Talk:Necessity and sufficiency

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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)

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)

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[edit]

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? 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). (talk) 08:59, 20 May 2008 (UTC)

"just in case", what?[edit]

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[edit]

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[edit]

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)
I think this is an important article. Maybe the articles you cite here could link to this article, rather than redescribe necessary/sufficient? --Andy Fugard (talk) 07:13, 30 September 2008 (UTC)

Why is there not a page on unnessesary?[edit]

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

This page could use a lot of improvement[edit]

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)

The mathmatics section is horribly unclear. I have no idea what it's supposed to mean, and I've taken some legit Philosophy department logic classes :(Floodo1 (talk) 08:23, 17 December 2008 (UTC)
Yes, this article is seriously important for ordinary usage of the terms, which is more in line with philosophy than the specialist maths examples. The value of an example is its ability to make something complex more specific and clear. Logic comes before Group Theory in pure mathematics, the examples are not really valuable even to mathematicians.
I hope the pictures and captions I added help. I think people will understand the usefulness of the ideas better if they see examples of each kind of condition, where it is important that the other kind of condition would not be the right description.
Mate, I'm swamped with other work, would you care to add some more simple, clear text to the article. Go right to the top and work on the lead. Don't delete anything, then no one can complain. But good simple clear text might lead others to have confidence the more tricky stuff isn't really needed.
There's some links that could help. Stanford Encyclopedia of Philosophy is excellent on topics like this. Without breaching copyright, following their example might give you plenty of ideas. Make this a holiday project mate! I'll cheer from the sidelines. ;) Just do it! Alastair Haines (talk) 23:08, 17 December 2008 (UTC)
I know this thread is a bit old, but I must agree with Manderr. I consider myself a reasonably intelligent person (although more on the liberal arts side), but I still have only a very foggy idea of the difference between a necessary and sufficient condition after reading this article several times.... Lithoderm 02:05, 18 September 2010 (UTC)

I totally agree that this article is confusing. I found this much better description in a philosophy page from hong kong...(apparently open source)[1]:

The concepts of necessary and sufficient conditions help us understand and explain the different kinds of connections between concepts, and how different states of affairs are related to each other.

§ M06.1 Necessary conditions

To say that X is a necessary condition for Y is to say that it is impossible to have Y without X. In other words, the absence of X guarantees the absence of Y. A necessary condition is sometimes also called "an essential condition". Some examples :

Having four sides is necessary for being a square. Being brave is a necessary condition for being a good soldier. Not being divisible by four is essential for being a prime number. To show that X is not a necessary condition for Y, we simply find a situation where Y is present but X is not. Examples :

Being rich is not necessary for being happy, since a poor person can be happy too. Being Chinese is not necessary for being a Hong Kong permanent resident, since a non-Chinese can becoming a permanent resident if he or she has lived in Hong Kong for seven years. Additional remarks about necessary conditions :

We invoke the notion of a necessary condition very often in our daily life, even though we might be using different terms. For example, when we say things like "life requires oxygen", this is equivalent to saying that the presence of oxygen is a necessary condition for the existence of life. A certain state of affairs might have more than one necessary condition. For example, to be a good concert pianist, having good finger techniques is a necessary condition. But this is not enough. Another necessary condition is being good at interpreting piano pieces.

§ M06.2 Sufficient conditions

To say that X is a sufficient condition for Y is to say that the presence of X guarantees the presence of Y. In other words, it is impossible to have X without Y. If X is present, then Y must also be present. Again, some examples :

Being a square is sufficient for having four sides. Being divisible by 4 is sufficient for being an even number. To show that X is not sufficient for Y, we come up with cases where X is present but Y is not. Examples :

Loving someone is not sufficient for being loved. A person who loves someone might not be loved by anyone perhaps because she is a very nasty person. Loyalty is not sufficient for honesty because one might have to lie in order to protect the person one is loyal to. Additional remarks about sufficient conditions :

Expressions such as "If X then Y", or "X is enough for Y", can also be understood as saying that X is a sufficient condition for Y. Some state of affairs can have more than one sufficient condition. Being blue is sufficient for being colored, but of course being green, being red are also sufficient for being coloured. § M06.3 Four possibilities

Given two conditions X and Y, there are four ways in which they might be related to each other:

X is necessary but not sufficient for Y. X is sufficient but not necessary for Y. X is both necessary and sufficient for Y. (or "jointly necessary and sufficient") X is neither necessary nor sufficient for Y.

This classification is very useful in when we want to clarify how two concepts are related to each other. Here are some examples :

Having four sides is necessary but not sufficient for being a square (since a rectangle has four sides but it is not a square). Having a son is sufficient but not necessary for being a parent (a parent can have only one daughter). Being an unmarried man is both necessary and sufficient for being a bachelor. Being a tall person is neither necessary nor sufficient for being a successful person.

Much clearer, maybe some ideas can be incorporated into this article... (talk) 14:50, 19 February 2014 (UTC)



Title discussion[edit]

I don't believe that the recent title change really reflects anything helpful to the reader. "Necessity" and "sufficiency" are themselves used in many different contexts, and I think that without some sort of qualifier of logic, the purpose of the article is unclear. MSJapan (talk) 19:23, 11 February 2012 (UTC)

The article is about the distinct, but related, concepts of 'necessity' and 'sufficiency', and not about 'necessary and sufficient conditions', which is only one of the four basic types: necessary and sufficient, necessary but not sufficient, sufficient but not necessary, and neither necessary nor sufficient. So, although the current title uses a phrase which may be used in other contexts – I would argue, however, that the logical concept is the primary meaning – the former title was misleading.
As for concerns of clarity, I don't think that disambiguation is needed at this time since we don't seem to have another article with a similar title. We generally do not disambiguate preemptively (e.g., we have Leroy Shield and not Leroy Shield (composer)) and the article's lead – "In logic, ..." – makes clear the scope of the article for anyone who is unfamiliar with the topic. -- Black Falcon (talk) 19:58, 11 February 2012 (UTC)

Definitions and letters[edit]

There's a fifty-fifty chance the misunderstanding is my fault and not the articles, but why in this world is the statement called S when defining necessary conditions, and N when defining sufficient conditions, particularly when the conditions are called N and S respectively? It results in both definition evaluating to the same string 'S implies N' although they should have, I presume, entirely different meanings. Would it be unreasonable for the statement to be defined by a single, not-S/N letter in both cases? Darryl from Mars (talk) 01:08, 26 July 2012 (UTC)

Venn diagram is NOT representative[edit]

Seems to me that the N(S) Venn diagram in the Relationships... section illustrates only ONE of the possible relationships between S and N. The caption makes it sound as if that is the ONLY relationship. In fact, the text directly next to the image states "... sufficient but not necessary". This is highly confusing. Am I missing something?

ScottHW (talk) 14:07, 21 August 2013 (UTC)

I'm not sure what you're complaining about. The diagram seems to accurately display the generic relationship between a necessary condition and a sufficient condition. — Arthur Rubin (talk) 18:15, 21 August 2013 (UTC)
This confused me also. After puzzling for some time, I understand that N and S in the diagram actually represent statements (eg N="x is a mammal", S="x is human") and do not actually represent the relationships "necessity" and "sufficiency". I changed the caption to be clearer, I hope. Krubo (talk) 22:26, 7 October 2013 (UTC)

Definitions section[edit]

"A true necessary condition in a conditional statement makes the statement true."

This is wrong. The conditional statement may still be false. That means it's an erroneous conditional statement. If you mean it makes the consequent true, this is still wrong. A true /sufficient/ condition in a conditional makes the consequent true.

People aren't typically interested in the truth-value of the conditional statement. They assume their conditionals are true. They're interested in the truth-value of the consequent, and they'll assume that "makes the statement true" means "makes the consequent true". A true necessary condition does not make the consequent true.

"A true sufficient condition in a conditional statement ties the statement's truth to its consequent." Every conditional statement's truth is tautologically tied to its consequent, so this statement is useless.

Do not mention the "conditional statement". We are discussing conditions, which are the left-hand side of a conditional statement, and nobody cares about the truth-value of the conditional statement. And this is all you need to say:

A true sufficient condition for the proposition P makes P true. A false necessary condition for the proposition P makes P false.

The truth table is correct, but its presentation is very confusing, particularly since it is re-using "N", which was just used to indicate a necessary condition, and now does not.

However, all of the above is still misleading. Necessary and sufficient conditions are not a set of necessary conditions plus a set of sufficient conditions. Being necessary and sufficient is a property of the entire set of conditions. You don't separate out those that are necessary and those that are sufficient. You typically collect a bundle of qualifying conditions that are true for everything in your category, and then add prohibitions that rule out everything not in your category for which the first bundle of conditions is true. The first bundle is not sufficient; an entity satisfying them may still fail to satisfy a necessary condition. The second bundle, of prohibitions, is necessary, but most of the things you think of as "necessary", e.g., "birds have wings", would be in the qualifying conditions, not in the prohibitions. "Necessary and sufficient" should be applied to the complete set of conditions; categories are not usually defined in ways that provide either a set of "necessary" nor a set of "sufficient" conditions.

Philgoetz (talk) 01:10, 21 January 2014 (UTC)

Yes please, be WP:BOLD.—Machine Elf 1735 16:28, 21 January 2014 (UTC)
@Philgoetz: I agree completely, the definitions are confusing. It seems to me to be because he preserves the meaning of N and S in the first parts as "necessary" and "sufficient" respectively. This is helpful if the question is "Which part is necessary/sufficient?", but the question most people will be asking is "Is the condition necessary/sufficient?". Keeping this in mind, the conditions established as necessary and sufficient should have the same name.
I attempted to rewrite the section with this paradigm (among other changes), but then I realized that all of this section's content is contained in the sections Necessity, Sufficiency, and Simultaneous Necessity and Sufficiency (except the truth table, which seems extraneous to me). So maybe Definitions should just be removed? Noblesp (talk) 20:52, 3 March 2015 (UTC)

Bachelor Example[edit]

"Example 1: In order for it to be true that "John is a bachelor," it is necessary that it be also true that he is: unmarried, male, and an adult, since to state "John is a bachelor" implies John has each of those three additional predicates." Should the list include human? If John is an unmarried adult male dog, that doesn't make him a bachelor. Alternatively you could replace 'is adult, male, and a human' with 'is a man.'OckRaz talk 19:02, 3 February 2014 (UTC)

Train Example[edit]

It seems to me that the train example in the image caption is actually flawed "That a train runs on schedule can be a sufficient condition for arriving on time (if one boards the train and it departs on time, then one will arrive on time)". This is probably a poor choice of example trains and rail networks are complex systems with many variables a train which departs on time may still fail to arrive on time due to breakdown of the vehicle or delays on the network for many reasons. I'm struggling to think of a better everyday example right now but thought I'd mention it in case someone has an idea. MttJocy (talk) 00:19, 25 July 2015 (UTC)

An Alternative to the Train Example[edit]

As MttJocy wrote above, the train example is quite a confusing one. I found a simpler example from Khan Academy (which can be used as a source). Here's the example:

"Boiling potatoes is a sufficient condition for cooking potatoes but is NOT a necessary condition for cooking them. This is because boiling potatoes is enough to cook them which makes this method sufficient. However, boiling potatoes is not a necessary condition to cook potatoes because there are other ways such as frying, grilling and baking that can cook potatoes as well." — Preceding unsigned comment added by Ragzputin (talkcontribs) 20:39, 14 June 2017 (UTC)

italicized uppercase letter & double quotes.[edit]

there's a problem with character spacing when an italicized uppercase*** letter ends a statement in double quotation marks. the letter and the first mark get smooshed together so instead of "if S then N", it looks like "if S then N', which could cause some confusion if an already confused reader thinks there is some new entity N prime.


A true necessary condition in a conditional statement makes the statement true (see "truth table" immediately below). In formal terms, a consequent N is a necessary condition for an antecedent S, in the conditional statement, "N if S", "N is implied by S", or N S. In common words, we would also say "N is weaker than S" or "S cannot occur without N". For example, it is necessary to be Named, to be called "Socrates".

(highlighted sections)

i added a single space in the middle of the following highlighted source markup, in all 20 instances of this issue.

"''N'' if ''S''" becomes "''N'' if ''S'' "

resulting in, "N if S" becoming, "N if S "

i know it's not syntactically correct, so if this really rubs someone the wrong way and they want to revert, i did it all in a single edit.

***oh, i also put the space in example 5 of Necessity_and_sufficiency#Necessity where it's a lowercase x. sensorsweep 04:36, 3 March 2015 (UTC)

Necessary AND sufficient?[edit]

"Being a male sibling is a necessary and sufficient condition for being a brother"

No it isn't.

It's a necessary condition, because, in order to be a brother, you must be a male sibling. The second in implied by the first.

It is not a sufficient condition, because you can be a male sibling and not be a brother. For example, father and son are male, sibling, non-brothers. — Preceding unsigned comment added by (talk) 03:22, 9 September 2015 (UTC)

What is your definition of a sibling? Bill Cherowitzo (talk) 03:31, 9 September 2015 (UTC)

Non-classical and modal logics[edit]

It is a bit of a lacuna in the article that these are not treated. — Charles Stewart (talk) 07:24, 2 May 2016 (UTC)

"And" or "or" in the caption[edit]

While the phrase "necessary or sufficient" is grammatically correct, it is only mathematically correct because we use the inclusive "or" in mathematics. There is a certain duality present in these terms, and while they can hold jointly, holding separately does not make much sense. Indeed, the statement that "a condition is either necessary or sufficient" conveys, at least to me, a state of befuddlement and not much more. I see absolutely nothing to be gained by using "or" in this caption and it is really stretching the English language to use it in this way. --Bill Cherowitzo (talk) 22:23, 27 July 2017 (UTC)

  1. ^