# Talk:Strict conditional

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## August 2005

The article stated: "In logic, a strict conditional is a material conditional that is acted upon by the necessity operator from modal logic".

While that is one way to view it, it is contrary to the history.

C. I. Lewis' original modal logic systems had Possibly, not Necessity, as basic.

Lewis (like J. Barkley Rosser) defined material implication [ p implies q ] as ~(p&~q). (It is not the case that p is true and q otherwise). And he defined strict implication as ~M(p&~q) (It is not possible for p to be true and q otherwise).

So... I did a reword.

-- [[User:Nahaj] Nahaj 2005-08-25

## Is the moon made of cheese?

I think that the example shown in this paper is slithgly misleading. The statement “the moon is made of cheese” used as the antecedent of all conditionals is typically false in all possible worlds that many are inclined to consider. While some people might believe that the moon is made of blue cheese, still this choice obscures the fact that strict conditionals can be used for facts that are assumed false but that would be more believable. For example, that the cervus elaphus canadensis is extinct is currently believed true, but yet one can consider the contrary as an actual possibility. I think that changing the antecedent to something that can be possible or not would improve the article. Suggestions? Comments? Paolo Liberatore (Talk) 18:58, 28 September 2005 (UTC)

Just a cultural note: I think possibly some subtle history is being missed here. When this issue was discussed after Principia Mathematica, by people that objected to the "material implication" given in it, "The moon is made of cheese" was the traditional example used in the discussions of what implication (or strict implication) should be. (And you see it sprinkled throughout papers in the early nineteen thirties.) Given some seventy years of tradition, I can fully understand why it was there. Nahaj 14:27, 27 October 2005 (UTC)

A question: what was the consequent used in the classical example? I mean, "if the moon is made of cheese then ..."? Paolo Liberatore (Talk) 20:05, 27 October 2005 (UTC)

To be honest, I don't remember. It would have to have been something true only by form. (It would not surprise me if it were 2+2=4). I'll be going back through some papers of the time next month, when I stumble over it I'll drop a note here. (: I assume you have a watch on the page. :) I think, by the way, that reading the papers of the time is a real eye opener on how far logic has come, and how the direction has changed. For example, Lewis' original papers on strict implication appeared mostly in "The Journal of Philosophy, Psychology, and Scientific Methods" and in "Mind; A quarterly review of Psychology and Philosophy", but most modern logicians probably don't consider Psychology the right forum. (And even as late as 1962 Anderson and Belnap's Journal of Symbolic Logic paper "A pure Calculus of Entailment" was funded in part by the [U.S.] office of Naval Research's Group Psychology branch. Nahaj 03:17, 28 October 2005 (UTC)

Not quite the reference you want... but close: "Implication and the Algebra of Logic" C. I. Lewis in Mind, New Series, Vol. 21, No. 84. (Oct., 1912), pp. 522-531. This is in a conjunction, making a point about implication. But, in 1912, it shows it was a standard example. (Nahaj)

Thanks for the reference. Yes, I have this page on my watchlist. Paolo Liberatore (Talk) 13:52, 28 October 2005 (UTC)

So far, what I've found is that around 1900 "The moon is made of green cheese" was the "canonical" example of a false statement, and used almost any time a false statement was needed for a discussion. The first use I can find of the use in the manner of the "Strict conditional" page example was in "On the Extension of the Common Logic", by Henry Bradford Smith in "The Journal of Philosophy, Psychology and Scientific Methods" Vol. 16, No. 14. (Jul. 3, 1919), and the consequent was "The angle-sum of a triangle equals two right angles". The consequent used varies over time and author, generally getting simpler over time. 2+2=4 starts appearing much much later. (And therefore probably can't be considered "classical" :) I assume that this answers your original question, and I'm not going to bother to research any further. Nahaj 16:50, 28 October 2005 (UTC)

## corresponding conditional

Edited definition/explanation & added link to main article. No need to say more about corresponding conditionals in this article, if indeed there is a need to mention them here at all. A bit off-topic really, I would have thought. --Philogo 23:05, 13 October 2008 (UTC) (84.100.243.3 (talk) 23:12, 1 March 2010 (UTC))

(Jean KemperN (talk) 05:03, 17 March 2010 (UTC))

## Logical hexagon

I have created an article for Logical hexagon and refactored a large amount of material contributed byUser:Jean KemperNN. The material is wonderful, but I think it is more appropriate in its own article.Greg Bard (talk) 22:59, 14 November 2010 (UTC) (Jean KemperNN (talk) 02:00, 31 December 2010 (UTC))http://www.grammar-and-logic.com/dossiers.php (Jean KemperNN (talk) 02:04, 31 December 2010 (UTC))http://erssab.u-bordeaux3.fr (Jean KemperNN (talk) 02:07, 31 December 2010 (UTC))(cf. here) —Preceding unsigned comment added by 79.90.42.155 (talk) (Jean KemperNN (talk) 16:33, 1 January 2011 (UTC))Greg Bard thinks that the logical hexagon of Robert Blanché is something interesting. He evokes "a wonderful material". In my opinion, the substitution of the logical hexagon for the traditional square will render more understandable the problem of strict implication. (79.90.42.155 (talk) 19:59, 1 January 2011 (UTC))(Jean KemperN (talk) 20:01, 1 January 2011 (UTC)) (84.100.243.244 (talk) 18:36, 9 January 2011 (UTC))(84.100.243.244 (talk) 09:03, 28 January 2011 (UTC))

## Why this?

Why does the article say, 'it is clearly not the case that 2 + 2 = 4 if Bill Gates graduated in medicine'? It seems to me that it clearly is the case. Ocanter (talk) 02:01, 29 April 2011 (UTC)

## Full Revamp

I have completely revamped this page to reflect better the aspects of strict conditionality. I have included sections on related strict conditionals, equivalencies to the strict conditional, distinctions between the strict conditonal, material conditional, and logical implication, and the work of C.I. Lewis on strict conditionals. I have included detailed citations with page numbers. Considering the incomplete coverage and the unorganized, uncategorized layout of the former page, I think the new page will be greatly welcomed. Hanlon1755 (talk) 07:12, 19 December 2011 (UTC)

Given the discussion at Wikipedia:Articles for deletion/Strict conditional, I think it's better to resolve some of the issues of fact here on the talk page BEFORE modifying a stable article that has broad consensus. In particular, I believe you're misunderstanding some of the key concepts, and conflating different meanings of the phrase "conditional statement." -- 202.124.72.22 (talk) 09:39, 19 December 2011 (UTC)
You aren't saying what exactly is the problem. What EXACTLY is the problem here? Unless you can adquately give me a real, concrete concern, YOU shouldn't modify the article! ALL my FACTS are backed up with very notable, respected, published references! So, what is your concern? Maybe I can fix your concerns here. Hanlon1755 (talk) 09:49, 19 December 2011 (UTC)
I also want to point out that my revision does not contradict anything that was previously in this article, so I am not "disputing" anything that was already in the article. I have simply added detail to make the article easier for others to understand. 202.124.72.22 (talk) believes I am conflating different meanings of the phrase "conditional statement." I strongly disagree; my editions have made clearer the difference between *strict* conditional statements and *material* conditional statements. Notice how "strict" and "material" are adjectives that modify the noun phrase "conditional statement." There are several different types of "conditional statements" ("conditionals"), what my work has done is make the difference clearer and easier for the reader to understand. What EXACTLY are the "key concepts" you believe I am misunderstanding? Please point out EXPLICITLY the sentences in my revision. Hanlon1755 (talk) 10:40, 19 December 2011 (UTC)
I think anyone can see that you've completely changed the meaning of the article, which is supposed to be about strict conditionals ${\displaystyle \Box (p\rightarrow q)}$. 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'm still waiting for you to give an EXPLICIT sentence in my revision that you believe is wrong! Hanlon1755 (talk) 11:21, 19 December 2011 (UTC)
• Both of you, please stop edit warring. I've asked for input from WikiProject Philosophy. Fences&Windows 21:05, 19 December 2011 (UTC)
(I was in the middle of writing this, sorry I will stop "warring" now.) Anyways, you seem to be confused because I am not using the notation ${\displaystyle \Box (p\rightarrow q)}$ right from the beginning. To clear up your concern I have added that notation, a type C.I. Lewis originally used, to a new equivalency, (2.), in the introduction of the article. It is important that you realize that today not everybody uses that notation. I have my references to back me up on that one. 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. On the discussion at AfD: I hope you realize that *I* was the one to withdraw the nomination. I did not withdraw it because I was wrong about some element of the content (which I was NOT); I withdrew it for organizational reasons. The editors of the AfD discussion are not "strongly against" my "suggested alternate article." Anybody can see in there that the editors are strongly against DELETING the article, not REVISING the article. There is a BIG difference there. And about your "PhD" in "logic": I really don't care. I don't need a PhD in logic to know a contradiction when I see one, as I see between your claims and mine on this very page. At this point I have addressed all of your concerns. But if, somehow, you still think something is "strongly" wrong, remember: I'm still waiting for that EXPLICIT sentence! Hanlon1755 (talk) 21:09, 19 December 2011 (UTC)
The AfD discussion speaks for itself. As to explicit errors, your whole "Variations of the strict conditional" section mixes up wording for strict conditionals (which are necessary) and wording for ordinary conditionals (which are not). Several of your cited sources are not about strict conditionals (and yes, I have checked them). Your "logical equivalences" section is incorrect, since you have dropped the modal operator on the conditional. There are other errors and instances of confusing wording; the original article was simply much better. -- 202.124.75.203 (talk) 23:43, 19 December 2011 (UTC)
You are now vandalizing the page since you broke the armistice, as ClueBot NG has confirmed. You are misunderstanding the AfD discussion. The consensus of the AfD discussion, which was agreed upon even by me, was that the page "Strict conditional" would not be deleted. Read the discussion again because you are not reading it correctly. Part of the agreement was that I recommended merging the two articles. I originally recommended merging "Strict conditional" into "Conditional statement (logic)," as I even say in the discussion, but have since decided the opposite merger would be better for the sake of organizing the content of the articles. Nobody in the discussion objected to that. That is very clear. You said you have checked the sources: you obviously aren't checking well enough. You seem to be overcome by subjective bias from the AfD discussion rather than rationally accepting the cited sources. 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. Furthermore, my "logical equivalences" section is not incorrect, as you claim, since I am using a different notation than the type you seem to be accustomed to. You then claim that "there are other errors and instances of confusing wording." I do not see any errors or instances of confusing wording, but if you have caught one: Please, explicity write down the sentence in this discussion so that the matter can be resolved here. Hanlon1755 (talk) 00:30, 20 December 2011 (UTC)
No, 202.124.75.203 is not vandalizing. Hanlon, the wholesale replacement of this article's text with your version is not an option:
Anybody can see in there that the editors are strongly against DELETING the article, not REVISING the article. There is a BIG difference there.
The consensus was clearly in favor of keeping this article. You're welcome to revise it by incorporating some of your text… However, please don't editorialize about “popular misconceptions”, the prior text explained the distinctions you seem to be concerned about much more clearly. You repeatedly cite the same page ranges for claims surrounding that, but those which I was able to review online failed WP:V. I couldn't find either of the Larson, Boswell, et. al. but these appear to be two editions of the same high school Geometry book, so perhaps it's better not to read so much into it? It would seem that there were some “other errors and instances of confusing wording”, but that's neither here nor there now.—Machine Elf 1735 03:33, 20 December 2011 (UTC)
You guys are terribly misinterpreting the AfD discussion. The editors of the AfD discussion were writing because they did not want to have no article, whatsoever, at Strict conditional. I now agree, strongly, with their position. I agree my decision to nominate the page was a stupid move, but the resulting discussion should not be taken as evidence that the article should not be modified. That's not what they mean. That's not what I mean, either. I believe it's incomplete. 202.124.75.203 (talk) is just confused, as are two editors of the Afd discussion, because I am using notation in the article that they are not accustomed to. I have since addressed those concerns. I will point out that the old version was just as bad at talking about popular misconcpetions by talking about "The paradoxes of material implication." In fact, I will merge the information about the paradoxes of material implication into my revisions. That way the article will be as complete as it possibly can be, since I did not previously mention it in my revisions. Everything else from the old article would just be redundant if I were to merge it into my revisions. Hanlon1755 (talk) 06:04, 20 December 2011 (UTC)
I think it's clear that the consensus here is AGAINST the wholesale removal of the original article. The obvious thing to do is to roll back to the original article, and for you to argue for specific changes, as per WP:BRD. -- 202.124.74.104 (talk) 09:06, 20 December 2011 (UTC)
I have addressed every concern that has been brought to my attention. It is clear you are not taking the time to actually read and appreciate the positive contributions I have made to the article. Most importantly for your case, I recommend that you realize that the strict conditional IS in fact the "ordinary conditional" we are so familiar with using. The ordinary conditional is not the material conditional; it is not some other type of conditional. It is the strict conditional. Please, I ask you from the bottom of my heart, read my contribution and realize this. Your understanding of this will change the way you think of conditional statements. Once you understand this, you will be truly enlightened. Hanlon1755 (talk) 09:44, 20 December 2011 (UTC)

This article has recently undergone massively large changes, without any preliminary discussion or review. I would request that subject matter experts in this area review these changes. --Hobbes Goodyear (talk) 06:08, 20 December 2011 (UTC)

## BRD Process

As requested, and in order to reach agreement, I have began the BRD Process for this article. I am proposing to modify the article 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. Hanlon1755 (talk) 17:42, 20 December 2011 (UTC)

Probably some of the information you've added is usable, but every single line you've entered violated WikiFormat guidelines. Propose changes here, before adding. — Arthur Rubin (talk) 18:08, 20 December 2011 (UTC)
Also, the truth table should not be here, as it's not truth-functional. — Arthur Rubin (talk) 18:09, 20 December 2011 (UTC)

## Proposing Changes

As discussed in previous sections "Full Revamp" and "BRD Process," I propose that the article be changed as outlined by the BRD Process I am currently running. Requesting input from other users. Hanlon1755 (talk) 18:11, 20 December 2011 (UTC)

You've been bold, been reverted. Now start discussing here. — Arthur Rubin (talk) 18:21, 20 December 2011 (UTC)
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)
I am a mathematician, with few knowledge in logic, but I have heard several talks in mathematical logic, especially about formal proofs. Here are some comments on the two versions.
• Both versions are difficult for a non logician. In both, an introduction is lacking, explaining the differences between the various conditionals. The reader should not be supposed to know or to learn what is a "material conditional" before reading the third line of the article. From this point of view Hanlon1755's version is the worst one.
• Hanlon1755's version begin with by "In ... mathematics ... a strict conditional is ...". This seem a wrong assertion: In mathematics there is not one logic, but many (first order or higher order logic, intuitionistic logic, logic with or without modus ponens, ... ). In none of these logic, the terminology of "strict conditional" is used. Thus, "in mathematics, the strict conditional is ..." appears to be a non sense.
• It is clear from the last Hanlon1775's edit, that he want to include his own original research in this page. This not acceptable unless he will provide a reliable citation for each change.
D.Lazard (talk) 20:07, 20 December 2011 (UTC)
Hanlon1755's basic premise is also wrong, and hence the additions are not acceptable. The ordinary (material) conditional, as in "Felix is a mammal ${\displaystyle \rightarrow }$ Felix is less than 10 metres tall" (true in our world, but not necessarily true) is not the same as the strict conditional "${\displaystyle \Box }$ Fred is an unmarried man ${\displaystyle \rightarrow }$ Fred is a bachelor" (necessarily true by definition). In mathematics, ordinary conditionals are not strict conditionals because they may contain free variables, e.g. "x is odd ${\displaystyle \rightarrow }$ x is prime" is true in a context where 1 < x < 9, but not necessarily true. However, if a variable-free mathematical statement is true, then it is necessarily true. -- 202.124.75.120 (talk) 22:20, 20 December 2011 (UTC)
Hanlon, rather than proposing change, you might want to try an approach wherein you propose a contribution to the article that you'd like to make.
“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.
We are trying to be helpful, but you're asking us to do so by not interfering. Declined: your efforts/proposals are still ‘not an option’. Perhaps you're not interested in making a contribution that has a lesser impact?
Original research is unwelcome, so to the extent we can say instead, that you've arrived at a synthesis (one you no doubt find compelling, but nevertheless…) on the surface, it seems peculiar to your own experiences, if not simply wrong. Please see http://plato.stanford.edu/entries/conditionals/ for a more circumspect treatment.
Ideally, an article can include more advanced material while remaining accessible to high school students. Perhaps you could develop a section with a suitable treatment of the material you deem appropriate? You can supply any verifiable information that was omitted by your teachers. Please do so without editorializing on how common, confusing or regrettable it might be for a student to find themselves in the “same boat”. Per WP:NPOV, all readers must be allowed to draw their own conclusion in matters of opinion, regardless of how challenging that may be. Please be advised that editors have commented on the inadequacy of your sourcing, but with proper attribution, it needn't necessarily be a problem if you prefer to focus on a single point of view. It will, however, preclude rewriting the entire article (for example).
Believe it or not, we're here to help… building the encyclopedia is a collaborative effort.—Machine Elf 1735 23:08, 21 December 2011 (UTC)

## Clarification

I have added a brief paragraph at the end of the article which may clarify the confusion: only conditionals which are tautologies are automatically strict conditionals. -- 202.124.73.25 (talk) 03:42, 22 December 2011 (UTC)

ALL conditional statements, whether true or false, are strict conditionals. I don't know where you got the notion that YOU somehow can just change the page, while I for some strange reason can't, but you did not discuss that change here on the talk page before making it. And sadly, I am apparently the more experienced one on the subject. The article still says nothing about hypothesis and conclusion, the basic, fundamental parts of a strict conditonal. The article also seems to have this theme that strict conditionals cannot be expressed in "if-then" form; in fact, it doesn't even say that's true anywhere, even though its a very important part of the strict conditional. The article instead has this underlying tone that "if-then" form is reserved for only material conditionals, which isn't true! In fact, some material conditionals are not even worthy of "if-then" form! The article is still very misleading, and I do not approve of this. I still would like at least some of my additions to be put on the page. Hanlon1755 (talk) 06:44, 23 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)
"Combining material from multiple sources to reach or imply a conclusion not explicitly stated by any of the sources", is not only original research but is also synthesis of published material that advances a position. Logical consequences can not be a justification to contribute what one wants. Just because one person feels there is a logical consequence does not mean this hypothesis is shared. I would argue, with the backing of consensus, that a "logical consequence", without supporting evidence, is conjecture and original research at it's best.
If content in an article is wrong then find the source that supports the position you are presenting. If you can not find a source that supports your position then conclusions can be reached that; 1)- Your position is not notable, or 2)- Your position is actually original research.
The last may be a problem spread over several articles. I have noticed a trend to use only general references. While this sometimes works it leaves an article vulnerable to multiple tags including verifiability. Content that is supported should be attributed.
You stated, "All my edits were cited", and this simply is not true. An editor could tag every single line that is only supported by a general source as, except for the one reference, text-source integrity is nonexistent. Content that is supported should be attributed.
I mention all this for a reason: Consensus is a fundamental process in building Wikipedia. The policy on verifiability is supported by 1874 editors (966 anonymous users) and has a section concerning material that is challenged that states, "...any material challenged or likely to be challenged must be attributed to a reliable published source using an inline citation." . The Wikipedia essay Inline citation section "When you must use inline citations" gives a further explanation of, "Any statement that has been challenged (e.g., by being removed, questioned on the talk page, or tagged with [citation needed], or any similar tag)" , and further this applies to material likely to be challenged. 128 edits and this talk page proves that a lot of material was and is challenged yet there is only one attributed reference.
Concerning other editors mistakes; If "there are multiple sources here that have the conditional statement wrong" then there should be a source somewhere that corroborates a correction. If any editor has an issue with content then tag such content and work towards corrections, as material that is referenced must still be included with implied or agreed upon consensus.
Conclusion: Providing information that is not original research, which means referenced, will last longer on Wikipedia. At some point some editor will challenge content that is not verifiable and at some period (after that point), the content will either have to be referenced or likely be removed. What good will all this have accomplished then? Please be advised that referenced material in no way means content does not have to pass consensus if challenged.
I will be adding a multi-tag because there are issues that need to be resolved including the sources and one reference listed. The article is listed as a "start class" but is really only a stub and needs work. I would hope that that a good article is more important than contributing original research. Otr500 (talk) 00:09, 26 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 12:00, 15 January 2012 (UTC)

## The definition of strict implication given at the beginning of the article is the definition adopted by scholars and must be respected as such

(84.100.243.150 (talk) 15:11, 8 September 2012 (UTC)) (84.100.243.132 (talk) 08:29, 14 August 2012 (UTC)) In logic, a strict conditional is a material conditional that is acted upon by the necessity operator from modal logic. For any two propositions p and q, the formula (p → q) says that p materially implies q while L (p → q) says that p strictly implies q.

L (p → q)and ~M (p & ~q)are equivalent expressions. They represent the strict implication of q by p not only in the articles of wikipedia but also in excellent authors like the John Lyons of Semantics 1. For this reason, I subscribe without hesitation to what Arthur Rubin writes below: It may be that you have a different definition of the strict conditional, but, unless it is published, it has no place in the Wikipedia article. — Arthur Rubin (talk) 09:54, 4 September 2012 (UTC) on, search

The definition of strict implication adopted by the contributors of wikipedia and by John Lyons says that p strictly implies q ,if we have L (p → q) or ~M (p & ~q), the latter expression being to be read It is im-possible to have together p and not-q.

L (p → q) and ~M (p & ~q) are equivalent expressions. According to De Morgan's laws, p → q means ~ ( p & ~q). In effect, the material implication of q by p, p → q signifies that one cannot have together p and not-q. p → q signifies therefore that one of two things, either p&q or ~p. For all three conjunctions: p&q, ~p & q, ~p & ~q obviously exclude p & ~q. p&q contains ~ ( p & ~q) and therefore p → q, ~p&q also contains ~ ( p & ~q) and therefore p → q, ~ p & ~q also contains ~ ( p & ~q)and therefore p → q.

In wikipedia and John Lyons, L (p → q) as as well as p ⇒ q symbolizes the strict implication , that is, the material implication p → q acted upon by L the necessity operator from modal logic. If in L (p → q), we replace p → q by the equivalent ~ ( p & ~q), we first obtain L ~( p & ~q) to be read It is necessary not to have the conjunction of p and not-q. It is clear that the necessity not to have is equivalent to the im-possibility to have Thus, instead of L ~( p & ~q) we can write ~M (p & ~q) to be read It is im-possible to have together p and not-q.

## The definition of strict implication given at the beginning of the article is perhaps insufficient

First remark: to define the strict implication by saying that it is equivalent to ~ M (p & ~q) is deficient in that the impossibility to have both the fact p and the fact not-q may result from the fact that p is im-possible and not from the fact that p is the cause of its effect q. If we have ~Mp i.e L~p, if p is im-possible, in other words if not-p is "necessary", if not-p is certain, it is im-possible to have p & q as well as p & ~q. ~Mp may be represented by the combination: ~ M (p & q) & ~ M (p & ~q). Therefrom, it clearly appears that ~ M (p & q) and ~ M (p & ~q) are not at all in-compatible. Both are true propositions if p is im-possible. Hence the necessity of adding Mp to ~ M (p & ~q)to eliminate the spectre of ~Mp.

But if the first two elements ~ M (p & ~q) and Mp are necessary, they are not sufficient.

Associated with ~ M (p & ~q), the second ingredient Mp eliminates the direful spectre of ~Mp im-possibility of p, that is, L~p certainty of not-p. To be able to say that a fact p is the cause of a fact q, it is evident that the fact p must be thought possible. How could we think that p has an effect q if p is said to be im-possible from the start ?

It is no less clear that if the fact q is certain in any case, whether p is the case or not-p is the case, it is absolutely im-possible to think that the certainty of the fact q is the effect resulting from the fact p exclusively. ~p → M~q is an expression saying that not-p implies M~q the possibility of not-q. Associated with the conjunction ~ M (p & ~q) & Mp, the expression ~p → M~q efficiently eliminates the second state of things incompatible with the strict implication symbolized in good authors like John Lyons by p ⇒ q wrongly held to be equivalent to ~ M (p & ~q).

— Preceding unsigned comment added by 84.100.243.132 (talk) 08:43, 14 August 2012 (UTC)

Note: the posting was refactored by 84.100.243.70 (talk · contribs) after Arthur Rubin’s reply. Why such people do not spend one minute to register an account? Incnis Mrsi (talk) 10:05, 1 May 2013 (UTC)
This no sense makes. Nor, as far as I can tell, does the blog mindnewcontinent. — Arthur Rubin (talk) 08:45, 3 September 2012 (UTC)

(84.100.243.70 (talk) 21:26, 12 September 2012 (UTC))

KNOLmnc 1 Something new about Maimonides’ Treatise on logic. On a difference between the canonical text of the Treatise on logic and the three Hebrew translations.

Shalom

Jean-François Monteil

Dear Sir, I answer. If p implies q strictly,if p ⇒ q, to use John Lyons'symbolization, p ≡ Lq to use mine that is to say if p is equivalent to the certainty of q, we have of course ~ M (p & ~q) the impossibility to have together p and not-q. But of itself ~ M (p & ~q) the impossibility to have together p and not-q is not equivalent to p ⇒ q (or p ≡ Lq). For ~ M (p & ~q) may result from ~ Mp, the impossibility of p. For if p is im-possible, it is impossible to have the conjunction of p and q, to have the conjunction of p and not-q as well. The impossibility of p: ~ Mp can be represented as ~ M(p & q)& ~ M (p & ~q). So, if you want to avoid ~ Mp, you must associate Mp with ~ M (p & ~q).

But if this addition of Mp is necessary, it is not sufficient. It is clear that if the fact q is certain in any case, whether p is the case or not-p is the case, it is absolutely im-possible to imagine that the certainty of the fact q results from the fact p exclusively. Lq, the certainty of q is equivalent to ~M~q, the im-possibility of not-q. If not-q is impossible, that means that you cannot have the conjunction of not-q and p and you cannot have the conjunction of not-q and not-p either. ~M ~q is equivalent to ~ M (p & ~q)& ~ M (~p & ~q). Once again, the insufficient ~ M (p & ~q) appears. What I call the third ingredient ~p → M~q signifies that not-p implies the possibility of not-q. So is eliminated the state of things corresponding to the potential fact that q should be certain in any case, whether p is the case or not-p is the case. The certainty of q, if it is to manifest itself, must be something resulting exclusively from p. Cordially. Jean-François Monteil — Preceding unsigned comment added by 86.75.111.62 (talkcontribs)

"If p implies q strictly,if p ≡ Lq " is wrong. If p → Lq, for some modal logics, it follows that L (p → q), which is one of the formulations of the strict conditional.
~p. M → M~q is not grammatically/syntactically meaningful.
It may be that you have a different definition of the strict conditional, but, unless it is published, it has no place in the Wikipedia article. — Arthur Rubin (talk) 09:54, 4 September 2012 (UTC)

All right, I submit. I must wait. Jean-François Monteil — Preceding unsigned comment added by 84.100.243.70 (talk) 12 September 2012

KNOLmnc 1 Crucial importance of the bilateral possible M(p), the third contrary fact represented in the logical hexagon of Robert Blanché applied to modal logic. KNOLmnc 1 Traité de logique modale KNOLmnc 1 About the main problem of modal logic. A formula of the strict implication of the fact q by the fact p: p ≡ Lq. The three ingredients of strict implication and particularly: ~p. M → M~q, the third one. p ≡ Lq seems to be the formula... KNOLmnc 1 The three elements of p ≡ Lq, the strict implication of q by p. The definition to be found in the John Lyons of Semantics 1 must be drastically critized.

(86.75.111.166 (talk) 06:58, 1 May 2013 (UTC))

Please, place the signature after your posting. How this message justifies insertion of a poorly formatted chunk of text loaned from the mindnewcontinentfrenchcorner.wordpress.com website? It is off-line currently (slashdot effect?), but I do not think that Google deceives me about the origin of the problematical text. Incnis Mrsi (talk) 10:05, 1 May 2013 (UTC)
BTW, could you first improve the fr:Implication stricte article? I do not understand what do you propose; maybe I will able to understand better something in French (English and French are equally non-native languages to me). Incnis Mrsi (talk) 10:13, 1 May 2013 (UTC)

Dear Incnis Mrsi, go to the entry implication stricte, then go to afficher l'historique and click on (actu | diff) 15 février 2012 à 13:42‎ 84.101.36.154 (discuter)‎ . . (9 321 octets) (+8 461)‎ (défaire). Thus, you'll get what I write about the three ingredients of implication stricte:(1) ~M (p & ~q) (2) Mp (3) ~p. M → M~q. The second ingredient Mp eliminates ~Mp; the third ingredient ~p. M → M~q eliminates Lq. Both ~Mp and Lq contains the first ingredient ~M (p & ~q)and the point is to eliminate ~Mp and Lq to obtain p ≡ Lq. ~M (p & ~q) alone cannot represent the strict implication of q by p, since clearly ~M (p & ~q) is compatible not only with p ≡ Lq but also with ~Mp and Lq. (86.75.111.166 (talk) 16:58, 2 May 2013 (UTC)) Jean-François Monteil — Preceding unsigned comment added by 86.75.111.166 (talk) 16:52, 2 May 2013 (UTC)

You confuse something. There were no edits in February 15, 2012. But I found the version of February 12. Is it your proposal? Incnis Mrsi (talk) 17:17, 2 May 2013 (UTC)
Your sneaky habitude to alter old postings is boring, Mr. Jean-François. Your habitude to make lengthy explanations of a simple thing expressed in only 8 digits is also boring. I hope, this is the text you refer to. I would not log off nor change my user preferences in fr.wikipedia (I never use Paris time) because you are not smart enough to specify a direct URL. Incnis Mrsi (talk) 18:03, 2 May 2013 (UTC)
Thanks, now I understood your point. You assert that The True Strict Conditional is not □(p → q), but something even stronger, which can be false if p is impossible. The answer is… not surprisingly… no.

Wikipedia is not interested in redefinition of already established concepts, at least while a redefinition attempt is not backed by serious researches published in peer-reviewed journals. Sorry, unless you can demonstrate a peer-reviewed paper where the “strict conditional” can be false for an impossible antecedent, your essays have not any chance in the article. Incnis Mrsi (talk) 18:44, 2 May 2013 (UTC)

Je m'en fous !

Jean-François Monteil

(86.75.111.166 (talk) 21:46, 2 May 2013 (UTC)) URLs redacted as not being helpful to anything — Arthur Rubin (talk) 01:04, 16 August 2013 (UTC) — Preceding unsigned comment added by 79.90.42.217 (talk) 21:16, 30 July 2013

Bon soir, Mr. Monteil. Votre nouveax sites personels? Incnis Mrsi (talk) 21:34, 30 July 2013 (UTC)

Although I agree that this article should be deleted, as it is part of the modal logic subject, thus it is a fragment of it. Please use the unicode decimal #10621 to write ${\displaystyle \Box (p\implies q)\equiv }$ pq. While this article is either fixed or deleted. — Preceding unsigned comment added by 189.140.161.209 (talk) 00:16, 2 декабря 2012 (UTC)