This is the archived discussion of the talk page of a redirected page |
Can anyone explain what "model of" is supposed to mean? How do models apply to logic?
I was directed to this page from LogicalImplication, and I was looking for a truth table. Can we put the truth table from the MaterialConditional page here? That would be helpful. Thanks. —Preceding unsigned comment added by 71.182.112.176 ( talk) 17:30, 22 July 2009 (UTC)
This entry is woefully in need of examples. There seems to be a contextual nuance that differentiates semantic from logical entailment, as well as from the meaning in pragmatism. This nuance isn't conveyed when the same words are used in all of the definitions. — BozoTheScary 16:11, 2 May 2006 (UTC)
What is the general consensus? Premise: A implies B. Conclusion: Not A implies not B. (Or would it be "Not A does not imply not B"?) And from that first conclusion, can it then be said "Not B implies not A" or even "B implies A"? -- 24.153.226.102 18:10, 28 February 2006 (UTC)
The
modus ponens rule is: If A is true then B is true.
The
modus tollens rule is: If B is false then A is false.
Those are the only two valid logical inferences of which I am aware in Propositional Logic.
capitalist 03:39, 1 March 2006 (UTC)
I don't believe that the reference to completeness and Godel's theorem is correct. Godel's theorem can be applied to logics that satisfy a completeness theorem (e.g. axioms of arithmetic on first order logic). The incompleteness theorem does provide a proposition that can't be proven or disproven but is satisfied by the "natural" model. But there are other models for which the proposition does not hold.
Maybe a better example for an incomplete logic would be the second order logic. Second order logic does not satisfy a compactness theorem. I think that this means that a proof system based on finite proofs will not work.
Turtle59 06:31, 13 March 2006 (UTC)
In the diagram, shouldn't B be a subset of A and not vice versa which is what the diagram is? -- Eok20 01:49, 1 July 2006 (UTC)
You're perfectly right and I allowed myself to add a subtext to the diagram, as well as correct the conclusion drawn out of it, saying now: "every B has to be an A" instead of "every A is a B", as before. - Frank.Lenzer@uni-jena.de 12 October 2006
If this diagram is showing what I think it is then it is wrong according to the "correction" underneath. Assuming the diagram is showing models of A and B then it shows A entails B. The definition of entailment says A entails B if all models of A are also models of B. Therefore A has less models than B and also A's models are a subset of B's models. Assuming the diagram is showing models then this should be cleared up because it refers to "A" and "B" whereas further up the page these are defined as sets of sentences. - b 16th November 2006
The diagram (an Euler, not a Venn as originally labeled) is misleading because it suggests that B has non-A members. However, A can entail B when B has no non-A members. I'll boldly remove it. Jcblackmon ( talk) 05:31, 15 December 2008 (UTC)
Are there specific words for the two arguments of an entailment? If we have that , is A the "entailer" or the "antecedent" or the "conditional" or what? Similarly, what is B called?
Also, what is the difference between the |= and |- symbols in implication? I'm having a hard time understanding this section... 169.232.78.24 ( talk) —Preceding comment was added at 04:42, 11 June 2008 (UTC)
Perhaps a little ramp is needed to map the peculiar notions so liberally assigned to conventional words in these articles on implication and entailment. Perhaps its an issue of tautological structure. A good clarifier I've found is the following: http://www.fallacyfiles.org/somernot.html —Preceding unsigned comment added by 72.136.100.3 ( talk) 20:24, 6 September 2008 (UTC)
The phrase "just in case" used in this article means something quite different in ordinary english english (where it can only mean "in the unlikely event that"). Here it seems to mean "only when" and these words would be better as they mean the same both sides of the pond. 88.11.129.94 ( talk) 20:35, 21 November 2008 (UTC)
I found an old version of this article which seems much nicer, what happened? —Preceding unsigned comment added by 76.10.150.120 ( talk) 20:17, 5 December 2008 (UTC)
⊧ redirects to this article. What does it mean? The list of logic symbols calls it "is a model of" which does not provide any semantics for a novice like me. Thanks for your help, -- Abdull ( talk) 17:49, 8 September 2010 (UTC)
This topic is in need of attention from an expert on the subject. The section or sections that need attention may be noted in a message below. |
Much of the content of this article ( Entailment) is duplicated at Material conditional and Logical implication. The difference between these concepts should be clarified and material should be (re-)moved from each article, as appropriate. - dcljr ( talk) 19:56, 15 January 2011 (UTC)
At first, I would leave material conditional alone. Is there any reason for having three separate articles on logical implication, logical consequence and entailment? Here are the lead sentences from each article:
There seems to be some agreement on the various talk pages that a merger should take place. The question is how to do it: which article should be the main article? Vesal ( talk) 23:17, 15 January 2011 (UTC)
It has been suggested that logical implication and logical consequence be merged into this article.
Comment The main article should be Logical consequence and content should be merged to that name. Greg Bard ( talk) 21:40, 17 January 2011 (UTC)
Support Entailment is the best title for a merged article (which is not to say that the article so currently entiled is necessarily the best or main article.) Philogo ( talk) 00:03, 18 January 2011 (UTC)
Just to round it out, I'll support logical implication as the title for the merged article, without preference for the content. CRGreathouse ( t | c) 01:40, 19 January 2011 (UTC)
Comment. I just checked how other people handle this, but there is no real consensus elsewhere either. SEP has an entry on logical consequence, while Simon Blackburn in the Oxford Dictionary of Philosophy follows the above proposal: "entailment" is the main entry and "logical implication" and "logical consequence" redirect to entailment ... Vesal ( talk) 03:36, 19 January 2011 (UTC)
Text and/or other creative content from logical implication was copied or moved into Entailment. The former page's history now serves to provide attribution for that content in the latter page, and it must not be deleted as long as the latter page exists. |
Philogo ( talk) 18:54, 20 January 2011 (UTC)
Text and/or other creative content from logical consequence was copied or moved into Entailment. The former page's history now serves to provide attribution for that content in the latter page, and it must not be deleted as long as the latter page exists. |
Philogo ( talk) 18:54, 20 January 2011 (UTC)
The merged in pages are at the bottom of the article: entailment#ex logical implication and entailment#ex logical consequence The article now needs editing to weave in the material therefrom pruning out duplicate material Philogo ( talk) 18:54, 20 January 2011 (UTC)
Re opening
Is it quite correct to imply thus that the term logical implication is applicable to the relationship between a set of sentences and a sentence rather than between a sentence and a sentence? The next sentnece in the lede (below, enphasis added) assumes not (as opposed to logical conseqnency) .
Cf eg http://planetmath.org/encyclopedia/LogicalImplication.html:
(although that definition does not differentiate Logical implication amd material implication!) and http://whatis.techtarget.com/definition/0,,sid9_gci833443,00.html Philogo ( talk) 16:23, 27 January 2011 (UTC)
The result of the move request was: not moved; there is no consensus or reason given for moving. ErikHaugen ( talk | contribs) 09:33, 12 February 2011 (UTC)
Entailment → Logical consequence — — Preceding unsigned comment added by Gregbard ( talk • contribs) 16:20, 4 February 2011 (UTC)
The article seeks to explain syntactic consequence as opposed to semantic consequence. We should ensure that it gets it right if it mentions the matter at all. There was quite a lot of discussion on the terms in talk:logical consequence. As I recall the consensus was that the terms semantic consequence and logical consequence were synonymous and NOT to be confused with syntactic consequence which was synonymous with derivablity. It would appear that entailment, semantic consequence, logical consequence are synonymous and the term logical implication is closely related if not also synonymous. None of them are synonymous with syntactic consequence. Philogo ( talk) 20:40, 5 February 2011 (UTC)
My personal interest in this page hinges on the Open world assumption. Is it feasible that this might also be included in the article as well? -- Ancheta Wis ( talk) 09:35, 6 February 2011 (UTC)
An editor has raised objections ("I disapprove of this organization...") to the merging/editing of this article at Wikipedia talk:WikiProject Philosophy#Duplication of content and general confusion . I have suggested that such discussion should take place here on this article's talk page. Philogo ( talk) 20:43, 6 February 2011 (UTC)
Unfortunately our article Logical Form is not a such quality that this article can rely on that article to explain matters (take a look), which is disappointing considering that it such a fundamental concept. The temptation of course is to say what needs to be said in this article but that of course sows the seeds of a future problem: if Logical Form is brought up to scratch then there will be duplication of content/possiblity of conflict between Entailment and Logical Form. (A similar problem exits/may develop (overlap/conflict) with the articles validity and contradiction. Philogo ( talk) 15:18, 9 February 2011 (UTC)
see new section Entailment#Limitations. Over to you, editors with expertise in the fields mentioned. Philogo ( talk) 19:35, 12 February 2011 (UTC)
Note that there are many links to there from articles, but that page points to a dab. Should it be redirected here? Incnis Mrsi ( talk) 18:51, 8 March 2011 (UTC)
This article seems to lack a discussion on the pre-theoretical notion, or existence thereof. See [4] for instance. Tijfo098 ( talk) 10:58, 5 April 2011 (UTC)
The fact that it gives The Concept of Logical Consequence as reference without ever discussing its thesis makes this article funny if not suspect. Tijfo098 ( talk) 11:08, 5 April 2011 (UTC)
I don't know who wrote the first three sections "Logical form" and "proof procedures", and "Relationship to other terms" but they're basically drivel—not even useful for teaching someone entailment in propositional calculus. The "Limitations" section (which is really about limitations of classical logic, not entailment) comes too soon. The "Explanation" section is what you'd expect in a discussion of entailemnt in FOL, which is fine by itself except for the title. "Accounts of logical consequence" is yet again on propostional logic, a bit better written that the first part of the article. Even if you want this to be Introduction to entailment, you should at least follow the structure of an introductory work, e.g. McKeon's IEP entry or his 2010 book ISBN 1433106450. Tijfo098 ( talk) 16:27, 5 April 2011 (UTC)
Also, if you want to actually touch on the philosophical issues, Stewart Shapiro appears to be a good wp:secondary discussion, incl. Tarski vs. Etchemendy etc. (It's a defense of the model-theoretic consequence; it's hard to find someone writing on this without an opinion of his own.) Shapiro also wrote a similar piece (but I suspect with less math detail) in Jacquette's A Companion to Philosophical Logic (given "resource" in the article). So, it's not like there's no good material on this. Shapiro really likes writing about this, here's the preprint of some paper/chapter on the same issue: [6]. So, it's even free :-) Also, Etchemendy revisits the issue here (2008). There's an old draft of that on citeseerx, but it says "pls, don't quote". Tijfo098 ( talk) 17:17, 5 April 2011 (UTC)
I see that part of the wierd structure an repetition in this article stem from having pasted this in it. (Not that it makes that much difference). Dumping together a bunch of poor quality articles will not result in a better one. Tijfo098 ( talk) 12:17, 7 April 2011 (UTC)
That redirects here, but this article fails to define it, or to explain the basic point that the consequence relation for a logic is usually infinite, which is why you bother with proof systems. (At least propositional proof system is not a red link). Tijfo098 ( talk) 12:02, 7 April 2011 (UTC)
Is this insufficient? — Philogos ( talk) 05:00, 9 April 2011 (UTC)
I wonder if other editors think that the lede has been improved by the recent changes shown here. Does the introduction of the symbolism clarify the meaning (or does it just restrict comprehension to those familiar with the notation, without adding any meaning)? Does the substitution of the term "proposition" for "sentence" make it clearer, and if not what is the poinst of the substitution? (the existence of propositions is controversial). Is the initial use of the term "logical proposition" helpful? (how is a logical proposition different from a "proposition" - the term subsequently used)?. — Philogos ( talk) 22:40, 31 July 2011 (UTC)
Ancheta: The second sentence was long, my bad, but your worthy to simplify it/break it up has altered the sense somewhat. Look at the dif [dir http://en.wikipedia.org/?title=Entailment&action=historysubmit&diff=444068939&oldid=443068685%7C here] What this sentence is TRYING to say is:
_________________
IF AND ONLY IF
Put another way
(S1 and not-S2 are logically inconsistent)
(Γ entails S2) (S2 is called the logical consequent of Γ) (S1 is said to logically imply S2)
—
Philogos (
talk) 01:55, 11 August 2011 (UTC)
Ancheta: Might this be better/clearer:
In logic, entailment is a relation between a set of sentences (meaningfully declarative sentences or truthbearers) and another sentence. If a sentence, S1, is the conjunction of the elements of a set of one or more sentences, Γ, then, Γ entails another sentence, S2, if and only if S1 and not-S2 are logically inconsistent. If a set of one or more sentences, Γ, entails a sentence, S2, then S2 is called the logical consequent of the conjunction of the elements of Γ, S1,and the conjunction of the elements of Γ, S1, is said to logically imply S2.
— Philogos ( talk) 12:32, 11 August 2011 (UTC)
It seems that entailment is not the same as material implication. Please explain the difference succinctly! Soler97 ( talk) 06:11, 25 September 2011 (UTC)
I am still confused. How is a sentence different from a proposition? Soler97 ( talk) 04:31, 27 September 2011 (UTC)
I remain confused. Could you give an example of a sentence and of a proposition, where the two are very similar except for the sentence/proposition difference? I'm sure I am not the only person who would like to see an explanation of the difference between entailment and material implication. Once it is clearly spelled out it should be added to the article. Soler97 ( talk) 23:14, 27 September 2011 (UTC)
I thought of another example, in
subjunctive mood. In this case, it is not necessarily true (
irrealis). Furthermore the sentence does not have to be true:
Now compare to the logical proposition:
My point is that an English sentence can have the capacity to express some things that a true/false up/down proposition cannot ever express, because a proposition will necessarily miss some subtleties which can be captured in the irrealis mood. -- Ancheta Wis ( talk) 02:31, 28 September 2011 (UTC)
Are you saying that some sentences are propositions but that others are not? Also, by "sentence" do you mean the ordinary meaning of this word in English grammar, or is it some technical sense that has not been specified? Soler97 ( talk) 23:43, 28 September 2011 (UTC)
If I understand you correctly, a sentence is just a grammatically correct utterance in a natural language. As such, it can express a wish, a question, a command, feeling a pain, a piece of sheer nonsense etc. This is very confusing, as the article on entailment is an article on logic, not linguistics. There is another use of "sentence" in mathematical logic ie http://en.wikipedia.org/wiki/Sentence_%28mathematical_logic%29 Are you certain this is not the one referred to in the entailment article? To talk about the logical consistency of questions, commands, utterances of pain etc seems nonsensical to me.
The article should be intelligible on its own. It should not require the lay reader to refer to links, except for definitions of technical terms. Soler97 ( talk) 22:59, 29 September 2011 (UTC)
During my involvement with this article, in which I have observed various editors attempt clarification/exposition, I have not seen a linguistic assessment of the various related terms vis a vis entailment, such as the material conditional. It is now becoming clear to.me that you appear to posit your original question from the POV of hindsight, where truth values are givens rather than TBDs (to be determined)s. That would explain to me how you could posit that all mathematical sentences have truth values. Entailment takes a different position. In the process of entailment, an inquiry is taking place before us, during which we examine arguments (that is, evidence ) for their truth value. This is intrinsically non-rhetorical because an investigation is occurring, which is distinctly different from a truth-functional which takes a rhetorical stance true or false, but not TBD. In entailment we admit things can be TBD, and seek to evaluate or at least admit we don't know yet, or cannot know because, ... etc. You get the gist.
Now compare this to material conditional, where the arguments have known values. As you can see, an investigation must already have occurred. It is a situation where hindsight reigns over a done deal. -- Ancheta Wis ( talk) 15:39, 30 September 2011 (UTC)
Can you comment on this, please: The difference between material implication and logical implication is contextual. The first is a statement of logic, the second of metalogic. The difference between "p implies q" and "p is a proof of q" is that the first is a statement within formal logic, the second is a statement about it. Soler97 ( talk) 01:10, 1 October 2011 (UTC)
Thanks for your efforts, but I think that (a) each of us is unable to understand what the other is saying and that further attempts at clarification are not going to lead anywhere, and that (b) you have failed to give a clear criterion of the difference between material implication and entailment. From the point of view of the lay reader, this is a big hole in the article. Perhaps someone else is willing to try. I would insert the formulation above (with terms defined) into the article, but no doubt you would immediately delete it. Soler97 ( talk) 21:57, 2 October 2011 (UTC)
Doesn't S1 entail S2 if and only if S2 is a tautological consequence of S1? That's what I got out of Barwise and Etchemendy's Language, Proof and Logic (2008), pages 110-113. This article as wrriten seems to imply that S1 entails S2 if and only if S2 is a logical consequence of S1. There are logical consequences that aren't necessarily tautological consequences. Isn't the introductory example where "John is a bachelor" does not entail "John is a man" an example of "John is a man" not being a tautological consequence of "John is a bachelor," but still a logical consequence? It seems as if this article makes several references to logical consequence when it should actually be referencing tautological consequence. Entailment should correspond exactly to tautological consequence, not logical consequence. Hanlon1755 ( talk) 07:51, 31 December 2011 (UTC)
My thanks to User:Incnis Mrsi for reverting my inadvertent change to this page, due to an inadvertent touch on a slow tablet. Sorry. -- Ancheta Wis ( talk) 09:44, 20 January 2012 (UTC)
It appears that the lead example involving John, being a bachelor, and being a man, is actually an example not of logical consequence as stated, but of tautological consequence. That is, if Γ = {“John is a bachelor”}, S1 = “John is a bachelor” and S2 = “John is a man,” then S2 is not a tautological consequence of Γ. S2 is still, however, a logical consequence of Γ. Comments, concerns? Hanlon1755 ( talk) 00:44, 22 January 2012 (UTC)
I understand that Logical consequence was merged into this page. Above, the proposal to rename this page "Logical consequence" was rejected. In the past two months, there have been repeated attempts to restore Logical consequence as a separate article, with repeated reversals of this move. This looks to me like an attempt to content fork? Should this issue be reopened and resolved one way or another so the extended reverting can come to an end? Good Ol’factory (talk) 02:49, 29 February 2012 (UTC)
The result of the proposal was moved. -- BDD ( talk) 16:37, 31 October 2012 (UTC) ( non-admin closure)
Entailment → Logical consequence –
A while back, the article Logical consequence was moved to Entailment. I subsequently proposed to move it back. However, it was not. I have always found this to be a very troubling development. Recently, I have been adding reference resources to articles and categories consistent with those resources. This is one that is not consistent (and I said it at the time.) Please take a look at SEP, InPho, PhilPapers, and IEP, none of which has an article on "entailment" independent of "logical consequence." The article itself is a bit scattered, and this has been a big stumbling block for me to improving it. It is only one of the most important concepts in logic. Please support this move, as it is consistent with the scholarly literature on the subject, and Wikipedia is the odd resource out in this regard. Greg Bard ( talk) 07:55, 24 October 2012 (UTC)
This is the archived discussion of the talk page of a redirected page |
Can anyone explain what "model of" is supposed to mean? How do models apply to logic?
I was directed to this page from LogicalImplication, and I was looking for a truth table. Can we put the truth table from the MaterialConditional page here? That would be helpful. Thanks. —Preceding unsigned comment added by 71.182.112.176 ( talk) 17:30, 22 July 2009 (UTC)
This entry is woefully in need of examples. There seems to be a contextual nuance that differentiates semantic from logical entailment, as well as from the meaning in pragmatism. This nuance isn't conveyed when the same words are used in all of the definitions. — BozoTheScary 16:11, 2 May 2006 (UTC)
What is the general consensus? Premise: A implies B. Conclusion: Not A implies not B. (Or would it be "Not A does not imply not B"?) And from that first conclusion, can it then be said "Not B implies not A" or even "B implies A"? -- 24.153.226.102 18:10, 28 February 2006 (UTC)
The
modus ponens rule is: If A is true then B is true.
The
modus tollens rule is: If B is false then A is false.
Those are the only two valid logical inferences of which I am aware in Propositional Logic.
capitalist 03:39, 1 March 2006 (UTC)
I don't believe that the reference to completeness and Godel's theorem is correct. Godel's theorem can be applied to logics that satisfy a completeness theorem (e.g. axioms of arithmetic on first order logic). The incompleteness theorem does provide a proposition that can't be proven or disproven but is satisfied by the "natural" model. But there are other models for which the proposition does not hold.
Maybe a better example for an incomplete logic would be the second order logic. Second order logic does not satisfy a compactness theorem. I think that this means that a proof system based on finite proofs will not work.
Turtle59 06:31, 13 March 2006 (UTC)
In the diagram, shouldn't B be a subset of A and not vice versa which is what the diagram is? -- Eok20 01:49, 1 July 2006 (UTC)
You're perfectly right and I allowed myself to add a subtext to the diagram, as well as correct the conclusion drawn out of it, saying now: "every B has to be an A" instead of "every A is a B", as before. - Frank.Lenzer@uni-jena.de 12 October 2006
If this diagram is showing what I think it is then it is wrong according to the "correction" underneath. Assuming the diagram is showing models of A and B then it shows A entails B. The definition of entailment says A entails B if all models of A are also models of B. Therefore A has less models than B and also A's models are a subset of B's models. Assuming the diagram is showing models then this should be cleared up because it refers to "A" and "B" whereas further up the page these are defined as sets of sentences. - b 16th November 2006
The diagram (an Euler, not a Venn as originally labeled) is misleading because it suggests that B has non-A members. However, A can entail B when B has no non-A members. I'll boldly remove it. Jcblackmon ( talk) 05:31, 15 December 2008 (UTC)
Are there specific words for the two arguments of an entailment? If we have that , is A the "entailer" or the "antecedent" or the "conditional" or what? Similarly, what is B called?
Also, what is the difference between the |= and |- symbols in implication? I'm having a hard time understanding this section... 169.232.78.24 ( talk) —Preceding comment was added at 04:42, 11 June 2008 (UTC)
Perhaps a little ramp is needed to map the peculiar notions so liberally assigned to conventional words in these articles on implication and entailment. Perhaps its an issue of tautological structure. A good clarifier I've found is the following: http://www.fallacyfiles.org/somernot.html —Preceding unsigned comment added by 72.136.100.3 ( talk) 20:24, 6 September 2008 (UTC)
The phrase "just in case" used in this article means something quite different in ordinary english english (where it can only mean "in the unlikely event that"). Here it seems to mean "only when" and these words would be better as they mean the same both sides of the pond. 88.11.129.94 ( talk) 20:35, 21 November 2008 (UTC)
I found an old version of this article which seems much nicer, what happened? —Preceding unsigned comment added by 76.10.150.120 ( talk) 20:17, 5 December 2008 (UTC)
⊧ redirects to this article. What does it mean? The list of logic symbols calls it "is a model of" which does not provide any semantics for a novice like me. Thanks for your help, -- Abdull ( talk) 17:49, 8 September 2010 (UTC)
This topic is in need of attention from an expert on the subject. The section or sections that need attention may be noted in a message below. |
Much of the content of this article ( Entailment) is duplicated at Material conditional and Logical implication. The difference between these concepts should be clarified and material should be (re-)moved from each article, as appropriate. - dcljr ( talk) 19:56, 15 January 2011 (UTC)
At first, I would leave material conditional alone. Is there any reason for having three separate articles on logical implication, logical consequence and entailment? Here are the lead sentences from each article:
There seems to be some agreement on the various talk pages that a merger should take place. The question is how to do it: which article should be the main article? Vesal ( talk) 23:17, 15 January 2011 (UTC)
It has been suggested that logical implication and logical consequence be merged into this article.
Comment The main article should be Logical consequence and content should be merged to that name. Greg Bard ( talk) 21:40, 17 January 2011 (UTC)
Support Entailment is the best title for a merged article (which is not to say that the article so currently entiled is necessarily the best or main article.) Philogo ( talk) 00:03, 18 January 2011 (UTC)
Just to round it out, I'll support logical implication as the title for the merged article, without preference for the content. CRGreathouse ( t | c) 01:40, 19 January 2011 (UTC)
Comment. I just checked how other people handle this, but there is no real consensus elsewhere either. SEP has an entry on logical consequence, while Simon Blackburn in the Oxford Dictionary of Philosophy follows the above proposal: "entailment" is the main entry and "logical implication" and "logical consequence" redirect to entailment ... Vesal ( talk) 03:36, 19 January 2011 (UTC)
Text and/or other creative content from logical implication was copied or moved into Entailment. The former page's history now serves to provide attribution for that content in the latter page, and it must not be deleted as long as the latter page exists. |
Philogo ( talk) 18:54, 20 January 2011 (UTC)
Text and/or other creative content from logical consequence was copied or moved into Entailment. The former page's history now serves to provide attribution for that content in the latter page, and it must not be deleted as long as the latter page exists. |
Philogo ( talk) 18:54, 20 January 2011 (UTC)
The merged in pages are at the bottom of the article: entailment#ex logical implication and entailment#ex logical consequence The article now needs editing to weave in the material therefrom pruning out duplicate material Philogo ( talk) 18:54, 20 January 2011 (UTC)
Re opening
Is it quite correct to imply thus that the term logical implication is applicable to the relationship between a set of sentences and a sentence rather than between a sentence and a sentence? The next sentnece in the lede (below, enphasis added) assumes not (as opposed to logical conseqnency) .
Cf eg http://planetmath.org/encyclopedia/LogicalImplication.html:
(although that definition does not differentiate Logical implication amd material implication!) and http://whatis.techtarget.com/definition/0,,sid9_gci833443,00.html Philogo ( talk) 16:23, 27 January 2011 (UTC)
The result of the move request was: not moved; there is no consensus or reason given for moving. ErikHaugen ( talk | contribs) 09:33, 12 February 2011 (UTC)
Entailment → Logical consequence — — Preceding unsigned comment added by Gregbard ( talk • contribs) 16:20, 4 February 2011 (UTC)
The article seeks to explain syntactic consequence as opposed to semantic consequence. We should ensure that it gets it right if it mentions the matter at all. There was quite a lot of discussion on the terms in talk:logical consequence. As I recall the consensus was that the terms semantic consequence and logical consequence were synonymous and NOT to be confused with syntactic consequence which was synonymous with derivablity. It would appear that entailment, semantic consequence, logical consequence are synonymous and the term logical implication is closely related if not also synonymous. None of them are synonymous with syntactic consequence. Philogo ( talk) 20:40, 5 February 2011 (UTC)
My personal interest in this page hinges on the Open world assumption. Is it feasible that this might also be included in the article as well? -- Ancheta Wis ( talk) 09:35, 6 February 2011 (UTC)
An editor has raised objections ("I disapprove of this organization...") to the merging/editing of this article at Wikipedia talk:WikiProject Philosophy#Duplication of content and general confusion . I have suggested that such discussion should take place here on this article's talk page. Philogo ( talk) 20:43, 6 February 2011 (UTC)
Unfortunately our article Logical Form is not a such quality that this article can rely on that article to explain matters (take a look), which is disappointing considering that it such a fundamental concept. The temptation of course is to say what needs to be said in this article but that of course sows the seeds of a future problem: if Logical Form is brought up to scratch then there will be duplication of content/possiblity of conflict between Entailment and Logical Form. (A similar problem exits/may develop (overlap/conflict) with the articles validity and contradiction. Philogo ( talk) 15:18, 9 February 2011 (UTC)
see new section Entailment#Limitations. Over to you, editors with expertise in the fields mentioned. Philogo ( talk) 19:35, 12 February 2011 (UTC)
Note that there are many links to there from articles, but that page points to a dab. Should it be redirected here? Incnis Mrsi ( talk) 18:51, 8 March 2011 (UTC)
This article seems to lack a discussion on the pre-theoretical notion, or existence thereof. See [4] for instance. Tijfo098 ( talk) 10:58, 5 April 2011 (UTC)
The fact that it gives The Concept of Logical Consequence as reference without ever discussing its thesis makes this article funny if not suspect. Tijfo098 ( talk) 11:08, 5 April 2011 (UTC)
I don't know who wrote the first three sections "Logical form" and "proof procedures", and "Relationship to other terms" but they're basically drivel—not even useful for teaching someone entailment in propositional calculus. The "Limitations" section (which is really about limitations of classical logic, not entailment) comes too soon. The "Explanation" section is what you'd expect in a discussion of entailemnt in FOL, which is fine by itself except for the title. "Accounts of logical consequence" is yet again on propostional logic, a bit better written that the first part of the article. Even if you want this to be Introduction to entailment, you should at least follow the structure of an introductory work, e.g. McKeon's IEP entry or his 2010 book ISBN 1433106450. Tijfo098 ( talk) 16:27, 5 April 2011 (UTC)
Also, if you want to actually touch on the philosophical issues, Stewart Shapiro appears to be a good wp:secondary discussion, incl. Tarski vs. Etchemendy etc. (It's a defense of the model-theoretic consequence; it's hard to find someone writing on this without an opinion of his own.) Shapiro also wrote a similar piece (but I suspect with less math detail) in Jacquette's A Companion to Philosophical Logic (given "resource" in the article). So, it's not like there's no good material on this. Shapiro really likes writing about this, here's the preprint of some paper/chapter on the same issue: [6]. So, it's even free :-) Also, Etchemendy revisits the issue here (2008). There's an old draft of that on citeseerx, but it says "pls, don't quote". Tijfo098 ( talk) 17:17, 5 April 2011 (UTC)
I see that part of the wierd structure an repetition in this article stem from having pasted this in it. (Not that it makes that much difference). Dumping together a bunch of poor quality articles will not result in a better one. Tijfo098 ( talk) 12:17, 7 April 2011 (UTC)
That redirects here, but this article fails to define it, or to explain the basic point that the consequence relation for a logic is usually infinite, which is why you bother with proof systems. (At least propositional proof system is not a red link). Tijfo098 ( talk) 12:02, 7 April 2011 (UTC)
Is this insufficient? — Philogos ( talk) 05:00, 9 April 2011 (UTC)
I wonder if other editors think that the lede has been improved by the recent changes shown here. Does the introduction of the symbolism clarify the meaning (or does it just restrict comprehension to those familiar with the notation, without adding any meaning)? Does the substitution of the term "proposition" for "sentence" make it clearer, and if not what is the poinst of the substitution? (the existence of propositions is controversial). Is the initial use of the term "logical proposition" helpful? (how is a logical proposition different from a "proposition" - the term subsequently used)?. — Philogos ( talk) 22:40, 31 July 2011 (UTC)
Ancheta: The second sentence was long, my bad, but your worthy to simplify it/break it up has altered the sense somewhat. Look at the dif [dir http://en.wikipedia.org/?title=Entailment&action=historysubmit&diff=444068939&oldid=443068685%7C here] What this sentence is TRYING to say is:
_________________
IF AND ONLY IF
Put another way
(S1 and not-S2 are logically inconsistent)
(Γ entails S2) (S2 is called the logical consequent of Γ) (S1 is said to logically imply S2)
—
Philogos (
talk) 01:55, 11 August 2011 (UTC)
Ancheta: Might this be better/clearer:
In logic, entailment is a relation between a set of sentences (meaningfully declarative sentences or truthbearers) and another sentence. If a sentence, S1, is the conjunction of the elements of a set of one or more sentences, Γ, then, Γ entails another sentence, S2, if and only if S1 and not-S2 are logically inconsistent. If a set of one or more sentences, Γ, entails a sentence, S2, then S2 is called the logical consequent of the conjunction of the elements of Γ, S1,and the conjunction of the elements of Γ, S1, is said to logically imply S2.
— Philogos ( talk) 12:32, 11 August 2011 (UTC)
It seems that entailment is not the same as material implication. Please explain the difference succinctly! Soler97 ( talk) 06:11, 25 September 2011 (UTC)
I am still confused. How is a sentence different from a proposition? Soler97 ( talk) 04:31, 27 September 2011 (UTC)
I remain confused. Could you give an example of a sentence and of a proposition, where the two are very similar except for the sentence/proposition difference? I'm sure I am not the only person who would like to see an explanation of the difference between entailment and material implication. Once it is clearly spelled out it should be added to the article. Soler97 ( talk) 23:14, 27 September 2011 (UTC)
I thought of another example, in
subjunctive mood. In this case, it is not necessarily true (
irrealis). Furthermore the sentence does not have to be true:
Now compare to the logical proposition:
My point is that an English sentence can have the capacity to express some things that a true/false up/down proposition cannot ever express, because a proposition will necessarily miss some subtleties which can be captured in the irrealis mood. -- Ancheta Wis ( talk) 02:31, 28 September 2011 (UTC)
Are you saying that some sentences are propositions but that others are not? Also, by "sentence" do you mean the ordinary meaning of this word in English grammar, or is it some technical sense that has not been specified? Soler97 ( talk) 23:43, 28 September 2011 (UTC)
If I understand you correctly, a sentence is just a grammatically correct utterance in a natural language. As such, it can express a wish, a question, a command, feeling a pain, a piece of sheer nonsense etc. This is very confusing, as the article on entailment is an article on logic, not linguistics. There is another use of "sentence" in mathematical logic ie http://en.wikipedia.org/wiki/Sentence_%28mathematical_logic%29 Are you certain this is not the one referred to in the entailment article? To talk about the logical consistency of questions, commands, utterances of pain etc seems nonsensical to me.
The article should be intelligible on its own. It should not require the lay reader to refer to links, except for definitions of technical terms. Soler97 ( talk) 22:59, 29 September 2011 (UTC)
During my involvement with this article, in which I have observed various editors attempt clarification/exposition, I have not seen a linguistic assessment of the various related terms vis a vis entailment, such as the material conditional. It is now becoming clear to.me that you appear to posit your original question from the POV of hindsight, where truth values are givens rather than TBDs (to be determined)s. That would explain to me how you could posit that all mathematical sentences have truth values. Entailment takes a different position. In the process of entailment, an inquiry is taking place before us, during which we examine arguments (that is, evidence ) for their truth value. This is intrinsically non-rhetorical because an investigation is occurring, which is distinctly different from a truth-functional which takes a rhetorical stance true or false, but not TBD. In entailment we admit things can be TBD, and seek to evaluate or at least admit we don't know yet, or cannot know because, ... etc. You get the gist.
Now compare this to material conditional, where the arguments have known values. As you can see, an investigation must already have occurred. It is a situation where hindsight reigns over a done deal. -- Ancheta Wis ( talk) 15:39, 30 September 2011 (UTC)
Can you comment on this, please: The difference between material implication and logical implication is contextual. The first is a statement of logic, the second of metalogic. The difference between "p implies q" and "p is a proof of q" is that the first is a statement within formal logic, the second is a statement about it. Soler97 ( talk) 01:10, 1 October 2011 (UTC)
Thanks for your efforts, but I think that (a) each of us is unable to understand what the other is saying and that further attempts at clarification are not going to lead anywhere, and that (b) you have failed to give a clear criterion of the difference between material implication and entailment. From the point of view of the lay reader, this is a big hole in the article. Perhaps someone else is willing to try. I would insert the formulation above (with terms defined) into the article, but no doubt you would immediately delete it. Soler97 ( talk) 21:57, 2 October 2011 (UTC)
Doesn't S1 entail S2 if and only if S2 is a tautological consequence of S1? That's what I got out of Barwise and Etchemendy's Language, Proof and Logic (2008), pages 110-113. This article as wrriten seems to imply that S1 entails S2 if and only if S2 is a logical consequence of S1. There are logical consequences that aren't necessarily tautological consequences. Isn't the introductory example where "John is a bachelor" does not entail "John is a man" an example of "John is a man" not being a tautological consequence of "John is a bachelor," but still a logical consequence? It seems as if this article makes several references to logical consequence when it should actually be referencing tautological consequence. Entailment should correspond exactly to tautological consequence, not logical consequence. Hanlon1755 ( talk) 07:51, 31 December 2011 (UTC)
My thanks to User:Incnis Mrsi for reverting my inadvertent change to this page, due to an inadvertent touch on a slow tablet. Sorry. -- Ancheta Wis ( talk) 09:44, 20 January 2012 (UTC)
It appears that the lead example involving John, being a bachelor, and being a man, is actually an example not of logical consequence as stated, but of tautological consequence. That is, if Γ = {“John is a bachelor”}, S1 = “John is a bachelor” and S2 = “John is a man,” then S2 is not a tautological consequence of Γ. S2 is still, however, a logical consequence of Γ. Comments, concerns? Hanlon1755 ( talk) 00:44, 22 January 2012 (UTC)
I understand that Logical consequence was merged into this page. Above, the proposal to rename this page "Logical consequence" was rejected. In the past two months, there have been repeated attempts to restore Logical consequence as a separate article, with repeated reversals of this move. This looks to me like an attempt to content fork? Should this issue be reopened and resolved one way or another so the extended reverting can come to an end? Good Ol’factory (talk) 02:49, 29 February 2012 (UTC)
The result of the proposal was moved. -- BDD ( talk) 16:37, 31 October 2012 (UTC) ( non-admin closure)
Entailment → Logical consequence –
A while back, the article Logical consequence was moved to Entailment. I subsequently proposed to move it back. However, it was not. I have always found this to be a very troubling development. Recently, I have been adding reference resources to articles and categories consistent with those resources. This is one that is not consistent (and I said it at the time.) Please take a look at SEP, InPho, PhilPapers, and IEP, none of which has an article on "entailment" independent of "logical consequence." The article itself is a bit scattered, and this has been a big stumbling block for me to improving it. It is only one of the most important concepts in logic. Please support this move, as it is consistent with the scholarly literature on the subject, and Wikipedia is the odd resource out in this regard. Greg Bard ( talk) 07:55, 24 October 2012 (UTC)