How is it possible that there are statements which appear to deal with contingent identity? It does at first seem to be the case that we use this type of identity statement commonly in our everyday language. However, Kripke disputes the idea that it is possible for these kinds of identity relationships to exist. Instead, he contends that such statements are actually matters that deal with necessary identity.
Whenever we say of two things, let’s call them x and y, something in the form of “x=y”, we are making a claim about their shared identity. Some examples of identity statements would be “water is H2O”, “Falvey is the professor”, and “the third planet from the sun is the earth”, but of course there are countless others of similar nature. Classically, identity statements can be differentiated as being either contingently or necessarily true. We consider a thing to be necessary if it is essentially true, or in other words, it can not possibly be false. “Water is H2O” appears to be a statement of necessary identity, as it refers to a seemingly unchanging chemical compound. On the other hand, something is contingent if it is not essentially true, or if it might have possibly been false. For example, “Falvey is the professor” seems more like a contingent identity statement, as it is very conceivable for another UCSB philosophy professor to have taught the class. We make allegedly contingent statements quite often in conversation; it seems almost intuitive for such identity relations to be existent.
However, Kripke opposes this claim, and instead argues that if an identity statement is true, it must also be necessary. He bases this argument on a couple fairly difficult to challenge principles. The first premise is the almost universally accepted Indiscernibility of Identicals, which states that for any two identical things x and y, if x has a certain property, then so too must y. Alternatively, if x and y are identical, to say that x shares the same properties with y is reducible to saying that x shares the same properties with x. The second premise has to do with the basic nature of identity, when given any single thing x, that thing x is necessarily identical with itself. This idea seems even more trivial than the first premise. When combined with one another, it becomes quite clear that given any two identical things x and y, and considering that therefore whatever is true of x is also true of y, it must be that if x is necessarily identical with x, then it is also necessarily identical with y. There is also a certain intuition in this line of thinking, albeit conflicting with the previous one. If two things are identical, there is really only one thing that is being referred to, which obviously holds all of its own properties, including that it must necessarily be identical to itself. Thus, Kripke argues that when we say something like “Falvey is the professor”, what we are really making is a necessary identity claim, and so we must find a way to remedy the apparently contradictory meaning of these kinds of statements.
Kripke’s solution to this problem is that there exists a distinction between a thing in itself and the ways in which we refer to it. Suppose we take a thing x, and imagine that we refer to it as both “the former senator of Illinois”, and “the current president of the United States”. It just so happens that we could truthfully state that “the former senator of Illinois is the current president of the United States.” Kripke would say that as an identity statement this must be necessarily true, but that it implies something different from what our common sense might tell us. If this statement were to mean that it is necessary the thing we call “the former senator of Illinois” is also the thing we call “the president of the United States”, it would at the very least be contradictory in a possible world where instead McCain was elected president, if not many others as well. Instead, it is saying that specifically the thing x, which we refer to as “the former senator of Illinois”, is necessarily identical with itself, and that we also to refer to it as “the current president of the United States”. This kind of identity statement is one that deals with definite descriptions, of the form “The x is y”. While it is true that x, which we happen to refer to by certain distinct definite descriptions, is necessarily identical with itself, the things referred to by these two specific definite descriptions are only contingently identical, and thus they possibly refer to two distinct things. In any case, it is not the actual claim of identity that is contingent, but rather the linguistic relation between the definite descriptions on their own.
Kripke then addresses identity statements that do not deal with definite descriptions, but rather with proper names. In the classic descriptivist view often linked to Russell, except for a select few logically proper names such as ‘this’ and ‘that’, ordinary proper names generally act as abbreviations of definite descriptions. According to Russell, definite descriptions do not act like pointers to entities, but rather denote them in the world by distinct attribute. One can make sense of statements like “zombie Professor Falvey does not exist”, because the sentence is not asserting the existence of the thing in question by its very mention, in this case zombie Professor Falvey, but rather simply denotes what we think might constitute such an entity. While we may even try and attach some sort of meaning to the phrase zombie Professor Falvey, it is not from the actual existence of such an entity, but rather our past experiences with zombie fiction and the real Professor Falvey, and it is only ever in a contextual sense like so that a definite description derives any meaning.
Kripke maintains the exact opposite view as Russell, instead arguing that proper names are actually devices he calls rigid designators. Such a designator refers to the same thing from every possible world in which the thing exists. It also literally points out the thing in particular, rather than indirectly referring to the possessor of some quality as a definite description might do. Let’s assume Russell to be correct however, that proper names are simply definite descriptions in disguise and refer to a thing by a distinguishing set of attributes. Suppose then that a person happens to know Samuel Clemens only as Mark Twain and as such, they could truthfully claim that “Samuel Clemens is Mark Twain”. However, imagine the highly plausible situation of a possible world where Samuel Clemens for some reason never grows up to assume the pen name Mark Twain. It would seem odd for that person to then be correct in claiming that Mark Twain does not exist. Kripke instead suggests that since both names are rigid designators to the same entity. The person might then be right in thinking ‘Mark Twain’ does not exist, but the reality of the situation is that from our perspecive both names, acting as rigid designators, pick out the same existent entity in all possible worlds, including his own. That he does not have ‘Mark Twain’ to designate the entity Samuel Clemens does not falsify its existence, as the designator is dependent on the entity, and not the other way around. This becomes of utmost importance to his theory of necessary a posteriori knowledge, which went contrary to popular belief at the time. If proper names pick out things in the world, and when we make statements about these proper names we are actually making a statement about the entity they necessarily pick out, claims about the identity of the entity become necessary by relation. For example, when we talk about water, we are making statements about the chemical compound H2O that exists unchanging in all possible worlds, and are therefore making empirical observations that are true by necessity.
Even if it may be far less plausible than my previous contingent claims, it still seems remotely feasible to construct a possible world in which “Hesperus is Phosphorus” is false. As implied by the sheer scale of our universe, there do seem to be countless configurations in which solar systems can form, and presumably ours could have turned out vastly differently than it did. Though it turns out that in our world both proper names happen to pick out the entity we call the planet Venus, the ancient Greeks originally thought they were two distinct celestial objects, so let’s take this to be the case. One of them goes passing through the sky in the morning, the other in the evening, and they are called Hesperus and Phosphorus respectively. Furthermore, the entity we call Venus does not exist, making the statement patently false in such a possible world, and must therefore merely be contingently true in general. At any rate, Kripke would say that what the celestial objects are called in each possible world is only a distraction from the reality of the situation. In our world, Hesperus and Phosphorus are both proper names that correspond to what we now call the planet Venus, and it is necessarily the case that this is true no matter what world you’re referencing it from. Conversely, in the other world, Hesperus and Phosphorus are another set of proper names entirely, and do not correspond with one another’s entity. From our perspective of such a possible world, there are two existent celestial objects, but they are not pointed to by our own Hesperus and Phosphorus, as that entity (the planet Venus) does not exist in their world. The exact proper names used are comparatively meaningless with the entities they happen to pick out, what is important is that when we talk about what is true of Hesperus and Phosphorus in our world, we are talking about what is true of the planet Venus itself, and likewise, statements about the Hesperus and Phosphorus of the other possible world are actually statements made about the two celestial objects they happen to pick out, and not their names in the least.
Kripke makes a lengthy and multi-faceted argument about the metaphysics of identity. First, I went over his assertion that only necessary claims of identity are possible, and that apparently contingent identity claims are simply a misperception. Next, I describe the asymmetry found in his system between Russell’s theory of description and the role played by proper names, and the significance of a posteriori knowledge. Lastly, I explained in depth how Kripke maintains the necessary truth of identity amongst complex possible worlds.