Talk:Logical implication

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Contents 1 Material implication 2 Introduction 3 Possible merge with Entailment 4 Fresheneesz' partial revert

[edit] Material implication

What the hell is the difference between Logical implication and the Material conditional ????? I propose a merge. Fresheneesz 07:35, 11 October 2006 (UTC)

A logical implication is a valid material implication (or material conditional). These are two different but often confused notions. The pages should remain separate, but the page on logical implication needs to be updated so as to reflect this distinction. 128.112.210.248 22:29, 7 November 2006 (UTC)

Actually both pages are a mess. Nortexoid 06:04, 10 December 2006 (UTC)

[edit] Introduction

The introduction of the article had been changed to read:

Logical implication is not to be confused with material implication (AKA material conditional).

In ordinary language, material implication is often expressed by sentences of the following form:

• If P then Q.

Here P and Q are propositional variables that represent propositions in a given language. In a statement of the form "if P then Q", the first term, P, is called the antecedent and the second term, Q, is called the consequent; and the statement as a whole is called a conditional. Assuming that the conditional is true, then the truth of the antecedent is a sufficient condition for the truth of the consequent, while the truth of the consequent is a necessary condition for the truth of the antecedent.

A sentence is valid (not to be confused with the property of an argument being valid) if and only if it is true on every interpretation. (See also logical truth, tautology.)

A logical implication is a valid material implication.

The rest of this article appears to be about material implications.

I found this introduction confusing, since it looks like discussion of the article rather than an introduction to the article. So I replaced the introduction with an earlier version. The above introduction is probably salvageable if it is modified to stop talking about what shouldn't be confused and start talking about what is to be understood. Michael Slone (talk) 23:52, 9 December 2006 (UTC)

[edit] Possible merge with Entailment

They are exactly the same concept, so why are there two distinct pages for them? This one is actually quite poorly written. I like the introduction though. Just kidding, I wrote it. This page should be scrapped (except for the great intro.) and redirected to Entailment. Is anybody going to make a stink about it if I do it? Nortexoid 23:38, 6 January 2007 (UTC)

Now that I've drastically edited the article, I don't think a redirect is in order, but rather a merge is. There is some useful information in the Entailment article that could be placed in this one, and then Entailment could be redirected to this article. Nortexoid 01:46, 7 January 2007 (UTC)

I'll support a merge, without really knowing much about entailment. I'll trust your judgment. Fresheneesz 21:49, 7 January 2007 (UTC)

[edit] Fresheneesz' partial revert

Yes, a lot was changed, but it would be appreciated it somebody qualified in disagreement reverted the article and gave good reasons for doing so. I notice that you ask what the difference between logical implication and the material conditional is at the top of the page. I feel your revert was unwarranted, simply because the article in its current state is awful. E.g., what exactly is the relevance of the Symbolization section, or for that matter the following section on Comparison with other conditional statements? What is all that talk of the Cond(x,y) function for? Nortexoid 21:47, 7 January 2007 (UTC)

I agree it was awful, maybe I shouldn't have reverted. I just felt like too much stuff I found useful was removed. I merged the two intros together, cause yours had lots of good stuff - but lacked some neccessary links and wording that made it a little hard to understand. I dunno about the Cond(x,y) junk - i'll look at merging some of the rest of the two versions right now. Btw, you have to admit, half a year ago, it was a little vauge (according to the articles) what the difference between material conditional and logical implication was. I don't need a degree in logic to know what makes sense. Fresheneesz 21:52, 7 January 2007 (UTC)

One thing I have a problem with is the model theory stuff. Is that really neccessary to understand logical implication? I'm not exactly sure what a "set T of formulas" would be - except that I suppose it could be a set of sets... Its just not clear to me. Fresheneesz 21:57, 7 January 2007 (UTC)

It's more general, as I clarified in the introduction, to use the model-theoretic (or valuation or interpretation) terminology rather than the valid material conditional one, because the logic may not have the appropriate semantic equivalent of the deduction theorem. E.g., if the logic does not have the property that if A logically implies B, then "if A then B" is valid, then "A implies B" cannot be stated as ""if A then B" is valid". They happen to be equivalent in classical logic but not for e.g. some many-valued logics.

"set Γ of formulas" means that the set Γ contains as elements formulas of some formal language L. Formulas are strings or sequences of symbols of L, usually constructed according to some inductive definition of 'formula'. But none of this has anything to do with the article. I suppose those terms (e.g. 'formula', 'set') could be linked to their respective pages. Nortexoid 00:09, 8 January 2007 (UTC)

Ok, I added back in your philosopical issues section, and killed the definition section (since thats covered in the intro). You can use your discretion on pruning the other sections - I just ask that you try to improve them, trim them, or truncate them, rather than deleting them entirely. Fresheneesz 22:01, 7 January 2007 (UTC)

Btw, pictures are nice - if you can get one or make one, I would personally be appreciative. Fresheneesz 22:01, 7 January 2007 (UTC)