Jlsperanza at aol.com
Jlsperanza at aol.com
Wed Jun 3 14:50:16 EDT 2009
"The hours of thoughtful vacuity I had spent."
A. R. Hope, My Schoolboy
F, 1875, p. 72
Further to R. B. Jones's considerations of the 'existential fallacy' in
some remarks on
(a) Grice -- 'vacuous names': two quotes by Grandy.
(b) Strawson -- on 'all' -- citing Grice. -- and Carroll citing Jones.
Grandy, in "Predication and Singular Terms" (Nous, vol. 11 -- pp. )
commenting on Burge:
"As Burge notes, we often want to make further distinctions as to the
EXISTENTIAL SCOPE of a singular term. His system can be extended to handle
these distinctions, but, as he remarks, 'the matter is tricky' [...] and the
ONLY SYSTEM in which such distinctions have been treated SYSTEMATICALLY
(Grice [Vacuous Names]) shows how complex such a system can be. (endnote: It
should be mentioned that Grice also had some other goals in mind for the
extension of his theory to definite descriptions [...])" (p. 165).
2. From Grandy's review of WORDS AND OBJECTIONS (Phil. Review, vol. 82,
"Paul Grice's contribution, 'Vacuous Names', is an attempt to formulate a
theory within which APPARENTLY CONTRADICTORY intuitions about logical form
and DENOTATION are reconciled. For example, ... he wishes to preserve
EXISTENTIAL GENERALIZATION without restriction [...] ... This is done by making
distinctions of SCOPE ... so that EXISTENTIAL GENERALIZATION always hold
for terms which have MINIMAL SCOPE. ... The system which Grice presents is
... equivalent to a system in which one replaces names by DEFINITE
DESCRIPTIONS and treats the resulting descriptions as always having minimal scope. ...
footnote: The semantics in this paper ['Vacuous Names'] could have been
made MORE PERSPICUOUS: the COMPLICATIONS in the definition of VALIDITY (pp.
137-138) would have been AVOIDED if
the residual sub-domain
was permitted to be empty,
the residual sub-domain
was never introduced."
"There is a trivial mistake in that
the SPECIAL sub-domain
should *not* be permitted to be empty, and a more serious one in that the
inference rule (15) is unsound." (p. 108).
(b) Strawson on 'all': From Introduction to Logical Theory (1952) citing
available online at:
CHAPTER 6 : SUBJECTS, PREDICATES, AND EXISTENCE -- THE TRADITIONAL SYSTEM
All x is y
No x is y
Some x is y
Some x is not y
"The system invites comparison with the predicative calculus. But there
are important differences."
All alcohol is poisonous
All elephants are long-lived
All tigers growl
All the guests sat down
All non-# is y
All x is non-y
All non-# is non-y
Instead of writing : * The inference-pattern
is valid ', I shall simply write down the first-order formula
xAy . yAz D x Az
The laws of the square of opposition, which give
certain logical relations between formulae in which the
terms, their quality, and their order are the same.
The Square of Opposition
The doctrine of the Square of Opposition concerns the logical
relations between any two statements of different forms having
the same subject and predicate. Since the terms, their position,
and quality are identical in the related statements, we can
symbolize the laws of the doctrine simply by using the letters
A, E, I, O. The doctrine is as follows : A is the contradictory
of O, and E of I; A and E are contraries, and I and O subcon-
traries ; A entails I, and E entails O.
Since there are four
figures, there are altogether 256 possible moods of the syllogism.
Of these 256 only twenty-four are recognized as valid;
THE ORTHODOX CRITICISMS OF THE SYSTEM
Criticisms of the traditional system have centred round the
question of whether or not, in using a sentence of one of the four
forms, we are to be regarded as committing ourselves to the
existence of anything answering to the description given by the
first term of the sentence. It is felt that this question cannot
be left unanswered ; for the answer to it makes a difference to
the validity of the laws. It is argued that the usage of the
ordinary words (e.g., * all ') corresponding to some of the con-
stants of the system varies in this respect.
that it would be absurd to claim that the man who says
'All the books in his room are by English authors'
has made a true
statement, if the room referred to has no books in it at all.
Here is a case where the use of * all ' carries the existential
On the other hand, it is said, we sometimes use
'all ' without this commitment. To take a classic example :
the statement made by
'All moving bodies not acted upon by
external forces continue in a state of uniform motion in a straight
may well be true even if there never have been or will be
any moving bodies not acted upon by external forces. The
consistency-problem for the traditional system is then posed
as follows. We must decide, with regard to each of the four
forms, whether it carries the existential commitment or whether
it does not.
But, for any plausible decision, i.e., any decision
which keeps the constants of the system reasonably close in
sense to their use as words of ordinary speech, we find that some
of the laws of the traditional system become invalid.
generally been assumed that, in the case of the particular forms,
i.e., I and O, only one decision was reasonable, viz., that they
did carry the existential commitment; and that whichever
decision was made for one of the universal forms, the same
decision should be made for the other.
So the problem reduced
itself to a dilemma.
Either the A and E forms have existential
import or they do not. If they do, one set of laws has to be
sacrificed as invalid; if they do not, another set has to go.
Therefore no consistent interpretation of the system as a whole,
within the prescribed limits, is possible.
We should normally accept
All the books in his room are by English authors
At least one of the books in his room is not by an English author
as contradictories. The
second sentence seems very close in form to
(Ex)(Fx . ~Gx)
which is the contradictory of
(x)(fx --> gx)
It is quite unplausible to sug-
gest that if someone says
' Some students of English will get
Firsts this year ',
it is a sufficient condition of his having made
a true statement, that no one at all should get a First.
this would be a consequence of accepting the above interpreta-
tion for I. Note that the dropping of the implication of plurality
in * some ' makes only a minor contribution to the unplausibility
of the translation. We should think the above suggestion no
more convincing in the case of someone who said "At least one
student of English will get a First this year".
The third table
of translations, then, does, if anything, less than the other two
to remove our sense of separation from the mother tongue.
someone says ' All John's children are asleep '. Obviously he
will not normally, or properly, say this, unless he believes that
John has children (who are asleep). But suppose he is mistaken.
Suppose John has no children. Then is it true or false that all
John's children are asleep ? Either answer would seem to be
misleading. But we are not compelled to give either answer.
174 SUBJECTS, PREDICATES, EXISTENCE [CH. 6
We can, and normally should, say that, since John has no child-
ren,, the question does not arise. But if the form of the state-
the correct answer to the question, whether it is true, would be
"Yes"; for 4 ~ (3tf)(/#) * is a sufficient condition of the truth
of * ~(3<r)(/# . ~gx) '. And if the form of the statement were
~(3XA ~&) *)(/)
or ~ (3x)(fx . ~gx) . (3x)(fx) . (3x)(~gx)
the correct answer to the question would be that the statement
was false; for * ~(3ff )(/#)' * s inconsistent with both these
But one does -not happily give either answer simply
on the ground that the subject-class is EMPTY.
One says rather
that the question of the truth or falsity of the statement simply
does not arise ; that one of the conditions for answering the
question one way or the other is not fulfilled.
The adoption of any of the explicitly existential analyses,
whether it be a negatively existential one or a con-
junction of negatively and positively existential components, forces us to
conclude that the non-existence of
any children of John's is sufficient to determine the truth or
falsity of the general statement; makes it true for the first
analysis, false for the other two. The more realistic view seems
to be that the existence of children of John's is a necessary pre-
condition not merely of the truth of what is said, but of its being
either true or false. And this suggests the possibility of inter-
preting all the four Aristotelian forms on these lines : that is,
as forms such that the question of whether statements exempli-
fying them are true or false is one that does not arise unless the
subject-class has members.
It is important to understand why people have hesitated to
adopt such a view of at least some general statements. It is
probably the operation of the trichotomy ' either true or false or
meaningless ', as applied to statements, which is to blame. For
this trichotomy contains a confusion : the confusion between
sentence and statement. 1 Of course, the sentence * All John's
children are asleep ' is not meaningless. It is perfectly signi-
ficant. But it is senseless to ask, of the sentence, whether it is
true or false. One must distinguish between what can be said
about the sentence, and what can be said about the statements
made, on different occasions, by the use of the sentence. It
is about statements only that the question of truth or falsity can
arise ; and about these it can sometimes fail to arise. But to
say that the man who uses the sentence in our imagined case
fails to say anything either true or false, is not to say that the
sentence he pronounces is meaningless. Nor is It to deny that
he makes a mistake. Of course, it is incorrect (or deceitful) for
him to use this sentence unless (a) he thinks he is referring to
some children whom he thinks to be asleep ; (b) he thinks that
John has children ; (c) he thinks that the children he is referring
to are John's. We might say that in using the sentence he com-
mits himself to the existence of children of John's. It would
prima facie be a kind of logical absurdity to say * All John's
children are asleep ; but John has no children '. And we may
be tempted to think of this kind of logical absurdity as a straight-
forward self-contradiction ; and hence be led once more towards
an analysis like that of Table 2 ; and hence to the conclusion that
the man who says * All John's children are asleep ', when John
has no children, makes a false statement. But there is no need
to be led, by noticing this kind of logical absurdity, towards this
conclusion. For if a statement S presupposes a statement S' in
the sense that the truth of S' is a precondition of the truth-or-
falsity of S, then of course there will be a kind of logical absurdity
in conjoining S with the denial of S'. This is precisely the rela-
tion, in our imagined case, between the statement that all
John's children are asleep (S) and the statement that John has
children, that there exist children of John's (S'). But we must
distinguish this kind of logical absurdity from straightforward
self-contradiction. It is self-contradictory to conjoin S with the
denial of S' if S' is a necessary condition of the truth, simply, of
S. It is a different kind of logical absurdity to conjoin S with
the denial of S' if S' is a necessary condition of the truth or falsity
of S. The relation between S and S' in the first case is that S
entails S'. We need a different name for the relation between
S and S' in the second case ; let us say, as above, that S pre-
Similar considerations hold for I; though mention of I re-
minds us of one not unimportant reservation we must make,
before simply concluding that the constants ' all *, ' some ',
* no ' of the traditional system can be understood, without
danger to any of the rules, as having just the sense which these
words have in the hosts of ordinary statements of the kind we
are discussing. And this is a point already made : viz., that
' some ', in its most common employment as a separate word,
1 Compare the discussion of the truth-functional system, Chapter 3,
178 SUBJECTS, PREDICATES, EXISTENCE [CH. 6
carries an implication of plurality which is inconsistent with the
requirement that should be the strict contradictory of A, and
I of E. So * some ', occurring as a constant of the system, is
to be interpreted as ' At least one . . .' or ' At least one of
the . . .', while * all ' and * no ', so occurring, can be read as
The interpretation which I propose for the traditional forms has, then,
the following merits : (a) it enables the whole body of the laws of the
system to be accepted without inconsistency ; (b) with the reservation noted
above, it gives the constants of the system just the sense which they have in
a vast group of
statements of ordinary speech ; (c) it emphasizes an important general
feature of statements of that group, viz., that while the existence of
members of their subject-classes is not a part of what is asserted in such
statement, it is, in the sense we have examined, presupposed by them. It is this
last feature which
makes it unplausible to regard assertions of existence as either the
whole, or conjunctive or disjunctive parts, of the sense of such ordinary
All the men at work on the scaffolding have gone home
Some of the men are still at work
This was the reason why we were unhappy about regarding
such expressions as ' (x)(fx --> gx) ' as giving the form of these
sentences ; and why our uneasiness was not to be removed by
the simple addition of positively or negatively existential for-
Even the resemblance between
There is not a single book in his room which is not by an English author
and the negatively existential form
' ~ (Ex)(fx . ~ gx)
The former, as normally used, carries the presupposition 'books-
in-his-room ' and is far from being entailed by 'not-a-book-in-
his-room ' ; whereas the latter is entailed by ~(3x)(fx).
So it is that if someone, WITH A SOLEMN FACE, says,
"There is not a single foreign book in his room
and then later reveals that there are no books in the room at all, we
have the sense, not of having
been lied to, but of having been made the victim of a sort of linguistic
Of course he did not say there were any books in the room, so he has not
said anything false.
Yet what he said gave us the right to assume that there were, so he has
For what he said to be true (or false) it is necessary (though not
sufficient) that there should be books in the room.
Of this subtle sort is the relation between,
'There is not a book in his room which is not by an English author'
'There are books in his room \ l
What weakens our resistance to the negatively existential analysis in this
case more than in the case
of the corresponding * All '-sentence is the powerful attraction
of the negative opening phrase * There is not . . .'.
To avoid misunderstanding I must add one point about this
proposed interpretation of the forms of the traditional system.
I do not claim that it faithfully represents the intentions of its
They were, perhaps, more interested in formulating rules governing the
logical relations of more imposing general statements than the everyday ones I
have mostly considered ; were interested, for example, in the logical
powers of scientific generalizations, or of other sentences which approximate
more closely to the desired conditions that if their utterance by anyone, at
any time, at any place, results in a true statement, then so does their
utterance by anyone else, at any other time, at any other place. We have yet
to consider how far the account here given of certain general sentences of
common speech is adequate for all generalizations.
"Some will say these points are irrelevant to logic (are ' merely prag-
matic *). If to call them *irrelevant to logic* is to say that they are
considered in formal systems, then this is a point I should wish not to
dispute, but to emphasize.
But to logic as concerned with the relations
between general classes of statements occurring in ordinary use, with the
general conditions under which such statements are correctly called * true
or ' false'' these points are not irrelevant.
Certainly a 'pragmatic ' con-
sideration, a general rule of linguistic conduct, may perhaps be seen to
underlie these points: the rule, namely, that one does not make the
(logically) lesser, when one could truthfully (and with equal or greater
linguistic economy) make the greater, claim.
Assume for a moment that the form
"There is not a single . . . which is not . . ."
into ordinary speech with the same sense as
~(Ex)(fx . ~gx).
Then the operation of this general rule would inhibit the use of this form
one could truly say simply
There is not a single . . . (or ~(Ex)(fx & ~Gx).
And the operation of this inhibition would tend to confer on the
form just those logical presuppositions which I have described.
The form would tend, if it did not remain OTIOSE, to develop just those
I have emphasized from the logic of the symbolic form it was introduced
The operation of this * pragmatic rule ' was first pointed
out to me, in a different connexion, by Mr. H. P. Grice."
* One way to unify some accounts here is to recall Grice's amusing
conversations on Marmaduke Bloggs in "Vacuous Names"
A: Where are you going?
B: Didn't you know. There's a special meeing of the Merseyside
A: What for?
B: We're honouring Marmaduke Bloggs. He climbed Mt Everest on hands and
A: But didn't you read? It was a lie. He was invented by the journalists.
B (shocked). Then someone is not going to be at the party.
A: Did you hear me distinctly? I said he doesn't exist.
B: And did _you_ hear me distinctly? That's what I implied, too.
And cfr. Lewis Carroll, Symbolic Logic -- cited by L. Horn in
CARROLL. Well, Jones, have you got your new club started yet?
JONES (rubbing his hands): Well, you'll be glad to hear that some of the
members (mind, I only say 'some') are millionaires! Rolling in gold, my boy!
CARROLL. That sounds well. And how many members have entered?
JONES (staring). None at all. We haven't got it started yet. What makes
you think we have?
CARROLL. Why, I thought you said that some of the members.
JONES (contemptuously). You don't seem to be aware that we're working on
strictly _logical_ principles. A particular proposition does not assert the
existence of its subject.
J. L. Speranza
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