We have already discussed Kripke’s first example of the necessary a posteriori: true identity sentences involving rigid designators. We now turn to the second class of necessary a posteriori truths: attributions of essential properties to objects. (The main discussion of this is at pp. 110-115, though Kripke returns to the topic briefly at pp. 126-127.)

1 Why essentialist claims generate examples of the necessary a posteriori

An essential property of an object o is a property such that o could not have existed without having that property o; or, put another way, it is a property such that o could not have been o without having that property. Properties of an object which are not essential are accidental.

(This is not to say that every property which satisfies this characterization is an essential property; the essential properties of an object might be a subset of those which hold of the object necessarily. But every essential property of an object is one which is such that, necessarily, if the object exists then it has this property.)

Let’s suppose for now that the idea of an essential property makes sense, and that there are some examples of essential properties. (We’ll defend both of these ideas in a bit.) How could essential properties generate examples of the contingent a priori? Let n be a name, and F be a predicate which expresses an essential property of the referent of n. Then the above explanation of the essential/accidental distinction is enough to show that Fn will express a necessary truth. But the proposition expressed by this sentence might well be a posteriori as well, since it might take empirical investigation to find out whether the referent of n in fact has the property expressed by F. As Kripke puts it:

We can approach a similar point another way (this is discussed by Kripke in his paper, “Identity and Necessity”). It might be the case that for some property, we can know a priori that, if some object has that property, it has that property essentially. For example, it might be the case that I know of each of you that, if you are human, you are necessarily (essentially) human. But it might take empirical work to determine that you are in fact human, rather than a cleverly disguised robot. In this case, we will have a necessary and a priori claim combining with a contingent and a posteriori claim to yield an example of the contingent a posteriori.

Consider, for example, the following argument:

Premises (1) and (2) are ordinary contingent claims that are, presumably, knowable only a posteriori. But if one knows (1) and (2), one is then in a position to deduce (3), which is an instance of the necessary a posteriori. But you might still wonder how we could know that (3) is a necessary truth; how could we ever know, or some a posteriori proposition, that it is necessary? Well, we might begin with a claim like (4), which seems like a necessary and a priori truth. Once we know (3) and (4), we are in a position to deduce (C), which says of our necessary a posteriori proposition (3) that it is necessary.

This argument thus shows how, on the basis of knowledge of necessary a priori truths and contingent a posteriori ones, we can come to know a that a certain a posteriori truth is necessary.

2 Kripke’s response to skepticism about essentialism

This case for the necessary a posteriori presupposes that essentialism makes sense, and that there are some examples of essential properties of objects. Kripke discusses two reasons for doubting that essentialism makes sense.

2.1 Quine on essentialism (pp. 39-42)

The first is due to Quine, and is familiar from our reading of his “Three Grades of Modal Involvement.” You will recall that Quine argued against quantifying into modal contexts on the basis of his claim that ‘necessarily’ creates referentially opaque context; we saw that if we cannot quantify into modal contexts, this counts against the intelligibility of de re modality (the idea that an object can have properties either necessarily or contingently (essentially or accidentally)), independently of a specification of the way in which that object is referred to.

Kripke has this to say about Quine’s argument:

Kripke replies that we do have an intuitive distinction between essential and accidental properties of things:

Kripke’s idea here is that in our pre-philosophical thought, we take it for granted that we can say things about which properties certain objects might have had or lacked.

It would be fair, at this point, to respond to Kripke as follows: granted, there is an intuitive distinction between essential and accidental properties. But Quine did not just say that the distinction was unintuitive; he suggested that, since we can easily generate cases in which there are two singular terms n and m, each of which refer to some object o, such that the two sentences

can differ in truth value, there is no sense to be made of the question whether o, independently of specification of some singular term which refers to o, necessarily or merely contingently has the property expressed by ‘is F.’ Surely this argument cannot be answered merely by citing our pre-philosophical intuition that this question does make sense. In fact, it’s hard to see how our pre-philosophical intuitions could even be relevant.

It is in response to this challenge that Kripke introduces the notion of rigid designation on p. 48:

The idea here is that when we are interested in whether some object o has a property, we can only test for this by looking at truth values of sentences of the form, Necessarily, n is F if ‘n’ rigidly designates o. For if ‘n’ does not rigidly designate o, then the truth value of the sentence in question depends on fact about whether objects other than o ‘are F.’ But if we are interested in the essential properties of o, it’s irrelevant how things stand, or could have stood, with objects other than o.

A defender of Quine might reply as follows: skepticism about de re modality involves skepticism about talk about talk about objects in various possible worlds rather than talk about whatever satisfies some description in various possible worlds. But the definition of rigid designation -- reference to the same object with respect to every possible world -- presupposes that we can make sense of talk about objects in various possible worlds. So it is illegitimate to use rigid designation as a response to Quine’s skepticism.

But it is at this stage that you might think that Kripke’s remarks about our pre-philosophical intuitions are relevant. You might think that the following kind of position about skepticism is plausible: if we have some pre-philosophical belief, one should abandon it as the result of a skeptical argument only if the skeptic, using propositions that we already accept, can show us that the belief is false. Kripke here makes a strong case that Quine has not done this. Quine’s arguments turn on their being no principled distinction between singular terms like ‘nine’ and ‘the number of planets.’ Kripke’s distinction, if intelligible, between rigid and non-rigid designators shows that there is. If the Quinean skeptic about de re modality wishes to question the intelligibility of Kripke’s distinction, we should need an argument for this. It is not enough for the skeptic simply to demand an explanation of some distinction in terms which the skeptic himself would accept; this is a demand which we can justifiably resist.

2.2 The problem of ‘transworld identity’

Another source of skepticism about the possibility of making sense of essentialist claims again has to do with the possibility of making sense of talking about the same object across all possible worlds. This has to do with questions about the metaphysics of modality, including questions about what sorts of things possible worlds are, and about whether we need ‘criteria of transworld identity’ in order to make sense of talk about objects in different possible worlds. Though this raises some very interesting issues, we will not have time to go into this in this course. If you are interested in this topic, an important statement of a view opposed to Kripke’s is in David Lewis, On the Plurality of Worlds.

3 Examples of essential properties

Suppose we grant Kripke that the distinction between essential and accidental properties is intelligible. To generate essentialist examples of the necessary a posteriori, we need more than this; we need the claim that there really are some essential properties of objects. Kripke thinks that there are, and gives some plausible examples.

3.1 Essentiality of origins (111-114)

Kripke suggests as a plausible essentialist principle the view that if a material object has its origin in a certain bit of matter, then it could not have existed without having that origin. He discusses the case of a particular table:

The example of the Queen’s parents.

3.2 Essentiality of constitution (114 n. 57, 126-127)

A similar principle about the material constitution of things. Could something composed of molecules have existed without being composed of molecules?

3.3 More trivial examples

You might also think that there are other, less interesting examples of plausible essentialist claims. Consider, e.g. the following: