Talk:Material conditional

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[edit] Problems with material implication

I was thinking that there should be a section about the "problems with material implication". Here's some text that I propose could be part of it:

There are several known issues concerning the standard truth-functional interpretaion of the material conditional. Such problems are sometimes referred to as the "paradoxes of material implication", though they are not quite paradoxes in the strict sense.

One such issue concerning material implication involves the truth-functional interpretation of the falsity of a conditional statement. Take, for example, the following conditional: If God exists, then the Earth is flat. If one were to think that this proposition is false (which seems reasonable), then, interpreted as a material conditional, the antecedent must be true and the consequent false—for that is the only case in which the conditional is false, according to the standard truth-functional interpretation of the material conditional. However, the antecedent is God exists. So, the standard interpretation seems to establish the existence of God from a simple false conditional in which the antecedent and the consequent are fairly unrelated. Of course, one way to respond to this would be to argue that the conditional in question is not a material conditional after all, but some other kind of conditional statement.

However, I don't know a great deal about this stuff. I thought some logic buffs might be able to create the section or help out. Any ideas? - Jaymay 18:43, 14 August 2006 (UTC)

This article is about the material conditional, as it is used in math and computer science. Some discussion of its relation to other types of conditionals is useful, but long digressions belong in the more philosophistical articles, of which there are many, as I'm sure you know. That can be handled via the requisite links in the <see also> section. Jon Awbrey 18:54, 14 August 2006 (UTC)
Jon, first, I apologize for changing the references format without discussion. I only figured that since there was no discussion going on already here that no one was really watching this article much anymore. However, by putting in the full URL to the reference that I added, I was not changing the references format, since there was no style on the article according to which "Eprint" was used. Thus, I believe you just changed the references style without discussion.
Second, I wasn't trying to be territorial by tagging this article with Wikiproject philosophy. I submit that you are being the more territorial by verbally tagging this article as restricted to math and computer science. I was trying to be pluralistic by adding philosophy-related stuff to this article, not by replacing anything with philosophy-related stuff.
Third, this article does not specify that it is about the material conditional only as it relates to math and computer science. If it is supposed to, then it should be titled "Material conditional (math and computer science)" and there should be a diambiguation article where we can distinguish a "Material conditional (philosophy)" article. There is a disambiguation article for Conditional, in which it says "Material conditional, in propositional calculus, or logical calculus in mathematics". The propositional calculus fits squarely into logic/philosophy. So, why would you say that it is restricted to "math and computer science"?
However, I think that it's a poor option anyway to create two separate articles. It's not a long article as it is. And, there is no reason that issues with the material conditional (philosophical or otherwise) should not be in this article. It need not be a "long digression" either, unless you think that any philosophically-related discussion is too long and a digression. Furthermore, while it's true that there are many philosophy articles on Wikipedia, there are none on the material conditional, except this one.
Fourth, cooperation is fun; hostility is lame. - Jaymay 22:03, 14 August 2006 (UTC)
I realize it's totally uncool to talk about one's expertise in WP, but my "commitment" here is shorter than it used to be, so maybe it will save some wasted breath to mention that I've been a student of logic in both mathematical veins and philosophical vains for 40 very odd years now, and so I'm quite familiar with all of the basic issues you mention here. But the article is titled what it is, and that is the kind of truth-functional implication that is used by mathematicians everywhere in almost (w)holy blessed ignorance of what some philosophers consider its "problematic" character. So the main aim of this article is to present the basics of material implication for the edification of those readers who came looking for that. Of course, it makes sense to make a hyper-side-long allusion to all those other issues, for which there are dedicated articles already on counterfactual conditionals, fuzzy logic, modal logic, relevance logic, and a host of others. That's the main thing. Will get to the other issues later. Jon Awbrey 01:06, 15 August 2006 (UTC)
Jon, no need to speak of your "expertise". I am well aware that the truth-functional interpretation is widely used and accepted as unproblematic. No doubt it is quite intuitive. Many philosophers recognize that. I think you misunderstood my point all along. I didnt' want to include issues with the material conditional because I thought that it has problems, in some serious sense. Fringe controversies are certainly not for an encyclopedia entry. However, issues that a large number of professionals on the subject discuss, including philosophers, are relevant to an encyclopedia entry.
However, it's really not a big deal. I just thought some people might be interested in expanding the article, since, I think, there are, from time to time, people browsing Wikipedia looking for issues surrounding material implication. But, I guess not. I'll leave it be. - Jaymay 03:58, 15 August 2006 (UTC)
Sorry if I am being brusque, but we have had some major mess-overs of related articles from both phil-logic and hard-ware folks, and since these are entry level articles my concern is not confusing initiates any more than they are likely to be already. But what I am saying about the problematique is that there are standard ways of coordinating groups of articles. In mathematical orbit, this is one of 16 on the binary connectives, and I worked a long time getting a consistent format for that group. By all means, add one or more brief sections on enrichment topics, perhaps using the {{main|...}} template under the subhead to link to the main articles on those topics. Many Regards, Jon Awbrey 04:44, 15 August 2006 (UTC)
I didn't realize you had collaborated and worked to get uniformity among various articles. I understand that you don't want all that work to be unecessarily tampered with. Besides, some issues are mentioned in the section on comparison with other conditionals. And I wasn't really planning on making the changes myself either. If anyone else what's to add info on this sort of thing, then they can.
By the way, maybe you should post something on the Talk page here warning that the article has pretty much been deemed satisfactory and that any changes should be discussed on the Talk page first. I know we're all supposed to do that first no matter what, but when the Talk page is blank or little is on it, one tends to think that no one is really working on it. - Jaymay 19:22, 15 August 2006 (UTC)
I am, of course, only expressing my personal opinions and preferences. And a note like that would probably be jes askin' fer trouble. Ha! Jon Awbrey 21:04, 15 August 2006 (UTC)


Is this right?

[edit] Subset?

Is the material conditional synonymous with the subset relation? If it is we should strongly note it or even consider merging the articles. Fresheneesz 21:44, 7 January 2007 (UTC)

Although it may be expressed in terms of sets, it is not synonymous. Gregbard 08:55, 28 June 2007 (UTC)

[edit] Proposed project

I have been working on all of the logical operators recently. I would like to see a consistent format for them. There is a wikiproject proposal for this at: Wikipedia:WikiProject_Council/Proposals#Logical_Operators. Also see Talk:Logical connective.

I would like to see the logical, grammatical, mathematical, and computer science applications of all of the operators on the single page for each of those concepts.

Gregbard 08:55, 28 June 2007 (UTC)

[edit] Material conditional vs. entailment

"The material conditional is not to be confused with the entailment relation ⊨ "


I was told by a philosophy professor they are the same. I'm a graduate student teaching logic for the first time, and I want to get it right for my students. —Preceding unsigned comment added by 24.208.177.188 (talk) 17:38, 22 April 2008 (UTC)

In Methods of Logic, Quine goes on a rant for a page or two about how we should not confuse the material conditional with implication. Truthfully, I don't understand how they're meaningfully different, but Quine says they are! Djk3 (talk) 21:10, 22 April 2008 (UTC)
They're much different. One is a relation (entailment) denoted in the metalanguage and the other is a connective (material implication) denoted in the object language. The connective takes two arguments, both of which are object-language propositions. The other takes two arguments, one of which is a set of object-language propositions and the other of which is an object-language proposition (or sometimes a set of them). For individual propositions A and B, A entails B iff the material implication from A to B is valid. (This assumes classical logic.) But it may be that for some model M, A materially implies B even though this is not true of every model (i.e. not valid), and hence A doesn't entail B. In a sense, entailment is not relative to a model, since it quantifies over all of them, while material implication is. It makes no sense to say that a material implication is true irrespective of a model unless all one means is that it is valid (and hence an entailment). Nortexoid (talk) 12:00, 23 April 2008 (UTC)