[hist-analytic] Vacuity

Roger Bishop Jones rbj at rbjones.com
Wed Jun 24 15:08:55 EDT 2009


On Saturday 13 June 2009 18:47:06 Jlsperanza at aol.com wrote:

>* 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.

But why should it be so?

If "the King of France is bald" is held to be false because he doesn't
exist then "Its not true that the King of France is bald" would be true
But "The King of France is not bald" looks more like complementing
the predicate than negating the assertion, and also implicates
the existence of the King of France. (I'm not saying this follows
from Russell's theory of descriptions, since I never do follow it)

You may think this a stretch, and I agree, for I like neither
alternative.  More to the point, neither satisfies my intuitions
about normal usage..

>(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.

Rings wrong to me.  I might say "Its not true, there is no such thing"
just to avoid asserting the negation, but again a definite negation
seems to me better than complementing the predicate.

>----  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 it!
>
>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 system (and in others of course) it isn't directly because
of ``the existential fallacy'' that one admits these extra
syllogisms, but of course, because of some alteration to the
semantics provoked by it.  In particular, because the nice
way to fix the semantics so that Aristotle's four examples
of "the fallacy" are true (i.e. not fallacious) is
to banish empty terms, which also happens to make sense
in Aristotle.  (Strawson mentions another rather bizzarre
solution, but I know no reason why it should be taken seriously).
If you put in that change to the semantics, then you get
not only Aristotle's four but also the other five (which
I first saw in Strawson but presumably were discovered
long before him).

To keep the four without acquiring the five would
require some compromise and I have no idea what that
might be, since I have not spotted any material
difference between them, though one must wonder
why some were included and others not.  Did he
not spot the others, or did he not think them
valid?  If the latter we might be inspired to look
harder for a way to exclude them.

>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?

The existential fallacy consists in inferring from a universal
to an existential, so the syllogisms involving it all have
A or E premises and an I or O conclusion.  This applies both to
Aristotle's and to the later ones.


Let me say a bit more about descriptions and truth values.

First, it seems to me that it may not often enough be
said that discussions about ordinary language of this
kind may not have definite answers because there may
be too much unsystematic diversity of usage, so that
in the end you can compare alternatives for how it
might be systematically be done, but not affirm that
language works uniformly in any way at all.

The question simply about whether there is a truth
value gap seems to me to be one, various issues
about how descriptions work are others.

So far as descriptions are concerned, Russell's is
I regret to say, the worst option I am aware of,
so I shall say little more about it.

The two most serious alternatives (if we were able
to chose) would be as follows (one with and one
without truth value gaps).

First we allow that the truth value of some
sentences is really neither true nor false,
lets call it "U" for undefined.
Note that saying the truth value is "U" is
not the same as making a statement of ignorance.
Its not that we don't know whether its true or false,
we might know that it is neither.

We can then also use U for the denotation of
descriptions which are not satisfied and make
predication "strict", i.e. if you put in U you
get U out.
Then you have to be more subtle with the logical
connectives, since they are not completely strict
(U in U out) and there are many alternative three
valued truth tables, but the most plausible are:

A B -A (A \/ B) (A /\ B)
T T  F    T        T 
T F  F    T        F
T U  F    T        U
F T  T    T        F
F F  T    F        F
F U  T    U        F
U T  T    T        U
U F  T    U        F
U U  T    U        U

And analogous treatment of quantifiers.
Anyway this is still pretty awful and a two
valued logic is much nicer.

So now we assume no truth value gaps and no
non-denoting terms.
The way it works is that we use ignorance instead
of undefinedness, ignorance turns out quite convenient.
We use term operators for descriptions, i.e.
Hilbert's choice function (for definite desciptions),
and someone else's iota for indefinite descriptions.

These work as follows.
All you know is the two axioms.

There exists an x s.t. D(x) => D(An x s.t. D(x))

and

There exists a unique x s.t. D(x) => D(The x s.t. D(x))
 
i.e. if there is something which satisifies D
then the reference "An x s.t. D(x)" satisfies D
and if there is a unique something which satisifies D
then the reference "The x s.t. D(x)" satisfies D

Now if D is not satisfied or not uniquely satisfied
then the relevant desriptions don't yield objects
satisfying the descriptions.  They still point to
something, but we don't know what.
So ignorance kicks in and influences how we
reason about failing descriptions.

This "The king of France" is a failing definite
description, which in this scheme doesn't mean it
fails to refer.  It means it fails to refer to
something satisfying the description.
So what is the truth value of

   "The King of France is Bald"

Well we have no way of telling, because the failing
reference might refer to anything, which might or
might not be bald.

We do know that the sentence has a truth value
and therefore that it either is or is not true,
so you might be able to say that:

   "Either the King of France is Bald or he isn't."

is true, but I wouldn't risk it myself since
the reference might be to a fit of pique, and
I would plump for:

  "Either it is true that the king of France is
  bald or it is false."

which is true under this scheme.

(or simpler "The King of France is Bald" is either
true or false, which I already said).

This as far as I am aware is the only scheme
which retains the laws of logic intact.
Russell's theory of descriptions is logically
disasterous unless you expand out the incomplete
symbol before you start to reason with it.

Roger Jones




More information about the hist-analytic mailing list