Talk:Necessity and sufficiency

In the previous version, the section on sufficient conditions had reversed which is the condition and which is the thing obtained. If you do it this way, it's hard to tell at a glance the main difference between necessary and sufficient: necessary is obtained-->condition, while sufficient is condition-->obtained. So I've switched Q and P so that one can see that. (this comment is hard to understand, but look back at the old version and you'll see) Motorneuron 21:08, 30 April 2006 (UTC)

It appears to me that you're rigidly applying "P is always a condition" and "Q is always the obtained". I think I understand this change, but I think this method is confusing also. If one misses the beginning phrase of the final statment in both sections, everything after looks identical and it's unclear what's going on. I favor preserving the order of the letters used (A sufficient for B, A necessary for B), and in that way one can see how the implication reverses direction between the two of them (B-->A, for necessity, A-->B for sufficiency).

The way I've heard the description of necessary/sufficient goes something like this: (A necessary for B) iff (Not A implies Not B). Note that this is logically equivalent to (B implies A)

Also, (A sufficient for B) iff (A implies B).

By preserving the order of A and B in the statements like this, when we get to "A is necessary and sufficient for B" it's immediately clear that "A-->B and B-->A". I plan on making this change in the article soon.--Rschwieb 17:37, 11 July 2006 (UTC)

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is this original work? for such a complex subject, that was sure rattled off quickly. had you already written it somewhere else? Kingturtle 03:12 Apr 18, 2003 (UTC)

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Previous version said:

[necessary and sufficient] should therefore not be too quickly conflated with iff

Correct me if I'm wrong, but I don't think this is correct. Necessary and sufficient is the same as iff, though neither are the same as logical equivalence. Evercat 23:40, 16 Nov 2003 (UTC)

I agree with Evercat. Can somebody explain that sentence? Otherwise I'm going to delete it. Timtzeptel 17:56, 14 Apr 2004 (UTC)

I agree as long as we're restricing this to mathematics and logic, where causality is not an issue. I'm slightly less certain in cases involving events occurring rather than propositions being true. But this locution "neither are the same", rather than "neither is the same" is weird. Michael Hardy 18:16, 14 Apr 2004 (UTC)

Examples used

Can someone rework this article with better examples? In the article itself are three different comments about how a particular example is confusing, and the smoke/fire example requires a footnote. I'm bad about thinking up "real-life" examples, but I'll give it a shot in a few days if no one else comes up with anything. Pagrashtak 5 July 2005 20:12 (UTC)

How about clouds and rain? 217.132.211.9 6 July 2005 05:40 (UTC)

I rewrote the example using thunder and ligthening. This may also be slightly confusing, but I understand the intent of using the confusing example of smoke and fire. It is to emphasize that causation and time ordering are not part of the definition of "necessary". I made this more explicit. Removed the stupid footnote. Let me know what you think of these changes.--Jeiki Rebirth 10:44, 9 June 2006 (UTC)

The thunder and lightening is a very poor example. Thunder and lightening are effects of the same physical phenomenon. To say one causes the other in any ordering will require a paragraph expalining eletrical current running through the air and how the two effects are produced. This example only serves to complicate the logical concept.

The Fourth of July example is logically flawed -- I would suggest that it is necessary but not sufficient that it be the Fourth of July for it to be Independence Day in the United States. If the year is 1730, for instance, there was a Fourth of July but not an Independence Day. Similarly, if an act of the United States Congress were to change the date for the celebration of Independence Day to, say, July 2 (as originally proposed by John Adams), then some future July Fourth could be July Fourth but not Independence Day. K95 18:05, 6 September 2006 (UTC)

Well then so is the thunder and lightning. If lightning strikes on another celestial body or in Earth's past/future where there is no atmosphere, there will not be any thunder. Similarly for card-based examples later - historically, or today in other countries, different suits were used.

Basically any examples we come up with will have the assumption (whether or not stated) that the situation is present-day Earth (and maybe some more specifics). Defining the situation/environment is inevitably required to use logic in all but the most abstract of fashions. (And even then, you need to define your notation at the least). 128.232.228.174 (talk) 08:59, 20 May 2008 (UTC)

"just in case", what?

I removed these sentences from the sufficient condition section "Necessary and sufficient conditions are therefore related. P is a necessary condition for Q just in case Q is a sufficient condition for P." Does this make sense to anyone? --Jeiki Rebirth 12:13, 9 June 2006 (UTC)

I also find "just in case" to be a bit obfuscating. "Push in case of emergency" means "If an emergency happens, then push". "Just in case" is taking on the meaning "iff". The way I under stand it, "(P sufficient for Q) iff (Q is necessary for P)" Try it out with Q=thunder and P=lightning.--Rschwieb 17:04, 11 July 2006 (UTC)

Role (or lack thereof) of causality in Necessary/Sufficient conditions

I removed the sentences mentioning causality because I felt that at their former location they interfered with the explanation, and I couldn't decide where to move it. If someone really feels it's a vital part of the explanation, might I recommend them to retrieve the info from before my July edits and organize them in an independent section about "causality and it's relationship with necessary/sufficient conditions?--Rschwieb 01:57, 19 July 2006 (UTC)

Deletion tag

I've (Shawn Fitzgibbons 19:40, 25 November 2006 (UTC)) nominated this article for deletion because it is redundant. There are already several articles that cover this topic. Here is a short list:

propositional logic
material conditional
logical implication

I've removed the prod tag. If you want this deleted you should take this to AfD. Paul August ☎ 02:39, 26 November 2006 (UTC)

Why is there not a page on unnessesary?

Why does unnessesary link here? Shouldn't there be a page on it? —The preceding unsigned comment was added by Ootmc (talk • contribs) 23:26, 14 February 2007 (UTC).

This page could use a lot of improvement

I think that as is, this article is too confusing to be useful to someone who is trying to understand the concept of necessary and sufficient conditions. Norman Swartz's article (in the external links page) is much clearer and simpler. I like how he makes it clear right away that necessary conditions are not the same thing as sufficient conditions, and vice versa.

One serious problem is the use of the language of implication in the explanations. If someone doesn't know what N/S conditions are, they probably won't know what implication is either. You can teach someone N/S conditions without mentioning implication.

Sorry I'm too lazy to fix anything at the moment. I thought I should point out the problems though. If the spirit moves me I will come do some editing. Manderr (talk) 10:02, 27 March 2008 (UTC)