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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
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)
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))
I have created an article for Logical hexagon and refactored a large amount of material contributed by User: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 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)
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)
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)
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)
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)
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)
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)
( 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.
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).
Type on Google: mindnewcontinent.
— Preceding unsigned comment added by 84.100.243.132 ( talk) 08:43, 14 August 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 ( talk • contribs)
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))
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)
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
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 p ⥽ q. While this article is either fixed or deleted. — Preceding unsigned comment added by 189.140.161.209 ( talk) 00:16, 2 декабря 2012 (UTC)
This article says that C.I. Lewis proposed strict conditionals as an analysis for indicatives, but Will Starr's SEP article says "C.I. Lewis (1912, 1914) defended the strict conditional analysis of subjunctives". Part of me thinks that C.I. Lewis couldn't have made that work for counterfactuals/subjunctives with the tools that existed in his day. But I'd also be surprised if Will Starr got that wrong. I don't have the time or energy to look into this, but wanted to flag it in case somebody else had the relevant knowledge. Botterweg14 ( talk) 15:07, 3 July 2020 (UTC)
This is the
talk page for discussing improvements to the
Strict conditional article. This is not a forum for general discussion of the article's subject. |
Article policies
|
Find sources: Google ( books · news · scholar · free images · WP refs) · FENS · JSTOR · TWL |
![]() | This article was nominated for deletion on 17 December 2011. The result of the discussion was nomination withdrawn, speedy keep. |
![]() | This article is rated Start-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | ||||||||||||||||||||||
|
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
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)
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))
I have created an article for Logical hexagon and refactored a large amount of material contributed by User: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 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)
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)
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)
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)
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)
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)
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)
( 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.
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).
Type on Google: mindnewcontinent.
— Preceding unsigned comment added by 84.100.243.132 ( talk) 08:43, 14 August 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 ( talk • contribs)
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))
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)
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
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 p ⥽ q. While this article is either fixed or deleted. — Preceding unsigned comment added by 189.140.161.209 ( talk) 00:16, 2 декабря 2012 (UTC)
This article says that C.I. Lewis proposed strict conditionals as an analysis for indicatives, but Will Starr's SEP article says "C.I. Lewis (1912, 1914) defended the strict conditional analysis of subjunctives". Part of me thinks that C.I. Lewis couldn't have made that work for counterfactuals/subjunctives with the tools that existed in his day. But I'd also be surprised if Will Starr got that wrong. I don't have the time or energy to look into this, but wanted to flag it in case somebody else had the relevant knowledge. Botterweg14 ( talk) 15:07, 3 July 2020 (UTC)