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Metaphysics: Kripke's Identity Statements

Updated on April 24, 2011

Just a preface: If you've never heard of Metaphysics before, you're going to be in for a ride. Metaphysics tries to explain the nature of fundamental being. As in, what makes us "be"? If you're interested, I've got another article that covers a couple of other Metaphysics theories here.

Kripke’s claim that identity statements of the form “a=b” where “a” and “b” are both "names" as necessary truths has many layers behind it that must be known to add up to it being a truth. One of the first things one must accept is the reason why identity statements themselves are necessary truths. Then, one must add in names and the notion of rigid designators, which to Kripke, solidifies the claim that identity statements involving names are necessary truths, even though some still find them contingent. To those who find contingency, Kripke demonstrates proof of necessary truth in these statements. “An argument like the following can be given against the possibility of contingent identity statements:”

To dive in, you must first accept that identity statements are necessary truths. This is shown through The Law of the Substitutivity of Identity, which states that “for all ‘x’ and all ‘y’, if x=y, then if ‘x’ has ‘f’, then ‘y’ has ‘f’.” Kripke then adds to this that all objects are self identical (Necessarily, x=x). Then you add a little more on to that by saying: If objects are self identical, then for all “x” and all “y,” if x=y, then if necessarily x=x, then necessarily x=y. Everything here adds up just fine, and he closes by saying for all “x” and all “y,” if x=y, then necessarily x=y, and if you are a person who is committed to The Law of the Substitutivity of Identity, then you must be committed to that last statement, which proves that identity statements themselves are necessary truths. If you were to be opposed to this logic, then you would have to be able to acknowledge that a thing could both have and lack the same property, which doesn’t make sense at all.

Now that identity statements are taken as necessary truths, Kripke must now show how identity statements involving names are necessary truths, and the biggest proponent to this would be rigid designators. A rigid designator refers to the same object in every possible world in which that object exists. The easiest way to describe this is by saying, “Brad Pitt is an actor.” In this sentence, Brad Pitt is the rigid designator, where actor is a non-rigid designator. Suppose there is a world in which Brad Pitt was a plumber. A world in which Brad Pitt is a plumber is still a world in which Brad Pitt is Brad Pitt. Through using names as rigid designators, it proves that identity statements using names are necessarily true.

Now, we “have to set up criteria of identity across possible worlds.” When we talk about these “possible worlds” where Brad Pitt is a plumber, we talk about them using words as if the “people” in the “possible worlds” use the same words the same way. Surely Brad Pitt was born and named here, but in another world, he could be named Bookshelf (this is why we talk about the alternative or possible worlds as though they use the same names and words as us). The entire point of these possible worlds is mainly to provide a framework of discussing what is possible in this world. When we ask what it is that Brad Pitt does in another world, we are talking about names of things we have in this world, and applying them to a possible world based on this one. To this, one could ask how we find out if the man we’re actually talking about is Brad Pitt. Kripke destroys this question by pointing out if “the phrase “possible worlds” is what makes anyone think some such question applies, he should just drop this phrase and use some other expression, say “counterfactual situation.””

Now that we’ve explored the foundation, let’s work our way up the tree of Kripke’s claim. Kripke now explains essential properties. As in which “properties, aside from trivial ones like self-identity, are such that this object has to have them if it exists at all.” They are properties that if the object didn’t have it, it wouldn’t be the object. So there are certain things that have essential properties. He then poses the example of a wooden lectern. Being that it’s a wooden lectern, let’s suppose it’s made of wood. If this is true, our intuition says it’s made of wood, and nothing else. Now we could say that this particular wooden lectern is necessarily made of wood and we could say that it’s not made of water. Therefore, the wooden lectern is necessarily made of wood, and necessarily not made of water. So now we’re left with this equation: Suppose we define P as “The lectern is not made of water.” If P, then necessarily P. All of this is learned a posteriori. Using this, we cannot conflate the necessity of claims with knowing them a priori. The point is to make clear that you cannot assume that necessity and knowability a priori go together. The mere fact that a truth has to be discovered before it’s known as a truth is not a reason for thinking it isn’t necessary. Remember, if P (something learned a posteriori), then necessarily P.

Now Kripke must reinforce identity cases with names as necessary. Since names do indeed seem to be rigid designators, identity statements must be necessary. So why then, other than appearance of a posteriori identity statements would someone thing otherwise? Attacks against the claim go a little something like this:

Identity statements are contingent given that names are rigid designators because they are often only knowable a posteriori. Well, since this one’s already been covered, I won’t dive any deeper into it, as long as it’s understood as incorrect. Next, they’re contingent given names are rigid designators because they are treated as metalinguistic. This states that when someone says a=b, what they are actually saying is “The name ‘a’ refers to the same thing the name ‘b’ refers to.” This is a very large misconception.

Yes, it is a contingent fact that things have their names. If identity statements are treated as being about names, then yes, they’re contingent. But, simply put, identity statements aren’t about names, they’re about the object. With identity statements, names are used. They aren’t mentioned or talked about, they’re used. Most of the time with words, we’re using them, but other times we mention or talk about them. For example - Steve likes Mountain Dew. The name Steve has five letters; it begins with an S, and has two E’s. The first sentence is using Steve; the second is mentioning the word Steve. When we say Hesperus is Phosphorus, we’re using the names. We’re not saying this name happens to refer to the same thing as this other name, we’re using objects. Thus, thinking identity statements are contingent fails, since identity statements are about objects, not words. The next claim against it is that we can imagine circumstances in which true identity statements would have been or would be false, or cases in which it really might not have been the case. An example would be that it might have been the case that Venus rose in the evening, but occupied a different position in the morning. That position might have been occupied by Mars in the morning. The problem is this isn’t using names as rigid designators. It’s giving a situation in which Phosphorus has different properties! Another example is with Cicero or Tully. If someone learns about the Roman orator Tully, and Cicero as a certain Roman author, they might not know that Cicero is Tully. The truth that he was an author or writer is contingent, so suppose we have a world in which Tully was an orator, but he never wrote anything. This fails miserably, since again, it’s not using names as rigid designators. This wouldn’t be a case in which Cicero wasn’t Tully; it would just a case in which Cicero wouldn’t be an author.

The idea here is, when you name something, you may get to the object by some properties the object has, but the name goes right to the object. The link between the name and the object is not mediated by some sort of description, even if the association is made through the description. Once a name is there, it’s free of description. Because of this, Tully is only contingently Cicero, since it could’ve been that the orator isn’t the writer. This is substituting description with the name, and confusing a reference description for the name.

Now onto a big philosophical payoff, which involves theoretical identities that we get through science, such as: water=H2O and heat=the motion of molecules. Since we use “heat” and “the motion of molecules” as rigid designators for something external that we can feel, and since “heat” is “the motion of molecules,” going by this entire argument, it seems obvious that heat is necessarily the motion of molecules. The view of contingency comes from the way that people react to heat (or the motion of molecules, at this point I’m leaving them defined as the same thing). Since heat contingently feels hot, you are defining heat by its contingent property, and not by what it actually is; the motion of molecules. The main problem that arises through this thought comes through the mind/body experience. If Kripke is right here, then there is a problem with the mind/body relation dealing with the contingent relationship between brain states and pain, which he ends by saying, “the next topic would be my own solution to the mind-body problem, but that I do not have.”

Through all of this, Kripke has clearly demonstrated that through the use of rigid designators, identity statements in the form of a=b where “a” and “b” are names are solidified as necessary truths. He debunked any theories that tried to bring contingency to his claim, and explained the differences between necessity and contingency. He also explained how knowing something a posteriori as opposed to apriori doesn’t take away the necessity of it, and why that is relevant. He clearly explained and demonstrated the proof of necessary truths in these situations.

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      Quentin 2 years ago

      What about if one were to deny that names are rigid designators outright? In counterfactual situations it doesn't seem that we're truly referring to the same object; only something very similar. By the indiscernability of identical two (?) objects are identical only if they share the same properties, but any object in a counterfactual is necessarily has a different property to its corresponding object in our world: namely that it isn't in our world.

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