ON RIGIDITY AND PERSISTENCE
Ti m othy WI LLI AMSO N
It is well known that the phrase "rigid designator" is used in a satiety
or n o n
•of these. (') The purpose of this note is to qualify some remarks which
eSalmon
q u i vmakes about the relation between two of his categories of
designator,
alent
defines an expression to be a 'le d designator ( * m o t h
s Salmon
e
it designates
ilie same thing with respect to every possible world in which
-s
n
that
thing
exists".
He define.* a persistent designutor to be an expression
0
e
r
)
i
f
e s .
"which
designates
the same thing with respect to every possible world in
N
awhich
t that thing exists, and which designates nothing with respect to possible worlds
in which that thing does not exist". ( ) Salmon finds both of
h
a
ihese
nouons
in Kripkes writings. He goes on to claim that his "formal
n
trenimem
or
definite
descriptions has the effect that all rigid definite
S
descriptions
musi
be
persistent".
(
a
lI r e
descriptions
-)m T h e opemtor.i. can denote something with tespeu to a enen possible
ro ieworld
a
l e only
v a ifnthat
t thing exists in the given possible world". (1)
The
nub
of
the
problem
a
m
e
s
p
e
c
t is easily stated. Suppose that our metaphysics
n
allows
a
s
I
tibeils,
for
example. did — that two possible individuals
ot
n
f
h
IICCU
n
o
t
b
e
C
OM
p
OSAib
it
.
( ) I n o t h e r w o rd s, t h e re a re w o r l d s i n w h i c h
ita
h
i
s
an
fs individual
s
o
ru exists,
m and aworlds in which an individual y exists, but no
worlds
in which both u and sexist. Ixt d beam
Ilg
designates
,li d e n nui with
t e respect to every possible world in which u exists.,
designates
y
with
d
e
s
c
r
i prespect
t i oto nevery possible world in which v exists, and
iv
w
h
i
c
h
a
e
d
n
"4
a
4
1
s
h I1)
ie (I)
i)R Mid go, 35.
n
)Ie See Fred d'Ascrobron —
l 0)
i
g LbIf e i b n i z Otharterflo
MiArgipkinai
24
p
i
C
o
m
p
o
s
e l i bof Selena tOxrdEd: Oxford linivaidayPr 91111)pp•14V-101•
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titrAtyPhynel
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end
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.
T witliAmsoN
designates nothing with respect to every other possible world. Then, sc.
cording to Salmon's definitions. d seems to be a rigid but not persistent
definite description. For instance, let a and b be names of u and v respectively gisen Salmon's treatment of definite treatment of definite descriptions and many standard treatments of names, the definite description
(ix) a v xtr tor will satisfy the condition on d. (
metaphysics
may not allow that two possibk individuals need not be corn4
possible.
) O fHowever.
c o the
u rquestion
s e , is in either
o case
u a rsubstantive one which
our semantic classifications should not prejudge.
The argument of the previous paragraph can be refined. In particular.
it is vulnerable as it stands to an objector who regards empty names as
semantically defective: for, they might argue, in whatever world the definite
description r (ix) (x -a v x•=1))' is supposed itself to exist, at Least one
of a and b will be empty, so that the whole description would presumably
be semamically defective, However, examples can be constructed using
monadic predicates rather than names. Thus suppose that there are values
of " V and " G ' such that : in some worlds there are Fs; in some worlds
there are Gal in no world arc there both Fs and Gs; any F in any world
is the one and only Fin any world in which it exists; any G in any world
is the one and only G in any world in which it exists. Or in operator symbolism. where the quantifiers range only ova what exists in the relevant
world:
(I) 4:>3x Fx
(2) 0 3 x a y
(
3 I i vx(Fx 1 :1 (3 y x•••)
(4)
(5)
,) v0 ylifx(Gx
( P y D (3y x=y v y ( G y xr•..V)))
—
•
•
x
Now consider the definite description "(gx)(PaNd G a r; call it d'. Hy (3)-O
(5). d ' is u rigid designator_ However, d' designates an F with respect to
( ) ) )
y
some worlds and a G with respect to other worlds in which that I': does
X
not exist, so d i s not persistent.
&
" f" and "(J" could be interpreted in such a way as to make (1)-(5) true
3
given some ontologies of facts. For example, suppose that it is contingent
X
G
x(
irt
) 6ntinolosy L e . Okla the) "timid dristnalc the same thins with respect to tsar" possible
',mid
) lop. cll. 9. 34).
I
t
'
o
f
f
i
c
e
s
ON RICI1311
-1
Y let
A an
N DF be a fact that P and a G be a fact that
whether Of not P. and
I ' l ' I R
- P, Presumably, there
is a fact that P( - P) if and only if P (- P); hence
S I S T E
Cl-(3) come out true-N ItC isE also not implausible that a fact that P (is essentially a fact that
9 P (- Pt and that there cannot be more than one
fact P( - P): hence (4)
1 and (5) also come out true. e )h is not for a t
onomy
n.
of designators to decide that such a theory of facts is incorrect.
Finally, it is worth nothing that most definite descriptions will be rigid
but not persistent on D a i d 1..dwiS
dividuals.
.
(') For the theory) 3 that no ordinary indisidual exists in (is
part
5 t of)
h emote
o rthan
y oneopossible
f
world. Thus a definite description such
as
w "the
o highest
r l dsolcano"
- b o
willube n
irivially
d rigid, and it will fail to be perNistern
i just because
n
there is more than one world in which there is a highest
volcano. (t)
Volteertily of Dublin
T i m o t h y
WILLIA14450M
Dept. of Philosophy
C
u
r
r
e
n
t
address:
Trinity College
U n i v r r s i t y
College
Dublin 2
O
x
f
o
r
d
° X I 4BH
Ireland
U
n
i
t
e
d
Kingdom
(
l (A)
7 - Th al p 88 of Kg Irne pp_
Minot
Nations to rhe a.watirs 4te IsNuited ,
F l) o41121
rst-O
r d cmoth
r
iestrkied
a
t hl e
q u a n i t t e e r s
M Choe ndto facts.
a
a
o
t
T (o h re o t r i e sn
quatigegidits
I 1
m
I
I
Salmon
informs one 'private coremunkultion) that his ',meal (1988) ••lete
P1
p Prolcssor
a
c
,
ea
It
0
s that
r I hr
p grnerato 001ktri of rigidity whii:11 he had intended to capture IMO which he belie
dekignare
Kripte
"does
c
•M
g
fs
th
d
e
in
ly
a
b
ro
n o t e else with respetA to any possible woad' to the * Mutant or w8
e p
l eoniethireg
r5i rtg i d 1
destinatoe'
A s1
1
-Nine
thin
nit
paper
9n
h
8
2 "Model
P Paradox:. P un and Couriierrbartʻ Points and Cowart pantile",
cino1
PA.
r
d
i
French,
n
g
T.F
ttlehlung
and Inc. Werner-in Ceds.k Mrdwest SturneTia Phitoeopay
e
aoi n M Enfititalamw (Minneapolis : University of Minnesota Pre%%. 1
iR 1
a
chhOdiell
t1 1
s h e al o I l ', nC
4
1M
7 5 • 1 2 0 , ,
w
1
i )i, . t pt p
e v
a
.
a
d
n
de
ii ef ff ei r e n t
a
n rni nt i do
c
n re. a , r t i
e
r A
or i
rg tf e i s
p
o
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e
d rN n
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e
a
o
f fm i