Nice question.

Causation is different from necessity and sufficiency how you define them. In diagnostic frameworks (say the DSM in psychiatry) there may be necessary and/or sufficient characteristics for diagnosis of conditions. This doesn't mean they have a causal role. A different way to think about causal roles is Pearl's do(x). If you do something that changes x (and nothing else directly, so nothing else not mediated by x), if y changes then x has a causal role. I recommend looking at Pearl's book Causality. I've attached an older paper on causality where I talk a little bit about necessity and sufficiency, but in a different field.

Article Causal and associative hypotheses in psychology: Examples fr...

Thank you very much [@Daniel_Wright7]. I liked Pearl's do(x) thought exercise a lot, but it is still difficult to implement in empirical studies. This gives me a few leads to investigate further, and I will get back to you. Thanks again.

Two empirical methods that can draw causal inferences on the basis of sufficient and necessary conditions are Qualitative Comparative Analysis (QCA) and Coincidence Analysis (CNA), both of which are centrally based on John L. Mackie's (1974) INUS theory of causation, but QCA and CNA enhance this theory in important respects.

What is essential to point out is that, per se, neither necessary nor sufficient conditions have any causal implications whatsoever. For example, being poisoned is necessary for being bitten by a rattlesnake (P

Thank you very much Alrik! That was such an extensive answer, and it gave me a lot of information and even more leads for diving deeper into the subject. I did talk with a colleague about the logical counter examples you mentioned. I can't wait till the weekend when I have the time to look more into the material you referenced. Thanks again.

I have to take issue with some of the discussion so far.  Necessary and sufficient conditions are by definition aspects of causality. Furthermore there is a temporal dimension to causality and conditions: and when dealing with complex systems such as organisms, it is effectively impossible to have a change with only one cause (pace Pearl).  I'll come back to the second and third points but first let's look at necessary and sufficient conditions.

QCA (I don't know about CNA) only infers that certain conditions may be necessary or sufficient - it may do so very strongly - but Younos Aboulnagi is quite correct, it is an inference.  Mills argument  that you can identify necessary and sufficient conditions  post hoc  is a fallacy. If we go back to first principles, we can get a better understanding of the issues.

First, a condition is a priori a requirement that precedes or is at least contemporaneous with a change in state and without which the change cannot occur.

A sufficient condition is one that is sufficient in and of itself to bring about a change.  It is and can only ever be treated as the single cause of the change.  Such sufficient conditions are extremely rare, if not infinitely so, when dealing with complex systems. If you have a sufficient condition, there are no necessary conditions.

A necessary condition is one that is necessary for the change to occur but not sufficient in and of itself.  Without the necessary condition the change cannot take place. However, a change may be (and usually is)  the result of several necessary conditions being met.  Often no condition is  sufficient on its own but taken together a number of necessary conditions generate the change.  In which case the co-occurrence of such conditions is the cause.  A necessary condition may also be a catalyst and seen as essential but not sufficient to some other 'cause.'  Yet if it is not present the 'other 'cause' is not sufficient so must also be treated as a necessary condition. 

When we can conduct a controlled experiment excluding unknown conditions, then we may make very strong inferences about causality, especially if we have a theory or hypothesis for the change.  Nevertheless, it is only an inference not absolute proof. However,  observations post hoc without controlling for unknown conditions (as occurs in QCA)  allows only weak inferences about causality and the necessary or sufficient conditions.  The likelihood of other unknown factors having a greater influence is significant.  The inferences we draw from QCA may be the best we can get and at least they are observations in vivo. However, the presence of unknown and uncontrolled variables weakens any inferences that may be drawn.

The temporal issue is also important.  Causality is premised on time passing in one direction.  If X, then Y.  Even in quantum physics, Y does not come before X, it may come at the same time but not before.  A post event state cannot be a condition for a prior event. 

Finally, changes in complex systems generally do not have simple causes.  There are two reasons for saying this.  First, a complex system is an interdependence of multiple factors interacting within the system.  Any changes in a complex system are the result of  such interactions.  A trigger may lead to change but the same trigger can have different results depending on when it is applied and where.

Second, many complex systems (such as organisms, societies)  exist in a dynamic environment and have multiple, often simultaneous interactions with that environment.  The system is different from moment to moment but more importantly, there are multiple variables acting on the system in different ways.  What one does is not the only factor affecting the changes in the system.  Just because one changes X and only X does not mean that nothing else changes.  A, B & C are likely to change and it is very difficult to exclude such changes from complex systems.   

Mr. Roberts argues that "Necessary and sufficient conditions are by definition aspects of causality." I would like to see an authoritative reference to a definition that directly associates the concepts of "necessity" and "sufficiency" with that of "causality", and that is used in the context of empirical data analysis for purposes of causal inference.

The standard Boolean-algebraic definition of an implication "A -> B", which is translated into plain English as "A is sufficient for B", or "B is necessary for A" or "If A, then B", in terms of the three fundamental Boolean operations "NOT" (¬), AND (*) and OR (+) is: A -> B := ¬A + B, which is equivalent with ¬(A * ¬B). In other words, claiming that some A is sufficient for some B means nothing beyond the claim that there exists no (or relatively few) case(s) of A which also exhibit the absence of B. This is the definition behind Mill's Methods, and it is also the definition used in QCA and CNA.

Mr. Roberts further argues that "QCA [...] only infers that certain conditions may be necessary or sufficient." This is plain wrong. QCA implements a theory of causality that assumes causal structures to be representable as Boolean expressions. Since causes must be difference-makers to their effects, QCA eliminates all redundancies (non-difference-makers) from sufficient conditions in the first stage, and all redundancies from necessary conditions in the second stage, using a purpose-built algorithm such as Quine-McCluskey, for example (with some modifications).

What Mr. Roberts describes as "the environment" is called a "causal field" in the INUS theory of causation. All potentially causal dependencies identified by QCA are always only interpretable against the background of a constant causal field.

Lastly, Mr. Roberts asserts that "If you have a sufficient condition, there are no necessary conditions", which is again plain wrong. For instance, all "if, and only if"-statements are based on conditions that are simultaneously sufficient and necessary. Such statements are captured by the EQUIVALENCE operator (also called bi-conditional; ).

I hesitated to respond because I don't want to put people off QCA or comparative case studies.  I am an advocate for Mill’s comparative case analysis and the method of difference. Comparative case studies and QCA look at phenomena post hoc and try to identify features common to different results, or at least present in several similar results. It is often the most appropriate way to collect evidence about complex situations where there are often multiple unknown variables and experimental methods are not suitable.

Causal inferences

That said, I disagree with the assertion that the method of difference does not attempt to draw causal inferences.  Why use them at all if you are not trying to draw causal inferences? 

Mill wrote of the method of agreement,

“If two or more instances of the phenomenon under investigation have only one circumstance in common, the circumstance in which alone all the instances agree is the cause (or effect) of the given phenomenon” (Mill 1967, p. 390).

He also wrote of the method of difference

"If an instance in which the phenomenon under investigation occurs, and an instance in which it does not occur, have every circumstance in common save one, that one occurring only in the former; the circumstance in which alone the two instances differ, is the effect, or the cause, or an indispensable part of the cause, of the phenomenon. (Mill 1967, p. 391)

Quite what Mill meant by ‘cause’ is debatable. As a philosopher Mill must have read Aristotle on cause. Aristotle recognised four different causes: 

• The material cause: “that out of which”, e.g., the bronze of a statue.
• “The formal cause: “the form”, “the account of what-it-is-to-be”, e.g., the shape of a statue.
• “The efficient cause: “the primary source of the change or rest”, e.g., the artisan, the art of bronze-casting the statue, the man who gives advice, the father of the child.
• "The final cause: “the end, that for the sake of which a thing is done”, e.g., health is the end of walking, losing weight, purging, drugs, and surgical tools.” (Stanford Encyclopedia of Philosophy)

Mill may have meant some or all of such ‘causes’ but the use of the word ‘effect’ suggests that he probably thought of cause pretty much as ‘efficient cause’ and probably very similar to current research ideas about cause, which is defined in the Oxford Dictionary as

‘that which produces an effect , or gives rise to an action, phenomenon or condition.’ (Oxford Dictionary)

I understood Dr Theim to follow Mill and assumed he meant that necessary and sufficient conditions are associated with causality. I may have misunderstood him but I am surprised that he now argues that they are not associated. It is difficult to see why one would bother if one did not intend to imply a causal relationship.  Indeed Dr Theim says as much when he wrote:

“Two methods that can draw causal inferences on the basis of necessary and sufficient conditions are …”

and

“QCA implements a theory of causality that assumes causal structures to be representable in Boolean expressions.”

Difference between co-occurrence and conditions

I accept the argument that Boolean logic, in and of itself, describes co-occurrence and says nothing about any possible relationship between phenomena, nor does it imply temporality between the events. 

However, when one starts talking about necessary and sufficient conditions, or ‘causes’ in Mill’s case, then one is describing a relationship.  Indeed it is a well-established principle in formal logic that a necessary or a sufficient condition describes a relationship between the two phenomena. It implies more than co-occurrence of the two phenomena. 

The characteristics of Boolean logic do not define the method of difference or the method of agreement (or their use in QCA).  Boolean logic is a tool used by QCA and the characteristics of QCA derive principally from the method of difference and the method of agreement.

I won’t write more on ‘conditions’ here, except that Dr Theim was correct when he pointed out that I omitted to mention that there are conditions that are both necessary and sufficient. N can only occur if S has also occurred (S is both a necessary and sufficient condition for N). 

My comment that “If you have a sufficient condition, there are no necessary conditions.” was poorly worded.  I meant of course that if one has a sufficient condition, then the change will occur without any separate necessary conditions.

Other causes

The problem I have is that observation post hoc does not allow one to identify whether a condition is ‘necessary’, or ‘sufficient’, or ‘necessary and sufficient’, or 'coincidental'. 

What if,

N can occur even when S does not occur

But we have not observed such an instance

Post hoc observation of complex, uncontrolled events cannot exclude the last possibility.  Co-occurrence may be totally unrelated or be the result of some unobserved, underlying causal factor.

Both Mill and Ragin recognise the alternative cause argument. Mill made an extended and cogent argument that “the method of difference is inapplicable in social science.” Schlosser et al reiterated the argument that such methods

“ … may not prove (stress in original) any causal relationship, because it is most often impossible (in social science at least) to test a clear and complete (preconceived) model of such links and to sufficiently “control” for other factors. They constitute, however, a valuable step toward eliminating irrelevant factors and approximating causal conditions in the “real” world." (Schlosser, Meur, Rihoux and Ragin 2008)

In other words the value of QCA is to test and falsify hypotheses.  It does not prove the relationship but it can invalidate the hypothesis. It can be used to identify evidence to test a theory.  It should not be used inductively to develop theory (see Sekhon 2004, Perspectives on Politics, 2 (2): 281).

I suspect that the difficulties of applying the methods of difference and agreement led some proponents of QCA to argue that necessary and sufficient conditions are not causal.   Such arguments reveal an inherent contradiction.

Such arguments that QCA or the method of differences are acausal go against the fundamental premises of the method of difference and the method of agreement.  To go back to the first two quotes in this post, Mill asserted that where an observed circumstance (or condition) is the only difference between phenomena (or is the only common factor) then it is the cause of the difference (or the common cause of the phenomena).  Ragin does not quite say this (though he does quote Mill on this point). However, the logic of the method of difference and the method of agreement (even in QCA) appears to lead inexorably to causal inferences.

We should be very careful about how we use the method of difference and the method of agreement; and be circumspect in what inferences we draw. Lieberson (1991, Social Forces, 70 (2): 307)) went further and argued that such methods should not be used without “more rigorous justification of heroic assumptions and a guard against possible distortions.” (p.307) 

Thank you very much David [@David_Roberts56] and Alrik [Alrik_Thiem]. Such a wonderful discussion, that left me speechless with gratitude for the amount of effort you put into answering my question. It also left me with so much reading to do; not the answers, but the references. In particular I will be reading about QCA and CNA, Mill's methods of Agreement and Difference, as well as Pearl's Do(x) calculus. I will not be able to finish all this and catch up during the weekend, but I will try to read more during my daily commute to catch up. Thanks again.

I am currently reading this book, which is a gentle inteoduction to the subject:

http://shop.oreilly.com/product/mobile/0636920033035.do