[hist-analytic] Vacuity

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

rbjones.com/rbjpub/pp/doc/t028.pdf


some remarks on

(a) Grice -- 'vacuous names': two quotes by Grandy.
(b) Strawson --  on 'all' -- citing Grice. -- and Carroll citing Jones.

(a)

1.  From
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, 
1973):

"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,

or, if

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
Grice:

available  online  at:

www.archive.org/stream/introductiontolo010626mbp/introductiontolo010626mbp_d
jvu.txt


CHAPTER 6 : SUBJECTS, PREDICATES, AND EXISTENCE -- THE TRADITIONAL  SYSTEM
OF CATEGORICAL
PROPOSITIONS l
:

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

xKy
yAz
.*. xAz

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.

"Everyone agrees
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
commitment.

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
line'

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.

It has
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

and

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.


But
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.

Suppose
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-
ment were

~(Ex)(fx.~gx)

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
either

~(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
formulae.

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-
supposes S'.

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,
pp. 68-69.



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
themselves.

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
statements  as

All the men at work on the  scaffolding have gone home

or

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-
mulae.

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)

was deceptive.

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
outrage.

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 
misled us.

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'

and

'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
principal  exponents.

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.


FOOTNOTE:

"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
not
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 . . ."

were introduced
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
where
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
introduced
form just those logical  presuppositions which I have described.

The form would tend, if it did  not remain OTIOSE, to develop just those
differences
I have emphasized from  the logic of the symbolic form it was introduced
to represent.

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
Geographical Society.
A:  What for?
B: We're honouring Marmaduke Bloggs. He climbed Mt Everest on hands  and
knees.
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.

---- (adapted)


And  cfr. Lewis Carroll, Symbolic Logic -- cited by L. Horn in
http://www.yale.edu/linguist/faculty/doc/horn97_eximport.pdf.

(pp.  160-161).
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.

Cheers,

J. L. Speranza

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