[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.

Deviant Logics

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.’”  

To review:

&,  +         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, 
say, "&"

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 
truth-functional operators.

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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