Jlsperanza at aol.com
Jlsperanza at aol.com
Fri Jun 12 08:46:38 EDT 2009
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
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
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.
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:
"The king of France is bald" is _false_ for Grice -- and R. B. Jones --
It's true-value gappy for
Strawson and Burton-Roberts
(this person calls himself a
"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
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
when it comes to handling of calculus; as if they do not care for any
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
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?
* 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
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:
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")
~3 F2 a1 (Also, "Pegasus doesn't fly, but as ascribed of
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.
* 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
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
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
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
J. L. Speranza
Grice, H. P. Vacuous Names', in Davidson/Hintikka, Words and
Grice, H. P. Studies in the Way of Words. Harvard. (esp.
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