# Talk:Material implication (rule of inference)

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## Gregbard's hatnote at Material conditional

I will revert such additions as [1] until the source where the rule of inference is called "material conditional" (not versa) will be demonstrated. Incnis Mrsi (talk) 07:03, 24 February 2012 (UTC)

The web sites given were not reliable sources, nor was the "book cover." The journal article was a WP:RS, but said that material implication was a connective (i.e. Material conditional), not a rule. -- 202.124.75.172 (talk) 08:49, 24 February 2012 (UTC)
I guess that Gregbard (talk · contribs) poorly understands the purpose and guidelines for WP:DABLINK hatnotes and probably confuses it with "See also" section. The purpose of DABLINK is to facilitate navigation to another topic known by the same name, where the name is either the article's title ({{for}} style hatnotes) or an inbound redirect ({{redirect}} style hatnotes). Incnis Mrsi (talk) 09:44, 24 February 2012 (UTC)
I'm sure well get to the bottom of it eventually, so I'm not worried about it. However, we can either merge the two into one article or have hatnotes on both. As of right now there are two articles, therefore there should be helpful hatnotes on both. I just don't see what the conflict is here?! The Hurley source is solid btw, so I have no idea what's up here. Please do help me out here Incnis. Greg Bard (talk) 09:55, 24 February 2012 (UTC)
Merge or have hatnotes on both?
• Space has a hatnote for Outer space, not conversely. Rationale: outer space is sometimes called just "space", but space (as a physical and mathematical concept) never is called "outer space".
• Dud has a hatnote for Dunedin International Airport (denoted as DUD), but the latter article has not any hatnotes because there are no other things in the Universe occasionally referred to as "Dunedin International Airport".
I am sure that hundreds of such examples may be extracted from English Wikipedia. So, I repeat the question: how a reader intended for an article about material implication (a rule of inference) may occasionally get the article named material conditional? These are only such cases what is treated with DABLINKs, and argument about the converse DABLINK is null and void. Incnis Mrsi (talk) 11:37, 24 February 2012 (UTC)
I'm not really interested in your examples, it's pretty clear when an issue arises as a result of the names used, and this is one of those times, very clearly. Some texts use "material conditional" and some use "material implication" for the connective as well as the rule which is basically the same concept. Greg Bard (talk) 22:15, 24 February 2012 (UTC)
Material implication is NOT, in fact, a rule of inference. -- 202.124.73.250 (talk) 22:06, 24 February 2012 (UTC)
Okay, this will shock and amaze you, but different texts use different terms. If you are just under the impression that there is just a right and a wrong term, and that others should be ignored, or disparaged, then I'd say you should really get some more experience reading different texts on the subject. "Material implication" in Hurley and Mates, and "Implication" in Parker/Moore. So, it is in use and needs to be accounted for. I am always very surprised at strong opinions and on what issue they are so strong. Greg Bard (talk) 22:15, 24 February 2012 (UTC)
You have not demonstrated that the term is in use FOR A RULE. "Material implication" and "Implication" are widely used to mean the CONNECTIVE Material conditional. -- 202.124.73.250 (talk) 22:20, 24 February 2012 (UTC)
In all of those cases it is referring to the rule, not the connective.Greg Bard (talk) 23:02, 24 February 2012 (UTC)
No it isn't, and you have provided no evidence that "Material implication" is used to mean a rule. -- 202.124.72.180 (talk) 10:46, 27 February 2012 (UTC)

## Bogged down in pedanticism

Okay, so there are many instances where concepts under "arguments," "theorems" and "rules of inference" have more than one article, and some where there is only one. There is this particular rule of inference here we are having a problem with right now. I wonder how you intend to address the larger issue? Is there some other name for this that you prefer? If we decide to merge many of these instances where more than one can be merged into one, it would be nice to make sure to provide for the rules of inference. If we make separate articles for each, it would be nice to provide a connection to the other articles expressing the same concept. In the case of material implication, I have to stand by the Hurley use "valid rule of inference that allows a horseshoe to be replaced by a wedge if and only if the antecedent is negated" He abbreviates it Impl as does Moore/Parker. I don't understand why anyone is ignoring that. However, what I would like to know is if you have a different name, or just are against this as a concept or what. Greg Bard (talk) 11:41, 27 February 2012 (UTC)

In the absence of a reliable source which gives a non-abbreviated name (yes, "Impl" is abbreviated, and it would be WP:OR to translate it as material implication), I would accept implication elimination, material implication elimination, or material implication (rule) as a standby, although the first name is used for modus ponens. They're all ambiguous and WP:OR, but are less likely to be used for something other than a rule. I argued against material implication redirecting to material conditional, but that seems a better choice for the use of the name than this one. "Material implication elimination", at least, has the advantage of being descriptive. — Arthur Rubin (talk) 14:13, 27 February 2012 (UTC)
"Material implication" or shortly "implication", but (p → q) ⇔ ¬p ∨ q is a rule of replacement, not an elimination. I already proposed Material implication replacement. Incnis Mrsi (talk) 19:25, 27 February 2012 (UTC)

Someone explain to me how Hurley is not a reliable source. It's in it's tenth edition at least. Also explain the reliable source which uses each of your proposals. Listen, I don't really feel strongly about it. Just figure out a name, and have a real good reason for moving it, and I'll go along. So far, tenaciously ignoring sources presented is not a good way to be. I would like to stay consistent with this transformation rules template. I would be open to moving it to material implication (rule of inference) if that avoids the issue somehow. But then why would that change anything? Greg Bard (talk) 20:27, 27 February 2012 (UTC)

## Disputed tag

Please note that, since the cited article says that material implication is a CONNECTIVE, the disputed tag should remain until resolved. I have not been able to access the cited book, but most books say the same thing (indeed, the phrase "material implication is a rule" gets zero hits). I believe the article author has misunderstood what they have read. It is of course a fact that ${\displaystyle P\rightarrow Q}$ is equivalent to ${\displaystyle \neg P\lor Q}$, but this fact is stated at material conditional. I recommend redirecting this article to that target. -- 202.124.73.250 (talk) 22:10, 24 February 2012 (UTC)

I note also that a book search for "material conditional or material implication" finds several books stating that the phrases both refer to the same connective, i.e. material conditional. -- 202.124.73.250 (talk) 22:18, 24 February 2012 (UTC)

I'm not saying I completely disagree, however doing a search on "Material implication replacement rule" gives an abundance of sources. Propositional logic has ten so called replacement rules, and all of them seem to be represented on Wikipedia in some form or another (Rule of replacement). That being a fact, this page in my opinion does have some merit. Mythio (talk) 11:45, 26 February 2012 (UTC)
This may indicate that the proper title for the aricle should be Material implication replacement, not "Material implication", the latter becoming a dab page. Incnis Mrsi (talk) 11:51, 26 February 2012 (UTC)
A web search for "Material implication replacement rule" finds at most one reliable source; a book search finds one online "book"; a google scholar search finds nothing. — Arthur Rubin (talk) 21:30, 26 February 2012 (UTC)
I note that the book by Hurley cited in the article is misrepresented: "material implication" is defined early on as the connective, and the later list of replacement rules simply includes the use of the definition of this connective. Accordingly, it makes sense to restore the redirect for this article, particularly as the author confuses "and" and "or" so badly. -- 202.124.72.180 (talk) 10:54, 27 February 2012 (UTC)
He uses the name for both, and he does so prominently. I haven't seen any name proposed that was backed up by anything.Greg Bard (talk) 20:47, 27 February 2012 (UTC)
Hurley, 11th edition, p. 414 seems pretty clear that he calls the rule "material implication". If I don't see anything to the contrary, I'll remove the tags shortly. However, this being a rule of replacement, the converse is also a rule, and should have a name. I question whether this is the most common name for the rule, but it is clearly a name. — Arthur Rubin (talk) 21:12, 27 February 2012 (UTC)
Yes, but earlier on in the book Hurley defines "material implication" to mean the connective. Likewise Copi defines "material implication" to mean the connective. -- 202.124.74.93 (talk) 11:25, 29 February 2012 (UTC)
Does the fact that Hurley is badly written make it unreliable? If not, "Material implication (disambiguator)" should remain a possible title for this article. If no one can come up with a better one .... 14:58, 29 February 2012 (UTC)

The material implication is not just any of the symbols ${\displaystyle \rightarrow ,\supset ,}$ or ${\displaystyle \Rightarrow }$.

This article and the related one material conditional pay too much attention in the meaning of the implication connective. That should be part of the article about logic. The problem that makes important the material adjective comes from examples like this:

elephants are pink, then 2+2=4

although the antecedent speaks about a different thing than consequent, it is a true statement because according to the true table for implication: false => true is true, moreover, one can conclude anything from a false antecedent, for that reason a set of premises should be consistent, false should not be obtained from them, otherwise any conclusion can be derived.

That is, the adjective material, is needed when one refers to implication with its meaning as the implication true table, to distinguish it from the deeper problem that gave rise to modal logics, barely speaking, the need to represent more accurately the relation between premises and conclusions.

The cited bibliography is introductory and do not address this problem in depth. This subject is better addressed in more philosophical books in modal logics, and the handbook of modal logic. This article seems written by enthusiastic, but confused, students, that have not that knowledge yet. Please refrain to write about subjects that you don't have a deep knowledge, an introductory course is not enough. This seems a growing problem in wikipedia, lowering it's quality and introducing many absurd disputes. As a computer scientist I could write this article, but I refrain from that because, doing that before in other articles where I can write something correct, was just a waste of my time, when the "owners of the page" fanatically erased my contributions. I do not know if this is the case with this article, but here some more observations:

Who wrote this article does not have clear several things. The symbol <=> is not a metasymbol, p <=> q is an abbreviation of (p => q) & (q => p). (s)he does not have clear what is understood by an axiomatic system. In the axiom (p => q) <=> (~p | q), the symbol <=> may be read as "is equivalent to", there is a relation between the implication =>, and the syntactic turnstile ${\displaystyle \vdash }$ — Preceding unsigned comment added by 201.103.56.195 (talk) 20:31, 14 June 2012 (UTC)

## Switcheroo

As I recall, Douglas Hofstadter referred to this as the Switcheroo rule in his book Gödel, Escher, Bach. --81.138.95.57 (talk) 08:51, 12 September 2012 (UTC)

## Article should be restored to a link

Prior to 2012 this article was merely a link to Material conditional. (Actually it should be the other way round: logicians usually refer to this logical operation as material implication.) Then some creative editor dreamed up the idea that material implication must be a rule of inference. This is simply false. Material implication, also known as classical implication, is a logical connective that is distinguished from other implications (such as intuitionistic implication and relevant implication) by virtue of satisfying Peirce's Law. When interpreted in two-valued logic material implication P → Q is false when P is true and Q is false and otherwise is true; as such it is equivalent to not-P or Q when negation and disjunction are present. Wikipedia should not be promoting the misleading idea that material implication is a rule of inference, which has no basis in logic. Vaughan Pratt (talk) 20:35, 21 October 2013 (UTC)

I'm afraid this is a rule of inference, although (I believe) rarely under the name "material implication". — Arthur Rubin (talk) 10:46, 23 October 2013 (UTC)i
On the contrary what you're referring to is a logical equivalence. Every logical equivalence vacuously gives rise to a derived rule of inference in which either side of the equivalence can be substituted for the other. Because it is vacuous one never dignifies any particular logical equivalence as a rule of inference in its own right. Conversely no rule of inference that has its own name gives rise to a logical equivalence. You will not find any reputable source that refers to this particular logical equivalence as a rule of inference. Furthermore material implication is neither a logical equivalence nor a rule of inference, it is an operation and it is simply wrong to call it anything else. Vaughan Pratt (talk) 20:56, 28 October 2013 (UTC)