The Necessary/Contingent Distinction
– A necessary proposition is one the truth value of which remains constant across all possible worlds.
– By contrast, the truth value of contingent propositions is not fixed across all possible worlds: for any contingent proposition, there is at least one possible world in which it is true and at least one possible world in which it is false.
The necessary/contingent distinction is closely related to the a priori/a posteriori distinction.
It is reasonable to expect, for instance, that if a given claim is necessary, it must be knowable only a priori.
Sense experience can tell us only about the actual world and hence about what is the case; it can say nothing about what must or must not be the case.
Contingent claims, on the other hand, would seem to be knowable only a posteriori, since it is unclear how pure thought or reason could tell us anything about the actual world as compared to other possible worlds.
While closely related, these distinctions are not equivalent.
The necessary/contingent distinction is metaphysical: it concerns the modal status of propositions.
As such, it is clearly distinct from the a priori/a posteriori distinction, which is epistemological.
Therefore, even if the two distinctions were to coincide, they would not be identical.
But there are also reasons for thinking that they do not coincide.
Some philosophers have argued that there are contingent a priori truths (Kripke 1972; Kitcher 1980b).
An example of such a truth is the proposition that the standard meter bar in Paris is one meter long.
This claim appears to be knowable a priori since the bar in question defines the length of a meter.
And yet it also seems that there are possible worlds in which this claim would be false (e.g., worlds in which the meter bar is damaged or exposed to extreme heat).
Philosophers disagree about what to make of cases of this sort, but if the above interpretation of them is correct, a proposition’s being a priori does not guarantee that it is necessary, nor does a proposition’s being a posteriori guarantee that it is contingent.
Finally, on the grounds already discussed, there is no obvious reason to deny that certain necessary and certain contingent claims might be unknowable in the relevant sense. If indeed such propositions exist, then the analytic does not coincide with the necessary, nor the synthetic with the contingent.