Testwiki:Articles for deletion/Conditional statement (logic)

The following discussion is an archived debate of the proposed deletion of the article below. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review). No further edits should be made to this page.

The result was not deleted. Despite its likely origin as a content fork, the article has now been set out to cover a different scope as strict conditional. The discussion below has also come to an agreement that while the article should not stand as is, deleting the page altogether is not the best solution, with most arguing for "deletion" actually meaning to turn it into a disambiguation page. Therefore, I believe that in this situation, deletion is obviously not the correct outcome, and the decision about the future of the page has become a pure editorial dispute which is beyond the remit of AfD. Editors involved in this deletion debate should continue to discuss constructively about the future of this page. Deryck C. 16:43, 23 January 2012 (UTC)

Conditional statement (logic)

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The author is competing with the Strict conditional article and had previously nominated that article for deletion. The discussion closed with the intent to make this a redirect to Strict conditional. Several editors have commented on verification problems, inclusive of all the sources cited, falsely supporting the author's admitted synthesis (or WP:OR). Please see the December 2011 discussions at Talk:Strict conditional and Talk:Material conditional. —Machine Elf ¹⁷³⁵ 04:50, 15 January 2012 (UTC)

Note: This debate has been included in the list of Philosophy-related deletion discussions. Machine Elf ¹⁷³⁵ 05:10, 15 January 2012 (UTC)

Strong keep. I am disturbed by this nomination. Almost all of the information in this article cannot be found in the article for the strict conditional. The article on the strict conditional says nothing about if-then form, other forms of expressing conditional statements, converses, inverses, contrapositives, when conditional statements are true and when they are false, and the comparisons of conditional statements to entailment. The missing information is very important to the topic and should not be deleted. All this information, which is in the current article, needs to be preserved. Also, the article under the given name is very noteworthy; many published sources refer to conditional statements and not "strict conditionals." This includes many of the cited sources on the current page. Many people will therefore be confused to references to strict conditionals when they are inquiring about conditional statements. At worst, this article should be merged with the article on the strict conditional. Hanlon1755 (talk) 05:38, 15 January 2012 (UTC)

• Keep per Hanlon 1755, and improve and expand as needed. Why should we delete a broader article with a broader and more common name, in favor of a narrower article with a less likely search term? Cullen³²⁸ Let's discuss it 08:52, 15 January 2012 (UTC)

WP:V? Machine Elf ¹⁷³⁵ 09:04, 15 January 2012 (UTC)

I should clarify, as the user's statements are misleading, (and a mockery of the concerns expressed in the AfD he brought against Strict conditional). It is not true that the author's synthesis is “broader”, although it is muddled. Their version is explicitly intended to be a replacement for Strict conditional, the product of well over 7 years of collaborative editing. If you would please review the suggested discussions in the three articles in which these tendentious edits have been attempted, and note the comments from various users who have reviewed them and the supposed sources… perhaps you'll also notice the user was just as emphatic about “strict conditional” being the better name.—Machine Elf ¹⁷³⁵ 11:41, 15 January 2012 (UTC)

• Strong Keep Very notable item. Totally encyclopedic, and distinct from Strict conditional. And a simple fact to see for any logician. History2007 (talk) 15:09, 15 January 2012 (UTC)

That's very interesting as those who reviewed the material at the three articles came to distinctly different but no less obvious conclusions. Unfortunately, the user is not interested in collaborating, so I'm not sure I understand how an article expressly created as a WP:CONTENTFORK can, in fact, be maintained as a separate fiefdom. Conditionals in general have not simply been overlooked on WP… You're correct that they're not simply identical to the conditional in modal logic, confusingly however, you're arguing against one of the user's central contentions—a problem that remains evident in their article. Finally, I'll point out once again that the sources do not verify the author's admitted synthesis.—Machine Elf ¹⁷³⁵ 18:35, 15 January 2012 (UTC)

Note: This debate has been included in the list of Science-related deletion discussions. • Gene93k (talk) 20:03, 15 January 2012 (UTC)

I did not admit that my contribution was synthesis. I had actually argued against that claim. MachineElf is drawing too many similarities between this article for the "conditional statement (logic)," and the articles associated with the "strict conditional," that these similarities, especially considering what MachineElf alleges as synthesis, would constitute synthesis itself. Hanlon1755 (talk) 21:40, 15 January 2012 (UTC)

You can deny it all you want, but you described your WP:SYNTH/WP:OR in elaborate detail. I'm spoiled for choice; here's what I'm alleging you've "admitted" (though obviously refuse to acknowledge):

OK. I am proposing to modify the article, in the manner provided through BRD, in order to ensure its completeness, accuracy, clarity and nonconfusion for future readers, and applicability to the appropriate fields of study (not just non-classical logic as the old version had been). This notably includes those fields of study that are known to use strict conditionals whether implicitly or explicity, but with different notation, and that are taught in many high school mathematics courses. As a high school student a few years ago, I became confused by the Wikipedia articles on "conditional statements." I was led to believe that the "material conditional" was the usual type of conditional statement; the type I had learned about in high school geometry and in other high school mathematics courses including Algebra II, Precalculus, and AP Calculus. I held this false belief for four and a half years. It was only through my own concerns, efforts, and research that I discovered I was wrong. The conditional statement I had learned in high school was actually the strict conditional, not the material conditional, and not some other type of conditional. I want to prevent confusion in future high school students that may be in the same boat as I. I want to include the more basic, high school side of the story in the article. Please aid me in these efforts by accepting my proposed changes to this article. Hanlon1755 (talk) 19:20, 20 December 2011 (UTC)

Most of your edits are your original research; however, all "strict conditionals" and "material conditionals" can be written in if-then form. — Arthur Rubin (talk) 07:57, 23 December 2011 (UTC)

All my edits were cited. Every sentence I added was either explicitly stated in at least one source or was a logical consequence of what was explicitly stated in several sources. I have read the section on original research and understand that this may constitute orignial research (but it may not considering my conclusions are logical consequences and cannot be implied in any other way). If it does though, then that is really a shame because there are multiple sources here that have the conditional statement wrong. People are going to continue to be misled and possibly even hurt by this inaccurate content. I still recommend putting at least some of my additions into the article. Hanlon1755 (talk) 08:43, 23 December 2011 (UTC)

It was clearly explained to you thereafter that your edits did indeed constitute WP:OR. That didn't stop you from making the same false claims at Talk:Material conditional:

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)

Is this your synthesis "argument"? (Not addressing me at the time… you quote your high=school geometry book?):

I am going to quote directly from Larson, Boswell, et al. 2007, p. 80, where "conditional statements" are discussed: "Conditional statements can be true or false. To show that a conditional statement is true, you must prove that the conclusion is true every time the hypothesis is true. To show that a conditional statement is false, you need to give only one counterexample." The key phrase there is EVERY TIME, as in IN EVERY CASE THAT, as in IT IS NECESSARY THAT. Therefore "conditional statements," as Larson, Boswell, et al. 2007 show, are strict conditionals. Therefore, your claim that "ordinary conditionals" are not necessary is untrue. I agree with you that several of my cited sources are not about strict conditionals, but it's important to note that I have those sources cited because I need to depict accurately non-strict conditionals in order to give a clearer notion of the distinctions between non-strict conditionals, and strict conditionals.

So they avoid the word NECESSARY? I wonder why… As I've confirmed, none of your other sources support your claim, aka, the "similarities" I draw too many of:

I think anyone can see that you've completely changed the meaning of the article, which is supposed to be about strict conditionals $◻(p\to q)$. These are not the same as ordinary conditionals, and your references to Rosen and Larson, Boswell, et al, for example, are completely misplaced, since they are not discussing strict conditionals. The discussion at AfD should make you realise that the consensus of editors is strongly against your suggested alternate article, which is both incorrect and confusing. And since my PhD is in logic, I'm fairly confident of my position here. -- 202.124.72.122 (talk) 11:15, 19 December 2011 (UTC)

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.

You've also been edit warring to redirect Template:Diff to your article, as opposed to entailment, as well as links, validity, for example… Perhaps History2007 briefly said it best: “What is going on here? Where is the sense of logic in this Afd?”—Machine Elf ¹⁷³⁵ 00:35, 16 January 2012 (UTC)

And I will continue to deny it. Nowhere in your long rant do I admit that my contribution was synthesis. It actually shows me proposing an argument against the claim. Hanlon1755 (talk) 01:31, 16 January 2012 (UTC)

To appease MachineElf, I have removed all alleged instances of synthesis from the article. I think MachineElf will be much more content with the outline of the article now. All stated facts in the article can be found, in their explicit form, somewhere within the cited sources. Given that none of the cited sources at any point explicitly drew an identity between conditional statements and the strict conditional, I do not recommend merging this article with strict conditional since that would in fact constitute synthesis and original research. Neither do I recommend merging this article with material conditional for the same reasons. I recommend keeping this article as is, without deleting or merging it. Although I have yet to come across them, it's very possible there are sources somewhere that would allow this article to be enriched further. Hanlon1755 (talk) 02:34, 16 January 2012 (UTC)

• Comment: This is a clear case of WP:PolicyFailure. Ironically, there is no logic here, but a personal and emotional discussion. I will not comment on this further but suggest that you two guys ask on the project page for someone else to come and fix it and do not edit it yourselves. You will never agree. This is a "very simple" issue and there are far more complicated pages on mathematical logic which have better presentations. There is no need for fighting here. When a neutral party comes over (if ever) a brief mention of logical implication at the proof-theoretic level vs the issues from the model-theoretic perspective should be made. I will not watch this any more. I will just shake my head in disbelief now and walk away. History2007 (talk) 06:24, 16 January 2012 (UTC)

• Delete. The topic makes sense only as a dab page, covering Material conditional, Strict conditional, etc. The current material is a WP:CFORK of those articles. -- 202.124.73.101 (talk) 08:20, 16 January 2012 (UTC)
• Almost every generalization may be characterized as Content forking if one could delete something, not improve the Wikipedia. Of course, the notion of conditional ( ≈ logical implication ) does exist, although in the framework of mathematical logic some more precise definitions are required. BTW why "logical implication" redirects to entailment? Look at de:interwiki: there are both de:Implikation ( = logical implication, redirects back) and de:Konsequenz ( = logical consequence ≈ entailment ). And meanwhile conditional statement is a dab, although conditionals in programming are yet another variety of conditionals. So, I propose to kick a dab off "conditional statement", move the article there (together with de:Implikation interwiki link and "logical implication" redirect), and expand the article such that it will cover conditional (programming) too. Incnis Mrsi (talk) 10:22, 16 January 2012 (UTC)

  P.S. I just discovered such brilliant example of WP:CONCEPTDAB in mathematics as Triangle center. Note that is it an article, not a dab page. If we have an article even about such undefined notion as triangle center, then we necessarily ought to have "conditional statement". The basic thing it needs is a warning hatnote about unsuitability of inbound links from articles about logic. Incnis Mrsi (talk) 20:07, 17 January 2012 (UTC)

• For the time being, I can go along with the idea of deleting the page and replacing it with a disambiguation page, as Incis Mrsi suggests. What would be helpful (to me, at least) is (1) no more TLDR posts on the AFD page and (2) a list showing all the articles related to conditionals. We often run into this sort of situation when we have a group of articles on distinct but closely related topics - the titles end up being somewhat nonsensical because they developed organically. I hope to have time before this AFD closes to look in more detail, but the dab option seems like it is a good solution to the content fork. — Carl (CBM · talk) 12:55, 16 January 2012 (UTC)

  I do not offer to convert an article to a dab, at least because in such case we do not solve the problem with de:Implikation. We ought to bind it with some article, along with ru:Импликация and probably articles in several other languages which are currently bound with entailment (some via redirect from logical implication). I am not sure that, in each case of linking "condition" an so on, we will be able to choose a target article with scientifically strict definition (from a list like: strict implication, material implication, entailment, conditional (programming)…), and I hope that there are enough RSs to make a pretty good outline article about the thing known as conditional/implication. Incnis Mrsi (talk) 13:26, 16 January 2012 (UTC)

• Comment on my recommendation to keep. I don't think anybody here would agree that all conditional statements are truth-functional. Hardegree's Symbolic Logic: A First Course (2nd edition) (p. 42-43) is a good source which demonstrates this, but Barwise and Etchemendy (p. 178-179) also explains it. I therefore do not recommend merging this article with material conditional on the grounds that not all conditional statements are truth-functional. Neither do I recommend merging this article with strict conditional on the grounds that that would be a synthesis of the cited sources. Hanlon1755 (talk) 23:35, 16 January 2012 (UTC)
  • I'm afraid you've misunderstood Barwise and Etchemendy. In any case, the definition of conditional currently given in the article is equivalent to material conditional, to which a merge might be appropriate. -- 202.124.73.135 (talk) 23:37, 16 January 2012 (UTC)

That's quite an outlandish thing to say considering I have the quote at hand, "As a result, many uses of if. . . then. . . in English just aren't truth functional" (179). Furthermore, I direct you to p. 42-43 of Hardegree. Non-truth-functional conditionals are also studied in modal logic, as can be seen in Hardegree's Introduction to Modal Logic, p. I-9. To quote Hardegree, "The problem is that, in elementary logic, we have no means of writing down a nontruth-functional if-then connective. Modal logic provides that connective." Hanlon1755 (talk) 00:29, 17 January 2012 (UTC)

No, not “outlandish”, articles already exist for English usage, for example, Conditional sentence. Good job removing the WP:OR, but with “(logic)” in the title, it should be merged to material conditional. That is to say, any relevant verifiable material not currently in material conditional should be contributed there, as Template:Diff, at Talk:Strict conditional.—Machine Elf ¹⁷³⁵ 00:33, 17 January 2012 (UTC)

As I've said and cited, non-truth-functional conditionals are studied in modal logic. Modal logic is a type of logic. Therefore use of "(logic)" in the title is only appropriate. This article should not be merged with material conditional on the grounds that, as I've already discussed, not all conditional statements in logic are truth-functional. Hanlon1755 (talk) 00:59, 17 January 2012 (UTC)

That quote applies to indicative conditionals in English, not to propositions in logic, which the article is about. -- 202.124.73.130 (talk) 01:26, 17 January 2012 (UTC)

This article is about propositions satisfying which are "true if and only if the conclusion is true in every case that the hypothesis is true... false if and only if a counterexample to the conditional statement exists" (quoting the article). That is equivalent to the definition of material conditional. In particular, it does not refer to modal logic. -- 202.124.73.130 (talk) 01:30, 17 January 2012 (UTC)

Your conclusions, if true, would constitue synthesis. At no point on the cited pages do Barwise and Etchemendy ever use the word "indicative." Neither do the sources which contend that conditionals are propositions satisfying which are "true if and only if the conclusion is true in every case that the hypothesis is true... false if and only if a counterexample to the conditional statement exists" (quoting the article) state that such propositions are equivalent to the definition of material conditional. In fact, I actually disagree with that claim (although I can't write this in the article because that would be original research). I will quote Hardegree again about logical non-truth-functional conditionals, "The problem is that, in elementary logic, we have no means of writing down a nontruth-functional if-then connective. Modal logic provides that connective" (I-9). It is obvious from his quote that there are non-truth-functional conditionals in modal logic. He later on refers to such logical conditionals as "strict conditionals." But, as MachineElf and others (perhaps even you) had argued, almost all of the information currently in this article cannot be put into the article for the strict conditional because that would be synthesis and original research. It is evident given all of this that the information in this article is best situated where it currently resides: in this article. Hanlon1755 (talk) 02:13, 17 January 2012 (UTC)

Not so. Barwise and Etchemendy use the phrase "in English." They are therefore talking about English sentences (indicative conditionals, counterfactual conditionals, etc.) not propositions. This article is (or at least is stated to be) about propositions (i.e. material conditionals). Furthermore, your Hardegree quote makes it clear that conditional propositions are truth-functional. There are indeed non-truth-functional conditionals in modal logic, but this article is not about modal logic, and much of what this article says would be false if it was viewed as talking about modal logic. -- 202.124.73.130 (talk) 02:22, 17 January 2012 (UTC)

Barwise and Etchemendy use the phrase "in English," but this is not the word "indicative." They need to explicitly use the word "indicative," otherwise it is synthesis and original research. Logical propositions can very well be written "in English." For example, for propositions a and b, the English statement "a and b" corresponds to the logical conjunction of a and b, which is itself a proposition. This article is about propositions, as you say, but it is about general conditional statements in logic. Modal logic is therefore included, being a branch of logic. In logic, there are both truth-functional conditionals (e.g. material conditionals) and non-truth-functional conditionals (e.g. strict conditionals). But I have already discussed the problems involving merging this article with material and/or strict conditional. It's apparent the best place for this information is right where it now is. Hanlon1755 (talk) 02:48, 17 January 2012 (UTC)

Barwise and Etchemendy use the phrase "in English," meaning that they are talking about English sentences, not propositions. Mapping sentences to statements in logic is far from trivial. In fact, strict conditionals were invented as one way of doing so. However, given that the lede of this article (which you wrote) does not apply to modal conditionals, modal logic must be excluded. If this article was intended to be an overview of conditionals of every kind, it probably needs to be blown up so we can start over. -- 202.124.72.207 (talk) 03:34, 17 January 2012 (UTC)

Whatever the case may be about the phrase "in English," it is not and will never be the same as the word "indicative." The lede of this article applies to all logical conditional statements, so it therefore applies to modal conditionals. I see no need to blow up this article: the intent of the article to apply to all logical conditional statements is well written in the title and the lede. Hanlon1755 (talk) 03:47, 17 January 2012 (UTC)

The word "indicative" is not the issue. Material conditionals are propositions; indicative conditionals and counterfactual conditionals are sentences (which Barwise and Etchemendy are talking about); strict conditionals are statements in modal logic. Not the same thing at all. The statement you wrote in the article "A conditional statement is true if and only if the conclusion is true in every case that the hypothesis is true. A conditional statement is false if and only if a counterexample to the conditional statement exists" is a rewording of the definition of material conditional. Conditionals in modal logic are defined differently, using possible worlds. Furthermore, you used the standard notation for material conditionals in the article. What exactly did you intend this article to be about? -- 202.124.72.207 (talk) 03:58, 17 January 2012 (UTC)

202 is correct… Halon, you deftly removed your WP:OR (I was calling it synthesis to be charitable, but if you prefer OR… so be it). Just because your source doesn't say something, doesn't make it synth, because countless other sources would make it perfectly clear. For better or worse, I've added sourced NPOV statements and quotations expressing the issue. As you've been informed, your source doesn't adequately address it, feel free to remove your source if you think it's synth.—Machine Elf ¹⁷³⁵ 04:10, 17 January 2012 (UTC)

The statement I wrote in the article, "A conditional statement is true if and only if the conclusion is true in every case that the hypothesis is true. A conditional statement is false if and only if a counterexample to the conditional statement exists," is not equivalent to the definition of material conditional. Here's an example: Let p be "I am running" and let q be "I am running northwards." Suppose both p and q are true. I am running and I am running northwards. The material implication p -> q is true. It is of the form T -> T, which is T. This corresponds to the first row of the truth table for material conditionals. But the conditional statement p -> q is false: a counterexample exists. I could be running, but running southward instead. Seeing that the material conditional has a different truth value than the conditional statement, it follows that material conditionals are different from conditional statements. Hanlon1755 (talk) 04:54, 17 January 2012 (UTC)

Is that a joke? If you assume both p and q are true, there is no counterexample. -- 202.124.72.2 (talk) 06:27, 17 January 2012 (UTC)

Just because p and q are true doesn't mean that they are true all the time. It is possible for p to be true, but for q to be false (aka, it is possible for me to be running, but for me not to be running northwards). This possible world (example) is your counterexample. So the material conditional p -> q is true, but the conditional statement p -> q is false. Hence the fundamental difference between material conditionals and conditional statements. Hanlon1755 (talk) 07:45, 17 January 2012 (UTC)

Classic, I hope you don't mind if I quote you.—Machine Elf ¹⁷³⁵ 18:33, 17 January 2012 (UTC)

Go right ahead. I don't see anything wrong with that argument. Hanlon1755 (talk) 00:34, 22 January 2012 (UTC)

• Delete, verify that nothing links to it (other than talk pages), and recreate as a disambiguation page. As noted above, it's a WP:POVFORK of strict conditional, so there's nothing here which needs to be or should be kept. However, strict conditional, material conditional, and probably others are all examples of conditional statements in logic, and so should be retained as a disambiguation page. Similarly, Conditional statement (grammar) should be created as a disambiguation including indicative conditional and contrafactual conditional, and possibly other examples listed in conditional sentence. — Arthur Rubin (talk) 03:47, 22 January 2012 (UTC)
  • I agree with that. — Carl (CBM · talk) 04:51, 22 January 2012 (UTC)

The above discussion is preserved as an archive of the debate. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review). No further edits should be made to this page.