ENGLISH AND ONTOLOGY
[1]

A.N. Prior

Dr. C. Lejewski refers in his article on 'Logic and Existence'
1

to the difficulty which English
speaking readers have in working intuitively with Leśniewski's singular
-
inclusion operator '
ε
'. The
source of this difficulty seems to be the fact that in English the two kinds of words which are
covered by Dr. Lejewski's p
hrase 'noun
-
expression' are very different in their syntax.


On the one
hand there are proper nouns like 'Socrates', 'Pegasus', etc., and on the other hand there are common
nouns like 'man', 'sun', dragon', etc.


To form a statement of a proper name or nam
es we use a
simple
verb

(transitive or intransitive) or an expression equivalent to this.


Thus we form the
statement 'Socrates smokes' out of the name 'Socrates' by means of the verb '
---

smokes'; we form
the statement 'Plato admires Socrates' out of the
names 'Plato' and 'Socrates' by means of the verb '
--
-

admires
---
'; and as a special case we have the verb '
---

is
---
', meaning '
---

is identical with
---
', as
in 'Tully is Cicero'.


But the operators which form statements out of common nouns are not sim
ple
verbs but expressions like 'Every
---

is a
---
', 'The
---

is a
---
', 'There is at most one
---
'.


And
different again is our operator '
---

is a
---
', which takes a proper name for its first argument and a
common noun for its second (as in 'Socrates is
a man').


What consequently puzzles us about
ontology is that its variables stand indifferently for proper and common nouns, and we have no
operators in our {p.2} language (except perhaps '
---

exists', which gives us so much trouble) which
are thus indiffe
rent as to whether they have proper or common nouns for arguments.


The same
difficulty seems to exist in French, though it is much less felt in Latin.

Most English and French expositions of ontology hitherto have attempted to solve this difficulty by
tran
slating Leśniewski's '
ε
' as either '
---

is
---
' or as '
---

is a
---
', and then where necessary forcing the
English operator to take 'unnatural' arguments.


It seems to me, however, that the odd
-
sounding
cases would be far fewer if we translated '
ε
' by 'The

---

is a
---
'.
2

Dr. Lejewski has very ingeniously
by
-
passed the problem by taking as his primitive operator not '
ε
' but '
⊂
', but in principle his solution
is the same as mine.


For '
⊂
' translates as

'Every
---

is a
---
', which resembles 'The
---

is a
---
' in that
the arguments which it 'naturally' takes (and which Leśniewski's name
-
variables are therefore taken
as
primarily

standing for) are common nouns (whether these in fact apply to one, less than

one, or
more than one object); so that we obtain odd
-
sounding cases only when the blanks are filled by
proper names.

This point is not without its relevance to Dr. Lejewski's main topic, existence and quantification.


In
what he calls the 'restricted' int
erpretation of the particular quantifier, the variables which it is
usually thought of as binding are ones standing for proper names; and proper names are thought of
as being {p. 3} somehow directly attached to actual individual objects, though there is so
me
departure from ordinary usage in this, as the case of 'Pegasus' shows.


But in what Dr. Lejewski
calls the 'unrestricted' interpretation, the variables which he takes the quantifier to bind are thought
of as standing primarily for common nouns; and comm
on nouns may of course just as easily apply
to no real thing as to one thing or more than one.


So his solution of the 'Pegasus' problem has at
least
something

in common with the orthodox solution of replacing the 'name which fails to name'
by an expressio
n containing the corresponding predicate (i.e. verb). He doesn't exactly do that; but
he does treat a proper noun as if it were a common one, and this must wear a very similar air in the
eyes of anyone accustomed to treating common nouns as logical constru
ctions out of predicates and
quantifiers.

This is not, of course, to deny the superiority of the Leśniewskian procedure on the side of formal
elegance.


It has a further importance too, in that it brings out the fact that the theory of
quantification need
not be thought of as exclusively a
predicate

calculus.


It is rather a quite general
operator
-
and
-
argument calculus.


We
can

interpret the operators as predicates and the arguments as
proper names, but we do not need to do this. We could equally interpret
the arguments as statements
and the operators as statement
-
connectives, as in Leśniewski's other discipline of 'protothetic'; or we
could interpret the arguments as common nouns and the operators as statement
-
forming operators or
common nouns, and if with
this interpretation we add to the operator
-
variables an operator
-
constant
('
ε
' or '
⊂
') with its own {p. 4} special axiom, we have 'ontology'.


With other operator
-
constants,
taking only non
-
empty common nouns as arguments, and other special axioms, we obta
in the
'formalised syllogistic' of Łukasiewicz.


From this point of view the most important and
illuminating passage in Dr. Lejewski's paper is that
3

in which he urges us to read '(
∃
x)(Fx)' not as
'T
here exists an
x

such that
Fx
' but rather as 'the non
-
committal "for some
x
,
Fx
."'


What is
important about this proposal is not merely that it removes the suggestion of existence, but that it
removes the suggestion that '
F
'
must

be a predicate and 'x' a proper name, and it is
by

removing the
latter suggestion that it removes the former.


A.N. Prior


Canterbury University College,

Christchurch, New Zealand.

1

This
Journal
, 1954,
5
, 115.

2

I have accordingly adopted this policy in my
Formal Logic

(forthcoming) III, iii.4.


As part of the
same policy, I read 'ex(
a
)' as 'An
a

exists' and 'ob(
a
)' as 'The
a

exists'.

[E
ditors' note: This footnote does not appear in the printed version in Brit.J.Phil.Sci.]

3

Op. cit. p.113.




[1]

This MS is kept

in the Prior Collection at the Bodleian Library, Oxford. It has been edited by
Sara L. Uckelman, Martin Prior
,

and Peter Øhrstrøm. It is an early version of the paper published in
Brit.J.Phil.Sci. vol. 6 no. 21 (May 1955), pp. 64
-
65. The author's original
three footnotes above are
kept apart from this editorial note.