Alan Gibbard on Contingent Identity

Gibbard’s paper is about contingent identity. That is, the thesis that two things can be the same thing, but only be contingently the same thing. It is not necessary that they are the same thing. He gives us an example a statue and a piece of clay. Or, more precisely, a statue made out of this piece of clay. He represents his position thus:

s = c    &◊ (s exists & c exists & s ¹ c)

To paraphrase: the statue and the piece of clay are identical. However, it is possibly the case that the statue could exist, alongside the clay, and that the two would not be identical.

Kripke famously argued that all identities are necessary. Gibbard argues otherwise. In fact Gibbard accepts to some extent what he thinks of as the traditional view:

a necessary truth can be known a priori

If it is a necessary truth we are talking about, it can be known to be true and necessarily true without relying on experience. An example of such a necessary truth would be:

1+1=2

As I said, Kripke rejects this view. Take this necessary identity (in his eyes):

If Hesperus exists, then Hesperus = Phosphorus

That is a necessary identity and truth but it can’t be known a priori. It is known a posteriori. It had to be empirically discovered that Hesperus and Phosphorus are identical. So according to the traditional view

Hesperus = Phosphorus

is true, but it is not necessarily true. Kripke rejects this account. According to Kripke, it is irrelevant how we came to know the truth of the above identity statement. It is still a necessary truth. It was known a posteriori and yet is still a necessary truth. What matters to Kripke is

whether it might have been false if the world had been different.

Kripke therefore argues that the above would have still been true even if things had been different. More than that, it would or is true in every possible world. And if it is true in every possible world, then it is necessarily true. So traditionally we had these formulations:

necessary – a priori

contingent – a posteriori

But now Kripke offers us:

necessary – a posteriori

Kripke’s position “undermine[s] accounts of reference which would make” the statement “Hesperus = Phosphorus” a contingent truth. What accounts of reference were these? Firstly, Russell’s theory of descriptions and

the later ‘cluster’ theory, [in which] a name gets its reference in some way from the beliefs of the person who uses it.

These are very subjective theories of reference. They make reference a very contingent matter. Gibbard goes into detail:

On Russell’s view, the heavenly body Hesperus…would be the thing which fitted certain beliefs they had about Hesperus…

What about the cluster theory?

[Hesperus] would be the thing which fitted a preponderance of [the ancients’] beliefs about it.

As I said, both theories are similar in that they are, as it were, mentalist. That is, based on the beliefs of persons. Thus the reference would not be, to use Kripke’s terms, “rigid” – it would be “flaccid”. But Kripke spotted a problem with these theories of reference.

It is possible that the ancient namers of Phosphorus and Hesperus had beliefs about one that didn’t coincide with their beliefs about the other. Perhaps these alternative beliefs were even contradictory. Or to use Kripke’s language. In some possible worlds certain beliefs could have fit Hesperus but not have fit Phosphorus. If it is beliefs we are talking about, therefore, then in some possible worlds Hesperus = Phosphorus would be false! Not only that, but it would be a contingent rather than a necessary truth. And it is of course Kripke’s belief that the identity statement is necessarily true; that is, true in all possible worlds.

In order for two things to be identical they must

start to exist at the same time and cease to exist at the same time.

If this is the case, the statue and the clay may not be identical. The piece of clay may have been hanging around for month before it became a statue. The statue, on the other hand, had “the property of being elephant-shaped” throughout its existence. They thus don’t have identical properties. The piece of clay does not have the property of being a statue throughout its existence.

However, there is the possibility that the

clay statue starts to exist at the same time as the piece of clay of which it is made.

Also, they cease to exist at the same time. Will the two in this possible situation be identical? Gibbard says he is “tempted to say…[that they] are identical”. This is why:

They began at the same time…they had the same shape, location, colour…at each instant in their history…If the statue is an entity over and above the piece of clay in that shape, then statues seem to take on a ghostly air.

More to the point. What does the statue have that the clay doesn’t? Still, Gibbard reiterates the contingent identity logical formula:

C = L   & (G exists and L exists and G = L)

To paraphrase. G and L exist now and they are both identical. However, it is possibly the case that both could exist and that they would not be identical.

Of course G and L may not have the same persistence criteria (unlike the earlier example). Gibbard writes:

For suppose I had brought L into existence as G…but before the clay had a chance to dry, I squeezed it into a ball. At that point…the statue G would have ceased to exist, but the piece of clay L would still exist in a new shape. Hence L would not [now] be G…

So L and G in the above scenario don’t have the same persistence criteria. Gibbard draws from his example the possibility, at this point, that L and G are only contingently identical.

Gibbard also talks about temporal parts. In the above example, the

statue is a temporal segment of the piece of clay.

Even though the clay as G and the clay as a ball are not identical, the clay as G is still a temporal part of L. Again, L could be G for its entire existence as L.

According to Kripke, if “L” and “G” are names for the same thing, that is, if they are rigid designators, then they necessarily name that thing at all possible worlds. But if Gibbard’s proof of contingent identity were true, “L” and “G” cannot name the same thing. That is, “L” and “G” must be different things. Gibbard, on the contrary, says that “L” and “G” do indeed name the same thing, but the identity between L and G is merely contingent. So “L” and “G”, in Kripke’s terminology, are flaccid designators.

As Gibbard says: “if the names “G” and “L” are both rigid designators” of the same thing in our world, then there could be a possible world in which G and L are not identical. Kripke denies this. However, Gibbard thinks he has shown this of our world

(i)                   In W⁰  G = L

but in another possible world

(ii)                in W¹ G = L

According to Kripke, if “G” and “L” denote the same thing in our world, then they denote the same thing in W¹ too. He therefore disagrees with Gibbard.

Sortal Concepts and Identity

According to Wiggins and Geach, we can talk about “the same statue” in different possible worlds, but not about “the same thing”. Identities come pre-packaged under sortal concepts.

According to Gibbard:

Proper names like ‘G’ or ‘L’ refer to a thing as a thing of a certain kind: ‘G’ refers to something as a statue; ‘L’ as a lump.

However, “one thing [can] be of two different kinds, with different persistence criteria. So L, for example, can fall under the kind [clay] and also under the kind [statue]. So that’s why the proper names ‘L’ and ‘G’ are different:

one proper name refers to [a thing] as a thing of one kind [i.e. a statue], another proper name [refers] to [a thing] of another kind [i.e. a lump].

Gibbard still accepts the theory of rigid designators. This is why he does so:

A designator may be rigid with respect to a sortal: it may be statue-rigid, as ‘G’ is, or it may be lump-rigid, as ‘L’ is.

In a sense, therefore, designators designate concepts or the concepts of things, not things simply qua things.

Gibbard gives us an account of Kripke’s theory of reference. In this thing there is a direct causal relation between the thing denoted and all subsequent users of a name:

thing denoted –  person who uses the name of the thing denoted ---

                         -  other people have the name passed on to them

To put this causal theory of reference more clearly. Gibbard says that the names ‘G’ and ‘L’

denote the thing they do because [he] applied those names to it directly and others got the name from me.

Gibbard also says that he gave the thing persistence criteria. However, his example does not appear to warrant the name “persistence criteria”. He simply said: “I name this statue ‘Goliath’.”

In theory, as was mentioned earlier, it is possible that both L and G can have the same persistence criteria. In that case, both names, ‘L’ and ‘G’, will denote the same thing. To the contrary, if he had given them different persistence criteria, he “might have named a different thing”.

Again, if

Hesperus = Phosphorus

then it is a necessary identity statement.

L = G

is a contingent one.

So:

The reference of a name in the actual world is fixed partly by invoking a set of persistence criteria which determine what thing it names. The name may then be passed on through a tradition, and the reference is fixed by the origin of that tradition.

Identity Across Worlds

Gibbard now talks about identity across possible worlds. He says that

identity across possible worlds makes sense only with respect to a sortal.

These are examples of sortals: statue, number, man, etc.

Kripke enters the picture again here. Kripke believed that

the number of planets in our solar system (i.e., 9)

 is a non-rigid designator because it is possible that there were 8 planets, not 9. The proper name ‘Nixon’, however, is a rigid designator because it names the same man in all possible worlds. Not the same thing. The same man. Sortals make the identity and are also a commitment to essentialism. That is, manhood is essential for all possible Nixons.

According to Kripke, unlike, say, David Lewis, possible worlds are stipulated. We invent them. He is not a realist about possible worlds like Lewis. If that’s the case, Gibbard argues, it would be best to call them “counter factual situations”. We don’t discover possible worlds or find out about them. We stipulate what they are to be like.

Can the famous Leibniz’ Law help us with some of the earlier problems. What is this law? It is often referred to as the general law of the substitutivity of identicals. This is the law:

If x = y, then for any property, if x has it, then y has it, and for any relation and any given things, if x stands in that relation to those things, then y stands in that relation to those things.

However, Gibbard doesn’t think that this law is true as it stands. He says it needs to be a “law about properties and relations”. That is, the

law so stated yields substitutivity of identicals only for contexts that attribute properties and relations.

To clarify:

Modal expressions do not apply to concrete things independently of the way they are designated.

Does this mean that reference fixing comes along with, say, concepts or definite descriptions?

Gibbard, unlike Kripke, thinks that within quantification contexts things must come with concepts or, more traditionally, with definite descriptions. On the Kripkean view, quantification must designate things without specifying properties, relations or concepts. But if

modal contexts do not attribute properties or relations to concrete things

Gibbard says

it follows that such contexts are not open to quantification with variables whose values are concrete thing.

This is an argument against direct reference.

So the sentence

  (L exists & x = L)

is “ill formed”.

This is because the variable ‘x’ does not stipulate an accompanying sortal. It would be true if it was taken to be a statue-concept, but it would be false if it were taken to be a lump of clay-concept

Variables that Range Over Concepts

Gibbard’s position is anti-essentialist in regards to individuals or things or objects, but not so with regards to concepts. He says that

[c]oncrete things will have no modal properties: there will, that is, be no such thing as de re modality for concrete things.

There will be no essential properties or attributes of concrete things.

So in Gibbard’s system, the name ‘G’ refers to a statue-concept, not to a statue. A concept, in this context, is the sense of a proper name. So different names can have the same sense, just as different sentences may express the same proposition. In a sense, sense and concept are synonymous.

It is the fact that these variables are in modal contexts which makes them range over concepts rather than over objects or individuals. So take this formula:

~ (Ex → Hx)

The variable x in the above ranges over concepts, not objects or individuals. The ‘E’ doesn’t now mean exists, it means a concept of an individual that exists. And ‘H’ does not stand for humanoid, but it stands for a concept of an individual that is humanoid. So to paraphrase the above. There necessarily exists an x, such that that x is a concept of an individual that exists and is also an example of a concept of humanoid.

The point of the formula above is that it is false when applied to L, but true when applied to G.

Also

~ (E L → H L)

is false. It isn’t necessary that L is an example of a concept of an individual that exists and necessarily exists as under the concept of humanoid. So, according to Gibbard, proper names do have senses when they refer, in accordance with what Frege said all those years ago. Or, to use Gibbard’s terms, a concept is attached to a name in modal contexts.

Gibbard makes variables range over concepts rather than individuals. Inside modal contexts variables range over concepts not variables. Outside modal contexts, variables range over individuals.

In Gibbard’s system, when we get the formula

a = b

both ‘a’ and ‘b’ are concepts of individuals, not the individuals themselves. If we were to paraphrase a = b we would say: The individual of which a is the concept is identical with the individual of which b is the concept. So concepts a and b are identical and they range over the same individual.

Essentialism

Gibbard quotes Quine, who said of essentialism that necessity properly applies

“to the fulfilment of conditions by objects…apart from special ways of specifying them”.

That is essentialism. Both Gibbard and Quine don’t accept this position. Quine rejects essentialism for all things. However, Gibbard rejects essentialism for concrete things but accepts it for individual concepts. Now it is concepts, rather than individuals or objects, which supply or create the necessity.

Gibbard goes into greater detail about his concept essentialism. He says that

it makes no sense to talk of a concrete thing as fulfilling a condition q in every possible world – as fulfilling q necessarily, in other words – apart from its designation.

He then goes on to say:

Essentialism, then, is false for concrete things because apart from a special designation, it is meaningless to talk of the same thing [the same what?] in different possible worlds.

How would we know what we were talking about? What thing would it be? How could we find or designate it without special designations of that object

So it

makes good sense…to speak of the same individual concept in different possible worlds.

There is no such thing as de re modality for concrete things. This means that in the formula

~Fx

the variable ranges over individual concepts rather than concrete things.

Gibbard makes a distinction of variables that fall within the scope of a modal operator and those that don’t. If the modal operator does fall under the scope of a modal operator, it ranges over individual concepts. But if x is outside the scope of a modal operator it will range over individuals. Take this formula:

(›y) [y = x & y & ~ (Ey  → Hy)]

This can be paraphrased thus:

There is an individual concept y which is a statue-concept, and is a concept of something humanoid in any possible world in which it is a concept of anything.

Again, concrete things have no de re properties, according to Gibbard. That is

~F

stipulates a necessary concept of a thing, not a necessary part or attribute of a thing. The ‘F’ in the above is a sortal. We can only affirm necessity and identity via a sortal. So ‘F’ in the above may be a statue-concept or a lump-concept.

Gibbard makes a distinction between the statue-concept and the lump-concept. Take

I squeeze x ~ → x ceases to exist

This would be true of the G-concept (the statue) but false of the L-concept (i.e., the lump of clay). At all possible worlds, if the statue, Goliath, is squeezed, it will cease to exist. However, L will not cease to exist.

Causal necessity is different from all the kinds of necessity we have thus far discussed. Causal necessity is scientifically bona fide. And, on some metaphysical positions, it is also metaphysically acceptable. Take this formula

 ~cq

This says “that it is causally necessary that q”, where q is extensional – contains no modal operators. This is de dicto necessity because it is about the formula “~cq” rather than, say

c~q

That is, it is necessary that q. That would be de re necessity.

Reference

Allan Gibbard’s ‘Contingent Identity’, from the Journal of Philosophical Logic 4 (1975)