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![]() | The contents of the Double negative elimination page were merged into Double negation on 27 February 2015. For the contribution history and old versions of the redirected page, please see its history; for the discussion at that location, see its talk page. |
The article currently states:
But it Does not. Its not a simple one liner like that and the notation is all wrong. I've never seen used this way myself, mostly or and this specific book uses , primitives are always lower case (p, not P) and would be
Book 1, Page 106 states that "proposition *2•14 with *2•12. constitutes the principle of double negation."
Where the proposition are
As the Book is pre 1923, its public domain so I can upload an image if need be (with proofs)
remember to check your sources Larek ( talk) 02:37, 14 April 2012 (UTC)
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The article commits the double sin of not defining its symbols and then mixing its (undefined) symbols. I fiddled with it, added some references and sourcing. If the article is ever expanded, there is something more in Kleene 1967:15 footnote 17: "Following Church 1956 p. 73, *49 may be called more specifically the "complete law of double negative"; 8 [implicative formula page 16: 8o. ⊧ ¬¬A ⊃ A ] the "law of double negation" simply; and the converse of 8 the "converse law of double negation".". In Kleene 1952:119 we see this converse law *49a. ⊦ A ⊃ ¬¬A, which is apparently not intuitionistically objectionable. In the years from 1952-1967 Kleene has changed his ⊦ to ⊧. Bill Wvbailey ( talk) 16:01, 14 April 2012 (UTC)
Actually the reprint is "official" and is of the 2nd edition first *52 sections. These are much different than in the first edition. I don't think folks realize this, and it takes careful scrutiny to figure out exactly what Russell changed. Entire sections are deleted and substitutions made for other sections, etc. Plus there's an important preface to the 2nd edition as well. I don't think the page number nor edition is terribly important. What is important was your complaint, which was valid and I hope I addressed. (Strangely, I could not find the 2nd quote, but it sounds familiar. I'm sure its in there somewhere.) Bill Wvbailey ( talk) 20:51, 14 April 2012 (UTC)
Should we add a section with the arithmetic equivalent of a logic Not and then algebraically show that Not Not is the original? This would help anyone not well versed in logic as the can type it into their calculator.
Its just a thought, to add some content to this tiny page Larek ( talk) 15:53, 15 April 2012 (UTC)
In the opening of the Double Negation page the following statement is made in which I believe is a false representation:
Like the law of the excluded middle, this principle is considered to be a law of thought in classical logic,[2] but it is disallowed by intuitionistic logic.[3]
The issue here I believe comes from the merging of 'Double Negation Elimination' into 'Double Negation'. In Intuitionistic Logic Double Negation Elimination is disallowed but Double Negation Introduction is allowed. The article is implying that all types of Double Negation is disallowed in intuitionistic logic which is not the case.
I think the article needs to be changed to have a summary of double negation, and then break out elimination and introduction into their own sub categories. — Preceding unsigned comment added by Chrisomills ( talk • contribs) 16:06, 15 January 2016 (UTC)
The article states that
but isn't actually instance of Modus Ponens, i.e. from and , infer ?
Mikko.nummelin ( talk) 18:21, 5 September 2023 (UTC)
![]() | This article is rated Start-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | ||||||||||||||||||||||||||||||||
|
![]() | The contents of the Double negative elimination page were merged into Double negation on 27 February 2015. For the contribution history and old versions of the redirected page, please see its history; for the discussion at that location, see its talk page. |
The article currently states:
But it Does not. Its not a simple one liner like that and the notation is all wrong. I've never seen used this way myself, mostly or and this specific book uses , primitives are always lower case (p, not P) and would be
Book 1, Page 106 states that "proposition *2•14 with *2•12. constitutes the principle of double negation."
Where the proposition are
As the Book is pre 1923, its public domain so I can upload an image if need be (with proofs)
remember to check your sources Larek ( talk) 02:37, 14 April 2012 (UTC)
---
The article commits the double sin of not defining its symbols and then mixing its (undefined) symbols. I fiddled with it, added some references and sourcing. If the article is ever expanded, there is something more in Kleene 1967:15 footnote 17: "Following Church 1956 p. 73, *49 may be called more specifically the "complete law of double negative"; 8 [implicative formula page 16: 8o. ⊧ ¬¬A ⊃ A ] the "law of double negation" simply; and the converse of 8 the "converse law of double negation".". In Kleene 1952:119 we see this converse law *49a. ⊦ A ⊃ ¬¬A, which is apparently not intuitionistically objectionable. In the years from 1952-1967 Kleene has changed his ⊦ to ⊧. Bill Wvbailey ( talk) 16:01, 14 April 2012 (UTC)
Actually the reprint is "official" and is of the 2nd edition first *52 sections. These are much different than in the first edition. I don't think folks realize this, and it takes careful scrutiny to figure out exactly what Russell changed. Entire sections are deleted and substitutions made for other sections, etc. Plus there's an important preface to the 2nd edition as well. I don't think the page number nor edition is terribly important. What is important was your complaint, which was valid and I hope I addressed. (Strangely, I could not find the 2nd quote, but it sounds familiar. I'm sure its in there somewhere.) Bill Wvbailey ( talk) 20:51, 14 April 2012 (UTC)
Should we add a section with the arithmetic equivalent of a logic Not and then algebraically show that Not Not is the original? This would help anyone not well versed in logic as the can type it into their calculator.
Its just a thought, to add some content to this tiny page Larek ( talk) 15:53, 15 April 2012 (UTC)
In the opening of the Double Negation page the following statement is made in which I believe is a false representation:
Like the law of the excluded middle, this principle is considered to be a law of thought in classical logic,[2] but it is disallowed by intuitionistic logic.[3]
The issue here I believe comes from the merging of 'Double Negation Elimination' into 'Double Negation'. In Intuitionistic Logic Double Negation Elimination is disallowed but Double Negation Introduction is allowed. The article is implying that all types of Double Negation is disallowed in intuitionistic logic which is not the case.
I think the article needs to be changed to have a summary of double negation, and then break out elimination and introduction into their own sub categories. — Preceding unsigned comment added by Chrisomills ( talk • contribs) 16:06, 15 January 2016 (UTC)
The article states that
but isn't actually instance of Modus Ponens, i.e. from and , infer ?
Mikko.nummelin ( talk) 18:21, 5 September 2023 (UTC)