Wednesday, April 29, 2026

necessary condition versus sufficient condition

 

If the necessary condition is present, the thing may occur. (If I am in MA, I may be in Boston. Being in MA is necessary to being in Boston.)

If the thing occurs, the necessary condition must be present. (If I am in Boston, I must be in MA. Since being in MA is necessary to being in Boston, when I am in Boston, I am in MA.)

Also, 

if the sufficient condition is present, the thing occurs. (If I am in Boston, I am in MA. Being in Boston is sufficient to know I am in MA.)

If the thing occurs, the sufficient condition may or may not be present. (If I am in MA, I may or may not be in Boston. While being in Boston is sufficient to know I am in MA, being in MA does not necessarily indicate I am in Boston.)


Note that while in every instance a thing occurring every necessary condition of that thing must occur, conditions which are sufficient for the thing to occur may or may not occur when that thing occurs. 

Being in Boston is a sufficient condition of being in MA. But, I can be in MA without being in Boston. This demonstrates that the thing (being in MA) can occur without the sufficient condition (Being in Boston) also occurring. There may be several "triggers" sufficient for a certain thing to occur. Any one of them is sufficient to trigger that thing occurring. For the thing to occur, a single sufficient condition could be triggered, or multiple, or even none. But every necessary condition will occur, every time. 


for example:

if it rains, the pavement will get wet 

rain is sufficient for to the pavement to get wet 

however, 

if the snow melts, the pavement will get wet 

snow melting is sufficient for the pavement to get wet

 
Note how the pavement could get wet either by rain or by snow melting. The pavement could also get wet if both things happen. The pavement could also get wet if neither of these things happen. It could get wet in an entirely different way. It could get wet because I paint it with bubble mix. If the pavement does get wet, all I know is that one of these things could have occurred, but I do not know that either or both did occur. 


on the other hand:

every time the pavement gets wet, it is slippery to walk on 

slipperiness is a necessary condition of the pavement wetness 

wetness is a sufficient condition of pavement slipperiness 

note that the pavement will be slippery to walk on every time it gets wet

however, 

If the pavement is slippery, this does not necessarily mean that it is wet. It could be slippery for other reasons. Curious George could have laid out a thousand banana peals on the pavement and thus made it slippery. However, if the pavement is wet, I do know that it is slippery. 

if the pavement is slippery, then it may be wet (the necessary condition does not guarantee the sufficient condition)

if the pavement is wet, then it is slippery (the sufficient condition guarantees the necessary condition)

if it rained, then the pavement is wet (the sufficient condition always implies the necessary condition)

if the pavement is wet, then it may have rained (the necessary condition may or may not imply the sufficient condition)

if snow melts, then the pavement is wet (the sufficient condition always implies the necessary condition)

if the pavement is wet, then snow may have melted (the necessary condition may or may not imply the sufficient condition)


When the sufficient condition is met, every necessary condition is present. 

When the thing occurs (AKA when every necessary condition is present), the sufficient condition may or may not have been triggered.