Necessary And Sufficient Conditions
by The Durable Leadership Team
September 24, 2021
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In philosophy, necessity and sufficiency are often used to discuss the degree to which a set (which can be one or many elements) of conditions has explanatory power for the causation of a particular outcome. When we analyze the relationship between a set of circumstances and a particular subsequent outcome, we attempt to identify direct causation or at least a very high degree of correlation that would warrant further investigation if the actual linkage is unknown. For a set of circumstances to be considered a cause of a subsequent event, it must be shown that it is a necessary and sufficient condition for the event in question. In other words, the presence of the alleged set of preconditions must guarantee the occurrence of that particular subsequent event without fail.
For example, suppose we want to show that smoking causes lung cancer. In that case, we must demonstrate that all smokers develop lung cancer. However, this is not always possible, as other factors may be at play. For instance, some smokers never develop lung cancer, while some nonsmokers do. As a result, demonstrating that smoking is a guaranteed singular cause of lung cancer is often difficult. Furthermore, the conjoined properties of necessity and sufficiency of a set of circumstances can be challenging to understand. So we will return to this shortly.
Neither necessary nor sufficient conditions.
Let’s start at ground zero. That is to say, where a particular circumstance is classified as neither necessary nor sufficient for the transpiration of a particular outcome. In other words, such a factor is said to have no impact on the outcome. So, for example, we can say that sleeping in a blue shirt is neither necessary nor sufficient to guarantee pleasant weather for tomorrow. In other words, there is no causal relationship.
A necessary condition is required for a specific result. Without the necessary condition being true, the result would not exist regardless of any other condition being present. For example, in a class where the professor has decided that for any student to pass the course, the student must attend no less than 12 out of 16 classes, the necessary condition for passing this course is that particular attendance requirement. In this hypothetical case, even if the student earned an A on the final exam but was absent for five classes, that student did not meet the necessary condition and did not pass the class. In this case, we would say that attendance is a necessary but insufficient condition to pass the class because while you cannot pass the class without proper attendance, you need a passing grade as well.
In some cases, no necessary conditions exist to guarantee a specific outcome. Yet, some set circumstances exist in which one or more (but not necessarily all) would result in the outcome. For example, to graduate from college, a student might need to pass a certain subset of classes in the catalog of general education courses. In this case, earning passing grades in any approved combinations of these core courses would be a sufficient condition for graduation. Still, no particular course is necessary for graduation.
Necessary and sufficient conditions.
The final combination is the existence of necessary and sufficient conditions to result in a particular outcome. For this example, we shall look at the qualifications for entering the selection process to become the head of the Catholic church. To be Pope, there are only two stated conditions:
- Be male.
- Be baptized in the Catholic church.
This means that neither a man who is not of Catholic faith nor a woman who is of the Catholic faith would qualify. Despite each having one necessary condition, neither has sufficient conditions. So, per the stated requirements, any Catholic man holds the complete set of necessary and sufficient conditions to qualify for the selection process.
Yet we know that any average man of the Catholic faith would still not automatically become Pope upon the vacancy of that position because one more unwritten necessary condition exists—the selection process conducted by the college of Cardinals typically excludes all except those from among their ranks. Since Cardinals are all male Catholics, this is, therefore, a wholly contained subset of the entire population of all male Catholics. So the complete collection of necessary and sufficient conditions to qualify for the selection process to become the head of the Catholic church is the following singular item:
- Be a Cardinal.
Remember that we are using this as an example of a necessary and sufficient condition to qualify for the selection process, not to become Pope.
While the philosophy of necessary and sufficient conditions can be difficult to grasp, it plays an important role in our understanding of how the world works. Having a firm understanding of these ideas will be useful in analyzing all events in general and the interplay of power dynamics in particular for our interests.
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