4 - Necessary and Sufficient Conditions
Necessary and sufficient conditions help to explain the connection between concepts and identify where causal relationships exist - as well as recognizing where they might seem to exist, but do not.
Necessary Conditions
To say that one thing is a necessary condition for another suggests that the first must exist for the second to occur.
Consider this: there must be oxygen for a fire to catch. This does not mean that oxygen causes the fire to catch, or that a fire can catch if only oxygen is present. However, it cannot catch without oxygen.
To dispute that one is necessary for the other, you must identify a situation where the necessary cause is absent, but the precipitating effect still occurs. That is, you cannot assert that mammals must live on land because whales are mammals.
The relationship between a phenomenon and its necessary causes is one-to-many - there may be multiple necessary conditions.
Sufficient Conditions
Sufficient conditions, meanwhile, guarantee that something else will be occur, or will have occurred. For example, in order to be a grandfather, you must have been a father (because you must have had children, who had children, to be their grandfather)
To show that one is not sufficient for the other, we list cases where one occurs and the other does not. For example, you cannot assert that to be a father, you must also be a grandfather (because your children have not yet had children of their own).
Describing How Two Things Are Connected
Considering any two phenomena
- One may be both necessary and sufficient for the other (being unmarried is necessary and sufficient for being a bachelor)
- One may be necessary but not sufficient for the other (oxygen is needed for survival, but it alone does not guarantee survival)
- One may be sufficient but not necessary for the other (having a son is sufficient to be a parent, but one may also be a parent of a daughter)
- One may be neither sufficient nor necessary for the other (having wealth is neither sufficient or necessary to be happy)
Much of this seems self-evident, given the simplicity of the examples, but failure to consider necessity and sufficiency (or mistaking one for the other) is a common cause of problems for more complex subjects.
For example, the claim that computers cannot think because they do not experience emotion presumes that emotion is necessary to thought. The person who disagrees defines "thought" differently, perhaps as deductive reasoning, and therefore argues that they can. The argument is not about the capability of the device, but the definition of the term.
Necessity and sufficiency are also important to defining terms adequately. A definition describes conditions that are both necessary and sufficient for the term it describes. It may not be comprehensive in that regard, and the degree to which it is comprehensive represents a risk in clarity when the definition is applied.
The Write-Off Fallacy
One problem germane to necessity and sufficiency is the write-off fallacy, which argues that something is unimportant (to be ignored) because it is not necessary or sufficient for something else. This generally reflects a difference between binary and probability.
For example, one might argue that democracy is unimportant because it does not guarantee quality of life for citizens, and cite as an example the culture that can exist in a benevolent dictatorship. This ignores the case that a democratic political system, by making the rulers beholden to the interests of their subjects, is far more likely to produce a positive culture.
Strictly speaking, democracy is not a necessary or sufficient cause of prosperity - but neither can it be assumed that the absence of democracy would be one.
Different Kinds of Possibility
Necessary and sufficient conditions are related to the concept of possibility and impossibility in a binary manner. But the nature of possibility and the way in which it is comprehended is mutable. To argue that "it is impossible to draw a red square without drawing a square" and "it is impossible to drink alcohol if you are under 18 years of age"
Possibility and impossibility are subject to certain laws, and the laws of man is far less binding than the laws of science. That is, it is entirely possible to drink alcohol if you are under 18 - it may not be permissible by the laws of the land, but it is not impossible.
In another sense, possibility derives from present reality. In the nineteenth century, it was impossible for a man to walk on the moon. In the twentieth, it was done. In the future, there may be a resort there.
When something is declared to be impossible, you must question: what causes it to be so? And consider if the reasons or valid or the conditions might change.
Exclusive Possibilities
Apart from causality and the possibility of things, there are also useful concepts that consider the probability of things - where one condition's truth might prevent another condition from being true. To say that someone is in Spain right now means it is not possible for them to be in Brazil.
It's also important to note that one condition might increase the probability of another: if someone is in Spain, they might be in Madrid, and have a higher probability of being in Madrid than if their location was unknown. It does not make it certain, but it does indicate it is possible.
There is also the notion of exhaustive possibilities, which provide a set of conditions for which one must prove true. A common mistake is believing that only one must be true, and the others must be false - which is not a characteristic of an exhaustive set, but of a mutually-exclusive set.