Speranza
As Grice and Warnock remarked, one is not accustomed in philosophy nowadays to the
assumption that one is either a Platonist or a Nominalist.
These venerable names, with their deceptive suggestion of
clear and sharp opposition, are no longer regarded as profit-
able banners under which to attack philosophical problems
and opponents, nor as party titles exhausting the possibilities
of disagreement. However, disputes couched in exactly
these terms are still keenly waged among mathematical
logicians. It is said that there is, attached to the study of
mathematical logic, a different and in some ways more
important enquiry t called Ontology : and that leading ques-
tions in this enquiry are, for example ; what abstract entities
there are in addition to the concrete objects with which we
are all familiar ; or whether, on a more radical view, there
may be no abstract entities at all. The central ontological
question is, it seems, the question whether there are abstract
entities. It is commonly supposed that there is no difference of
principle (though certainly there are very many differences of
some sort) between properties, relations, concepts, numbers,
classes ; that all of them are in some way reducible to
classes, and so that the admission of these lets in all the rest.
And accordingly as one does or does not make this admission,
one is a Platonist or a Nominalist.
1 This is an extensively revised version of a paper originally published in
the Proceedings of the Aristotelian Society for 1950-51. That paper was very
defective, being confused at many points, in some passages irrelevant, and
written also in a rather disagreeable polemical tone. The present version,
though still directed at the same targets, is milder, shorter, and, I hope, much
clearer. I am most grateful to the editor for allowing me the opportunity to
make these changes.
75
y6 ESSAYS IN CONCEPTUAL ANALYSIS
It is, as one would expect, exceedingly difficult to come
to grips with this debate, since the doctrines between which
one is to choose are so curiously worded. Do we believe
that there is a 'reality behind linguistic forms' ? Surely we
do. But Professor Quine regards this as the thin end of the
Platonic wedge, 1 which we must be prepared to extrude if
we wish to 'renounce abstract entities'. Are we willing, or
not, to make this renunciation ? But we do not know what
it is that we are invited to renounce. It would be both
arrogant and rash to assume that these queer-looking dis-
putes are quite without substance, but it does not appear at
first sight that any sensible choice could be made between
such alternatives.
Professor Quine has made numerous highly expert
attempts to sharpen the ontological issue for us. However,
in this paper I shall seek to show that the apparatus which
he brings to bear does not clearly or naturally apply to some
at least of the fields in which he has advocated its employ-
ment. I believe that some scrutiny of the logical symbolism
and logicians 1 devices which he uses, and some comparison
of these with certain features of ordinary language, will
reveal that the logician's apparent sharpening of the issue
involves in part the manufacturing of unnecessary problems,
and In part a distortion of what may be quite serious pro-
blems ; and I shall suggest that this may come about through
an insufficient sense of the perils involved in imposing the
neat simplicities of logic upon the troublesome complexities
of language. It is hardly necessary to say that 1 pick no
quarrel with mathematical logic itself, but only with some
of the peripheral uses to which its weapons are sometimes
put. The particular weapon which is, as I shall suggest,
importantly misused in the present case is the existential
quantifier.
A preliminary distinction should be made at once. The
central ontological question is, as I said above, the question
whether there are abstract entities. But this question is in
1 *On Universals', Journal of Symbolic Logic, September 1947.
METAPHYSICS IN LOGIC 77
an important sense secondary to the question whether some
given system of discourse implies that there are abstract
entities. The initial problem is said to be that of detecting
the ' ontologica! commitments J of a language or some depart-
ment of a language ; thereafter the different question can be
raised what language, and hence what commitments, one is
to adopt. It is not suggested that any strictly logical tests
will serve to answer the latter question, which seems to be
regarded as 'pragmatic' ; it is, however, claimed that the
question of ontological commitment falls within the purview
of the logician. As Quine puts it, 'perhaps we can reach no
absolute decision as to which words have designata and
which have none, but at least we can say whether or not a
given pattern of linguistic behaviour construes a word W as
having a designatum' ; I and one is held to be ontologically
committed to the existence of such entities as must be
designated by those expressions of one's language which
one takes to be designating expressions. A nominalistic
language will be such that all expressions in it which are
taken to have designative uses designate only concrete
objects ; a platonistic language will be such that it contains
expressions, construed as having designative uses, the desig-
nata of which must be abstract entities. The first pro-
blem, then, is that of deciding whether a given language or
part of a language is platonistic or nominalistic; and if
satisfaction were obtained on this point, it would be possible
to proceed to the further question, which is the proper sort
of language to use.
(l) 'WHAT IS THERE?'
Are there classes ? Do numbers exist ? Are there such
things as abstract entities ? Quine has on more than one
occasion boiled down such typical ontologists* questions to
the simple and uncompromising formula, 'What is there ?'
It needs no argument to show that this way of posing
1 'Designation and Existence *> Journal of Philosophy > 1939.
G
7 8 ESSAYS IN CONCEPTUAL ANALYSIS
the question, perhaps never meant to be taken seriously, is
unprofitable; It appears to invite a quite indefinite and
possibly endless range and variety of answers. There is a
pen in my hand ; there is a pain in my ankle ; there is a
virtue in necessity ; there is general confidence in the dollar.
These are all correct expressions, and what they state may
well be true. It cannot be supposed, however, that to add
to such truths at random is the proper way to solve the
ontological problem. We are really more interested in the
question what kinds of things there are are there abstract
as well as concrete entities ? and even this question is, as
has been pointed out, strictly secondary to the question what
kinds of things we are committed to believing that there
are. So let us try to approach this latter question more firmly.
(2) DESIGNATION
One method of approach to the problem begins with
the unexceptionable assumption that, if a given expression
designates something, then there is something which it
designates ; or more cautiously, that if an expression has a
designative use, there is something which in that use it
designates. If, for example, 'Tito* has a designative use,
then there is such a person as Tito. It is taken for granted
that there are concrete objects, such presumably as Tito,
which may be designated ; it is a question whether ex-
pressions which, if they had designative uses, would desig-
nate abstract entities, are in fact taken to have designative
uses. If they are so taken, then we must hold that there are
abstract entities ; if not, not or at any rate not unless
they turn up in some other way.
We require, then, tests by which to decide what ex-
pressions are taken to have designative uses, and hence
what we must hold that there is to be designated. Quine
has more than once described two such tests, admitting
that they are not absolutely conclusive. I shall seek to show
that the case is worse than this.
METAPHYSICS IN LOGIC 79
The most important of these tests consists In an operation
called 'existential generalization'. Suppose I say
(i) Leeds is a City
Then, since there is in fact a city of which 'Leeds' is the
name, I am presumably entitled to state that there is some-
thing of which my statement is true. That is, I can safely
assert
(la) Something is a city. Or
(i) There is something which is a city. Or even
(ic) There is an x such that x is a city.
If on the other hand I had said
(2) Valhalla is mythological,
I would certainly wish to convey that there is actually no
such place ; and it is assumed that I must object to the
inference that there is something which is mythological. I
must not allow
(20) There is an x such that x is mythological,
since my point was that there is not a place called ' Valhalla'.
It is then argued that this difference between the logical
behaviour of 'Leeds' and 'Valhalla 1 can be attributed to the
fact that ' Leeds' is, and 'Valhalla* is not, taken to designate,
name, or refer to an actual place. It might seem, then, that
we have in this device a method of deciding in general
whether or not a given expression is regarded as having a
designative use, or (to put the point more insidiously) as
designating something.
Suppose then that we try to apply this test of existential
generalization to disputed cases say to 'appendicitis', or
'17', expressions which, it is held, must designate abstract
entities if they designate anything at all. We might say,
for instance,
(3) Appendicitis is painful. Or
(4) 1 7 is a prime number.
Now is there something of which each of these statements is
true ? Can we infer that something is painful, that some-
thing is a prime number ?
go ESSAYS IN CONCEPTUAL ANALYSIS
But here we encounter a curious difficulty. How can we
possibly decide whether or not to tolerate these inferences ?
The trouble is that
(30) There is something which is painful, and
Something is a prime number,
are wholly odd and mystifying sentences, for which it is
difficult to imagine plausible contexts of utterance. And
for this reason it seems impossible to pronounce generally on
the question of their admissibility.
But let us see what can be done. Suppose someone says,
'He is suifering from appendicitis'. I might, if I were un-
certain about this diagnosis, reply, ' Perhaps he is ; he is
certainly suffering from something 7 ; and it might turn out
in the end to be appendicitis. Or suppose I have worked
out a sum, and found the solution of it to be 17; but I forget
this, and later when I try to re-work the sum I get stuck.
In such a case I might well say, with an air of dogged be-
wilderment, 'Well, something was the right answer* per-
haps in order to insist that the sum does work out somehow,
is not insoluble. There are thus some cases at least in which
one might use 'something' where, if one had more or better
evidence, or exact knowledge, one would instead have said
'appendicitis' or ' 17' ; and so perhaps one would have no
reason to object, though one might be extremely puzzled,
If one were invited to reverse the usual procedure and to
replace 'appendicitis' or '17' by 'something'. One decides,
let us say, to accept existential generalization in these cases.
What does this prove ? It is supposed to prove that one
is thereby recognizing appendicitis and 17 as ' somethings',
entities, and, furthermore, as abstract, Platonic entities. But
surely it does not prove anything like this ; for at this point
one begins to encounter the invaluable non-simplicity of
ordinary speech. The difficulty is that * something' does not
behave in the way required in the logician's argument. For
if I inform a bored or inattentive listener that Valhalla is
mythological, it would be perfectly in order for him, if
METAPHYSICS IN LOGIC 81
questioned about our conversation, to say, 'He was telling
me that something or other was mythological 1 ; and this
use of 'something* would not be taken as evidence that he
thought there really was such a place, nor would his report
be condemned as self-contradictory. And if I say, secret-
ively, that I am imagining something, I do not thereby evince
belief in the actual existence of what I imagine. If one were
to use the queer-sounding sentences, * There is something
which is mythological 1 , or "There is something which I am
imagining', one would certainly perplex one's hearers ; but
the use even of these odd sentences cannot be said to be flatly
ruled out merely because the mythological does not, and the
imagined may not, actually exist. Still less (indeed in no
way) conclusive is the mere use of ' something *, without
1 there is', in sentences of a quite different construction.
It is in fact pretty obvious that one's readiness or reluct-
ance to use 'something' in the cases mentioned has really
no sort of connexion with the question whether or not one
supposes that diseases, numbers, etc., are abstract entities,
possible designata of abstract expressions. The word
'something' has an entirely different function. One is
ordinarily disposed to use the word 'something' in cases
where one does not know what in particular, or where for
some reason one does not wish to specify ; and there is no
sharp restriction upon the sorts of expressions which in such
cases one cannot or does not wish to use, so that one has
recourse to the use of 'something'. Hesitation in admitting
such sentences as (30) and (40) is indeed justified not,
however, because their admission would entail acceptance of
any philosophical doctrine, but because it would be very hard
to see when or why one might wish to say such things, or what
one could possibly be getting at if one did.
The failure of existential generalization to do for us what
is required can be explained, in part, briefly as follows. In
manipulating the symbolism of logic, if I have the expression
' Fa', I am undoubtedly entitled to write down the expression
'(3x)Fx'; and in so far as the rules for the use of this
82 ESSAYS IN CONCEPTUAL ANALYSIS
expression are fixed, there is no uncertainty as to what is
meant. But if I come across the expressions ' 17 is a prime
number' or ' Valhalla is mythological', I cannot be sure
that I am right if I say, * Something- is a prime number',
nor can anyone else be sure that I am wrong if I say, ' Some-
thing is mythological'. For the former sentence is doubt-
fully admissible as English, the latter might be intelligible
and true in suitable contexts. In any case it would be quite
impossible to say, simply on the basis of someone's readiness
to employ these sentences, that he was a Platonist or self-
inconsistent ; for in the ordinary language in which they
purport to be expressed, they simply would not have the
implications thus imputed to them.
But perhaps a yet more important consideration is this.
The test of existential generalization is most simply em-
ployed as a device for revealing how names of actual persons,
cities, etc,, may be made to function differently in some con-
texts from story-tellers' names for mythical or fictitious
persons and cities. But it is further supposed that the very
same device can be applied at once to the job of detecting
the existence or non-existenee of abstract entities. This
assumption appears to embody the supposition that the
question whether there are or are not abstract entities is
just like the question whether there is or is not a city called
4 Leeds ' ; that, if there are no abstract entities, then appendi-
citis, etc., belong in the same list as Pegasus, Apollo, Mr.
Pickwick; that, if '17' does not designate anything, it fails
to do so in the same way as 'Cerberus' fails.
Now here again it is surely in point to draw a contrast
between logic and language. If we have a form of discourse
already reduced to the pattern of quantificational logic, then
doubtless we can draw a simple distinction between ex-
pressions allowed to be ' substituends ' for bound variables,
and expressions debarred from such employment. But there
is no warrant for the belief that expressions in ordinary
language can be dichotomized in a similarly simple manner.
It seems almost too obvious that no one device could force
METAPHYSICS IN LOGIC 83
'Pegasus', '23', ' intelligence ', 'redness 1 , and 'republican-
ism' into a single bag. No doubt none of these designated
a concrete object, but they fail to do so If indeed they can
be said even to fail in ways that are utterly diverse.
' Pegasus J designates no concrete object, and it is true that
there is no such thing as Pegasus ; ' republicanism ' designates
no concrete object, but that there is no such thing as re-
publicanism is, of course, straightforwardly false ; ' 23 ' does
not designate a concrete object, but that there is no such
thing as 23 is so queer a remark that, unless further explained,
it must defy the assignment of any truth-value.
At this point a protest might also be entered against the
alleged dichotomy between concrete objects and abstract
entities. It is manifest that, unless this distinction is clear,
we do not clearly know what Platonism or Nominalism is,
and also that, unless it is exhaustive, we do not know that
these are necessary alternatives. But consider such a list as
the following: (i) 'gravitational field'; (2) 'the North
Pole' ; (3) 'the Heaviside layer' ; (4) 'the Common Law' ;
(5) 'shadows'; (6) 'rainbows'; (7) 'the Third Republic'.
Any of these expressions may occur in true or false state-
ments not in fiction or myth. There is such a thing as the
Common Law ; there are such things as rainbows ; there
was such a thing as the Third Republic, etc. None of these
things could be called a Universal; none has 'instances';
some require the definite article ; yet none would naturally
be called ' concrete ' ; and it is at least uncertain which, if
any, should be labelled 'particular'. What is referred to by
(2) or by (3) has a definite position ; shadows and rainbows
have dimensions ; and the Third Republic had a definite
duration. But shadows and rainbows, though visible, cannot
be touched, heard, or smelt; the Common Law cannot be
seen, and also has no position, shape, or size ; the Heaviside
layer can move, but cannot be seen or heard or felt to be
moving. And so on. Again, it may very well be that in the
symbolism of logic some clear distinction can be made
corresponding to that alleged between the abstract and the
84 ESSAYS IN CONCEPTUAL ANALYSIS
concrete ; but that this is so, if it is so, settles nothing when
we return to ordinary words. The distinctions here are per-
haps not useless, but they are certainly neither precise nor
exhaustive. It surely follows that outside logic no
definite sense can be attached to the supposed assertions and
denials of the Nominalist, just as no definite results could be
obtained by the device of existential generalization.
The second test by which it has been hoped to identify
expressions having designative uses is the converse of existen-
tial generalization, and is called ' application'. We have
so far attempted to decide whether or not (say) 23 is an
entity, or is thought to be so, by asking whether what is true
of 23 is thereby true, or thought to be so, of an x, a some-
thing. It is now proposed that we take some formula which
we know to be true of all x's, and ask whether it is thereby
true of (say) appendicitis. Suppose we agree that, for all
values of x, x=x ; can we proceed to infer that appendicitis
= appendicitis ?
This is not much help. In addition to the over-simplifica-
tions already noted, there is here the further defect that the
conclusion to be drawn (or rejected) by application seems
merely fantastic. Why should such an expression as ' ap-
pendicitis = appendicitis' ever be written down, uttered,
asserted, or denied ? It says nothing whatever about any-
thing ; it is not a mathematical equation ; it does not look
like any sort of logicians 1 theorem. And if we were for any
reason persuaded to allow this sort of expression, it would
be hard indeed for the speaker of plain English to see why
any version of it should be, or indeed how it could be, denied.
Pegasus = Pegasus' looks odd, but not deniable ; there seems
to be nothing wrong with 'pink=pink', nor yet with 'if=if '.
If this is a test for designative use, then every expression
designates.
Let me say again, at some risk of being tedious, what I
think it is that goes wrong with, the logico-ontologist's argu-
ment. It is supposed that because, in the symbolism of logic,
certain distinctions can be clearly drawn and certain infer-
METAPHYSICS IN LOGIC 85
ences made, the same should be true of discourse in general ;
that since we can be clear what sorts of logicians 8 expressions
may be used, and how they may be used, in contexts of
existential quantification, it should be possible similarly to
discover the 'existential commitments* of ordinary talk.
This is, however, not so. For the expressions supposed
to correspond to the existential quantifier ('There is . . .',
c . . . exists 5 , "Something . . .', 'There is something
which . . .') are too diverse and intricate in their uses to
yield the necessary results; and the supposed distinction
between abstract and concrete entities is too wavering and
non-inclusive. The Nominalist, launched with this inappro-
priate equipment upon the field of ordinary discourse, is
obliged ('There is no such thing as appendicitis') to conduct
his campaign in a manner so exceedingly awkward that
doctors and other philosophical non-combatants must in-
evitably be assailed along with the Platonic army.
(3) FRAGMENTATION OF SENTENCES
I would next like to enter, consistently with my general
thesis, a mild protest against another logicians' practice,
doubtless innocent enough in many contexts, but liable to
cause much perplexity in the present case. Consider the
straightforward statement
(5) There is a prime number between 13 and 19.
This might indeed be called though for reasons given
below only with due caution an existential statement, so
that it should be a fair case for the use of the existential
quantifier. But even here the conventions of logicians are
fraught with some peril. For in their hands such a sentence
is apt to become, by accepted translation of the symbolism,
(50) There is something which is a prime number
and is between 13 and 19.
It is important to notice that into this transformed version
86 ESSAYS IN CONCEPTUAL ANALYSIS
an 'and ' has mysteriously entered, so that the whole sentence
now appears to contain as a proper part the sentence, * There
is something which is a prime number', or 'There is a prime
number'. But how is this surprising appearance generated ?
It is of course an accepted rule of logic that from (gx)(Fx.Gx)
we may without qualms derive (3x)Fx ; there is no doubt
that the latter expression is well formed, or that it is entailed
by the former. From this, however, it does not follow that
the first half of (5) or (5*) is by itself an impeccable and
intelligible sentence in English ; on the contrary, it is clearly
not so. For if someone were to say, ' There is a prime number ' ,
and then stop, one would wait expectantly for the rest of his
observation; one would not suppose that he had already
come to the end of it. One does not assert bare Being. ' Go
on J , one might say, ' what about it ? ? And if he were merely
to repeat, ' There is a prime number', this being the whole of
his contribution, one would be left in bewilderment. What
can he be getting at ? Can he suppose that anyone has ever
said that there is not a prime number ? And even if someone
had ever said this, in what would the disagreement .have
consisted ? If one takes it for granted that the baffling frag-
ment, * There is a prime number' is really a proper part of a
conjunctive sentence and so could stand alone, it may seem
necessary since it has no ordinary use to invent some
curious sense for it, to interpret it as meaning something odd
that there is an object called a prime number, an Entity,
one of the things that are. Here indeed we seem to be tread-
ing Platonic ground ; but it is easy to see that by this path
at least we would never have got there, if the original plain
statement had not been broken in two. In general : Sen-
tences of English cannot usually be taken to pieces in the
way in which their corresponding formulae can be.
(4) EXISTENTIAL QUANTIFICATION
Let us now make a final and more head-on attack upon
the logico-ontologist's apparatus. It is sometimes said, with
METAPHYSICS IN LOGIC 87
a view to clarifying the issue, simply that we must admit
into our accepted ' universe of entities' ail those things which
we allow to be values of the bound variables of quantification.
We may discourse of classes, as Boole does, or of proposi-
tions, as in the prepositional calculus, without thereby com-
mitting ourselves to Platonism ; for we can discourse in these
ways without taking the fateful step of * quantifying over J a
class, or a proposition. If we take this crucial step, however,
we fall into the ontological grip of the existential quantifier.
Let us begin at a point where all seems reasonably clear.
We may, for example, wish to indicate that some algebraic
formula holds for all values, or for at least one value, of the
variable occurring in it ; and here ' values J has the familiar
sense of ' numerical values '. Dealing with integers we might
say, 'For all values of x, 2x is even', or 'For at least one
value of x, x=7~3'. And the first of these expressions
states that whatever integer we choose, if we multiply it by
2 we have an even number ; the second that there is at least
one integer equal to 7 minus 3.
But a statement of this latter kind has been thought to
raise a peculiar difficulty. It might be described as an
existential statement, and if so, do we not by making it
commit ourselves to the important view that a certain
number (in this case 4) exists ; and so, since a number is
presumably an abstract entity, to the acceptance of Plato-
nism ? Are we not thus trapped by the existential quantifier ?
To this there appear at once to be the following objections.
First, the existential statement in question, whether true or
false, can be shown to be true or false by purely mathematical
operations. In fact every schoolboy knows quite well that
it is true, even if he has never so much as heard of Plato,
and there could be no serious argument about it. Further,
even if one were to call for a full demonstration, one would
be offered no contentious philosophical arguments, but
only a bit of mathematics. The whole matter is entirely
remote from the arena both of Platonic and of anti-Platonic
philosophizing.
88 ESSAYS IN CONCEPTUAL ANALYSIS
And in any case, second, the statement does not state
that the number 4 exists, but only that there Is an integer
equal to 7 minus 3 a very different matter. To say that
there is a number of a certain sort is not at all the same as
to mention a number and then assert that it exists. The
question whether there is an integer equal to 7 minus 3 is
closed, once we have said and if necessary shown that 4 is
such a number. Whether the number 4 itself exists is, if
there could be any such question at all, a quite different
question a different sort of question; and certainly we
do not answer it in the affirmative merely by answering
affirmatively the other question.
However, it seems, I suppose, tempting to argue that, if
there is an integer equal to 7 minus 3, and 4 is such a number,
then at least there must be such a number as 4. This I take
to be odd, rather trivial, but presumably true. But even
this does not either require or license us to say that the
number 4 exists \ for the phrases 'There is . . .', 'There is
such a thing as . . .', and '. . . exists' are not, as they are
so often assumed to be, synonymous and interchangeable.
Consider
(6) There are tigers in Africa.
(?) Tigers still exist.
(8) There are such things as tigers.
First, clearly (6) would sound odd and incomplete if we
omitted from it the words 'in Africa'. It would then be, in
fact, a mere fragment of a sentence, just as * There is a prime
number* was a fragment of a sentence. Sentence (7) is per-
fectly natural, in as much as it contains the word 'still', and
thus would be understood as conveying the information that
tigers are not extinct. f Tigers exist ' would be by compari-
son queer ; it is not easy to see why anyone should want to
say such a thing, though perhaps it might be intelligible
enough in some suitable context. I think that (8) would
usually be understood as a denial of the idea that tigers are
fictitious or mythological beasts, employed to distinguish
METAPHYSICS IN LOGIC Bg
tigers from phoenixes and unicorns. It might have other
uses, but this would be typical enough.
Now it is no doubt the case that the seriously made
statement 'There are tigers in Africa* would not be true
unless (a) tigers still existed, were not extinct, and (3) there
were such things as tigers, non-fictitious , non-mythological.
But it is equally clear that to say that there are tigers in
Africa is not to say that tigers still exist, nor is it to say that
there really are such animals. Of course there are con-
nexions, but there are also marked differences, between these
three statements ; the situations, questions, counter-asser-
tions, etc., which would naturally call for their utterance are
quite distinct.
Consider next
(9) There are shadows on the moon.
There is no doubt that this is both intelligible and true. But
in this case there seems to be no plausible counterpart to
sentence (7). What could be meant by saying that shadows
(or, the shadows) exist ? There is no question of shadows
being or not being extinct of their still, or perhaps no
longer, existing. Certainly we should not say that the
shadows on the moon do not exist ; this would be too much
like saying that they are not really there (but are really seas,
or due to defects of eyesight, etc.). But if we say that the
shadows on the moon exist, or in general that shadows
exist, might we not appear to be suggesting that shadows
lie about on things as sheets do that perhaps they could
be taken up and erected for shelter ? After all, a shadow
is in many ways more like the absence of something than the
presence of anything ; in a way, there is nothing there
when we say there's a shadow. And so, if someone were to
ask whether shadows exist, we should not know what he had
in mind, we should feel reluctant to answer either yes or no.
We do not in fact use the word * exist' in talk about shadows.
What then of * There are such things as shadows* ? The
most plausible use that I can think of for this is an ironic
90 ESSAYS IN CONCEPTUAL ANALYSIS
one, calling attention to the obvious addressed, for in-
stance, to a painter who always leaves the shadows out of
his pictures. Similarly, one might say 'There are such
things as tigers* as an ironically phrased reason for not
spending the night in the open. These remarks are clearly
quite unlike the enigmatic 'Shadows exist ', or ' Tigers exist'.
In this connexion numbers, classes, properties, etc. re-
semble shadows rather than tigers. We can say * There is
a number which, multiplied by 3, gives 21'; but we feel
wholly baffled by the question whether this number is,
whether it exists, whether numbers exist. No one surely
supposes that numbers might be extinct, or that they figure
only in legend and fiction ; and every one knows that there
is such a subject as arithmetic, that in this sense there are
such things as numbers. Of course one does not wish to
deny that numbers exist one does not use the word
'exist' at all, in talk about numbers.
The expressions I have been considering are of course
familiar ones, and it is really pretty obvious that they have
different uses. However, employment of the existential
quantifier is liable to blind the logician's eye to just such
points as these. To this one device is given the job of sym-
bolizing such phrases as 'There is . . .', 'There is such a
thing as . . .', '. . . exists', and even 'Some . . .', 'At
least one . . .', and 'There is something which . , .'. Be-
cause all these phrases are ordinarily dealt with by the use
of the existential quantifier, it is easy to assume that they
are interchangeable, all really the same; it may even be
naively supposed that logic has somehow proved that they
are really the same, and that one must be wrong if neverthe-
less one insists that they are different. (Too often the boot
gets on the wrong foot in this way as if a map-maker
should complain that the mountains were inaccurate.) It is
of course possible that/0r some purposes perhaps for most
of the purposes of logicians the phrases in question are
not relevantly different, and so that a single symbolic device
may be more or less workable. If there is, say, a green
METAPHYSICS IN LOGIC 91
book on my table, then it is at any rate true, for what It Is
worth, that there is something of which I could say i It is a
green book J ; that there is at least one book which is green ;
that there is such a thing as a green book ; even, perhaps,
by stretching matters a little, that some books are green and
that a green book exists. But for many other purposes the
differences between these locutions will remain of vital
importance. It will often be highly important to remember
that where, for example, it is intelligible and true to say
'There is such a thing as x', to say that there is x or that x
exists may be unintelligible, and even if not unintelligible
will usually be different. Those who use expressions of the
sorts supposed to correspond to the existential quantifier are
not all saying the same kind of thing, nor can there be any
single philosophical position to which they are committed
by their readiness to use such expressions. The proper
understanding of these expressions- is not assisted, but on
the contrary rendered almost impossible, by the lavish intro-
duction of quantifiers. For thus the harmless will constantly
be transformed into the peculiar ; progress will be held
up by unnecessary questions, needless scruples, and false
dilemmas ; and in the obscurity Plato's ghost will seem
to be lurking.
I have been arguing in this paper that the efforts of the
logician to clarify problems of ontology fail, since the devices
employed all turn on notions of quantificational logic, par-
ticularly on the use of bound variables and the existential
quantifier ; and that this apparatus has little or no clear
application to the ordinary words and idioms in which the
problems are initially expressed. I need finally to defend
this argument against the charge of irrelevance. Professor
Quine has recently written l that t the philosophical devotees of
ordinary language are right in doubting the final adequacy
of any criterion of the ontological presuppositions of ordinary
language', since 'the idiomatic use of " there is" in ordinary
1 From a Logical Point of View, p. 1 06.
92 ESSAYS IN CONCEPTUAL ANALYSIS
language knows no bounds comparable to those that might
reasonably be adhered to in scientific discourse painstakingly
formulated in quantificational terms '. However, he observes
that this is a minor affair, since the enquiry into ontological
commitments is properly concerned, not with ordinary lan-
guage at all, but with 'one or another real or imagined
logical schematization of one or another part or all of
science J . If so, it would of course follow that my argument,
though within its own limits possibly sound, has been sub-
stantially beside the point. Now one way in which I might
seek to ward off this charge would be by maintaining, first,
that most of the last ten years' literature of ontology embodies
no such awareness as Quine now expresses of the limitations
of symbolism in application to ordinary language; and
second, that there is also little evidence in that literature of
any particular concern with science, except for one or two
brief statements that some unspecified science is the subject
ultimately in view. However, to adopt either of these
courses would involve much rather acrimonious citation of
texts, with much risk of distortion, misconstruction, and mis-
understanding ; it would be a mere exercise in post mortem
polemics. In any case I think that it is more to the point
to make a counter-charge of irrelevance. If it is true that
ontology in its modern dress can get firmly to grips only
with scientific discourse really or imaginedly schematized,
then certainly it can have little relevance, if any, to philo-
sophical problems about universals, concepts, etc. abstract
entities in general, the supposed subject-matter of the
enquiry. For these problems arose from, can be posed,
clarified, discussed, and (in their way) settled in, quite
ordinary, unregenerate language ; they can neither be con-
fined to, nor settled in, language of any specially regimented
pattern. If one cannot deal with philosophical problems of
ontology upon the field of discourse in general, one cannot
deal with them at all ; one can only pass them by. This
itself, if admitted, would be a useful conclusion to reach.
At least it would be clear that there are problems which we
METAPHYSICS IN LOGIC 93
cannot look to the logician to settle for us, and that the old
problems of ontology remain among them.
Perhaps after all this is really to say no more than that
they are philosophical and not logical problems. But in
uttering this highly charged platitude, I suspect that one can
only be pretending to have arrived at an absolutely uncon-
troverslal terminus.
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