[hist-analytic] Topdogma Attacked
Jlsperanza at aol.com
Jlsperanza at aol.com
Mon Feb 2 21:05:05 EST 2009
"... that I can always be relied on the
defense of the underdogma"
Grice, "Meaning Revisited' WOW.
I will select [in my mind] a few passages from B. Aune's message forwarded
by S. Bayne, as they relate to 'and'; since I have written extensively on that
(to little avail, so far, but hey, such is the history of analytic
I'm not sure I follow Quine in joining truth-functional operators with
'quantification' and 'identity' in terms of Goedel on completeness. I draw quite a
boundary between truth-functionality (as far as my thought-processes are
concerned) _and_ quantification _and_ identity.
Quine mentions 'if' and 'and', but I'm far less sure (than perhaps he was)
that I understand 'if', so I'll stick with 'and'.
Plus, I should stick to "&", since, well, natural languages, if I may be
analytic, _are_ natural languages!
Quine makes a reference to something like &-intro and &-elim.
“anyone who affirms a conjunction and denies one of its components, is
simply flouting what he learned in learning to use ... ‘and.’”
&, + p
"p & q"
&, ~ p & q
"anyone who affirs a conjunction ("p & q") and denies one of the conjunts
("p") is ..." _not_ abiding by "&, ~".
But what *is* "&, ~"?
When it comes to "not" (Quine's reference here to "Excluded Middle" seems
relevant) I feel we are treading trickier ground as it were. For ~ is not
really a truth-connector, but a truth-functor, and I hold that "Excluded Middle"
is a law about ~, rather than, say "or" ( p v q).
"The king of France is not bald"
would be _true_ (rather than truth-value gappy) if 'the king of France'
fails to refer (I'm here with Grice, WOW, "Presupposition and Conversational
But back to "&". I take "&, +" and "&, -" (and Grice formalised them
exactly like that in his contribution to the Quine festschrift, Words and
Objections, ed. Hintikka/Davidson) are _natural_ deduction rules (Gentzen) -- but are
they _syntactic_ or _semantic_? I take they are _syntactic_ and thus do not
really _concern_ *meaning* (so Quineean anti-semanticists should not worry).
It takes an interpretation (I under a system S) to provide truth-tables for,
p & q
1 1 1
1 0 0
0 0 1
0 0 0
Now, I think it was via Susan Haak I learned about these things. Not only
her "Philosophy of logics" but her Dutch-published book, "Deviant logics" --
relying heavily, as I recall, on Quine.
So, it would seem that Quine was in fact responsible to bring into the
analytical forum, as it were, the very possibility of a _deviant_ (the expression
is perhaps not too happy) logics, where, ... er, things _get_ defined
Now, if Quine is right that Carnap was wrong about 'semantical rules' about
'truths which are not logical yet true by virtue of the meaning of its
components" (I'm expressing vaguely), I'm less sure about what kind of _claim_ is
it that we make when we just deal with the consistency or lack thereof of our
Perhaps the pragmatist direction along the right lines is something like
Gazdar's work on implicature (PhD, Reading -- book for Academic Press). He would
reason along 'transcendental' lines. Why is it that we _need_ something like
an "&" operator with such a _truth_ table? Is it conceivable that some
'foreign' community can do _without_ 'and'? What about _mere_ conjunction, as when
Russell & Whitead suggest "pq" as formalisation for "p and q". What kind of
claim is our claim about 'and'.
Grice has a charming fragment about this in, I think, "Further notes" or
"Presupposition" (but not I think in the WOW reprint version). He suggests, it's
not a matter of our use of the vernacular 'and'. Even if we start using the
ampersand sign, "&" -- as I may do in hanwriting a letter -- that does not
mean that the 'implicature(s)' of 'and' will _detach_; '&' will, in spite of
the logicists, retain what he calls 'metaphysical excrescences'!
--- But what would philosophy _be_ if not a gate for us to _be allowed_ to
contemplate 'deviant' logics, if only to criticise them? Or is it because we
call them 'logics' (and yet 'deviant') that they are _beyond_ criticism!?
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