P. F. Strawson on H. P. Grice

Strawson searches for an interpretation for The Square of Opposition -- the A, E, I, and O forms -- for which all the laws of the traditional Aristotelian system hold good together. 

A E
I O

Affirmo, nego.

Strawson argues that there are, at least, two distinct, though related, methods by which this can be done. 

One method illuminates some general features of conversation. 

A second method has only a limited and formalistic interest.

But though the two methods are very different in certain respects, the ways in which the two methods operate to save the consistency of the system are closely related. 

Strawson presents the formalistic method first, partly for the sake of completeness and partly for the light it casts on the other realistic method. 

One method consists simply in a tweak on the kind of interpretation in class or quantificational terms. 

It is a kind of "ad hoc" patching up of the Aristotle's old system in order to represent it, in its entirety, as a fragment of the new -- which we may call neo-traditionalism.

The method is to encounter every breakdown in a traditional law by amending the class or predicative interpretation suggested in such a way as to secure its validity. 

E. g. one attempt at providing a translation in terms of positively and negatively existential formulae leaves one with at least *three* laws of the Square of Opposition invalid. 

So Strawson introduces an ad hoc prevention of these breakdowns. 

Thus Strawson makes A and O contradictories. 

Now:

A 

is 

(A) ~(Ex)(Ax and ~Bx) and (Ex)(Ay) 

whereas 

O 

is 

(O) ~(Ex)(Ax and ~Bx) 


The contradictory of an expression of the form 

 ~p . q 

is the corresponding expression of the form 

p v ~q.


Strawson accordingly decides to make "O" of this form by re-interpreting it as 

(Os) (3x)(fx . ~gx) v ~(3x)(fx) 

Strawson has turned A and O are contradictories. 

Similarly, Strawson re-interprets "I" as 

(Is) 


so that it is the contradictory of "E," which is 

(Es) 


Strawson thinks he has, by his neo-traditionalist manoeuvre, saved the law that I and O are subcontraries (i.e., that corresponding statements of these forms cannot both be false). 

This law for Strawson breaks down for the un-strawsonised interpretations because corresponding statements of these forms could both be false, in the case where the corresponding statement of the form 

* ~(3x)(fx) ' 

is true. 


But on Strawson's neo-traditionalist interpretation, the truth of this statement is a sufficient condition of the truth of both I and statements, since 

' q Dp v q 

is analytic. 

Nor do we sacrifice any of the OTHER laws of the Square of Opposition in saving these three 'laws.' 

A and E have not been altered, so they remain contraries. 

The laws * A D I ' and 'EDO' remain valid. 

For the old form ofI entails the strawsonised form of I, and A entails the old form of I.

Hence A entails the new form of I. 

Similarly, E entails the strawsonised O.

Further amendments, however, are required. 

Although Strawson thinks he has saved all the laws of the Square of Opposition, he has not altered E.

So the simple conversion of E remains invalid. 

Moreover, Strawson's amendments so far made render invalid the simple conversion of I. 

If we transpose the terms (i.e., the predicative variables) in the formula 

(3x)(fa .gx) v ~(~ix)(fx)

we obtain 

(3aO(gff./aO v ~(3aOfeaO 

And these formulae are by no means equivalent. 

For 

 ~(3a?)(/k) , (3x)(gx) 

entails the first and is inconsistent with the second. 

The reason for the breakdown of the conversion of E was that 4 ~(3)(#&) ' [or ' p = '] is consistent with ~(3a)(/* #*) (3*)(/ar) [or P = O . a * 0] but not with its simple converse ~(3x)(gx .fa) . (3x)(gx) [or p* = O . (B * O]. 

The term-symmetry of E can obviously be restored, Strawson thinks, and the breakdown prevented, by adopting the interpretation ~(3)(/ **) (3*0(/aO . (3*)fea?) [or ap = . a 4= O . p 4= O] 

Similarly, the term-symmetry of I can be restored by re-interpreting it as (3x)(fx.gx) v ~(3aO(/fc) v ~0a0tor) which also maintains its status as the contradictory of E. 

Adopting these readings for E and I will obviously force us to make further alterations in the other forms in order to preserve their logical relations. 

Since, by the rule of obversion, 

' xAy ' 

is equivalent to 

' x&y' 

we can obtain the appropriate interpretation for A simply by negating the second term ( c g ' or 4 P ') throughout the latest form of E; which gives us or ap == . a 4= O . p 4= O] 

Finally, O, as the contradictory of A, must be re-interpreted as PT.

So we have, as our final interpretation : 

A ~(3*)(/ ~&) (3)(/*) - (3a?)(~#r) 

E ~(3*)(/* **) - (3)(/ff)'. (3*)te) 

I (3a?)(/aj .#*) v ~(3a>)(/0) v ~(3)fe) 

O (3o?)(/ . ~#r) v ~(3*)(/*0 v ~(3*)(~*}. 

For this interpretation, all the laws of the traditional Aristotelian logic hold good together ; and they hold good within the logic of classes or quantified formulae ; as a part of that logic. 

So the consistency of the system can be secured in this way. 

But the price paid for consistency will seem a high one, if we are at all anxious that three constants or formal devices, a truth-functor and two quantifiers of the system -- "~" "(Ax)" and "(Ex)" should faithfully reflect the typical modernist logical behaviour of "not" (and "no," as in "no king"), "all," and "some (at least one)."

It is quite unplausible to suggest that if an utterer utters 

i. Some students of English will get Firsts this year.

the proposition expressed by 

ii. No one at all should get a First. 

is a sufficient condition for the utterer's having made a true statement. 

But this, Strawson thinks, is a consequence of accepting the palaeo-traditionalist interpretation for I. 

The dropping of the implicatum of plurality (cf. Warnock, 'Metaphysics in logic') in "some" and have it, as Grice suggests as "some (at least one)" makes only a minor contribution to the unplausibility of assuming "I" to be the logical form of "Some students of English will get Firsts this year."


We should think the above suggestion no more convincing in the case of an utterer who utters

ii. At least one student of English will get a First this year.

Strawson's neo-traditionalist proposal, then, does, if anything, less than the modernist proposal to remove our feeling of separation from the vernacular.

So let us start again.

Suppose an utterer utters 

iii. All Smith's children are asleep.

or

iv. Every child sleeps.

Obviously an utterer will not normally, or properly, utter (iii), unless he believes that Smith has children, who are asleep.

But suppose the utterer is mistaken. 

Suppose Smith has no children.

If Smith has no children, is (iii) true or false?

"It is true" or "It is false" would seem to Strawson to be misleading. 

But Strawson suggests that he be not compelled to give either answer, in spite of what Aristotle says about the Tertium Exclusum.

Suppose the utterer utters:

v. The proposition is neither true nor false -- since, since John has no children,, the question whether the proposition is either true or false, does not arise, or rather it's a meaningless question.

If the logical form of the statement is the modernist one. 

~(*x)(fx.~gx) [Table 1]

the correct answer to the question, whether it is true, would be "Yes," for " ~ (3tf)(/#)" is a sufficient condition of the truth of * ~(3.

And, if the form of the statement is 

~(3XA ~&) *)(/) t

or

 ~ (3x)(fx . ~gx) . (3x)(fx) . (3x)(~gx) 

the correct answer to the question would be "False," for * ~(3ff)(/#)' is inconsistent with both these formulae. 

But Strawson feels one does not happily give either answer simply on the ground that the subject class is empty or vacuous.

Strawson feels one might say, rather, that the question is a meaningless question, even if Aristotelian, or that the alleged 'question' regarding the truth or falsity of the statement simply does not arise.

Here comes J. L. Austin, doing erotetics.

One of the conditions (or presuppositions, to echo Collingwood), Strawson thinks, 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 conjunction of negatively and positively existential components forces us to conclude that the lack of existence of any children of Smith's is sufficient to determine the truth or falsity of the general statement.

A modernist proposal makes it true for the first sub-analysis, false for the two sub-sub-analyses.

A more realistic view seems to Strawson to be that the existence of children of Smith's is a necessary pre-condition (or presupposition, to use Collingwood -- cfr. Kneale on 'suppositio' in his Oxford seminar on "The Growth of Logic" -- not merely of the communicatum or explicatum being true, but of its being true or false. 

And this suggests to Strawson the possibility of interpreting all the four Aristotelian forms -- A, E, I, O -- on these lines; i. e. as forms such that the Collingwoodian question of whether statements exemplifying them are true or false is one that is meaningless or does not arise unless both who makes the question and who is prepared to give an answer believe that the subject class has members, and is not vacuous.

It is important to understand why philosophers, Occam included, have hesitated to adopt such a view of at least some specimens of a 'general' (or 'universal') statement. 

Strawson thinks that it is probably the operation of the false trichotomy 'either true or false or meaningless ', as applied to statements, which is to blame. 

For this false trichotomy -- 'p' is either true or false or meaningless -- contains a confusion, viz. the confusion between and statement -- the communicatum or the explicatum -- and a sentence -- the 'utteratum,' as Austin jocularly calls it -- the 'expressum,' or Grice the 'explicitum.'

Of course, the sentence qua expression 

All John's children are asleep.

is not 'meaningless.' 

It is perfectly significant, or 'meaningful'

'All Smith's children are asleep' 'means' that all Smith's children are asleep.

iff

By uttering 'All Smith's children are asleep,' U means that all Smith's children are asleep.

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 that he is referring to Smith's children. 

c) he thinks that he is truthfully predicating 'being asleep' to them. 

In Strawson's parlance, borrowed from but never returned to Quine, by using the utterance, the utterer 'commits' himself to the existence of children of John's. 

A theory is committed to those and only those entities to which the bound variables of the theory must be capable of referring in order that the affirmations made in the theory be true. 

(Quine 1948: 33)

It would prima facie be a kind of absurdity to say 

All John's children are asleep ; but John has no children '. 

cf.

'The king of France is not bald, since France is a republic.'

Grice agrees that uttering

'The king of France is bald'

if France is a republic is uttering something false.

'The king of France is bald and France is a republic'

is not a valid cancellation because the existence is ENTAILED, not IMPLICATED, in the affirmative case.

And we may be tempted to think of this kind of absurdity as a straightforward self-contradiction ; and hence be led once more towards a neo-traditionalist analysis; and hence to the conclusion that the man who says, in the affirmative, All John's children are asleep ', when John has no children, makes a false statement. 

The modernist will say he makes a TRUE statement, because 'all' (Ax) involves 'if'

"Every S is P"

"(x) If Sx, Px."

where the 'if' is taken as the horse-shoe.

But Strawson claims that there is no need to be led, by noticing this kind of absurdity, towards this conclusion. 

For, Strawson claims that, if, with Collingwood, we say that a statement S 'pre-supposes' ('supponit,' alla Kneale, 'implicates,' alla Grice) a statement S' in that the truth of S' is a precondition of the truth-orfalsity of S, of course there will be a kind of absurdity in conjoining S with the denial of S'. 

This is precisely the relation, in our imagined case, between the statement

All Smith's children are asleep (S) 

and the statement that 

Smith has children, that there exist children of John's (S'). 

But we must distinguish this kind of 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 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 expression for the relation between S and S' in the second case.

Let us say, as above, with Collingwood, -- cf. Kneale on 'supponit' -- that 

S pre-supposes S'.

cf. Grice

S implicates S'.

Underlying the failure to distinguish sentence and statement, and the bogus trichotomy of 'true, false, or meaningless,' we may detect a further logical prejudice which helps to blind us, Starwson thinks, to the facts of 'ordinary' language. 

We may describe this as the belief or, perhaps better, as the wish, that if the uttering of a sentence by one person, at one time, at one place, results in a true statement, the uttering of that sentence by any other person, at any other time, at any other place, results in a true statement. 

It is, of course, incredible that any formal logician should soberly believe this. 

(cf. Russell's egocentricity). 

It is, however, very natural that they should wish it were so; and hence talk as if it were so. 

And to those tempted to talk as if it were so, the distinction Strawson insists upon between sentence and statement will not occur or will seem unimportant. 

Why this wish-belief should be natural, in principle, only to an "'ideal'-language" philosopher -- unless you are such an "'extra-ordinary' language" philosopher as Grice is! 




What Strawson is proposing, then, is this. 

There are many ordinary sentences beginning with such phrases as 


UNIVERSAL:

"all"

 "all the"

"no"

"none of the"

EXISTENTIAL:

"some (at least one)"

"some (at least one) of the"

which exhibit, in their standard employment, parallel characteristics to those Strawson describes in the case of a representative ' All . . .' sentence. 

i. e., the existence of members of the subject-class is to be regarded as presupposed (in the special usage Strawson describes) by statements made by the use of these sentences; to be regarded as a necessary condition, not of the truth simply, but of the truth or falsity, of such statements. 

Strawson is proposing that the four Aristotelian forms should be interpreted as forms of statement of this kind. 

Will the adoption of this proposal protect the system from the charge of being inconsistent when interpreted? 

Obviously it will. 

For every case of invalidity, of breakdown in the laws, arises from the non-existence of members of some subject-class being compatible with the truth, or with the falsity, of some statement of one of the four forms. 

So Strawson's neo-traditionalist proposal, which makes the non-existence of members of the subject-class incompatible with either the truth or the falsity of any statement of these forms, will cure all these troubles at one stroke. 

We are to imagine that every logical rule of the system, when expressed in terms of truth and falsity, is preceded by the phrase c 

Assuming that the statements concerned are either true or false, then . . .' 

Thus the rule that A is the contradictory of O states that, if corresponding statements of the A and forms both have truth-values, tthey must have opposite truth-values.

The rule that A entails I states that, if corresponding statements of these forms have truth-values, if the statement of the A form is true, the statement of the I form must be true ; and so on. 

The suggestion that entailment-rules should be understood in this way is not peculiar to the present case 

(Compare the discussion of the truth-functional system, Chapter 3, pp. 68-69.) 

What is peculiar to the present case is the requirement that, in order for any statement of one of the four forms to have a truth-value, to be true or false, it is necessary that the subject class should have members. 

That the adoption of this suggestion will save the rules of the traditional Aristotelian system from breakdown is obvious enough for all the rules except, perhaps, those permitting, or involving the validity of, the simple conversion of E and of I. 

That the subject class referred to in a statement of either of these forms must be non-empty in order for the statement to be true or false does not guarantee, in the case of the truth of an E statement or the falsity of an I statement, the non-emptiness of the predicateclass. 

This is the reason why the interpretations requires three components for each form instead of two. 

But, whilst this is true, it does not constitute an objection, nor lead to the breakdown of the rules as we are now to understand them. 

Thus perhaps a statement of the logical form 

* xEy ' 

might be true while the corresponding statement of the logical form 

* 7/Eo? '

 was neither true nor false. 

But all that we require is that so long as corresponding statements of the logical forms 

' xl&y ' 

and 

fc yE*x r 

are both either true or false, they must either be both true or both false. 

This is secured to us by interpreting 

* x&y '

 as the logical form of hosts of ordinary statements, beginning with 

* No . . .' or ' None of the . . .', 

of the kind described in this section. 

Similar considerations hold for I.

Mention of "I" reminds us of one not unimportant reservation we must make, before simply concluding that the constants "not" (or "no") and the quantifiers, "all" and "some (at least one") of the traditional system can be understood, without danger to any of the rules, as having just the SENSE which 'not,' 'no,' 'all' and 'some (at least one), have in the hosts of ordinary statements of the kind we are discussing. 

And this is a point already made (by Warnock, "Metaphysics in Logic,") viz., that 'some (at least one)', in its most common employment as a separate word, carries an implicature of plurality which is inconsistent with the requirement that should be the strict contradictory of A, and I of E. 


So 'some (at least one),' occurring as a constant of the system, is to be interpreted as 'some (at least one'), or 'some (at least one) of the ...', while * all ' and * no ', so occurring, can be read as themselves.

Strawson feels that the neo-traditionalist interpretation for the traditional forms has, then a few merits.

a) Strawson thinks the neo-traditionalist reading 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: 'not,' 'no,' and the quantifiers 'all' and 'some (at least one)' just the SENSE which these devices 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 -- EXPRESSUM, EXPLICITUM -- 



in such statement, it is, in the sense we have examined, alla Collingwood, presupposed -- OR CONVENTIONALLY, or CONVERSATIONALLY (in the case of the negative) IMPLICATED -- by them. 





It is this last feature which makes it unplausible to regard an assertion 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 Strawson is unhappy about regarding such expressions as 

' (x)(fxDgx) ' 

as giving the logical form of these sentences ; and why Strawson's uneasiness is not to be removed by the simple addition of positively or negatively existential formulae. 

******************* ENTER GRICE **********************

Even the resemblance (for Grice, equivalence in terms of 'iff' -- cf. his account of what an syntactically structured non-complete expression ) between 

(G) 

There is not a single book in his room which is not by an English author.

and the negatively existential form 

 (LFG) 

~ (Ex)(Ax . ~ Bx) 

is deceptive. 

It is not the case that there exists an x 

such that 

x is a book in Strawson's room and

 x is written by an Englishman. 

FIRST,

'There is not a single book in my room which is not by an English author'

-- as normally used, carries the presupposition -- or entails, for Grice -- 


 (G2) 

Some (at least one) book is in my room. 

SECOND, 


'There is not a single book in my room which is not by an English author.'

is far from being 'entailed' by 

(G3e) It is not the case that there is some (at least one) book in my room.

****

If we give

(G) 

There not a single book in my room which is not by an English author.

the modernist logical form

(MLF)  

~ (Ex)(Ax . ~ Bx) 

we see that 

(MLF) is 

ENTAILED by 

(MLF2) 

~ (Ex)Ax

So it is that if someone, with a solemn face, says 

(G) 

There is not a single foreign book in his room.



and then later reveals that 

(G3) There are no books in the room.

-- at all, we cannot get the feeling of having been lied to -- or been confronted with an initial false utterance --, because we have not.

But Strawson gets the feeling of having been made "the victim of a sort of communicative outrage."

"What you say is outrageous!"


outrage (n.)

c. 1300, 

"evil deed, offense, crime; affront, indignity, act not within established or reasonable limits," of food, drink, dress, speech, etc., from Old French outrage "harm, damage; insult; criminal behavior; presumption, insolence, overweening" (12c.), earlier oltrage (11c.).

From Vulgar Latin 

ultraticum 

excess," from Latin ultra 

beyond" (from suffixed form of PIE root *al- "beyond").

Etymologically, "the passing beyond reasonable bounds" in any sense.

The meaning narrowed in English toward violent excesses because of folk etymology from out + rage. 

Of injuries to feelings, principles, etc., from 1769.

outrage (v.)

c. 1300, outragen, "to go to excess, act immoderately," from outrage (n.) or from Old French oultrager. From 1580s with meaning "do violence to, attack, maltreat." Related: Outraged; outraging.

But Strawson gets the feeling of having been made "the victim of a sort of communicative outrage."

When it is only Grice trying to tutor  him in logic!

Of course it is not the case that Grice is explicitly conveying or expressing that there there is some (at least one) book in his uncle's room.

Grice has not said anything false. 

Or rather:

It is not the case that Grice utters an utterance which is not alethically or doxastically satisfactory.

Or it doesn't seem to be the case.



Yet what Grice (about the books in his uncle's room, none of them being 'foreign')  


gives Strawson

us the defeasible, cancellable, license to to assume that Grice thinks there is at least one book.


Thus, 

Grice, unless he goes on to cancel the implicature, misleads Strawson,

For what Grice explicitly conveys to be true (or false) it is necessary (though not sufficient) that there should be books in the room. 

What if the 'not' is external:

(G4) It is not the case that my uncle has a library and in that library all the books are autochthonous to England.

In fact:

(G5) It is not the case that my uncle has a library; for starters, it is not the case that I have an uncle.



Of this SUBTLE


nuantic

or cloudy or foggy

"slight or delicate degree of difference in expression, feeling, opinion, etc.," 1781, 

from French nuance "slight difference, shade of colour" (17c.), from 

nuer "to shade," from 

nue "cloud," from Gallo-Roman 

nuba, from Latin 

nubes "a cloud, mist, vapour," from PIE 

*sneudh- "fog,"

source also of Avestan snaoda "clouds," 

Latin obnubere "to veil," Welsh nudd "fog," Greek nython, in Hesychius "dark, dusky").

According to Klein, the French usage is a reference to "the different colours of the clouds." 

In reference to color or tone, "a slight variation in shade," by 1852; of music, by 1841 as a French term in English.

 'sort' is the relation between

(G) 

There is not a volume in my uncle's library which is not by an English author

and 

(G2) There are volumes in my uncle's library.


ENTER GRICE




Some may rightly say that a fine point such as this, which Strawson's tutor call the 'implicatum', is irrelevant to logic.

It is 'merely pragmatic,' Grice would say -- distinguishing between

logical point
pragmatic point

logical inference
pragmatic inference

entailment
implicature

conveying explicitly
conveying implicitly

stating
implicating

asserting
implying

what an utterer means
what the expression 'means'

-- but cf. Nowell-Smith, who left Oxford after being overwhelmed by Grice, "this is how the rules of etiquette inform the rules of logic -- on the 'rule' of relevance in "Ethics," 1955.


If to call such a point, as Grice does, as "irrelevant to logic" is vacuous in that it may be interpreted as saying that that such a fine foggy point is not considered in a modernist formal system of first-order predicate calculus with identity, this Strawson wishes not to dispute, but to emphasise. Call it his battle cry!


But to 'logic' as concerned with this or that relation between this or that general class of statement occurring in ordinary use, and the attending general condition under which this or that statement is correctly called 'true' or 'false,' this fine foggy nice point would hardly be irrelevant. 

GRICE'S FORMALIST (MODERNIST) INTERPRETATION:

Certainly, a 'pragmatic' consideration, or assumption, or expectation, a desideratum of conversational conduct underlies and in fact 'explains' the implicatum.

If we abide by an imperative of conversational helpfulness, enjoining the maximally giving and receiving of information and the influencing and being influenced by others in the institution of a decisions, the sub-imperative follows to the effect:

Thou shalt not make a weak move compared to the stronger one that thou canst truthfully make, and with equal or greater economy of means.


Assume for a moment that the form 


There is not a single . . . which is not . . . 

Or

It is not the case that ... there is some (at least one) x that ... is not ... 

is introduced into ordinary speech with the same sense as 

~(Ex)(Ax and ~Bx)

Then the operation of this imperative inhibits the utterance of the form where the utterer can truly and truthfully simply convey explicitly 

There is not a single ...

i. e. 

~(Ex)(Fx). 

And it is this inhibition which tends, ceteris paribus, to confer on the prolixic form ('it is not the case that ... there is some (at least one) x that is not ...')  just that kind of an implicatum which Strawson identifies.  

But having detected a nuance in a conversational phenomenon is not the same thing as rushing ahead to try to explain it BEFORE exploring in some detail what kind of a nuance it is.

The mistake is often commited by J. L. Austin, too! 

(in "Other Minds," and "A Plea for Excuses")

and by H. L. A. Hart (on 'carefully')

and by R. M. Hare (on "good")

and by P. F. Strawson on 'true,' (Analysis) and 'if.'

just to restrict to the play group.

Grice tries to respond to anti-sense-datum in "That pillar box seems red to me."





The form ("It is not the case that there is some (at least one x) such that ... x is not ...") would tend, if it does not remain otiose, to develop or generate just those baffling effects in one's addressee ('outrage!') that Strawson identifies, as opposed 

to the formal-device with which the the vernacular counterpart is co-related. 


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 one may add a point about the neo-traditionalist interpretation of the forms of the traditional Aristotelian system. 

Strawson is not claiming that it faithfully represents this or that intention of the principal exponent of the Square of Opposition.

Appuleius, who knows, was perhaps, more interested in formulating this or that theorem governing this or that logical relation of this or that more imposing general statement than this or that everyday general statement that Strawson considers. 

Appuleius, who knows, might have been interested, e. g., in the logical powers of this or that generalisation, or this or that sentence which approximates more closely to the desired conditions that if its utterance by anyone, at any time, at any place, results in a true statement, so does its utterance by anyone else, at any other time, at any other place. 


How far the account by the neo-traditionalist of this or that general sentence of 'ordinary' langauge is adequate for every generalization may well be under debate!