The Nachlass of A.N. Prior
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Department of Information Studies - University of Copenhagen
and
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Logical and Grammatical Predicates

By Arthur N. Prior on NA/NA/1964

This text has been transcribed and edited by David Jakobsen, Martin Prior, and Peter Øhrstrøm

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Logical and Grammatical Predicates
1

A.N. Prior

The following

Some thinkable has all the other perfections and is real

∴

Something that has all the other perfections is real

∃
x (Tx & Ox & Rx)

∴∃
x (Ox & Rx).

Something is a real dragon

∴
Some dragon is real.

When D. pu
t up the argument, one opponent Gaunilo said existence isn’t a perfection or even a property, but
is
presupposed
in having perfections or properties. Kant said existence isn’t a predicate. And many later
writers, such as Russell, have said that e
xistence isn’t a predicate. What does this mean?

Let’s see at first what it
seems

to mean, because what it seems to mean is either trivially
true or false. Most
of us learn
t to use the word
“
predicate
”

in grammar lessons, and in grammar it means part of a sentence.
Now where a predicate is a part of a sentence

(1)

Existence isn’t a predicate

w
ithout any quotes is ob
viously true
–

existence
–

your

existence, m
y existence, any existence
–

is
n’t part of
a sen
tence. And even with quotes

(2)

“Existence” isn’t a predicate

i
s trivially true to
o

–

a predicate has to be a verb or a verb phrase, and “existence” isn’t a noun. But let’s look
at another case.

{
p.
2}


We might say that

(3)

“Smokes” is th
e predicate of the senten
ce “Socrates

is smoking”.

And we might express so
mething v
ery like this by saying

(4)

The sentence “Socrates

s
mokes” predicates smoking of Socrates
.

Similarly we might say

(5)

“Exi
sts” is the predicate of “The Queen

of England exists.”




1

This MS is kept in the Prior collection at the Bodleian Library, Oxford. It has been edited by
David Jakobsen,
Martin
Prior and Peter Øhrstrøm.
It is handwritten and untitled. The above title is the suggestion of the editors.
It has not dated,

but it must
have been writte
n after October 1964, since Haro
ld Wilson is mentioned as Prime Minister, cf. note 5.

And

(6)

In “The Queen

of England

exists”, e
xistence is predicated of the Queen of England
.

a
nd more generally

(7)

“Exists”
(
sometimes
)

can be the predicate of a sentence

a
nd

(8)

Some sentences predicate existence of objects.

And maybe (1) just denies (7) or (8). But in that case isn’t it false? Surely “exists”
can

be the predicate of a
sentence, and some sentences do predicate existence of objects.

Well, maybe that’s true about English, but perhaps it
’
s not true in a more tidi
ed up language, and when
people say that existence isn’t a predicate what they mean is perhaps that “exists” won’t be one of the
predicates of a tidied up language.

Until

late in the 19
th

century, the tidied up lang
uage that logicians used was one

derived
from Aristotle, in
whi
ch people studied sentences {p. 3}

constructed from common nouns,
of these 4 principal
f
orms


Every

X is a Y


Some X is a Y


No X is a Y


Some X is not a Y

The X’s and Y’s were common nouns, and were called terms, and the 1
st

one was called the subject or
subject term and the 2
nd

one the predicate or predicate term.

In modern logic we don’t have symbols for common nouns but only for indi
vidual names

and verbs. A
predicate is anything that forms a sentence from an individual n
ame or names
–

the F in Fx, or Fxy or Fxyz.
And “Existence isn’t a predicate”, said by a modern person, means that in predicate logic we don’t need a
predicate “exists”, but always express what we ordinarily means by using this predicate in other ways.


Li
ons exist =
∃
xLx


Unicorns don’t exist =
-
∃
xUx.

The
real

predicate of “Lions exist”, we might say, is the predicate hidden in the apparent subject “Lions”, i.e.
the predicate “is a lion”, and when we
set
it out in symbols that’s the only predicate we need
a predicate
letter for: the “exists” part of it has gone into the quantifier.

{p.4}

Similarly if we say “
A

lion exists”. That is again just
∃
xLx; “Something
is a lion
”.

”A lion” was called by
Russell an
indefinite description
; and i.d.

is just a common noun preceded by the indefinite article; and what
modern logicians say is that even where this is used as the grammatical subject of an English sentence, it’s
really just part of the predicate “is a lion”
–

you can rephrase the sentence s
o that this predicate is seen to
occur.

Sometimes, however, we use “exists” with a
definite

description
, i.e. a common noun preceded by

the
definite article


The Queen of England

exists
.


The King

of
France

doesn’t exist.

Here again the real predicate is t
he one buried in the apparent subject, and the “exists” part goes into the
quantifier, only now it’s a more complicated quantifier.


The Queen of England e
x
ists = Exactly one thing is a Queen

of E
ngland
.



∃
xQx
2


i
.
e.

∃
x(Qx &
-
∃
y(Qy & y
≠

x)
)

The King of

France

doesn’t exist



∃
xKx


=

-
∃
x(Kx &
-
∃
y(Ky & y
≠

x))
.

{p.5}

So neither in


Lions exist

n
or in


The Queen of England

exists

i
s

existence a predicate, i.e. something that forms a sentence from a name. Rather, it forms a sentence from a
predicate. It amounts to


e
ither

∃
x(


)x


o
r

∃
x(

)x,

w
here the gap is filled by a predicate, not to anything like



∃
(


),

w
h
ere the gap is fil
led by a name
.

But don’t we sometimes want to say things like

“Mr
. Wilson exists but Mr. Pickwick

doesn’t”?

Russell says
that we must distinguish between a
grammatical proper name

and a
logical proper name
. Read his chapter on
“
Knowledge by Acquaintance
and Knowledge by Description
”
3

in
Problems of Philosophy
.





2

Editors’: Prior is using a special symbol


to indicate unique existence.

A logical
proper name has no function exce
pt to pick out an object
–

the object we want to talk about. A
g.p.n.
4

seldom does
just that; if the object isn’t

right there in front

of us, it really wo
rks by an element of
description, probably a rather long description and possi
bly a different description

with different people.
“Mr. Wil
son exists” means there is such a person as
the person who is either Mr. Wil
son and is now Prime
Minister of England
5

and so on “Mr. Pickwick

doe
sn’t exist”

means

&c
.

Quine

suggests that we invent verbs corresponding to
each

proper name and summing up these

description
s
,
whatever they are
, so that “Mr. Wilson exist
s
” means “Somebody Wil
sonises”,
∃
xWx,

and
“Mr Pickwick
do
e
s
n’t exist” {p. 6}

mean
s “Nobody Pickwickises”. For a l.p.n
.
6

you have to go to something more like a
demonstrative. “
This

is real” would re
ally be of the form Fx; “Mr. Wil
son is real” isn’t really of that form
but is more like


∃
xWx &
∀
x(Wx
→

Fx).

So for

“exist
s
” really to be used as a predicate we’ll have to have some example like “This exist
s
”.

Russell
say
s

this is just meaningless.
I’m not sure why he says this.
Moo
re says that if it’s meaningful

it’s true, and
similarly if “This doesn’t exist” is mean
ingful it’s false. And you could get a predicate that means “exist
s
”
even in Russell’s system if you l
et it be “
—

is identical

with something”
:


E
a =

y
(a=y).

But now notice this is a theorem


⊦

∃
y(a = y).

Simple to prove it

(1)

a = a


= I

(2)

∃
y(a = y)

1. EI
7
.

Another 2 assertions about
‘
exist
’
.


1

Socrates

is ill
→

Socrates

exist
s


Fs
→

Es



Socrates

doesn’t exist
→

Socrates

is not ill

-
Es
→

-
Fs


2

x is im
aginable
-
|
-
� x exists







3

Editor
s
’

note: Prior writes “Aq and Descr.”. Russell, B.: The Problems of Ph
ilosophy, London 1912, cf.
http://www.ditext.com/russell/russell.html

4

Editor
s
’

note: ’g.p.n.’ is an abbreviation of ‘grammatical proper name’.

5

J. Haro
ld
Wilson was Prime Minister of the United Kingdom from October 1964 until June 1970 (i.e. 8 months
after
the death of A.N. Prior).

6

Editor
s’

note: ’l.p.n
.
’ is an abbreviation of ‘logical proper name’.

7

Editor
s’

note: ’EI’ is an abbreviation of ‘existential introduction’.


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18-12-2018 13:52:29 (GMT+1)