[hist-analytic] Vacuity

Jlsperanza at aol.com Jlsperanza at aol.com
Sat Jun 13 13:47:06 EDT 2009

A brief comment, I hope, on a few lines --  having now seen the updated pdf 
-- excellent! -- by R. B. Jones. These are his  lines in his "Re: 
Davidson's Hume", but I'm taking the liberty of appending them  to the thread on 

R. B. Jones writes in his reply to S. Bayne  on "Davidson's Hume":

>Having just read Strawson I think he would say,  and I would agree,
>that e having a unique cause is presupposed here and  that the
>sentence has the status of being true whenever it has a  truth
>value, but in many possible worlds lacking one.
>Though one  might very reasonably insist that in those cases it
>is  false.

Excellent application.

For the record, three  things:

* Strawson did use 'imply' in "On Referring" (predating  Introductin to 
Logical Theory by four years?). This I find fascinating, because  he later did 
introduce 'presuppose' which links nicely with the 'continental'  
philosophical tradition -- I can think of Collingwood on 'presupposition' and  the 
whole idea of 'suppositio' in mediaeval logic. When Grice coined 'implicate'  
he was obviously having 'imply' in mind; and when in "Presupposition and  
Conversational Implicature" he is thinking of 're-coining' Strawson's  
'presuppose' as 'implicate' it's like the full circle.

* ASYMMETRY of the  'alleged' gap. Part I. Strawson puzzled everyone, "The 
king of France is bald"  _and_ "The king of France is not bald" (oddly he 
uses 'wise') are _neither true  nor false_. They lack a truth-value. They 
diplay a truth-value gap (I tend to  think the coinage of that phrase is 
Quine's?). But there is some asymmetry here,  Grice feels, that Strawson  ignores:

"The king  of France is bald"  _is_ *false* if there  is
no king of France.

This is, Grice does (and I would) claim -- drawing on  G. E. Moore's own 
coinage of 'entailment' -- because 'The king of France is  bald' _entails_ 
there is a king of France -- Russellian expansion -- three prong  analysis.

* ASYMMETRY of the 'alleged' gap. Part II. What about the other  claim by 
Strawson, "The king of France is not bald" is neither true nor false  when 
there is no king of France? Grice claims the picture is perfectly  opposite:

"The king of France is not bald" _is *true* if  there
is no king of France.

(I wonder what Strawson _was_ thinking). This is  because it's a mere 
matter of 'cancellable' implicature (or presupposition).  Surely it's wittily 
cancellable, "The king of France is not bald; there is no  such thing". Grice 
plays with "contextual" cancellation even, "The Loyalty  Examiner won't be exa
mining you" -- his example in WOW, op. cit.

----  This and R. B. Jones's document. I will have another look at the 
document, which  pleases me bunches -- I can _see_ Jones's enjoyment in building 

I  would think that on account of that asymmetry of 'negation' one would  
re-consider the five odd syllogisms Strawson thinks 'valid' but only on 
account  of the existential fallacy.

In my previous I provided some formalism for  the treatment of '~', and I 
would wonder if there is an effect on what  syllogisms are valid (regardless 
or not regardless) vis a vis this 'asymmetry'.  It seems to me that those 
involving "~" (E and O, in Aristotle) would be valid  regardless, and only A 
and I -- affirmative -- would ask for the deployment of  the 
existential-fallacy tweak? 


Negation is fascinating. I  don't know what exactly Grice, Aristotle, or 
Kripke, or Wittgenstein meant by  that. I would think that nature does abhor a 
vacuum. Imagine if all we knew  about the world (the totality of state of 
affairs, Wittgenstein says)  were:


A big fat noth!


Grice's subscript device and  square-bracket device are realistic along 
Aristotelian lines. As R. B. Jones  notes, it would be _otiose_ (or odd) to 
display a detailed taxonomy of things  (and define them, too -- picky as the 
Stagirite is on that front) to add, "But  all this may be vacuous".)

So, while ~Fa does not display its  _phylogenesis_, Grice notes that:

1. If  Fa is introduced at one stage of the conversation
2. And  ~Fa at a later stage, one may want to say that [Fa]  _is_
cancellably  presupposed.

This 'phylogenesis' is best shown in the subscript device.  If the ordinal 
attached to "F" is _greater_ than that attached to "~", there is  _no_ way 
to avoid the existential  fallacy:

~-3 F-2 a-1

---  shows that the order is, first posit "a" (hence the ordinal 1), then 
F, hence  the ordinal 2, and then ~, hence ordinarl 3. In that formula, ~ 
would _not_ have  maximal scope.

What fascinates me is that ~ differs from &, v, and  --> in various 
respects. It's an operator on a _phrastic_  direct:

V      the king of France is bald 

(Grice uses  this symbolism in "Aspects of Reason". The "radix" of "The 
King of France is  bald"). Should it include the ~? Is ~ part of the phrastic 
or part of the  neustic?

V    the king of France is not  bald

V  ~ (The King of France is bald)

--- I can make sense of that, but,  how do we distinguish it  from
~  V   The king of France is bald

--- Grice is well aware, and  this is his wording, that 'the crunch comes 
with negation' -- but he adds that a  conversational-implicature approach to 
the trickiest and darkest problems of  value gaps and presuppositions will 
_be_ available.

In a way, the  truth-functionality of ~ is at the core of this. But unlike 
the operators which  are dyadic (and connect, &, v and -->) "~" does _not_ 
connect. So what  kind of a functor is it? It's a monadic functor that 
_inverts_ the truth-value  of the 'atom'.

Gazdar notes that there are at least three other monadic  functors like  

p           ~p              Rp            Cp         Tp
1            0                1             0           1
0            1                1             0          0

Gazdar --  in his PhD for Reading -- notes that only "~" gives a 
conversational  contribution. "Tp" maintains the truth-value of the atom, Rp yields 
true  regardless, and Cp yields false regardless.


The issue of  'vacuity' I find fascinating. I am with R. B. Jones that 
'vacuous' and 'empty'  should be distinguished. In various and many ways -- and 
perhaps this would be a  good reminder that Carnap perhaps over-reacted to 
Heidegger's dictum, "Nothing  noths"!


J. L. Speranza  

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