (w)holy blessed ignorance of what some philosophers consider its "problematic" character. So the main aim of this article is to present the basics of material implication for the edification of those readers who came looking for that. Of course, it makes sense to make a hyper-side-long allusion to all those other issues, for which there are dedicated articles already on counterfactual conditionals, fuzzy logic, modal logic, relevance logic, and a host of others. That's the main thing. Will get to the other issues later. Jon Awbrey 01:06, 15 August 2006 (UTC)

Jon, no need to speak of your "expertise". I am well aware that the truth-functional interpretation is widely used and accepted as unproblematic. No doubt it is quite intuitive. Many philosophers recognize that. I think you misunderstood my point all along. I didnt' want to include issues with the material conditional because I thought that it has problems, in some serious sense. Fringe controversies are certainly not for an encyclopedia entry. However, issues that a large number of professionals on the subject discuss, including philosophers, are relevant to an encyclopedia entry.

However, it's really not a big deal. I just thought some people might be interested in expanding the article, since, I think, there are, from time to time, people browsing Wikipedia looking for issues surrounding material implication. But, I guess not. I'll leave it be. - Jaymay 03:58, 15 August 2006 (UTC)

Sorry if I am being brusque, but we have had some major mess-overs of related articles from both phil-logic and hard-ware folks, and since these are entry level articles my concern is not confusing initiates any more than they are likely to be already. But what I am saying about the problematique is that there are standard ways of coordinating groups of articles. In mathematical orbit, this is one of 16 on the binary connectives, and I worked a long time getting a consistent format for that group. By all means, add one or more brief sections on enrichment topics, perhaps using the {{main|...}} template under the subhead to link to the main articles on those topics. Many Regards, Jon Awbrey 04:44, 15 August 2006 (UTC)

I didn't realize you had collaborated and worked to get uniformity among various articles. I understand that you don't want all that work to be unecessarily tampered with. Besides, some issues are mentioned in the section on comparison with other conditionals. And I wasn't really planning on making the changes myself either. If anyone else what's to add info on this sort of thing, then they can.

By the way, maybe you should post something on the Talk page here warning that the article has pretty much been deemed satisfactory and that any changes should be discussed on the Talk page first. I know we're all supposed to do that first no matter what, but when the Talk page is blank or little is on it, one tends to think that no one is really working on it. - Jaymay 19:22, 15 August 2006 (UTC)

I am, of course, only expressing my personal opinions and preferences. And a note like that would probably be jes askin' fer trouble. Ha! Jon Awbrey 21:04, 15 August 2006 (UTC)

Is this right?

Subset?

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)

Although it may be expressed in terms of sets, it is not synonymous. Gregbard 08:55, 28 June 2007 (UTC)

The material conditional $(A\rightarrow B)\Leftrightarrow (\neg A\lor B)$ is related to the entailment relation $A\Rightarrow B$ in the same way,

as the set operation $A^{c}\cup B$ is related to the subset relation $A\subseteq B$ . Lipedia (talk) 18:41, 27 July 2009 (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 08:55, 28 June 2007 (UTC)

Material conditional vs. entailment

"The material conditional is not to be confused with the entailment relation ⊨ "

I was told by a philosophy professor they are the same. I'm a graduate student teaching logic for the first time, and I want to get it right for my students. —Preceding unsigned comment added by 24.208.177.188 (talk) 17:38, 22 April 2008 (UTC)

In Methods of Logic, Quine goes on a rant for a page or two about how we should not confuse the material conditional with implication. Truthfully, I don't understand how they're meaningfully different, but Quine says they are! Djk3 (talk) 21:10, 22 April 2008 (UTC)

They're much different. One is a relation (entailment) denoted in the metalanguage and the other is a connective (material implication) denoted in the object language. The connective takes two arguments, both of which are object-language propositions. The other takes two arguments, one of which is a set of object-language propositions and the other of which is an object-language proposition (or sometimes a set of them). For individual propositions A and B, A entails B iff the material implication from A to B is valid. (This assumes classical logic.) But it may be that for some model M, A materially implies B even though this is not true of every model (i.e. not valid), and hence A doesn't entail B. In a sense, entailment is not relative to a model, since it quantifies over all of them, while material implication is. It makes no sense to say that a material implication is true irrespective of a model unless all one means is that it is valid (and hence an entailment). Nortexoid (talk) 12:00, 23 April 2008 (UTC)

This needs to be explained in the article. Currently it asserts that they are different without giving a clue as to in what way they differ, at least not before it slips into impenetrable formal jargon. The article on entailment has the same problem.

Also, what on Earth could "the entailment relation (which is used here as a name for itself)" possibly mean? Nathanielvirgo (talk) 13:34, 26 July 2009 (UTC)

Done. The entailment tells, that the material conditional is always true, respectively never false. You need a quantifier to express the entailment.

Anyone who thinks they are the same, should ask himself if the statement $A\subseteq B$ and the set $A^{c}\cup B$ are also the same for him. Lipedia (talk) 18:56, 27 July 2009 (UTC)

The explanation of the difference between material and logical implication is difficult to understand. The problem is that the explanation of entailment is too abstract. 72.83.207.14 (talk) 14:53, 28 August 2009 (UTC)

I am addressing the comment of the anon, who tagged the entailment article, which I have reversed; it may be useful to include Peter Marcuse's comment that things might be 'true for the wrong reason'. In other words, material implication can be 'true for the wrong reason' (see the Venn diagram). BTW Peter Marcuse used to have his own wiki page which was deleted for non-notability; I disagree with that assessment. --Ancheta Wis (talk) 19:48, 28 August 2009 (UTC)

If one examines the proof in entailment#Discussion (see the Venn diagram) then one sees that material and logical implication differ in the following way:

• in logical implication, given that (A $\Rightarrow$ B), then "A → B", and also "A without B is never the case".
• in material implication, given that (A → B), then "there can be cases when B is true but A is not".

--Ancheta Wis (talk) 21:42, 29 August 2009 (UTC)

Why is it that "logical" implication, aka entailment, is not listed as a "logical" connective while material implication is? This seems very counter intuitive. Bbippy (talk) 23:23, 30 October 2011 (UTC)

Implication in natural language

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)

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)

Summary

The summary for this article does not meet wikipedia guidelines for being understandable by the broadest possible audience. —Preceding unsigned comment added by 74.202.89.125 (talk) 19:47, 25 February 2009 (UTC)

Amen to that! It's not even understandable to this guy with a total of 4 degrees in mathematics and computer science! It comes off like so many philosophers and logicians talking to each other, and that's not what introductory paragraphs are for. Further down the article says "People often confuse material implication with logical implication," but offers no help in distinguishing between them.

Is it possible to add a real-world, everyday example or two, or at least an analogy or two?—PaulTanenbaum (talk) 22:55, 26 February 2010 (UTC)

Commutativity?

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)

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)

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)

Contradictory example?

In "Example" it says:

Finally, if the first proposition proves false (Chris is standing at the Sydney Opera House), and the second proposition also proves false (Chris is in Sydney, Australia) then it is a false statement.

But in the truth table it is shown that F → F gives T.

Isn't there a contradiction? Dart evader (talk) 20:32, 23 June 2009 (UTC)

Does it? If Chris is not standing on the Eiffel tower then he is not in Paris. What happens if Chris is standing in the Louvre? Does that mean that he's not in Paris? - Tbsdy lives (formerly Ta bu shi da yu) ^talk 05:48, 25 June 2009 (UTC) Let me look at the example I gave and get back to you. I'll revert for now. :( Tbsdy lives (formerly Ta bu shi da yu) ^talk 05:51, 25 June 2009 (UTC)

OK, so the example is "If Chris is standing on the Eiffel tower then he is in Paris."

I actually think now that I've made a boo-boo. However... if both propositions were false, then Chris is not standing on the Eiffel tower and Chris is not in Paris. Thus it would make the statement true. Wouldn't it? - Tbsdy lives (formerly Ta bu shi da yu) ^talk 05:56, 25 June 2009 (UTC)

I suppose it would. Dart evader (talk) 14:46, 25 June 2009 (UTC)

Unintelligible!

{{Technical|date=September 2010}} (Yes I have put a second {{technical}} tag here.) I can be as abstract as the next guy, but this article is practically opaque. As the comments peppered throughout this talk page indicate, the article needs big help! Grad students in logic have heartburn with it. Please, somebody, at least create an introductory paragraph that gives a notion of the definition that laymen can fathom, rather than just a grab-bag of properties stitched together rather unhelpfully.—PaulTanenbaum (talk) 23:04, 26 February 2010 (UTC)

If that tag belongs anywhere, it would be on the article. -- 202.124.75.219 (talk) 01:47, 30 April 2010 (UTC)

This article effectively assumes that the reader knows as much or more about its subject matter than that which the article actually explains. In that respect it is typical of the babel of technical articles in Wikipedia. It uses letters to stand for sentences with hidden logical structure, which seems to be part of how the article ends up defining logical implication as a claim that a material conditional is "always true" (another phrase bound to leave the general reader shaking his or her head). Keep it simple. A logical or formal implication is automatically true, for instance pq logically implies p; for instance, if John's here and John's smiling, then John's smiling; if the logical structure is adequately exposed, a logically true conditional can be proven without investigation of its empirical claims (e.g. is John actually smiling?). If a claim of a logical implication turns out false, then it wasn't a logical implication. As for relevance logics and all the rest, save them for later mention, start with the ABCs. Well, maybe I'll try my hand at it when I have some time. The Tetrast (talk) 15:33, 11 April 2010 (UTC).

And this is why you SHOULDN'T be editing this article. Nortexoid (talk)

Well, maybe I should say instead that a sentence whose schema (e.g. "p → p") is valid is true in all universes, or some such, and that (logical) implication is the validity of the conditional, and is not itself called true, etc. But I stand by that which I meant, that a logical implication (at least in Quine) is not a claim of a conditional's having a valid schema, and that the article says otherwise, and neglects the common practice (according to Methods of Logic) in 1st-order logic of dealing with schemata that lay all relevant logical structure bare. On the other hand, I don't know what your complaint about my informal comment is. I also stand by my statement that the article assumes the reader's knowledge of that which is being explained. It's as if it were written by students for their professor, rather than by logicians for the general reader. Eventually, if I have time, I will do some cleanup (unless your or others do it first), and I'll source it with footnotes. The Tetrast (talk) 15:40, 12 April 2010 (UTC).

I think I see the problem here. It seems that maybe you have in mind logical implication and logical equivalence in terms of set theory or simulated set theory. I've been thinking just in terms of ordinary 1st-order logic, where (logical) implication is the validity of the conditional, and a sentence with the consistent but invalid schema $\forall$(G→H) is not taken announcing a logical implication G$\Rightarrow$H. Such terminological tangles need to be addressed without getting tangled in them for the general reader. The Tetrast (talk) 21:57, 12 April 2010 (UTC).

Duplication of content

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

Connective versus implication

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)

That seems to have originated from an earlier version of this article. I am going to very aggressively remove a lot of material which I consider nonsensical. Take the example:

$A\subseteq B\Leftrightarrow (x\in A\Rightarrow x\in B)\Leftrightarrow \forall {x}(x\in A\rightarrow x\in B)$

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)

Made clearer the differences between material implication and strict implication

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)

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)

Article inaccurate, proposal to change several parts

I dispute several parts of this article. I propose to modify the article, such that it agrees with the facts about strict conditionals. See Talk:Strict conditional for an overview of this overall discussion. Not all material conditionals can be put in "if-then" form, as this article currently suggests. "If-then" form is a type of expression reserved for only strict conditionals, not necessarily material conditionals. Furthermore, it is disputed whether or not a "material conditional" is even a type of conditional at all. What is instead the case is that all conditional statements (those that can be written in "if-then" form) are strict conditionals, which are not necessarily material conditionals. This article lacks pretty much any citations, never mind exact page numbers where this material can be found. Furthermore, it has been my expierence that some of the respected, notable, published literature on this topic is in error. Just because somebody said something about material conditionals is true doesn't necessarily mean it actually is, whether it was an "expert" or not. I want the part that material conditionals can be written in "if-then" form taken out of this article, because it isn't true. And if an entire section of this article can be about "paradoxes" or apparent "misconceptions," I propose to add to this article, at least, a sentence or two distinguishing between material conditonals and strict conditionals, and how the misconception that all material conditionals can be written in "if-then" form is not actually true. The article as currently written is very misleading and I myself am horribly a victim of it. Please aid me in these efforts to modify this article. Hanlon1755 (talk) 07:06, 23 December 2011 (UTC)

You need evidence that not all material conditionals can be written in if-then form — this means from reliable sources, not just your imagination. — Arthur Rubin (talk) 08:03, 23 December 2011 (UTC)

Every sentence I added was cited. It was either explicitly stated or was a logical consequence of what was explicitly stated in several sources. This includes the position that not all material conditionals can be written in "if-then" form. And all my sources were reliable sources. I still recommend modifying the article to improve its accuracy. Hanlon1755 (talk) 08:47, 23 December 2011 (UTC)

In mathematics, it certainly is true that every statement $A\to B$ can be stated as "A implies B" or "if A then B". (See, I just did.) The issue that some philosophers worry about is that "if A then B" could mean different things depending on the intention of the speaker. But one thing that phrase can mean is a material conditional, and every material conditional can be trivially rephrased in that way. — Carl (CBM · talk) 14:55, 23 December 2011 (UTC)

One of the sources used by Hanon1755 included Barwise who is no dummy, but for my part I don't have any of the source texts that Hanon1755 referred to. This article is about the material conditional, and only tangentially about the linguistic form "if...then...". I think that two questions are raised here:
1. The practical question is whether, in the study and application of logic, one commonly utters it "if p then q" - the general reader, coming here to learn about the material conditional in logic, deserves to be told the answer up front, i.e. in the lead, and the answer is an affirmative which we probably can source to Quine and which I seriously doubt is contradicted by any of Hanon1755's cited sources. The lead is not the place for a revisionist silence about common practice in formal, symbolic, or mathematical logic.
2. The linguistic question is, how well does "if p then q" represent "p→q"? - on which the article pretty much admits that "if p then q", as an utterance in logic, is just an imperfect convenience for "p→q". The article notes that the respective negations in everyday English do not seem equivalent to each other; i.e., the article alerts the reader to be aware of the divergence of formal logic's "it is false that if p then q" from the same form in everyday English. It would be nice if logicians pushed for use of some synthetic phrase or word like "nand not" or "nandn't" for "→" but, with few exceptions (Quine's "excl-or"), logicians resist synthetic words for connectives (whereas mathematicians seem happy to coin words for their objects and relations). The Tetrast (talk) 17:25, 23 December 2011 (UTC)

I disagree with Carl who says that $A\to B$ "can be" stated as "A implies B," on the grounds that that's not what "A implies B" means. "A implies B" means that every time A is true, B is also true. As you should be able to see, that means "A implies B" is a modal claim, talking about all possible worlds. The material implication does not talk about all possible worlds. It only talks about a single given case in which A is either true or false, and B is either true or false. The material implication is therefore not worthy of being expressed in the form "A implies B." If you have any doubt about this, I refer you to look at Larson, Boswell, et al. 2007, p. 80 and how this is in conflict with Rosen 2007 p. 6-7. A clear contradiction can be seen between these two sources as to what a "conditional statement" is, and along with it, the method of expression "A implies B." Hanlon1755 (talk) 23:33, 24 December 2011 (UTC)

As editors pointed out at Talk:Strict conditional, the citations fail WP:V. Most numerous are cites to a high school Geometry textbook, (Larson, Boswell, et al.) I couldn't find a copy of this one online, but maybe the hypotenuse and cosecant “can not always be written in "if-then" form, since it is not necessarily a strict conditional.” And yet…

“I disagree on your claim that "strict conditionals are not the same as ordinary conditionals." The ordinary conditional is the proposition that can be written in "if-then" form, but that is precisely what a strict conditional is to begin with! Refer to my sources if you need to. I also disagree with your claim that "Larson, Boswell, et al.,... are not discussing strict conditionals." While they may not use the explicit words "strict conditional," the conditionals they are using are nonetheless strict conditionals as defined by C.I. Lewis. They do not have to use the exact wording "strict conditional" to be using a strict conditional! The type of conditional they are working with has all the properties of the strict conditional, and only the strict conditional. Please, look at the sources yourself and understand this. This latter claim of yours strikes me as outlandish considering it is just downright wrong. It seems to show that you haven't even bothered to check the source yourself.”

I've checked rest of the rest of the sources, (which are WP:RS for logic: Rosen; Hardegree; Barwise and Etchemendy), however, none of them support the user's “dispute/proposal”.—Machine Elf ¹⁷³⁵ 11:17, 25 December 2011 (UTC)

Afd: Nominated for deletion; see Wikipedia:Articles for deletion/Conditional statement (logic)

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)

What dispute?

Why has the dispute tag been added back?—Machine Elf ¹⁷³⁵ 19:42, 17 January 2012 (UTC)

Yes, I dispute that all material conditionals are if-thens, and that all if-thens are material conditionals. Not only do I believe this, but it is a logical consequence of published facts. See WP:Articles for deletion/Conditional statement (logic) and Talk:Strict conditional for more. Hanlon1755 (talk) 02:08, 21 January 2012 (UTC)

Well, that has been discussed… I think you've established that you believe it, for reasons you no doubt find compelling. As was explained, WP nonetheless considers it synthesis or original research. But you know all this, you did a great job bringing Conditional statement (logic) into compliance with policy in that regard. You removed the tag with your Jan 17 edits. As there were many problems, I reverted and instead used the content from the SEP "Conditional" article, which you "cited" several times. It touches on many of your concerns, but as you restored the dispute tag after my edit, apparently that's not satisfactory. Is it intolerable that WP:UNDUE weight isn't given to your peculiar notions? According to Edgington, it can found in every textbox and like Etchemendy, another one of your "sources", she stressed that, it's truth-functional role is uncontroversal in this regard.

In fact, while you're not disputing that "if then" is commonly used, you did, however remove every instance of "if then" phrasing; sometimes replacing it with "and", as you've done elsewhere. The WP:NPOV policy prohibits you from removing material that you merely find inimical to your point of view. I won't belabor the point that you're knowingly misrepresenting your sources, none of which support some kind of unconditional rejection, so to speak, much less the quixotic activism. The lengthy demonstration paraphrased WP:OR you've tried elsewhere and the remaining editorial was mostly duplicated in two sections, perhaps inadvertently. The dispute tag isn't a memento of the forums you've shopped. It says: “This article's factual accuracy is disputed. Please help to ensure that disputed facts are reliably sourced…”—Machine Elf ¹⁷³⁵ 17:33, 24 January 2012 (UTC)

I never even once cited the SEP "conditional" article, as you claim I did. As this shows, you do not fully understand my efforts. Even with your new additions, the lead of this article still implies that material implication is "typically read "if p then q" or "p implies q," suggesting that such a reading is OK. I dispute that; I do not believe such a reading is OK. At the very least, the lead of this article is misleading. Hanlon1755 (talk) 02:26, 27 January 2012 (UTC)

It's not my claim, it's a matter of record. You cited the SEP "conditional" article four times, click the diff. I can't say I understand, no. But I do try… so there's that at least. Believe what you please, but sincerely, ask yourself: “What if it's just wholesome Boolean goodness through and through? What if you want it to be something it's not?”—Machine Elf ¹⁷³⁵ 03:36, 27 January 2012 (UTC)

Truth function or logical connective?

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)

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)

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). Copyedit. The Tetrast (talk) 20:45, 20 February 2012 (UTC)

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).

Additional citations

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 [{{Refimprove|date=April 2010}}] [{{No footnotes|date=January 2010}}] 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.

1. -
2. -
3. -

Any editor who is able to help with citations that would be helpful. NewbyG ( talk) 20:52, 20 February 2012 (UTC)

March 2012

Could someone answer 3 questions:

• Where it was a "WP:POINTy shuffling"?
• About which "repetition" did Machine Elf 1735 speak?
• How many modern sources (even based on classical logic) assert that ¬p ∨ q or something like that is the definition(sic) of p → q? (not a "property", a "theorem" or even an "axiom")

How many Machine Elf 1735's changes will I revert depends on how many questions will be answered, and how promptly. Incnis Mrsi (talk) 16:00, 4 March 2012 (UTC)

I still wait for constructive proposals how to improve the article, either for pedagogical usage or something else. From here and forth, I will silently ignore any libelous accusations in WP:DISRUPT or so, hence don't waste precious edit summary space for this. BTW this article become a cause célèbre for my essay WP:Foundations of mathematics. Incnis Mrsi (talk) 08:16, 5 March 2012 (UTC)

Thank you so much for that. Continued slights and blue-links in edit summaries can be considered as being edit warring, that's right. Sorry, but it is more productive when editors hold their tongues, and ignore minor heat-of-the-moment niggles, then we get back on track sooner. It may take time, but all input should be welcomed, in a good way. Thanks NewbyG ( talk) 09:47, 5 March 2012 (UTC)

That is WP:POINTy and I suggest you read both WP:NPOV and of course, WP:LEGAL. Feel free to delete the quote from your source's abstract. Or is that another petty threat?

8 hours later…

“ (no sources indicate that Machine Elf 1735's "definition of material implication" is a majority view, either in mathematics or by laymen. while it is not proven, there is no preferred definition) ” — Incnis Mrsi (talk) 8 hours later…

What makes it “Machine Elf 1735's "definition of material implication"”? LOL, I don't got one and I'm not bothered. It's self-evident that the existing article is the de facto consensus, as opposed to your “cause célèbre”, absent someone to clean-up behind you. The simple copy edits aren't controversial, but between your WP:BATTLEGROUND tactics and petty abrasiveness, it's impossible to collaborate with you. Obviously, not a win in your game.

No surprise you should ask about repetition, I certainly can't accuse you of contributing can I? You'll notice however, that when you ghettoized “Classical Logic”, you stacked text from different parts of the article… No doubt it's in your essay, but let's see if we can find your so-called “PoV” issue here in this article, shall we? M is for moved:

==Definition → In classical logic==

+	In [[classical logic]],
-	The material conditional is associated with an [[logical operation|operation]] on two
+	The material conditional is associated with a [[truth function]] of two
	[[logical value]]s, typically the values of two [[proposition]]s, that produces a value of
-	false
+	[[false (logic)|false]]
	just in the case when the first operand is true and the second operand is false
-	the compound sentence p→q (typically read "if p then q" or "p implies q")
+	the compound p→q
M	is logically equivalent to the negative compound: not both p and not q Thus the compound p→q is false [[if and only if]] both p is true and q is false By the same stroke, p→q is true if and only if either p is false or q is true (or both) Thus → is a function from pairs of [[truth value]]s of the components p, q to truth values of the compound p→q, whose truth value is entirely a function of the truth values of the components Hence, the compound p→q is called [[Truth function|truth-functional]] The compound p→q is logically equivalent also to ¬p∨q (either not p, or q (or both)), and to ¬q → ¬p (if not q then not p) But it is not equivalent to ¬p → ¬q, which is equivalent to q→p
-	A material conditional is often simply called a conditional

I don't see it. Realistically, your “throw away” comment was quite specific. You don't fancy it, so it can be deleted. It's a WP:DONTLIKE issue, not a “PoV” issue:

Truth function or logical connective?

“ 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)

A user stepped in and simply fixed what appeared to be a minor omission. It's a shame you can't do likewise without pretending you're fighting the bad guys.

We're kicking “not p or q” to the curb are we? Why don't you tell us exactly how many.—Machine Elf ¹⁷³⁵ 12:41, 5 March 2012 (UTC)

There was actually no consensus about definitions in this article, and now there is yet no consensus. What is not correct, or maybe omitted, in my version? I explained why the version from January 2012 was incorrect. "Truth function" in the lede was not only a PoV, but virtually another topic (just a truth function of the material conditional). So, anyone can make a mistake. I know, there were some reasons for this article to be underdeveloped, but now the situation is changed. I repeat the question one time more: what is wrong with my text? Incnis Mrsi (talk) 13:01, 5 March 2012 (UTC)

WP:DONTHEAR. All three are different. Tortured prose in triplicate is more than I care to deal with… so congratulation, you win another edit war. You got a problem with that?—Machine Elf ¹⁷³⁵ 13:41, 5 March 2012 (UTC)

My goal was to improve the article, not to "win an edit war". I just reverted edits which made the article confusing. Incnis Mrsi (talk) 07:43, 6 March 2012 (UTC)

You missed. Lie all you want about what you “reverted”.—Machine Elf ¹⁷³⁵ 14:58, 6 March 2012 (UTC)

Yeah, thanks for cutting out the name calling, peoples, and naming, please, Focus on content Keep discussions focused, comment on content not contributors, please NewbyG ( talk) 13:05, 5 March 2012 (UTC)

You're not helping. Enough with the accusatory section titles.—Machine Elf ¹⁷³⁵ 13:12, 5 March 2012 (UTC)

I've restored the 'standard' or 'classical' definition to the lead paragraph, this time explicitly as "classical." A sentence there that clearly assumes the classical definition was never even removed and now flows better again with the definition restored [(insert) and I added the word "classical" into said unremoved sentence.]
Next I would suggest that somebody expand the article with information actually about non-classical conditionals. That would be more constructive than pursuing removal of mention of classical logic from the lead paragraph in order for the kind of 'neutrality' that hinders the general reader - especially the kind of general reader who doesn't already know what a material conditional is. The standard classical elementary conditionals in Quine's Methods of Logic and plenty of other textbooks, and standard in logic circuits, is the place to start.
Once non-classical material is added to the article, then it would make more sense to work something about non-classical conditionals into the lead paragraph. The Tetrast (talk) 03:59, 6 March 2012 (UTC).
I just noticed that the article already has a little material on non-classical conditionals, but in comment above I was thinking of a paragraph or more, dedicated to a discussion of such. The Tetrast (talk) 05:30, 6 March 2012 (UTC). Edited with an insert The Tetrast (talk) 07:07, 6 March 2012 (UTC).

It would be a mistake to think that even classical views on the material conditional are represented well. Yes, it is equivalent to a form with one negation and one disjunction. But why and how are these forms equivalent? Current version is still a bit confusing because of ambiguity about the foundation of the biconditional tautology (p → q) ↔ ¬p ∨ q. Is the material conditional just a syntactic sugar for ¬p ∨ q, analogously to the converse situation with negation in intuitionism? Is it an axiom? If not, which axioms entail it? Incnis Mrsi (talk) 07:43, 6 March 2012 (UTC)

Won't that depend on exactly what connectives you choose when you formalize the logic? If you take {∨, ¬} as the connectives, then → is just an abbreviation. On the other hand if you take {→, ¬} as the connectives then ∨ is just an abbreviation. In a system where NOR is the only basic connective, all the usual ones are abbreviations. But in a system where all the connectives are included, the equivalences between various expressions are theorems rather than definitions. — Carl (CBM · talk) 12:18, 6 March 2012 (UTC)

Good point. Logical connective#Functional completeness should be enriched with this reasoning. BTW the article, not surprisingly, has a heavy classical logic PoV. Incnis Mrsi (talk) 12:46, 6 March 2012 (UTC)

Article inaccurate, proposal to change several parts

• "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)

Per exportation, those are the same. — Arthur Rubin (talk) 00:20, 16 July 2012 (UTC)

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)

There was a second concern about "For example, in intuitionistic logic which rejects proofs by contraposition as valid rules of inference, (p → q) ⇒ ¬p ∨ q is not a propositional theorem, but the material conditional is used to define negation.", it has been said it was an arbitrary definition choice rather than a fundamental property, and than intuitionnist logic could be defined using the not connective as a primitive connective. What do you think about that here ? TomT0m (talk) 13:54, 19 July 2012 (UTC)

Monotonicity

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)