[hist-analytic] Vacuity

[Jlsperanza at aol.com]

In a message dated 6/11/2009 3:52:03 P.M. Eastern Daylight Time,  
rbj at rbjones.com writes:
But for Aristotle "izz" isn't merely set  inclusion,
for the sets here are part of something like
a taxonomy (either  of substance of some category
of attributes).  They do not correspond  to
aribitrary descriptions but to definitions,
about which Aristotle is a  bit picky.
When you consider this as a taxonomy it's natural
enought to  expect all the defined concepts to
be non-empty. ... When we look at "hazz"  the situation is different.
Here we do not need to insist on non-empty  extensions
(and my last model does not) because, in effect,
syllogisms  never quantify over the extension of
an attribute.  If an individual  attribute is
the subject of a predication then the predication
must be an  "izz", and the syllogism rather than
saying anything about the objects in the  extension
of the attribute is simply stating that the
attribute is IN some  universal, e.g. red is a colour.
Aristotle's logic+metaphysics as I  understand it at
present (mainly at second hand) doesn't allow you
to say  "All red things are coloured".


-----
 
As I said in my ps for "Re: Pirotologica", I am fascinated by the post by  
R. B. Jones on vacuity. My reference to Strawson was meant historically for  
various reasons:
 
i. I do think he was a master in capturing the nuances of
   ordinary language like nobody before or after did.
 
ii. It's _his_ nuances that Grice took seriously when
   developping that side of his programme connected
   with logic.
 
iii. Grice/Metaphysics/Strawson/Aristotle overlap too,
    in that Grice was closely aware (and he says
    uncrediting contributing) to Strawson's  masterpiece
    in Metaphysics: His Individuals.
 
etc.
 
-----
 
In this post I would like to mention what Grice found a syntactical device  
to deal with Strawson's problems. The easiest access is in WOW, Strand 6 -- 
I  think: modernism versus neo-traditionalism.

As R. B. Jones notes, it's difficult to check with Strawson: how much  is 
"Aristotelian" and how much is just "traditional". In this respect, I should  
say I loved to teach logic -- I recall one seminar where we set to music 
all the  'barbara celarent' little ditty. Since the Chair of the Department 
was not happy  in hearing my class sing, I had to find a reference to back me; 
and I did: a  book called "Barbara Celarent" -- printed in London. I should 
have the complete  reference somewhere. 
 
Now, where Grice gets in:
 
Indeed,
 
"The king of France is bald"  is _false_ for Grice -- and R. B. Jones  -- 
and me.
                                           It's true-value gappy for 
Strawson and Burton-Roberts
                                           (this person calls himself a 
neo-Strawsonian)
 
"The king of France is not bald" is thus _true for Grice, Jones, and  me.
                                           It's true-value-gappy for 
Strawson and Burton-Roberts
 
(Oddly, Burton Roberts worked marvels with the Square of Opposition in  
connection
with necessity in "Implicature and Modality" -- he is a linguist rather  
than a philosopher,
so be careful there -- I find that linguists and some logicians are pretty  
inconsidered
when it comes to handling of calculus; as if they do not care for any  
metaphysical
reverberation this or that technical tweak may have on the system).
 
Now, this is indeed all about Russell
 
(Ex) Kx     &    (                     ) & ~Bx
 
The king of France is bald (skipping the uniqueness clause).
 
Grice mentions Sluga for some considerations into the interpretation  of 
the 'iota' operator:
 
(ix)Kx & ~Bx.
 
So I will use (ix) as iota operator and avoid the uniqueness clause  
altogether -- but recall it's _three_ conjuncts in the Russellian  expansion.
 
Now, as Grandy I believe  notes in the two quotes on Grice's Vacuous  
Names, Grice seems to be saying that ~ shall always have maximal scope:
 
~(ix)(Kx & Bx)
 
I.e. it is not the case that the king of France is bald.
 
This is the only thing that
 
"The king of France is bald" _means_. The implicature that there _is_ a  
king of France arises because of considerations of trivial (or non-trivial,  
sometimes) "common-ground status" of "There is a king of France" --  (ix)Kx.
 
(The point about 'trivial' and 'nontrivial' is somewhat complex:
 
           A: I loved  that concert
           B: My aunt's  cousin went to that concert, and loved it too.
 
It would be otiose to _expect_ that A knows that B has an aunt ("let alone  
that B's aunt has a cousin"), so it's not so much 'common ground' but  
non-trivial/trivial knowledge worth sharing or not).
 
Now, Grice seems to have _preferred_ to keep the _natural_ order of the  
surface formula:
 
It's not like we do say:
 
~(ix)Kx    &  ~(ix)Bx
 
 
"There is not a king of France, and he is not bald".
 
Rather we do say, at one fell swoop -- if that's the expression, "The king  
of France is not bald" and it would be otiose to be asking for 'it is the 
case'  reformulations. Strawson oddly considers this under 'not' in 
"Introduction" and  he insists that "~" represents "It is not the case" only, not 
plain "not". I  would follow him, since I'm Italian and the Italians are 
redundant, but honest,  to be saying, It is the case that the wife married her 
husband, instead of the  shorter, "The wife married her husband" seems a bit 
too much -- for surely if  'it's not the case that ...' is necessary for 
negative propositions, 'it is the  case that' should be symmetrically preferred 
for affirmative sentences  too.
 
So Grice was following what he called 'wisdom', when he says (in  WOW):
 
  What the eye no longer sees the heart no longer grieves for.
 
His idea is to get _rid_ of the impilcature even in the surface form.  How?
 
TWO METHODS.
 
* In "Vacuous Names", it's his subscript notation. He corresponded with  
Boolos and Parsons on that, and G. Myro helped him there. Myro has an  
interesting "Rudiments of Logic" which covers much of this ground. In this  
subscript notation we would need to subscribe each element of the formula. Let's  
call the king of France 'Bob' 
 
                 Bob hazz bald
 
                 It is not the case that Bob hazz bald
 
                Bob  hazz no bald
 
                 etc.
 
I'll settle for the iii, albeit cacophonically. In the subscript system it  
comes out as
 
        Bob-1 hazz-2 no-3 bald-4.
 
Each element is giving a scope ordering and index. In this case, as I  
recall, Bob has a lower index than no (Bob has 1; no has 3), so the implicature  
could be _defended_ on logical grounds. But Grice wants to say that the 
neutral  preferred ordering is with "no" giving maximal scope:
 
         Bob-2   hazz-3 no-1 bald-4
 
Syntactically, it's a teller. He then goes on to propose 'interpretation'  
in the systems for one or the other reading.
 
I recalled I found it witty and easy to digest at one time:
 
           ~Fa
 
Surely that's ambiguous:
 
            ~1  F2  a3
 
is less so
 
The fact that he uses subscript makes for a nicer outlook.
 
In that way, 
 
          ~1 F2   a3     ("Pegasus doesn't fly")
 
differs from
 
          ~3     F2   a1  (Also, "Pegasus doesn't fly, but as ascribed of  
the non-vacuously
                                named Pegasus -- and I agree with R. B. 
Jones that one should
                                distinguish between 'vacuous' and 'empty'.
 
(Stanford Univ. was editing a collection on "Empty names" and I  wrote to 
the editors: I hope you credit Grice -- they replied back, "And  then NOT get 
the book published? This is supposed to be new, edgy stuff" Ah  well -- 
Unfortunately when "Vacuous Names" was felt as if it needed a  reprint, it was 
only a _partial_ one, in "Definite Descriptions", MIT -- a  reader.
 
Of course Grice is aware of 'x pegasises', so the counterparts for the two  
formulae above in Quinean -- and Grice calls his system Q in honor of Quine 
 -- I write 'honor' without the 'u' because Quine _is_ (WAZZ?)  American. 
(HAZZED American).
 
-----
 
* The other device is studied by Robert Harnish -- the (Kantian-Fregean)  
philosophically minded of the group Harnish/Bach -- I love Bach, too -- in  
"Logical form and implicature". This is the 
 
                     SQUARE-BRACKET DEVICE
 
and it's cute. Grice loved square brackets but here they mean 'immune to  
negation'. He presented it in WOW iv and Retrospective Epilogue. Also in  
"Presupposition and Conversational Implicature" -- his example, the slate for  
"Arrest the intruder! Should the intruder exist!")
 
What this does is respect the surface-form of the utterance (One of Grice's 
 supermaxims, Be perspicuous -- falls under the category of MODE, so he has 
to be  careful HOW the info is presented). 
 
So, the square bracket device allows for a way to avoid the  fastidious
 
~(ix)Kx   & ~(ix)Bx
 
We could write the shorter:
 
~[(ix)Kx] & Bx
 
I think.
 
Here is where I think Sluga's considerations enter. Should we take the  
definite description as a _term_ or as a quantified expression? (I'll omit the  
details but should get back to them)
 
In any case, what "[ ... phi ... ]" represents is that _it is common  
ground_ and thus immune to negation that phi.
 
If we bracket in squares "There is a king of France" we cannot then go  
_and_ deny that. 
 
Grice is pragmatical here: he loves his square-bracket device, but realises 
 Russellians will hate him (G. Bealer once quoted a paper, "Definite 
Descriptions  in Russell and the Vernacular", by Grice). 
 
So, as prolixic Grice is for the steps of introducing the square-brackets  
he also is in providing steps for their elimination.

The elimination relies on simplification of formula and repetition,  too:
 
~[(ix)(Kx] & Bx)
 
becomes indeed, via elimination of the square brackets, the original  
verbose formula where we make it clear which of the three Russellian conjuncts  
_gets_ denied: the last one, that the king is bald:
 
(ix)(Kx & ~Bx)
 
But surely Grice wants to say that CETERIS PARIBUS and on logical  
principles, it's the maximally located ~ that trumps any other consideration.  This 
above is the 'surface' form for the implicaturally loaded expression, in  
case someone should not be as careful as Grice and think that the utterer _is_ 
 'presupposing' the existence of the king of France when denying his  
baldness.
 
It's "~(ix)(Kx & Bx)" that is the right thing to do, in  formulation.
 
------
 
In "Life and Opinions" as I think I shared with the forum, Grice goes back  
to the problem of "explanation" with empty sets, but on re-reading those  
commentaries, I find he is more into the ultimate metaphysical claims of a  
unified scientific approach -- and he is pretty open as to what options are 
open  for the metaphysically-oriented scientist or philosopher. 
 
Grice writes in his Vacuous Names that it creates no "Meinongian jungle"  
but in other writings (Life and Opinions) he criticised Quine for preferring  
dessert landscapes in springtime! So one has to be careful -- especially 
when  one sees indeed that the Modified Occam Razor may even contradict his  
"Ontological Marxism" (not so, but on the face of it)
 
In considering his extension to 'definite descriptions' besides the idea of 
 'dossier' that G. Evans took up in "Varieties of Reference" with a credit 
(in a  footnote), I liked Grice's expression, 'by a stroke of a pen', 
whatever that  meant. He said that -- in his funny scenario where the butler mixed 
his and his  friend's hat. It turns out that the butler was the gardener. 
So Grice says, "the  butler whoever he is mixed my and my friend's hat" -- It 
would do to play with  non-existentials here. If they were mixed, by chance 
-- since there is no  butler, I _suppose_ the 'whoever he is' (whatever it 
is, etc) may be  expanded to cancel the unwanted 'existential fallacy':
 
              'whoever he is, if he is _anything_ at all'
             
Bellorophon owed Pegasus.
Bellorophon owed Pegasus, whoever he was, if he was at all.
Bellorophon, whoever he was, if he was at all, owed Pegaus, whoever he was, 
 if he was at all.
 
etc. Recall that Grice wants to say that even if he didn't exist, Pegasus  
possibly _could_ fly -- for Apollodorus says it's so. But if that's not a  
Meinongian jungle it's not the desert of Gaza, either.
 
"The present king of France" is more of a political dogma. I'm sure there  
are royalists in France who think that a particular individual _is_ the 
present  king of France. I know in Italy they do vis a vis the present King of  
Italy!
 
Cheers,
 
J. L. Speranza
 
     Ref.:
       Grice, H. P. Vacuous Names', in  Davidson/Hintikka, Words and 
Objections.
       Grice, H. P. Studies in the Way  of Words. Harvard. (esp. 
"Presupposition and
             Conversational Implicature") 
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