[sci.lang] Fun with the semantics of paradox

sp299-ad@violet.berkeley.edu (Celso Alvarez) (01/28/89)

From an absolutely non-technical, lay perspective, here are some ideas about
the truth value of "The current king of France is bald".  My intuition is
that the logic paraphrasis of the sentence is

>> "There exists an x, such that x is the current king of France and x is
>> bald."  [which is false]
(Diana Smetters <diana@cis.ohio-state.edu> in article
<32698@tut.cis.ohio-state.edu>).

Compare:

	"The king of France [Louis XIV] was bald"

is true; but both

	"The current king of France is bald", and
	"The current king of France WAS (used to be) bald"

contain a linguistic presupposition (rather than an assumption)
that a king exists in France that is 'current'.  Since this is false,
the falsehood of the entire proposition lies on the fact of the non-
existence of a king in France, not on whether he is or used to be
bald (verb tense makes no difference).  (In fact, aren't we dealing with
several, embedded logical propositions?).  And since the statement

	"The current king of France" 

(uttered while pointing at a portrait or photograph) is false in itself,
why claim that the whole sentence is "meaningless"? (cf. Christopher A.
Welty (weltyc@cs.rpi.edu) in article <374@rpi.edu>):

CW>The point is that we, as humans, are able to form sentences like this and
CW>understand that there is no `truth value' associated with it - it's
CW>meaningless.

In fact, I have the feeling that people understand that the whole statement is
false (fallacious) precisely because there is no king in France, that is,
precisely due to
powerful mechanisms of linguistic pressuposition.  While the statement does
not *assert* that there is a current king of France, it *presupposes* it
linguistically, in very much the same way as the statement "The sun shines"
presupposes `The sun is' (for clarity, I hope, compare the meaningless of

	The current kangkt of France is bald ,

where the presupposed proposition `The kangkt is' cannot be true nor
false.  Or not?).

Celso Alvarez
sp299-ad@violet.berkeley.edu

lee@uhccux.uhcc.hawaii.edu (Greg Lee) (01/29/89)

From article <19625@agate.BERKELEY.EDU>, by sp299-ad@violet.berkeley.edu (Celso Alvarez):
" ...  (In fact, aren't we dealing with several, embedded
" logical propositions?).

Yes, and together with the fact that only a non-embedded clause
can be straightforwardly denied, I think that's all there is
to it.  If in a conversation the problem sentence is stated,
and one replies 'No', this would be taken as denying that the
guy is bald.  That's because 'is bald' is predicate of the
matrix sentence -- it has to do with the *syntactic* relation
between assertion and response.  If one wishes to deny that
there is a king of France, which is also part of what was
stated, a simple 'No' won't do.

Although we haven't discussed here the definiteness of the
description 'the king of France', the above is roughly along
the lines of Russell's analysis.

I see no warrant here for distinguishing between assertion and
presupposition if this means any more than matrix versus embedded.
I think the intuition that the sentence is meaningless in the
event there is no king of France is founded on a confusion
between a sentence's being false, on the one hand, and the
syntactic resources offered by natural language for conveying
that it is false, on the other.

Mind the syntax, and the semantics will take care of itself.

		Greg, lee@uhccux.uhcc.hawaii.edu

weltyc@cs.rpi.edu (Christopher A. Welty) (01/31/89)

In article <19625@agate.BERKELEY.EDU> sp299-ad@violet.berkeley.edu (Celso Alvarez) writes:
> [...] since the statement
>
>	"The current king of France" 
>
>(uttered while pointing at a portrait or photograph) is false in itself,
>why claim that the whole sentence is "meaningless"? 

You are adding here a context to the statement, implying that the more
formal meaning of the statement is `This is the current king of
France'.  But that, I would claim, is a COMPLETELY different statement
than just "The current king of France", because this statement is NOT
false.  It is based upon the presupposition (which, as you point out,
is the correct term) that there IS a current king of France.  But the
statement itself DOES NOT make this claim.  I claim that the
understanding of this statement requires a notion beyond that of truth
or falsehood.


Christopher Welty  ---  Asst. Director, RPI CS Labs
weltyc@cs.rpi.edu             ...!njin!nyser!weltyc

sp299-ad@violet.berkeley.edu (Celso Alvarez) (02/01/89)

In article <429@rpi.edu> weltyc@cs.rpi.edu (Christopher A. Welty) writes:
CAW> In article <19625@agate.BERKELEY.EDU> sp299-ad@violet.berkeley.edu
CAW> (Celso Alvarez) writes:

CA>  the statement "The current king of France" (uttered while pointing at a
CA>  portrait or photograph) is false in itself,

CAW> You are adding here a context to the statement, implying that the more
CAW> formal meaning of the statement is `This is the current king of
CAW> France'.  But that, I would claim, is a COMPLETELY different statement
CAW> than just "The current king of France", because this statement is NOT
CAW> false.

If for you "The current king of France" is NOT false (your emphasis), then
it is true.  Its meaning is `There is a king in France at present'.  But "The
current king of France is bald" must be false, because, while there happens
to be a king, there happens to be no bald person who is the king of France.

Without adding a (temporal and spatial) context, however, "The current king
of France" is true.  It just depends on when the statement was uttered.
My point is, the context affects the truth-value of "The current king of
France" as much as it affects that of "The current king of France is bald".

CAW> I claim that the understanding of this statement requires a notion
CAW> beyond that of truth or falsehood.

I don't see any basic difference between "The current king of France"
and "There is a king in France at present" in terms of propositional
content.  The problem is that truth/falsehood is linguistically built in
presuppositions.  The typical example of linguistic presupposition (profusely
employed by lawyers and other experts of interrogation) runs along the
lines of "Did John stop drinking heavily?"; the fact that John didn't use
to drink heavily cannot be denied just with a simple "yes".

I prefer to see the truth-value of utterances in terms of native (e.g.
speakers') categories.  If the categories employed in philosophy of
language or logic contradict those of natural conversationists, speech
act theory is futile.  While most people probably recognize the
difference in the falsehood of "The current king..." and that of "The
Earth is square", if presented with the statement about the king, people
would probably say 'It's false', 'It's absurd' or 'It makes no sense'.
If forced to choose between true-false, some might say 'It's false,
because it makes no sense'.  But I doubt anyone would reason 'It's
TRUE, because it makes no sense'.

And how about the logicity of these non-sequitors (I'll translate)?:
	It was Thursday, yet it was raining ("Era jueves, y sin embargo llovia")
	Although Camoes was Portuguese, he was one-eyed ("Camoes, aunque era
			portugues, era tuerto").
or...
	It's half overcrowded in here.
	I'm mildly/fairly exhausted.
	The prisoner was sort of riddled with bullets.

Celso Alvarez
sp299-ad@violet.berkeley.edu

laverman@prismab.prl.philips.nl (Bert Laverman) (02/01/89)

In article <429@rpi.edu> weltyc@cs.rpi.edu (Christopher A. Welty) writes:
  (As well as many others)
>>
>>	"The current king of France" 
>>
>> [.. many statements about him and those statements deleted ..]

This morning in the newspaper I found an article telling that the current
claimer of the French Throne died in a skiing accident. Fate let the
(supposed) descendant of `guillotined' Louis meet a steel cable at
appropriate height.
So anyway, whatever statement about the current King of France will
alas be invalid. :-/
BTW I saw his photo: He had enough hair!


# Disclaimer:
# I don't post
# If I do, certainly not on behalf of my employer

lee@uhccux.uhcc.hawaii.edu (Greg Lee) (02/04/89)

From article <505@aipna.ed.ac.uk>, by rjc@aipna.ed.ac.uk (Richard Caley):
" In article <3038@uhccux.uhcc.hawaii.edu> lee@uhccux.uhcc.hawaii.edu (Greg Lee) writes:
" >From article <479@aipna.ed.ac.uk>, by rjc@aipna.ed.ac.uk (Richard Caley):
" >" ...
" >" 	"The current king of France is bald."
" >Russell said it was
" >false.  I agree with Russell.
" 
" Obviously this is a matter of opinion, but I can't agree it is false
" since I would not say that
" 
" 	"No he isn't"
" 
" Is the natural responce.

I agree that that is not the natural response.  Neither is "No, there
isn't." This has to do with syntactic constraints between assertion and
reply in conversations -- to a first rough approximation, a reply
must correspond to the main clause in what it is a reply to.  If we thus
distinguish between the sentence *being* false and the circumstances
that determine whether we can give a *reply* to the effect that it is
false, we can avoid resorting to a peculiar third truth value (in this
specific case, anyway).

So, I say, the sentence means the same as "There is a (unique) current
king of France, and he is bald," but it has a different structure and so
is not syntactically equivalent in that the two sentences admit of
different replies.

The description of such examples in terms of presuppositions and third
truth values is a pre-theoretical taxonomy.  It doesn't tell us what is
really going on, but just supplies a terminology for enumerating the
facts.

		Greg, lee@uhccux.uhcc.hawaii.edu

rjc@aipna.ed.ac.uk (Richard Caley) (02/09/89)

In article <3201@uhccux.uhcc.hawaii.edu> lee@uhccux.uhcc.hawaii.edu (Greg Lee) writes:
>From article <505@aipna.ed.ac.uk>, by rjc@aipna.ed.ac.uk (Richard Caley):

>" "The current king of France is bald."		(1)

>" I would not say that

>" 	"No he isn't"					(2)

>" Is the natural responce.

>I agree that that is not the natural response.  Neither is "No, there
>isn't." This has to do with syntactic constraints between assertion and
>reply in conversations -- to a first rough approximation, a reply
>must correspond to the main clause in what it is a reply to.

But there _is_ no subordinate clause, unless we introduce one as a
crowbar to get the facts to fit the theory. A perfectly respectable
responce ( not a reply, however ) would be

	"but there _is_ no king of France"		(3)

I would never say 

	"No, there isn't"				(4)

would even be a candidate, since (1) makes no _assertion_ of existence,
it just presumes it. 

>If we thus
>distinguish between the sentence *being* false and the circumstances
>that determine whether we can give a *reply* to the effect that it is
>false, we can avoid resorting to a peculiar third truth value (in this
>specific case, anyway).

Ok, I don't like third truth values either, however I don't think that
the way to go is to add more and more complexity to the 'meaning' we
ascribe to an utterance. I don't think that (1) has a meaning in
isolation any more than

	" This is black "				(5)

does. Without knowing what I am pointing at you can neither agree nor
disagree with (5), you can only decide that I am foolish for saying it.

>So, I say, [ (1) ] means the same as "There is a (unique) current
>king of France, and he is bald," but it has a different structure and so
>is not syntactically equivalent in that the two sentences admit of
>different replies.

Here is a shot at trying to change your mind. ( not original by any
means ). If (1) is false ( as it must be if it has the meaning which you
give it ) then, assuming we do not throw out the law of the excluded
middle, its negation must be true - ie either

	" The current king of France is not bald "	(6)

or, more conservativly,

	" It is not true that the current king of 	(7)
	  France is bald "

Certainly I would not assert (6). If (7) is true but (6) isn't then we
must explain why they are not logically equivalent - I think most people
would say that they were. On your reading, (6) means

	" There is a unique king of France and he is	(6')
	  not bald "

whereas (7) means

	" Anyone who is king of France is either	(7')
	  not bald or shares the throne "

( I think I have done my rewriting correctly, no doubt someone will
correct me if not ).

Now, I can't give a cast iron proof that (7') is an incorrect reading,
certainly it seems rather farfetched to me.

>The description of such examples in terms of presuppositions and third
>truth values is a pre-theoretical taxonomy.  It doesn't tell us what is
>really going on, but just supplies a terminology for enumerating the
>facts.

Why is this so for presuppositions and third truth values and not for
syntactic constraints on replies?

Certainly 3-valued logics can be defined just as formally as syntactic
constraints, as can rules for deriving presuposition sets from sentences.

>		Greg, lee@uhccux.uhcc.hawaii.edu

-- 
	rjc@uk.ac.ed.aipna	AKA	rjc%uk.ac.ed.aipna@nss.cs.ucl.ac.uk

	    "Give me a beer and money sandwich: hold the bread"
			- Waldo 'DR' Dobbs

lee@uhccux.uhcc.hawaii.edu (Greg Lee) (02/11/89)

From article <529@aipna.ed.ac.uk>, by rjc@aipna.ed.ac.uk (Richard Caley):
\>" "The current king of France is bald."		(1)
\
\>reply in conversations -- to a first rough approximation, a reply
\>must correspond to the main clause in what it is a reply to.
\
\But there _is_ no subordinate clause, unless we introduce one as a
\crowbar to get the facts to fit the theory.

Did I say there was?  (I might resort to a crowbar, but I haven't
yet.)

\...
\Here is a shot at trying to change your mind. ( not original by any
\means ). If (1) is false ( as it must be if it has the meaning which you
\give it ) then, assuming we do not throw out the law of the excluded
\middle, its negation must be true - ie either

Correct.  Its logical negation must be true.  Neither (6) nor
(7) below is the logical negation of (1), however.  Your (7'),
or something along those lines, is the logical negation of
(1).

\	" The current king of France is not bald "	(6)
\
\	" It is not true that the current king of 	(7)
\	  France is bald "
\
\Certainly I would not assert (6). If (7) is true but (6) isn't then we
\must explain why they are not logically equivalent - I think most people
\would say that they were.

Yes, I'd say that, too.

\ On your reading, (6) means
\
\	" There is a unique king of France and he is	(6')
\	  not bald "

Yes.  The negative in the main clause of (6) goes with the corresponding
clause in (6').

\whereas (7) means
\
\	" Anyone who is king of France is either	(7')
\	  not bald or shares the throne "

No, of course it doesn't.  You've made a theory here that putting 'it is
not true that' in front of a sentence (of English) gives its logical
negation, then attributed that theory to me, apparently.  Straw man.

\>The description of such examples in terms of presuppositions and third
\>truth values is a pre-theoretical taxonomy.  It doesn't tell us what is
\>really going on, but just supplies a terminology for enumerating the
\>facts.
\
\Why is this so for presuppositions and third truth values and not for
\syntactic constraints on replies?

Syntactic constraints on replies are there anyhow -- that's just a
fact.  Describing one set of facts in terms of others -- what I
proposed -- is an explanation.  Devising a terminology for some
facts in a way that does not do this -- what you propose -- is
not an explanation.  That's the difference.

\Certainly 3-valued logics can be defined just as formally as syntactic
\constraints, as can rules for deriving presuposition sets from sentences.

I don't see what formalization has to with it.  You don't think that
bad theories are incapable of being formalized, do you?

		Greg, lee@uhccux.uhcc.hawaii.edu