[hist-analytic] The Old Wykehamites

Jlsperanza at aol.com Jlsperanza at aol.com
Tue Feb 3 16:49:11 EST 2009

Here in fond memory of  Wykeham!

---- Thanks to B. Aune for his comments in "Notes on  Conjunction", etc. 
Don't feel like pressurising anyone, if that's the word,  but (have some time 
in my hands -- don't expect a reply, please note*) but have  these notes that 
I composed this morning and have been burning with me  since!)

* (this caveat, "Don't  feel obliged to reply or event comment on this" was a 
typical  turn
of phrase  in Verdi's and Boito's correspondence, I  read)

** Hopefully, D. Frederick  will jum in, too. I enjoy his fresh approach to 
the history of analytic  philosophy!

In a message dated 2/3/2009, Bruce Aune writes in "Notes on  Conjunction, 

>JL Speranza’s latest note, partly in response to  
>an earlier note of mine, contains some observations on 
>Quine’s  and other logicians treatments of 'and.'  
>I agree with many of JL’s  observations, but I want to 
>call attention to the fact that  knowledgeable logicians are 
>well aware of the fact that the  *truth-functional* conjunction, 
>often represented by an upside-down 'v'  but sometimes by ‘&’, 
>is a sentence or [truth-evaluable] *clause*  connective, 
>not a true counterpart to the English ‘and.’ 
>The  latter, unlike the former, can properly 
>connect expressions from many  categories other 
>than clauses.  It can connect noun phrases, as in  
>‘Tom’s dog and Mary’s cat,’ 
>verb phrases, as in  
>‘slipping and falling,’ 
>adjectival phrases, as in ‘powerful and  threatening,’ 
>and adverbial phrases, such as ‘cautiously and  prudently.’  
>(I speak of phrases here, instead of simply nouns,  verbs, 
>adjectives, and adverbs, because longer verbal, adverbial,  
>etc. units can also be joined by ’and,’ ‘or,’ ‘neither,’ ‘nor,’  
>and other vernacular conjunctions.)  
>To say this is not to  criticize the logician’s familiar symbols.  
>Sometimes ‘and’ and so  forth are used as *clause* connectives 
>for which operations such as  commutation holds, as in 
>‘2 + 2 = 4 and 3 + 2 = 5.’  
>Of  course, as J.L. observed, commutation sometimes 
>fails for the  truth-functional ‘and,’ 

---- Is 'fail' the right word? I think the whole  point of Grice's 
_programme_ so called, is that it's _speakers_ who 'fail'! :)  More on this below (on on 
another post, I hope!).

I know it's pedantic to  focus on a turn of phrase in a post meant for a 
discussion internet forum (D.  Frederick got into some little trouble on another 
list for just using a  colloquial expression -- but one cannot spend the 
eternity re-reading for  editorial improvements! :).

>as in 
>‘Tom sat down and started  to eat,’ 
>which might be written more perspicuously as 
>‘Tom  sat  down *and then* he started to eat.’  
>G.H. Von Wright once  had a little calculus featuring an 
>‘and then’ connective. 

---- I  believe Grice (and he loved von Wright's neologisms, not just 
'alethic', but  'prothetic' -- _Aspects of Reason_) and this temporal-sequence one, 
which I  think Grice uses in his 'traditionalist' critique of Davidson's  
actions-and-events theory in the perhaps not too originally entitled (knowing  
Grice) essay, "Actions and Events" in Pacific Philosophical Quarterly,  1988.
I want to say that von Wright was perhaps into  something more than the 
search for a 'and then' operator? I think he  used

"p / q"   -- where, I think, he would read, "q, as brought  about by p" -- 
but I may be confused. There seems to be an element of  'causality' brought into 
the picture, too. Oddly, Urmson -- who's sticking to  Wittgenstein (the 
early) and Russell, rather, uses in "Philosophical  Analysis":

"He went to bed and took off his trousers"

which is  _temporal_ alright. On the other hand, I think it was Ryle 
(Dilemmas) who  used,

"He died and he swallowed the pill"

-- which is, naturally,  _temporal_ *and* causal.  And I agree that most uses 
of 'and' _are_  confused. I wish we could go back to the old Latin lingo, 
where they merely  appended '-que' at the end of things. Ditto for Greeks, and 
the 'men'/'de',  enclitics if ever there were some. B. Aune continues:

>A moral of my  observations here is that, 
>to avoid error, we have to be very careful  
>when putting vernacular inferences 
>into symbolic notation.   If an 'or' *isn't* 
>used as a *truth-functional* _clause_-connective,  
>it should not be represented by a logician's '&'.

--- Well,  I'm glad I have seldom occasion, if that's the expression, to use 
'or'. I recall  Jennings's noting (in "Genealogy of Disjunction") that the 
original _sense_ as  it were, is 'other', as in "every other day". I realise that 
the Latins here  were a bit otiose in having sive _and_ vel, but I'm glad the 
logician's 'wedge'  is supposed to represent the 'vel' only. 

Oddly, Grice apparently never  discussed the inclusive 'or' +> exclusive 'or' 
-- where '+>', after  Levinson, I use for 'conversationally implicates'. He 
(Grice) rather focused on  the implicature of 'or' to the effect that the 
utterer does not have  not-truth-functional evidence for the disjunction). 
Similarly, it's odd Grice  did not discuss the so-called 'if' +> 'iff' -- as Pears 
does, in "Ifs and  Cans"; Grice focusing merely again on a correlative 
implicature, that the  utterer does not have non-truth-functional evidence for either 
antecedent or  consequent. B. Aune writes:

>J.L. also comments on Excluded Middle,  
>saying he thinks it is really a law about the tilde 

--- Oddly,  P. Smith (in his "Logic", CUP) calls it, and I guess I liked it, 
the  'squiggle'.  I read the 'tilde' is actually the Spanish 'grandee' sign 
for  the thing that goes above the "n". Odd.

>rather than ‘or’ (or  ‘v’).  I think it is “about” both 
>symbols if it is about  either.  

That was a good one, in trying to formalise:
p v ~p /  v, ~ ---> "p v ~p" / v, ~
if "p or not p" is about 'or' or 'not', it's  about 'or' _and_ 'not'.   :).

>Actually, it uses both and  mentions neither.  

Good! I guess I was trying to think of  Russell-Grice's view on "The King of 
France's baldness" versus Strawson. For  some reason, Strawson discusses the 
King's _wisdom_, but let that be.  In a  formalisation of, "There is a unique 
king of France and he is not bald", I  wouldn't use 'or', yet the whole 
paraphernalia of truth-value gaps spring.  Although it is true that a corollary would 
be that,  For Strawson, "Either  the King of France is bald or he is not"
would bear a truth-value gap  (_contra_ Russell-Quine-Grice). As Russell 
would add, in a _triple_ disjunction,  " ... or else he is wearing (since a 
Hegelian likes a synthesis) a wig."  (Incidentally, I have read Dummett's discussing 
the similarly monarchic  statement, to a different purpose, of

"Queen Elizabeth II wore a wig --  as she was bald"

-- as an example of 'unverifiable by evidence', since  it's quite a remote, 
anti-intuitionistic thing. Oddly, my mother who likes opera  was commenting 
yesterday on how impressed she was by this version of "Roberto  Devereux" (by 
Donizetti), when, in the final scene, Elizabeth II throws away her  wig. But I'm 
disgressing). B. Aune: 

>But Excluded Middle holds only  for 
>sentences (or clauses) that have a 
>determinate meaning  

--- and 'bald', alas, is not one of them. But I'm using in an absolute  sense 
to mean, 'no hair whatsoever' 

>and satisfy the principle of  Bivalence: 
>when they are either true or false 
>but not  both.  
>Sentences containing vague predicates 
>such as ‘fat’  

-- or indeed 'bald' some say. 

>don’t (without regimentation)  
>satisfy bivalence and so provide counter 
>instances to Excluded  Middle. 
>Jack Sprat is clearly thin and his wife is 
>clearly fat,  but if Jack’s brother is a borderline case, 
>neither clearly fat nor  clearly thin, then 
>the sentence ‘Jack’s brother is fat’ is  
>(without regimentation) neither true nor false, 
>‘Jack’s brother is fat v ~( Jack’s brother is fat)’ 
>is not true  and so is an exception to Excluded Middle. 

-- also if he doesn't exist,  I guess.

>For various reasons, Carnap thought that 
>the meaning  of some predicates, including 
>vague ones, can usefully be clarified  incompletely 
>by ‘A-Postulates.’  

Some say he was a charming  man, but this 'usefully clarify incompletely' 
beats me! :)

>If I wish  to use the predicate ‘fat’ in a discussion 
>where I want my meaning to be  relatively clear, I 
>might offer a partial clarification of its meaning  by 
>offering two A-postulates:
>(x)(x is fat -> ~(x is  thin))
>(x)(x is obese -> x is fat).

I would think Julia  Hirschberg would disagree. She invented what she called, 
I think,  'rank-implicatures'. As much as the Sargent-Major (who tucked me in 
my little  woden bed) is _not_ a private, she wouldn't say (most ordinary 
speakers would  say) an obese person is fat. But surely we can keep the true 
conditional as a  true semantical rule, and treat the 'rank' phenomenon as clearly 
 _implicatural_.  B. Aune: 

>Carnap regarded A-postulates as  semantical rules, 
>so the two formulas I have just given could be  considered true 
>by virtue of the semantical rules of a certain  system.  

It dawns on me that Geach's pleonetetic may also play a  role here, but I'm 
_not_ good at grading gradual predicates! It would entail  considerations on 
'many' (fats), and even "too many". So a fat person would be  one who has a body 
who has too many cells with too many fats. An obese person  would be a fat 
person who has _far_ too many cells with _far_ too many fats in  them. And so 
on. Apparently, the way doctors judge it is easily in terms of a  _ratio_: if 
Jack's brother is x high and weighs y, then provided x/y is within  the range of 
a bound variable (to quote Quine), he would be, if  not  _thin_, _okay_.  B. 

>As such they would count as analytic  truths 
>of that system. I defend Carnap on this matter in 
>chapter  3 of my recent book; 
>I can think of no enable objection to 
>his  procedure.
>My thanks to JL for the comments.

No, no enable  objection, no noble objection, either! Only perhaps what I 
called "Highly  Powerful System G".

You see, Grice, since he was _kind_, called his  system, "System Q" (in 
"Words and Objections"). George Myro, in some unpublished  work, but notably in his 
contribution to "P.G.R.I.C.E.", ed. Grandy/Warner,  speaks of "System G", 
rather.  I speak of "System G(sub h-p)" i.e. highly  powrful, if not hopefully 
plausible" system G. 
Now, a  system -- should it stop at syntactic and semantic rules? I would 
think, perhaps  no, and that _pragmatic_ considerations may enter, as in 
connection with  cancelling implicatures of the type "The king of France is not bald; 
he died  many years ago and _never_ was seen with a wig, or with a bare 
cranium". Or of  the type, "Well, he is fat; he is obese". "Well, I do have three 
children; I  have fifty children", etc. 
The larger picture would  relate to B. Aune's concluding remarks in his post 
on "the Analytic/Synthetic  Distinction". I said I'd dedicate a longer day. He 
says (words to the effect):  

"How precisely can it be drawn? Can it be defended?"

I would  transfer those questions to the topic that fascinated Grice (_only_ 
after  Strawson had to put it 'in his mouth' by saying that there _are_ 
differences in  _sense_ between the vernacular 'devices' ('and', 'or', --- Grice 
indeed lists  seven: 'not', 'and', 'or', 'if', 'all', 'some' and 'the') and their 
_formal_  counterparts. 

How precisely their connection should be described, if at  all? I know that 
when I talk to some logicians (or pretend to talk, as when I  browse through 
George Myro's posthumous, _Rudiments of Logic_) I have to pretend  there's _no_ 
As for  _can_ the lack of connection be defended? I guess it can! I used to 
call this  the C. P. Snow's "Two cultures" war. B. Aune speaks of 
'knowledgeable  logicians'. But Grice speaks rather of 'philosophy of logic'. While the 
online  dictionary (Merriam-Webster, I think) defines Grice as "British 
logician", I  think he is being underdescribed. (But then, can you believe it, the 
current  OED3 has him as a "British _linguist_"! Please mailto:oed.co.uk, my 
messages  _bounce!)). 

LARGER HISTORICAL PICTURE.   I note that as far as  Oxford is concerned there 
are now _two_ chairs of Logic! One the usual one,  Merton-college bound, 
Wykeham chair of Ayer fame ("You may be a boxer, but I'm  the former Wykeham 
professor of logic"). The other is, across the road, in  something called "The 
Department of Mathematics", I think, and it's called  "Mathematical Logic", I 
think. Now _they_ have a right to disassociate things  like that, but we good ole 
Wykehamites just _can't_!


J. L.   

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