[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
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! :).
>‘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
--- 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
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
>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
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
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_!
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