Roderic Allen Girle
A Thesis Submitted for the Degree of PhD
at the
University of St Andrews
1975
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ABSi'RACT
In t h i s essay a theory of proper names i s developed and applied to the c o n s tr u c ti o n of q u a n ti f i e d modal lo g ic s and to a
d is c u s s io n of problems concerning i d e n t i t y across p o ssib le worlds.
The theory i s then used to aid d is c u s s io n of e s s e n t i a l i s m , empty
s in g u la r terms, q u a n t i f i c a t i o n i n t o epistem ic c o n te x ts, and F r e g e ’ s problem with i d e n t i t y .
In the f i r s t c h a p te r, a f t e r a prelim inary d is c u s s io n of
R u s s e l l ’s and F r e g e ’ s th e o r ie s of names, a theory i s developed. I t i s argued t h a t in the giving of a name a r e l a t i o n i s e s ta b lis h e d
between the name and what i s named. That r e l a t i o n i s the sense of the name. I t i s a lso argued t h a t names can be given to imaginary, f i c t i o n a l , and o th e r such n o n -e x is te n t things..
The second ch ap te r i s devoted to a d is c u s s io n of Quine’ s programme f o r e lim in a tin g s in g u la r term s. I t i s th e re argued t h a t the programme cannot be j u s t i f i e d .
The t h i r d c h ap te r c e n tr e s around the c o n s tr u c tio n of
lo g i c a l systems to deal with i d e n t i t y across p o s sib le worlds. I t i s assumed t h a t once a name i s given and i t s sense thereby e s ta b li s h e d
the name i s a r i g i d d e s i g n a t o r . Q u a n t if ic a t io n a l systems are c o n stru cted
w ithout modal o p e ra to rs yet in terms of which cross world i d e n t i t y
can be d isc u s s e d . Modal o p e ra to rs are then introduced to f a c i l i t a t e
a d is c u s s io n of e s s e n t i a l i s m and I d e n t i t y . At each point the formal systems are c o n stru cte d in accordance with c l e a r l y s t a t e d assumptions about c o n sta n t s i n g u la r terms, the domains of q u a n t i f i c a t i o n , and the
giving accounts of such changes, and a d isc u s s io n of the idea th a t primacy should be given to the sense which a name has in one p a r t i
c u l a r world.
The f i f t h c h ap ter i s a d is c u s s io n of empty s i n g u l a r terms
and fre e lo g ic s . There i s a d is c u s s io n of the nature of the values o f empty s in g u la r terms in the formal semantics of fr e e lo g ic s , and a
d iscu ssio n of tiie o b je c tu a l and s u b s t i t u t i o n a r y i n t e r p r e t a t i o n s of
q u a n t i f i e r s .
The f i n a l c h a p te r i s a d is c u s s io n of q u a n t i f i c a t i o n and
i d e n t i t y in ep istem ic lo g ic . I t i s argued t h a t the theory of proper
names developed i s of use in c l a r i f y i n g q uestions about q u a n t i f i c a t i o n in to epistem ic co n tex ts and about F r e g e ’s problem with the co g n itiv e
values of •- a" and = b" when both are tr u e .
A Thesis for
the Degree of Doctor of Philosophy
'Proper Names and Possible Worlds
record is my own, and th a t th is work has not been accepted in any
previous application for a higher degree.
}
Philosophy. My Supervisor has been Hr. G.B.B. Hunter of the I
i
Department of Logic and Metaphysics, For the f i r s t three terms I
worked as a fu ll-tim e student, and for the other twelve terms I
have worked as a part-time external student.
U n iversity o f St Andrews have been f u lf il le d in th e case o f
Mr Roderic A llen G irle.
Signed
INTRODUCTION
CHAPTER I THE WEANING AND REFERENCE OF NAMES
Russell on names Theories of meaning Frege and id e n tity Names and naming
Name g i v i n g and acquaintance
Empty names
The sense of a name
CHAPTER II FORMALIZING AND SINGULAR TERMS
The elim ination of singular terms
Naming predicates
Reference by d escrip tio n Divided reference
Id e n tity and divided reference
Singular reference
CHAPTER III NAMING ACROSS POSSIBLE WORLDS
Time and h istory
In div id u als, worlds and id e n tity
Q u antification, transworld i d e n tity , and no modal operators
Formalizing
E;? :
E'::
I d e n tity and e s s e n ti a l properties Modal systems
I d e n tity and modality
Q u antification and modality
Quantifying Into modal contexts The Barean formula and others The preferred systems
The in d isce r n ib ility of id e n tic a ls
Rigid designators and d e fin ite d escriptions Definite descriptions
Empty d e f in ite d escriptions
CHAPTER IV ESSENTIALISM
CHAPTER V
Common properties Radical differences Matter and d escription Worlds and designators Language and esse n tialism FREE LOGIC
CHAPTER VI
APPENDIX I
APPENDIX I I
APPENDIX I I I
Empty singular terms Free modal logic
The values of variables The range of q u a n tifie rs
Su b stitu tio n al in te rp re ta tio n
Reference
T ru th -value gaps
KNOWING REFERRING AND QUANTIFYING Epistemic logic
Quantifying into epistemic contexts Oratio recta and Oretio pblioua F reg e ’s problem
CONCLUSION
A type theory basis for a theory of proper names A type for symbols
Naming and re fe rrin g I d e n tity and sense Divided reference
The systems = ( 1 ^ 4)
The systems M7Q “ ( 14 i< 4) The systems M^QF (14’ i 4 4 ) Epistemic Logics
F ic tio n a l c h aracters, animals or places are often given
names. Those names, such as "Pickwick” , "Pegasus” or "C airParavel", are then used when we ta lk about such f ic tio n s . A philosophical
consideration of the use of such names has raised the question, How
can we ta lk about something which does not e x is t, since there is
nothing about which to talk?
At f i r s t sight th is question may strike us as ambiguous
because of a kind of play upon the words "something” and "nothing".
So l e t us consider b r ie f ly the way in which Russell came to the
conclusion th at the names of f i c t i o n s , and probably most other names
also, are disguised d e sc rip tio n s. The way in which Russell proceeded
w ill give point to the question posed above,
"A name," says Russell, " i s a simple symbol, d ir e c tly
designating an individual which i s i t s meaning, and having th is meaning in i t s own r ig h t , independently of the meanings of a l l other
w o r d s , F o r Russell, the bearer of a name i s the meaning of th a t
name, Russell also assumes th a t in a genuine subject-predicate
0
proposition'- the meaning of the subject term is whatever is desig
nated by th is term. Under R ussell's assumptions the assertion
"Socrates is wise" can be analysed as saying of the bearer of the name
'S o c ra te s ’ th a t he has the c h a r a c t e r i s t i c of being wise. But i f the
bearer does not e x is t then the subject term is meaningless and the
asse rtio n meaningless. Only i f the bearer e x is t s can the asse rtio n
Russell, Introduction to Mathematical Philosonhv. Allen and Unwin, London, 1920. P. 173.
9
be either true or fa ls e . How then could we assert meaningfully that
Excalibur was brandished, or th a t the round square does not exist?
The question is even more acute in the case of the round square
because we can hardly be assertin g that there is an object which i s not.
Russell iiolds th a t the meaning of a proper name is i t s
bearer. This is a key assumption. I f there is no bearer e x is te n t, as in the case of f i c t i o n a l c h aracters, then the name is meaningless, and tiie assertio n s in which such names occur are meaningless. Since we cannot agree that assertions about f ic tio n a l characters and such
like Eire meaningless i t follows th a t e i t h e r Russell was mistaken
about proper names or, as he was to suggest, most of the terms which
we c a ll proper names are not proper names at a l l . Most of what we
c a l l proper names Eire r e a lly disguised d esc rip tio n s, says Russell,
so th a t
whenever tlie grammatical subject of a proposition can bo supposed not to e x i s t without rendering the proposi
tio n meaningless, i t is plain th a t the grammatical
subject i s not a proper name, i . e . , not a name d ir e c tly representing some object. Thus in a l l such cases, the
proposition must be capable of being so analysed th a t ^
what was the grammatical subject shall have disappeared.' Russell then proposed analyses in terms of d e fin ite d e sc rip tio n s.
Our concern in th is essay is with proper names. V/e
w ill not be much concerned with the theory of descriptions as such.
Our main concern w ill be to consider the statu s of names in language
Eind what can be said about t h e i r meaning.
We begin to develop a theory of proper names by discussing
R u sse ll's assumptions and Freg e's th e o rie s. In the course of d iscu s sion we w ill consider R u s s e ll's idea th a t i f a sentence i s lo g ic a lly of the subject-predicate form, "then the very fact of i t s being
proper names w ill then be proposed, a theory somewhat in the stylo of
Frege's theory with emphasis on the sense of names*
Even so, a theory of proper names would be somewhat
redundant i f i t were possible to purge a language of a l l names. So
we discuss Quine’s programme for the elimination of singular terms.
The theory of proper names w ill then be applied to
discussions of several questions of current in terest in the philosophy
of logic. F i r s t wo discuss the problems of i d e n tity across possible
worlds, then essentialism , free logic and quantification into
epistemic contexts. At the conclusion of the l a s t discussion the
theorv i s applied to one of F ren e's problems about i d e n t i t é .
R u ssell’s two assumptions about proper names were th a t (a) the meaning of a proper name Is it s bearer, and (b) the only bearers of proper names to be countenanced are real or ex istin g ob jects. We
consider f i r s t the notion th a t the meaning of a proper name is it s bearer.
One is tempted to say straigh t away t h a t R ussell is
plain ly mistaken when he says th a t proper names have any meaning at
a l l . I f one were asked what was the meaning of some proper name,
such as "Robin", one would be lik e ly to reply eith er th a t names don’t
have meanings, or to reply by asking the questioner what the point of
h is question was. Of course, the questioner might be asking the kind
of etymological question which can be given an answer such as "'Robin
means 'courageous and j u s t * " , or "'Emmanuel’ means ’God with u s , ' "
There is also the weak sense in which " B ill" means "male", but then
" B ill" has been used as the short name fo r women named "Wilhelmina".
The temptation to say that Russell i s simply mistaken
can be resisted i f we take into account some comments which he makes
about the use of the term "meaning". In his lectures on Logical Atomism he says
As to what one means by 'meaning*, I w ill give a illu s tr a tio n s . For instan ce, the word 'S ocrates', you
w ill say, means a certain man; the word 'mortal* means
a certain quality; and the sentence 'Socrates is mortal' means a certain fa c t. But those three s o rts of meaning
are e n tir e ly d is tin c t, and you w ill get in to the most hopeless contradictions i f you think the word 'meaning*
has the same meaning in each of these three cases. I t is
very important not to suppose th a t there i s j u s t one thing
which is meant by 'meaning', and that therefore there i s
not a name a t a ll, i t i s a noise.^
So i t ' s reasonable to say th a t R u ssell's account of
proper names is th a t they simply designate in d ivid u als. There are
other points in his account of proper names, but they need not
concern us j u s t now because they bear ch iefly on the s ta tu s of what
is designated, and the relationship between the user of a proper name
and what i t designates. We can u sefu lly label R u ssell's account of
proper names as a Simple Re fere ni.i a.l theory. The term "Simple" is used in order to h ig h lig h t a contrast which can be drawn between
R u ssell's account of proper names and Frege’s account.
Theorjes^of
Before going on to consider Frege's account of proper
names we need to be clear about what the la rg e r story i s in to which
these various accounts of proper names f i t . The larger story w ill be some theory of meaning. I t w ill s u ffic e , for our purposes, to adopt
2
what Dummett says about theories of meaning in h is study of Frege.
Although what Dummett says is sp e c ific to Frege's work, we can generalise from what he says without prejudicing any contrasts we
may want to h ig h lig h t, in th is essay, between Frege and other philosophers such as B u ssell.
What Dummett says can be put as fo llo w s. F i r s t , for any
theory of meaning the sentence i s the unit of meaning. Secondly,
^"The Philosophy of Logical Atomism" in Logic and Knowledge, Ed. R.C.
Marsh. Allen
&
Umvia, London, 1956, pp.l86«187.?'Michael Dummett, Frege; Philosophy of Language. Duckworth, London,
i t must explain also how the meaning of each sentence ( i s ) determined
from i t s in te rn a l structure . . . . i t must be a semantic, and not
merely a syn tactic, analysis."^ Thirdly, a d estination can be drawn
between the sense and the tone of a sentence or expression; "to the sense of a sentence belongs only th a t which is relevant to
determining it s tru th or fa ls ity ; any feature of i t s meaning which
cannot e ffe c t i t s truth or f a ls it y belongs to it s tone. Likewise,
to the sense of an expression belongs only that which may be relevant
to the truth or f a l s i t y of a sentence in which i t might occur; any 2 element of it s meaning not so relevant as part of i t s tone." An
example of expressions with the same sense but d iffere n t tone i s the
p a ir; "and" and "but".
R u s s e ll’s account of proper names can be seen as saying
th a t the sense of a name c o n sists j u s t in i t s having a certain referent
But th is account does not s a tis fy Frege.
Ejm e-jM JdentitX
I f proper names simply designate individuals and have no
other v i t a l ch a ra cteristic, then there is s problem which a r ise s.
The problem concerns id en tity-p rop osition s such as "Cicero is Tully"
and "The morning star i s the evening star." About id e n t i t y Frege asks, "Is i t a relation? A rela tio n between ob jects, or between names
or signs of objects?" The f i r s t a ltern a tiv e, that id en tity is a
^Ibido, p. 2c
^'Ibidc, p. 2c
3G. Frege, "On Sense and Reference" in Translat ions from the Philosophical ^frlH nqs,of Gottlob Frege, Eds. P. Geach and M. Black. Basil Blackwell,
wise" can be analysed as saying of the bearer of the name "Socrates"
th a t he has the c h r a c t e r i s t i c of being w ise, "Cicero i s Tally" should
bs analysed as saying of the bearers of the names "Cicero" and "Tully”
that they have the ch aracteristic of being id en tica l with each other. Taking the f ir s t altern ative Frege says.
Now i f we were to regard equality as a relation between
th a t which the names *a* and 'b' designate, i t would seem
th a t S“ b could not d i f f e r from apa ( i . e . provided s™b
i s tr u e).
Blit is d ifferen t from "Srk"« The difference that concerns
Frege here is not simply a syn tactic difference but a difference in
terms of inform ation. "a.~a" conveys quite d i f f e r e n t information from the information conveyed by "^b". "The two sentences," says Frege,
2
"do not have the same cognitive value", and t h is is ju st what is
meant by saying th a t the information conveyed by one i s d ifferen t
from the information conveyed by the other.
As Dummett says.
The notion of ’information’ being appealed to here does
not require any elaborate e x plication; I acquire
information when I learn something which I did not previously know, and Frege is asking how i t is possible
that I may be in a position to know the sense of an
id entity-statem ent, i . e . to understand i t , and yet
learn something th a t I did not know before by being told
th at that statement i s tru e.3
I t is important to rea lize that im p licit in Frege’s
c r it ic i s m of a simple referen tia l account of the sense of ’a/ and
*b’ in ”^“ b" is the notion t h a t "a theory of meaning i s a theory of
^Ibid. p. 56.
O
he understands Now, i f when a person understands being
a name he knows it s referen t, and sim ilarly fo r ' b ' , then that person
w ill know that ^ rb . " I f the sense of a name co n sists merely in i t s
reference, anyone who understands two names having the same re fe re n t
o
must know th a t they have the same r e fe r e n t." ’
Although th is looks lik e a most powerful c ritic is m of
R u ssell's account of proper names, Russell has a ready reply. The reply i s contained in the follow ing statements of R u ssell's:
For a lo g ic a lly p erfect language, there w ill be one
word and no more for every simple o b j e c t , . . ,
. . . a l l the names th a t i t would use would be private to
t h a t speaker and could not enter into the language of
another speaker.^
Russell rea lly does meet Frege head-on here. Real proper
names would be able to be used only by people who know the referent
of the name, and i d e n t i t y statements would be non-existent because
they would be u s e le s s. I t is j u s t because Russell conceives of an
id e a l language in t h i s way that h is account is u n r e a listic , but i t
i s c o n sis te n t. We w ill retu rn again to th is question of the user of
proper name having to be acquainted with the name's referen t. Taking the other a ltern a tiv e, th a t i s th a t id en tity is a relation between names, Frege argues th a t "a~b" i s ju st not an assertion about words. I f we take "apb" to say th a t the name 'a /
^Ibido p. 92.
h h i d c p. 95.
^ O p .c it,, p. 197.
these words as names for the same ob ject, whatever th a t object might be. "In that case the sentence ^=b would no longer r e f e r to the
subject matter, but only to i t s mode of designation; we would express
no proper knowledge by i t s means. But in many cases th is is ju st
what we want to
Frege then presses his argument even further and says th a t
we cannot, anyivay, look upon names simply as objects of some s o rt,
for example, typographical ob jects. We have to take account both
of what a name re fe rs to ( it s reference) and the way in which a name
designates an object ( it s sen se). I t is not altogether c le a r ju st what Frege is talking about when he talks about the mode of designation.
He says;
I f the sign 'a* is distinguished from the sign only
as object (here, by means of i t s shape), not as sign ( i . e . not by the manner in which i t designates something). The cognitive value of becomes e ss e n tia lly equal to that
of apb, provided a=b is true. A difference can a ris e
only i f the differen ce between the signs corresponds to
a difference in the mode of presentation of that which
i s designated.2
One way of seeing Frege's argument and point here is to
see him as saying th a t names cannot be distinguished one from the
other simply by means of syntax. and 'b ' are not d ifferen t names simply because they are two d ifferen t items on a l i s t of prim itive symbols. So i f they are d ifferen t names t h e i r difference must l i e in
th eir having d ifferen t relationship s with the one thing to which both
refer. As Dummett explains; ^OpoCit. p. 67
e i t h e r name, although i t happens th a t i t Is the same
object which s a t i s f i e s the two pairs of conditions of
such id e n tific a tio n ,!
Frege then explains th at,
The regular connection between a sign, it s sense, and i t s
reference is of such a kind th a t to the sign there
corresponds a d e fin ite sense and to th a t in turn a
d e f in i te reference, while to a given reference (or object)
there does not belong only a single slgn,^
In th is way the sense of a proper name has i t s place in determining
the truth-value of any sentence in which the proper name occurs, "The sense of a word — as opposed to any other ingredient i t s
meaning may have — c o n s titu te s the contribution which i t makes to
determining the tru th -co n d itio n of sentences in which i t occurs precisely by associating a c e r ta in reference with i t . " ' Yet, even though the sense of a name associates a c e rta in reference with i t ,
for each name there w ill be a d ifferen t way of associatin g i t s
referent with i t , and because of the differences between these ways of association the names w ill be d iffe r e n t.
Names aM _me&nim
From what Frege says about id en tity taken as a relation between names i t is not altogether clear that he is not ju st wrong. He expounds th is a ltern a tiv e, as we have seen, as "What is intended
to be said by |p b seems to be that the signs or names ’a ’ and 'b*
designate the same thing, so th a t those signs themselves would be
^Op.cit, p, 95 ^Op.cito po 58
trary, and (b) that i t makes a-'b no longer " r e f e r to the subject
2
matter, but only t) i t s mode of designation," '
I t is not alto g e th er c le a r ju st what F reg e’s f i r s t
criticism amounts to , but i t is hard to see how one can avoid the conclusion th a t names are a rb itra rily chosen end given to people, places and things, e tc . I t may be that th is c ritic is m springs partly from Frege's in clu sion of d e fin ite descrip tion s, such as "the
morning star", in the general category of proper names. But even
i f th is criticism does spring partly from the way in which d e f in ite
descriptions are categorised i t is hard to see how the criticism survives Frege's own example of a mountain with the two names 'A fla'
3
end 'Ateb', These two names are a rb itra rily chosen, even made-up, words. Once chosen and declared to be names then the words can be used by any speaker of the language to r e f e r to some p a r tic u la r . Words
can be declared to be names by any one of several ways such as by
being used in a r ite such as baptism, or by some declaration of an overt kind like "The man, whose name was 'B rinklethorpe', , . or
ju s t by being used in litera tu re with a c a p ita l f ir s t le tte r .
Although the choice of some word as the proper name of some particular
may be quite arbitrary, th a t is not to say that there i s a subsequent
randomness about the use of such words or the category to which they are seen to belong. "Peter", "Rover" and "Ateb" have a q uite firm
status as names, and as three d ifferen t names.
^Op.cit. p. 56
^Ibid. p. 57
3
in the category and what status the word then has in a language, we need to note also th a t a name is not merely a phonological or typo graphical object, token or even type,
III most languages a, is the same name as a, and b is a
d ifferen t name. In most languages we t e l l th a t a name ^ is the same name as the name a, because the typographical tokens are both of the
same typographical type. Sim ilarly, we distin guish n from b typo graphically, This practice can be the source of a confusion. We
could confuse the nature of the sim ila r itie s and d ifferences between
typographical marks (or spoken words) with the nature of the sim ilar
it i e s and d ifferences between names.
There are the sorts o f languages suggested by Searle^ in
which there is some convention for changing the typographical or
phonological object in order as we use a name. For example, the f ir s t
time we use some given name we use the mark * V \ the second time the
mark "b", the th ird time the mark "ej% and so on.
So, in th is sense, Frege i s correct when he says that we
cannot look upon names simply as typographical ob jects, or objects of
some other sim ilar so rt. But, although we cannot look upon names as objects of that kind, i t does not follow that we cannot take ”s
5
"b"to be saying something about names i n th eir role in a language as
names. Hence, i f we take i t at the outset th a t i t i s names that we
are talking about, not typographical ob jects, then ".s-b” can be about names as such, and not be about typographical ob jects.
Frege himself uses the term "sign" when talking about
names. We could say th a t there is a cla ss of signs which is the c lass
of names. These names are to be distinguished sy n ta c tica lly . They
are, in fa c t, a set of syntactic o b je cts. But then, i t might be
objected that we ere s t i l l le f t with the problem of how "John" and
"James" are rea lly two d is tin c t elements in the s e t of names. Our arguments to show that one name can be expressed typographically (or
phonologically) in several d ifferen t ways w ill only give added force
to the objection that perhaps "John" (in the typographical sense) is
expressive of the same name as "James" in the typographical sense. Frege would say that they are d i f f e r e n t because th eir senses are d iffe re n t. I f there is no need to provide other than syntactic
c r ite r ia for sameness of names then Frege's bringing in of the senses o f names is unnecessary. I f there is a need to provide other than syn tactic c rite r ia for sameness of names then Frege's bringing in
of the senses of names is dangerous to his own account. I t is
dangerous because there is not usually some one way of associating the referent of a name with the name which is understood by a l l those who
use the name m eaningfully.
This la st point is not th a t the notion of a name's having
sense and reference is somehow self-d efea tin g . Provided vie accept
th a t there are names, and th a t the syntax of the language indicates
which names are which, then the notion of these names' having both
sense and reference is not unreasonable, and i t i s also not unreasonable
to agree th a t the sense of a name may vary from speaker to speaker.
"Frege , . . was p erfectly w ell aware of the va ria tio n s in sense
attached by individuals or a t d ifferen t times to the same expression,
and of the haziness of the senses so attached,"^ The point a t issue is
t h a t we cannot use e i t h e r sense or reference as c r i t e r i a for id e n tity
of names them selves. Here we have to rely on s y n tac tic c r i t e r i a .
We now come to Frege's second c r itic is m . His c ritic is m is
th a t i f we say th a t "jgrk" says th a t what is named by *.a' i s also
named by ' b ' , then "s.“ b" no longer refers to the subject matter but
only to i t s mode of designation. From th is i t would follow that no
real information would be imparted about the referen ts of end %%
I f there is an argument here i t is c e r ta in l y in valid ,
but more importantly, i t is ju st not true that i f we say that says th a t what is named by 'a / is also named by 'b*, then no longer refers to the subject matter but only to it s mode of designa
tio n , Apart from the fa c t th a t i t i s strange to hear Frege talking
about what "a-b" i s referring to in terms of p articu lars, there is a
form alization of which i s illu m in atin g. I f we l e t mean "x names y". then we have the following formalization of the view
c r itic ise d :
& = b = N' b\ K
The definiendum
can be read as
"The item which 'Ij* names is named by 'a.',"
In t h is case the subject matter, i . e . the item named, is most certain ly
discussed and the information imparted is not equivalent to a
lo g ical truth. There
is
proper knowledge about the referent in "spb"of 'a'and of 'b.%
Although F reg e's c r itic is m of the simple reference account
of proper names has point, i t is not c le a r th a t much credence can
he
put upon his c ritic is m of the view th a t "apb" says that what 'a* names
i s also named by ' b ' . The c o n tra st between R ussell and Frege is
i t is not surprising that Frege's c ritic is m of the "naming" view
should f a i l , because Frege's own account of proper names in terras of
sense and reference is very sim ila r to the "naming" view.
We have seen how the sense of a name, for Frege, co n sists
not merely in it s reference, but in a p a rtic u la r way of id en tifyin g
an object as the referent of the name. At the r is k of suggesting
something sim ilar, i t is clear th a t one common way of id en tify in g
the object to which a name refers is to find out which object has
been so named. Given th a t there is a syntactic category of names,
when an assertion is made using one or more of these names i t is
ju s t assumed that each name used has been given to something. I f
a name is given to something or someone then the naming relation has been established between some one element of the category (or
s e t) of names and a thing, place or person.
Name giving and acquaintance
Several things need to be noted about the naming re la tio n ,
F i r s t , although i d e a l ly the naming relation is a function from a
domain of names (the arguments) to a domain of what i s named (the
values), in natural languages t h i s is not the case. There are, for
example, many people who have the same name. N evertheless there is
a tendency in everyday l i f e for people to be given names which w ill bring the ordinary language naming r e la ti o n clo ser to the id e a l. So
we get the notion of a person's " f u l l name", a notion which seems to
give expression to the hope that no two people w ill have the same
f u l l name. Array s e r ia l numbers work th is way also .
Secondly, the act of giving something a name is quite
John Austin seems to have held th a t naming i s a
momentous act, which ju s t not anyone casually can
perform; i t would take the rig h t person in the rig h t
circumstances using the rig h t performative formula; and
I am not at a ll sure th a t he would have counted me a
valid ly ordained namer, or my baptismal formula fo r
Pauline as a valid sacramental form. Well anyhow, I
claim the rig h ts to r e f e r to any young lady of my acquain
tance by the name "Pauline" for the course of th is
discussion; and I think the difference between such use
of a name jprq ha^ v ice and the more o f f i c i a l conferment
of a name is only of legal or anthropological, not of
lo g ic a l, importance.%
Thirdly, we must not confuse the giving of the name with
it s subsequent role as an argument for the naming rela tio n . At the
same time I t is v i t a l to remember that names call be given in other
than the o f f ic ia l settin g s of such things as ch risten in gs, or the
launching of ships, or the claiming and naming of te r r ito r ie s by explorers. When logician s claim th a t genuine proper names must name
some ex istin g object or particular i t seems to me th a t they are for
gettin g that there i s a vast range of situ ation s in which names are
given. I f the giving of a name does e s ta b lis h the naming relation
between a name and something named then i t w ill not be untov/ard to
consider some cases of the giving o f names.
There are three so rts of cases which are of i n t e r e s t .
There are those cases where, in the presence of the p a r tic u l a r , a
name is given i t . The b est example i s that of a christen ing. Here
there is no doubt about eith er who i s named or th a t the parson so
named e x i s t s . There are, secondly, those cases where, in the absence
of the particular but in the knowledge, or at le a s t the b e l i e f , th a t
i t e x i s t s , a name i s given i t . Such a case is the case of the giving
of the name "Vulcan" to a planet which some astronomers believed
existed in an o rb it inside Mercury's. This is an in terestin g case.
because once the name was given both those who believed Vulcan
existed and those who didn't used the word "Vulcan" as a name. There
are a range of v a ria tio n s in these cases through those who know t h a t
the p a rtic u la r e x i s t s , and those who claim to know, and those who
believe tru ly, and those who b elieve fa ls e ly , to those who guess or
postu late. There is no need to go through every variation .
Thirdly, there are those cases where, in the knowledge t h a t
what is to he named does not e x i s t , a name is given. This is the
case ty p ified by the w riter of fic tio n giving names to the characters, animals, objects and places in his work.
Several things need to be noted about these various cases
of the giving of names. F ir s t, there is the in terestin g feature of
ordinary language th a t one can take some new word, invent i t as i t
were, and by the act of name-giving that word becomes part of the
syntactic category of names. Freg e 's 'Ateb' and 'A fla' are cases in
point. There are, of course, already a large stock of words in
ordinary language which can be put together in various combinations
to make up a f u l l proper name. But, by name-giving a word becomes a
name. Secondly, although in one kind of case the name giving goes
with an acquaintance with th a t to which the name is given, in many
cases there is no acquaintance with that to which the name is given.
A name is often given to something which has been id e n tif ie d descrip tiv e ly , and often the d e sc rip tio n i s not really a d e fin ite description.
For R ussell, the sorts of name-giving where there is
lack of any acquaintance with th a t to which the name i s given are
not r e a lly name-giving. Furthermore, anyone who uses a word as a
name must be acquainted with the bearer of th a t name.
A name, in the narrow logical sense of a word whose
meaning is a p a r tic u l a r , can only be applied to a
We are not acquainted with Socrates, and therefore
cannot name him. When we use the word 'Socrates', we ore
r e a l l y using a d escrip tio n .1
This follows from R u ssell's account of proper names. I f
the sense of a proper name is i t s referent and a speaker knows the
sense of a given name, i . e . understands the name, then the speaker
must know the re fe re n t of the name. To know the referent of a name
i s , for R ussell, to foe acquainted with i t .
R u ssell's claim that we must be acquainted with a p a r t i
c u la r before being able to use a word as it s name makes understandable
h is further claim th a t "the only words one does use as names in the
2
lo g ica l sense are words like ' t h i s ' or 'th a t'." For, "One can use
' t h i s ' as a name to stand fo r a p a r t ic u la r with which one is acquainted
at the moment. We say 'This is w h ite'. I f you agree th a t 'This is
w h ite ', meaning the ' t h i s ' th a t you can see, you ai'e using ' t h i s ' as
3
a proper name." Of th is approach Hlntlkka remarks, "Here one fe e ls ,
something has gone amiss. Not only i s i t strange to c a l l ' t h i s ' and
' t h a t ' names. i t seems p o sitiv e ly perverse to allege t h a t they are
our only proper names properly so c a lle d ." ^
R u ss e ll's requirement th a t we must be acquainted with the
bearer of a name in order to use a word as a name means t h a t , for him, we cannot use the word 'Socrates' as a name. "We are not acquainted
with Socrates, and therefore cannot name him. When we use the word
'S ocrates', we are rea lly using a descrip tion . Our thought may be ^Op.cit. p. 201.
^Op.cit. p. 201.
^Ibid. p. 201.
lîiîîtiîska, "E xistential Presuppositions and E x isten tia l Commitments".
K ■
rendered by some such phrase as, 'The Master of Plato,*
Geach emphatically denies t h is point of R u ss e ll's when he
w rite s , "It is indeed esse n tia l to the role of a name that the name
can be used in the presence of the object named as an acknowledgment
of i t s presence. But equally e sse n tia l to the name's role is i t s use
to ta lk about the named object in absentia," But Geach does agree
that- acquaintance is e s s e n tia l at some point: "There must in the f ir s t
q
instance be someone acquainted with the object named."'" Once there has been th is i n i t i a l acquaintance then the name may be used to talk
about the named object in absentia , and in perpetuum. "Plato knew
Socrates, and A ris to tle knew Plato , and Theophrastus knew A ris to tle ,
and so on in apostolic succession down to our own tim es; that is why
we can legitim ately use "Socrates" as a name the way we do."^
Although Geach denies the extreme th esis put forward by
Russell, he supports the central notion th a t acquaintance is e s s e n t ia l
to a word's becoming a name,, or being properly used as a name. So,
for Geach, since no one has seen Vulcan, the word '"Vulcan" i s not
r e a l ly a proper name. I t was not a proper name even when soma
astronomers believed Vulcan ex isted , and now th a t i t i s f a i r l y c e r ta in
th a t Vulcan does not e x ist i t i s also quite certain th a t "Vulcan" is
not a proper name. The same can be said for a l l those words which
were (and are) supposed to be the names of f i c t i o n a l , mythical or imaginary bei ngs.
^Russell, o p .c it, p, 201,
Geach, Logic M atters. Blackwell, Oxford 1972, p,154,
EsnptY names
I f logicians lik e Russell and Geach are co rrect most of
what has been described above as name-giving is not r e a l l y name-givii
For Geach, the giving of a name to something which does not e x i s t is
r ea lly the giving of a quasi-name. He says:
Suppose we hear of a man who dreams of the same g ir l
night a f t e r night , as happened in a story of H, G,
Wells; for convenience of conversation, we may say he
dreams of Petronella every night, without eith er committ ing ourselves to the view th a t there is a real liv e g i r l
he is dreaming o f, or meaning th a t the name "Petronella"
is the name he gives the g i r l in his dreams. For us,
"Petronella" is then functioning not as a name but as a
quasi-name. and also
Names and quasi-names are of course grammatically proper
nouns.2
I t seems to me th a t Geach is trying to have his cake and ea t i t . He
wants to say th at re a l names designate only e x istin g th ings, but
since names like "Petronella" (he says: 'the name "Petronella"') are
bestowed on characters in dreams he w ill have quasi-names. I t is a
d i s t i n c t i o n without a difference fo r which he can give, on his own
3
word, no sa tisfa cto ry account. But above a l l , he cannot stand
imaginary e n t i t i e s . " I allow no such e n t i t i e s as imaginary g i r l s in
my universe of discourse,"^ Geach i s not alone in th is p ro h ib itio n is t
attitu d e to imaginary e n tit ie s .
R u ssell's a ttit u d e to the bearers of names is quite
unequivocal, indeed ru th less, as we have already seen.'' For in the long
^Op.cit. p. 161.
% bid. p. 163. ®Ibicl. p. 165. ^Ibid. p .156,
run R u ss e ll's lin e on proper names leads to the virtu al elim ination
of singular terms and the almost exclu sive use of d e f i n i t e descriptions
in his lo g ic . But the view need not be pressed th a t far. Frege i s in general agreement with R ussell. In a
properly constructed formal language " it must be impossible to form
a proper name lacking a reference."^ Dummett explains th at, for Frege, a sentence containing a proper name without a referent was a
sentence without a truth-value. And " it is impossible to give any
coherent account of the functioning of a language in which i t is
9
possible to construct well-formed sentences which lack truth-value.""
Natural language is im perfect, and we make do with i t . There are
proper names in natural language without reference, but we under stand what is said in s p ite of being unable to give t r u t h - value to
the sentences in which empty names occur.
Frege says, "A lo g ic a lly perfect language should s a tisfy
the conditions; th a t every expression well constructed as a proper
name out of signs already introduced sh a ll in fa c t designate an
object; and th a t no new sign s h a ll be introduced as a proper name
3
without being secured a reference." For example, Frege in s is ts th a t
in arithm etic one does not create numbers by d e f in i tio n and then give them names such as "zero", "one", e tc . "Zero" i s a proper name, but
"Only when we have proved th a t there e x ists one object and one only
with the required property are we in the position to give th is object
the proper name 'zero'."^ We must secure a reference for the name,
^Dummett, o p . c i t . p. 167
^Ibid. p, 167
Even though Frege held to the d e sir a b ility of every name's
referring to an o b ject, in p ractice, Frege's doctrine of sense and
reference enabled him to cope with the s itu a tio n where a name did
not have a r e f e r e n t. Frege's solution for the problem of what i t
amounts to to use a name like "Vulcan" is to say th a t, as Dummett
puts i t ,
Such an expression has a sense because we have a
c r iterio n , perhaps quite sharp, a t any rate a t lea st
as sharp as for most names having a genuine reference,
for an o b j e c t ’s being recognised as the referent of the
name : but i t lacks a reference, because as a matter of
fact there i s nothing which would id en tify any object as the referent of the name ; there i s no object which
s a t i s f i e s the condition determined by the sense fo r
being i t s referen t.
Dummett concludes that Frege "had no need to postulate any realm of
shadowy non-existent objects which yet had being, and could therefore
be talked about and were talked about whenever we used one of these
2
empty proper names." In practice then Frege did not go the way of
Russell and Geach and declare the names of Vulcan, Petro n e lla , Pegasus
and Pickwick not to be names a t a l l . Frege accepts such names for
what they are, and in as much as he does th is his account i s that
much more i n t u i t i v e l y acceptable.
But, once again, in Dummett as in Geach, Quins and others, we see th is disparaging reference to "the shadowy realm of non
ex isten t objects." But there is nothing shadowy about Pickwick, Pegasus or Cair Paravel. There are quite clear accounts of who, what and where they are. But of course, that is not what Dummett and the
others are talking about, yet there does seem to be some lack of c la r ity . I t is one thing to guard against the confusions which can 3Dummett, o p . c i t . , p. 160,
a rise when a name is used and i t is not c lea r whether what is named e x ists or not, i t is another thing to say that we cannot, in some
log ical sense, name non-existent o b je c ts. As Hlntikka says of th is
view;
The c r i t e r i a by means of which we recognise an expression
as being a proper name do not involve ascertaining th a t
there i s a unique person (or object.) to which i t refers.
Otherwise i t would bo a lo g ica l and not merely a factu al mistake to be deceived by a pseudonym. The p ecu liarity
of 'Bourbaki' w ill not lead us to repudiate it s namehood. Empty names are s t i l l called names ;. .
Our ordinary language includes amongst the things of which
we we speak a myriad of non-existent ob jects, but we are able in ordinary language to distin gu ish between real and imaginary, ex isten t
and non-existent. Why should we not then be able to do the same in logic?
This question i s asked, not simply to throw down some sort
of lo g icia n 's g a u n tle t, but because there i s a problem, one so lu tio n
to which demands th a t we be able to do some such thing in our formal
systems. The problem can be posed in the form of a question. In
posing the question Î w ill use the le tte r s 'EP* for " e x i s t e n t i a l
presupposition", and take i t th a t names interpreted in an EP way are names in te rp re te d to be non-empty. The question i s : I f we are given
a formal language which is to be in te rp re te d in an EP way with respect
to names, is i t possible to consider situ ation s in which those named individuals did not ex ist?
In the chapter on free logic I hope to show th a t the best
way of considering s itu a tio n s in which named individuals do not e x i s t
i s to abandon an EP in t e r p r e t a t i o n of names, because the EP i n t e r p r e t a
tio n of names makes for considerable d iffic u lty in the consideration
of such s itu a t io n s .
The sense of a name
We s h a ll also explore the notion that words are entered
in to the sy n tactic category of proper names by t h e i r being given as
proper names and th a t what Dummett c a ll s "the c r i t e r i o n fo r an objects*
being recognised as the referent of the name" is given in some basic
sense at the name-giving — sometimes by the circumstances, as with
a baptism; sometimes by an author in the form of a description;
sometimes by stip u la tio n , or some other means. But in many cases
there is no c r i t e r i o n which would sa tis fy a demand for a d e f in ite
d e sc rip tio n other than saying th a t a is j u s t the item to which the
name 'a.* was given. I t does make sense simply to ask, when looking
f o r the person who is called "Who is a,?” We sh a ll explore the
implications of assuming th a t i f we see the naming re la tio n as the
f i n a l irred u c ib le c r i t e r i o n for an o b je c t’s being recognised as the
rolhient of a name, then we can interpret the notion of the sense of
a given name as the r e l a ti o n established by th a t name's having been
given to something.
I t is possible to give a formal account of the naming
r e la tio n and the sense of a proper name as outlined above. This is
done in d e ta il in Appendix I . Use is made there of the work of
1 2
Church and Rennie. The formal system developed there r e lie s on the
basic idea th a t there are four categories of item s, they are truth
values, in d iv id u als, possible worlds, and syntactic item s. The
logic there is developed in terms of the relationships of a functional
^A. Church "A formulation of the Simple Theory of Types", The Journal
of Symbolic Logic Vol. 5, 1940, pp.56-68,
211. K. Rennie, Some uses of type theory in the analyses of Lanquaoe.
typa which can e x is t between these categories and categories b u i l t
upon them. Our main in ter e st is in the s e t of functions from names
to in d ivid u als.
I f a name is given to an ind ividu al, say 'a / is the name
of a,, then the rela tio n between the name and the individual can be represented se t-th e o r e tic a lly by I t can also be
represented by {^<the individual named by * â '> ] ^ Either of these can be treated as the sense of ‘a.** and i t is quite clear that
the sense of is d is tin c t from the sense of *b' provided that *b*
i s a d i f f e r e n t syn tactic item to
When a word is used as a name i t is placed in a relation
to that which i t names. I t i s , of course, an item In the category of syntactic item s, but within that category i t becomes a member of
the set of names. This i s not to say th a t the sense of a name i s 9
" i t s having been assigned whatever reference i t has been assigned",
as Wiggins says. I t i s the resu lt of it s having been assigned a
referen t, the s e ttin g up of the designation r e la t io n . Once the word
has been assigned i t s referent i t then has a sense. Indeed, Wiggins
goes on to in d ic a te j u s t th is when he says, " I f standing for i t s
referent is what a proper name's having a sense con sists in , then
there is no room for discrim ination of sense arising from the p arti
cular circumstances under which a proper name may have been learn t. Such contingencies are overcome as they are overcome in the learning
3
of the sense of any other sort of expression."
^The convention here i s th a t the value of the function i s to the le f t .
o
"D. Wiggins, "Essentialism, Continuity and Identity". Synthèse, 23,
1974, p. 338. '
