In a message dated 3/19/2016 8:52:51 A.M. Eastern Daylight Time,
donalmcevoyuk@xxxxxxxxxxx considers the utterance:
i. The solar system consists of only the following bodies (list).
and its alleged status as a universal statement (which McEvoy denies).
Since Putnam's first language was French, I should say:
Touché.
Two points though:
First, Putnam is arguing I think that Popper would take BOTH (i) _and_ (ii)
not as universal statements, so we may want to consider (ii) too.
Second, regarding (i) itself, I guess a weakened case may be made to the
effect that the LOGICAL FORM of (i) *includes* [as part of its entailment]
the occurrence of "∀x", i.e the universal quantifier. Suppose we rephrase (i)
as
ib. The solar system is beautiful.
and now compare (ib) with Russell's (ic):
ic. The present king of France is bald.
Russell, and for that matter, Grice (and I am pleased that Grice quotes in
"Vacuous Names" authors such as Boolos and Parsons who had good
associations with Putnam) analysed (ic) as a CONJUNCTION of three quantified
statements:
(A)
The first conjunct admittedly features the existential quantifier only:
There is an x such that x is currently King of France.
In symbols:
∃x[K(x)]
(using 'K' for 'currently King of France')
(B)
The second conjunct, however, features the universal quantifier, as applied
to variables x and y (it is only natural that Putnam is thinking this way
seeing that Quine's "On What There Is" was what made him a philosopher,
more or less).
For any x and y, if x is currently King of France and y is currently King
of France, x=y
(i.e. there is at most one thing which is currently King of France).
In symbols:
∀x∀y[[K(x) & K(y)] ⊃ y=x]
(C)
Finally, again the third conjunct features a universal quantifier:
For every x that is currently King of France, x is bald:
In symbols:
∀x[K(x) ⊃ B(x)]
(using 'B' for 'bald')
Mutatis mutandis for 'solar system' and 'beautiful', and Putnam's and
Popper's utterance in question.
The issue is about how to provide a conceptual analysis for what "the
[then] new generation of logicians" (as Popper calls Putnam) referred to,
following Whitehead and Russell -- for everything old is new again -- as "the
iota operator", that translates in English as 'the' -- and that Grice lists as
one of the seven 'formal devices' along with their vulgar counterparts
that it has become a wrong commonplace in philosophical logic to think that
they don't pair. They do! (The seven devices listed by Grice correspond to
the vernacular "not", "and", "or", "if", "all", "some (at least one)" *and*
"the"). If there is any divergence between the conceptual analysis of 'the'
as provided in the three clauses above and its vulgar use, this divergence
is only implicatural (and bound to go unnoticed by those who disregard
conversational factors such as candour, informativeness, and clarity), and,
the interesting thing too, as Putnam would agree, is that we don't need to
bring in the dubious (Strawsonian) concept of 'presupposition' or the
controversial metaphysical concoction of a truth-value gap, either!
Cheers,
Speranza
References:
Grice, H. P. "Vacuous Names", in "Words and objections: essays on the work
of W. V. Quine.
Grice, H. P. "Definite descriptions in Russell and in the vernacular"
Grice, H. P. "Presupposition and conversational implicature" in Studies in
the Way of Words.
Whitehead and Russell, Principia Mathematica
