The notion of rigid designation figures prominently in Saul Kripke's Naming and Necessity. (See Naming and Necessity p. 48.) There has been much confusion about rigidity, even among professional philosophers. I hope this brief note helps to eliminate some of that confusion.
Kripke holds the following rigidity thesis:
KRT Proper names are rigid designators.
It's a simple
enough thesis, but the concept of rigidity has made it difficult for
some to understand. What would it be for a name to be a rigid
designator? Let's focus on a particular individual, Jill Beck, and her
name, "Jill Beck." Presumably, Jill Beck is, like the rest of
us, merely contingent; there are worlds in which she exists and worlds in
which she does not exist. We, here, in this the actual world can talk
about her and what she does in some of the other possible worlds in which
she exists. Let w1 be a possible world in which she exists, is not the
president of L.U., but is the president of Carleton College. Here in the
actual world, if we wanted to say something about her in w1, we can use
her name: we can say, for example,
(1) In w1 Jill Beck lives in Minnesota.
When we, here
in the actual world, make such a claim, KRT entails that our utterance
of "Jill Beck" in our utterance of (1) refers to, or
designates, Jill Beck--the woman who is the actual president of L.U..
Contrast this with
(2) In w1 the president of L.U. lives in Minnesota.
that in w1 the president of L.U. is our current actual Provost, David
Burrows, and that, like every other provost of L.U.,
David Burrows lives in Wisconsin. Hence, (1) truly attributes to
Jill Beck the property of living in Minnesota in w1, and (2)
falsely attributes to David Burrows the property of living in Minnesota in w1.
Now, in the actual world terms, "Jill Beck" and "the president
of L.U." codesignate, but, as we here in the actual world use them
to talk about w1 they do not co-designate: "Jill Beck"
continues to be used by us to designate what we use it to designate when
we talk about the actual world, but "the president of L.U."
does not continue to be used by us to designate what we use it to
designate when we talk about the actual world. That's because the proper
name "Jill Beck" is functioning as a rigid designator, and the
definite description "the president of L.U." is not. Let's try
the following definition
Def Singular term, T, rigidly designates object, x (at world w) =df T designates x at w & as used by inhabitants of w to talk about another possible world, w', T designates a inhabitant of w' iff T designates x at w'.
according to KRT, since "Jill Beck" is a rigid designator,
when we use "Jill Beck" to talk about other worlds, if our use
of "Jill Beck" designates something, it designates the very
person it actually designates. This is not the case with "the
president of L.U." It actually designates Jill Beck, but it varies
in what it designates as we use it to talk about certain possible
be clear about this notion, let's make sure that we understand that KRT
does not imply certain things that others have mistakenly thought that
First, some have mistakenly thought that KRT implies both the falsehood that Jill Beck is named "Jill Beck" in every world in which she exists and the falsehood that there is no possible world in which something other than Jill Beck is named "Jill Beck." Here is an example,
- Kripke argues against this view [i.e., contingent identity] using the concept of rigid designator--if a term (or name) refers to an object, then it necessarily refers to that object. (Jack S. Crumley II, in Problems in Mind: Readings in Contemporary Philosophy of Mind, Mayfield, 2000, p. 95)
That's simply not the case--and this is
not an isolated example. There are plenty of worlds in which Jill
decided against naming her "Jill" and plenty of worlds
wherein someone other than Jill Beck is named "Jill Beck."
Let's suppose that w2 is such a world; hence, as we here in the actual
world use it
(3) In w2 Jill Beck is not named "Jill Beck,"
(4) In w2 the person named "Jill Beck" is not named "Jill Beck,"
(5) In w2 Jill Beck is not Jill Beck,
are false. KRT
does not imply either that Jill Beck is named "Jill Beck" in every
world in which she exists or that there is no world in which something
other than Jill Beck is name "Jill Beck."
Second, KRT is frequently falsely taken to imply that definite descriptions are not rigid designators. It does not, but Kripke, himself would surely assert that many definite descriptions are not rigid designators. The definite description, "the president of L.U." is not a rigid designator, whereas, provided it designates, on standard interpretations of mathematics, the definite description, "the sum of 2 and 2" is a rigid designator--as we use it to talk about other worlds, it designates just as rigidly as the numeral "4."
© 2000 Thomas C. Ryckman/Revised to reflect changes in the Administration of Lawrence University 2004/2006 (November)