Contingent a priori and necessary a posteriori

It was once the consensus that all a priori knowledge was necessarily true and all a posteriori knowledge was contingently true. In fact, this consensus is seemingly itself a priori knowledge. However, the philosopher Saul Kripke has shown that this could be wrong. He proposes examples that successfully demonstrates how an a priori knowledge could be contingently true, and also how an a posteriori knowledge could be necessarily true.

For the uninitiated, I'll give some quick and simple background information. The idea was that a priori knowledge was knowledge that could be confirmed in the absence of experience. For example, the proposition "all bachelors are unmarried men" would be an a priori knowledge. A person, if they understand that proposition, can verify the proposition without appealing to any experience as the very essence of the term "bachelor" is that it refers to unmarried men. That is, we need not find all of the bachelors in the world to see that all bachelors are unmarried; we know this to be true if we understand the meaning of the proposition's constituents. Also, the proposition is necessarily true, as it is impossible to present a case in which that proposition is false.

The proposition "some unmarried men are not bachelors" would be considered a posteriori knowledge. In this proposition, we must appeal to our experience to make sure that there are cases in which an unmarried man is not a bachelor in order to verify the proposition. Since we know that the Pope is an unmarried man and not a bachelor, we know that this proposition is true. However, since this proposition could be false (say, a deadly virus wipes out all unmarried men that are not bachelors), we say that this proposition is contingent. To see if a proposition is true contingently or necessarily, you can perform this test: negate the proposition (in the contingent case, "no unmarried men are not bachelors") and check to see if there are any inherent contradictions. No contradictions means that the original proposition is contingently true, while an inherent contradiction means that it is necessarily true.

If this is something new to you, take a moment to reflect on the idea of a priori/a posteriori and necessity/contingency. I think you will find that the two have very hard to break the relationship, though, as you should be able to tell from the purpose of this post, not impossible.

Kripke offers two examples: one that demonstrates necessary a posteriori knowledge and another that demonstrates contingent a priori knowledge.

Necessary A Posteriori

The Greeks often gave celestial entities names by which to identify them. The name Hesperus was given to an evening star, and Phosphorus was given to a morning star. As you might imagine, Hesperus appears only in the evening, while Phosphorus appears only in the mornings. Their positions relative to other celestial entities (that is, their position to the background stars) were dramatically different. There was little in common other than perhaps their luminosity.

But it turns out that, upon further investigation, both Hesperus and Phosphorus are in fact a single entity. It just so happens that both Hesperus and Phosphorus are Venus. Since Hesperus=Venus and Phosphorus=Venus, we can say that Hesperus=Phosphorus is necessarily true. After all, they ARE one in the same, and to negate it would lead to a contradiction. However, we would not know that Hesperus=Phosphorus unless we know what Hesperus and Phosphorus are and that they both refer to Venus. In order to know this, we must appeal to empirical evidence, thus making this a posteriori knowledge.

While this demonstrates a case in which a posteriori knowledge is necessarily true, many people might find the whole idea of identity and the process of naming a bit uneasy. Of course, this is certainly pertinent to the case presented here (as well as any other necessary a posteriori cases that I can think of), but this leads us down a very complex path. That said, please feel free to contribute to this point if you wish; I just don't have the balls to get into this on my own.

Contingent A Priori

Take the proposition "a meter stick is a meter long." This statement can be verified without appealing to experience: we don't need to go check how long a meter is and compare it to the length of a meter stick, for however long a meter happens to be, we know that a meter stick will also be that long (after all, it is the essence of a meter stick to be a meter long).

Or do we need to check? There is a bar in Paris that is supposed to be the defining measurement of a meter; the standard meter bar, if you will. We also know that a bar, as with any other physical objects, could potentially fluctuate in length when exposed to different temperatures. You can, then, imagine a world in which the average temperature is significantly higher such that the standard bar is actually a bit longer than in our world. While this might be a little confusing, you can say that the proposition "a meter stick is a meter long" is true a priori but is contingent: we know that a meter stick is a meter long (duh) but, at the same time, it's possible that a meter stick (say, a meter stick in our world) is not a meter long (as measured by the standard bar in the hotter, alternate world).


Much progress has been made on this, particularly in the domain of language since it is there that this peculiarity seemingly resides. Instead of me going into difficult and painstaking details here (which I lack the capacity to do so in any respectable manner, anyway), I'll save myself (and you) the pain and instead encourage you to leave your thoughts in the comments.