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'Nor' in the World's Languages

From:Yahya Abdal-Aziz <yahya@...>
Date:Sunday, August 6, 2006, 6:36
Hi all,

I'm forwarding a (rather long) reply I recently made to Maarten van Wijk about a
question he raised on the Linguist list. My main question to you all is:

In your conlangs, what kinds of logical connectives have you implemented?
Examples would be:
1. A and B - AND
2. A or B or both (A and B) - the "inclusive or", OR
3. A or B but not both (A and B) - the "exclusive or", XOR
4. If A, then B - "A implies B"
5. A only if B - "A is implied by B"
6. A if and only if B  - "A and  B imply each other", "A and  B are equivalent"
7. not A - ie the statement A is not true - cf Malay "tidak" for logical negation, below
8. M is not a N - ie the thing M is not one of the things N - cf Malay "bukan"
for categorical negation, below
9. neither A nor B - ie not A and not B

A secondary question is, if you wish to comment, how strictly do they match the
logician's view of those connectives?


-----Original Message-----
From: Yahya Abdal-Aziz
Sent: Monday 10 July 2006 22:41 pm
To: Maarten van Wijk
Subject: 'Nor' in the World's Languages

Hi Maarten,

On the Linguist list, you recently wrote:
For my dissertation on the emergence of logical connectives in natural language
I'm trying to debunk an argument by Gazdar and Pullum (1976) on what they call
non-confessionality, which is supposed to be principle that rules out nand, but
also nor as a natural language truth-functional connective.

The basic argument runs as follows:

There is psycholinguistic evidence that negations are hard to compute for human
minds, and computation time increases exponentially for each extra negative
element added (Hoosain 1973; Clark 1974, both cited by Gazdar and Pullum 1976).
Therefore there can be no connective C that causes the truth value of a
proposition conjoined by C to be true when both of the arguments of C are false.
This is supposed to explain why NAND, IFF and IF are not natural language
connectives. After all, A if B is true if neither A nor B is true.

However, NOR would be non-confessional as well, and still it is found in many
natural languages.

Gazdar and Pullum acknowledge the existence of neither...nor in modern English,
but they accommodate this by proposing that neither...nor is derived
syntactically from either...or by incorporation of NEG. Such syntactic claims
have been made. (I don't have the citations handy).

This seems like a bit of an argument out of convenience to me. I can see that
English nor certainly gives the impression of being composed out of not and or.
I'm wondering whether this is true in other languages of the world as well,

Does anyone know of any language in which the word for NOR doesn't look at all
like the particle for negation? And what is your general take on the
'incorporation of negation' argument? How seriously should I take this
generativistic argument? I myself work in an evolutionary linguistics framework.

I don't know whether the following will help you or

_1)  Malay certainly uses a standard "logical" negation
"tidak" for a "logical" /neither ... nor .../ construction.

Malay uses a phrase : "juga tidak", literally "also not"
eg "I neither knew nor wanted that" would be
"sahaya tidak tahu juga tidak mahu itu", literally
"I not know also not want that".

This form, using "juga", differentiates it from an implicit
conditional structure, such as the following proverb:
eg "[If you] don't know, [you] don't want" would be
"tidak tahu, tidak mahu", literally
"not know, not want".

_2) There is also a separate word in Malay for "categorical"
negation: "bukan", which you would need to use for a
"categorical"  /neither ... nor .../ construction.

eg "Neither fish nor fowl" would be
"Bukan ikan juga bukan ayam [pula]", literally
"Not-fish also not-fowl [again/likewise/furthermore]".

This shows that a language with two kinds of negation
may require or allow two kinds of /neither ... nor .../. ;-)

_3)  This little logical digression is not directly apropos your
question.  But I wonder whether we may be hasty in so readily
equating the logical operations of natural language with those
of formal logic, binary mathematics or computers.  I invite you
to consider my arguments below, and make of them what you
will ...

It's a truism that language is not logic.  So it should be
no surprise that some natural language constructions, which
use words we have adopted as models of logical operations,
such as "if", "not" and "and", are not strictly logical in using
those very same words.  And any attempt in everyday speech
to use those words very precisely is usually derided as
pedantry, or just "being smart".  You know all this, I'm sure!

But this is why I take issue with the analysis we so often
make of the logic of "IF".  In a binary-valued logic calculus,
we demand that each operation on propositions produce a
binary-valued result.  (This I call the Aristotelian error.)
Therefore we say something like:
"Well, if neither A nor B is true, we still need a binary value
for the proposition 'if A then B'.  Which value can we assign

And so we decide, that for consistency in our binary world,
we will *choose* to say that 'if A then B' is true in that case.

But this is not what happens in the real world of everyday
language use!  We say instead "We don't know".  (Always
assuming we don't go round making rash assumptions ...)
At least, if we are being reasonable, skeptical empiricists,
we do.  This particular case simply doesn't add any evidence
to the proposition "if A then B".  I can diagram this with
truth tables:

______Case	| 1 2 3 4
________A	| T T F F
________B	| T F T F
___~(A&~B)	| T F T T
_____(A=>B)	| T F T T
__if A then B	| T F ? ?

The logical operator => (implies) is usually *defined* to be
the equivalent of not both A and not B.  This appears as row
three of the table, ~(A&~B).  Its truth value is well defined
in each of the four cases 1, 2, 3 and 4.  So the truth values
of => are also all well defined; its truth table is full and it is
a well defined operator.

But, taking a commonsense evidentiary approach, only cases
1 and 2 provide us with evidence for the truth or falsity of
'if A then B'.  Case 1 provides positive evidence; case 2
provides negative evidence.  But any case, such as 3 or 4, in
which the antecedent A is false gives us *no* evidence for
the truth of the implication when the antecedent is true.

Two farmers are looking at a pig.

Brown: "Look at my duck!"
Green: "That's no duck, it's a pig!"
Brown: "It flew around the barnyard this morning.  If it
flies, it's a duck.  You wouldn't call it a chicken, would
Green: "Flew, you said?  It's not flying now, is it?  Yes,
it might be a chicken at that.  I've never seen it fly.  Until
I see it fly, you can't tell me it's a duck."

You don't even need a *good* implication to see that the
absence of evidence does not support the implication.
Mind you, I'm not saying that absence of evidence is
evidence of absence ...


Good luck with your dissertation!  If you ever do find a
convincing reason why we don't have NAND in natural
English, I'd love to know!


      Yahya Abdal-Aziz
      Melbourne PC User Group
      Convener, Graphics Interest Group
      Convener, Music Interest Group

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Yahya Abdal-Aziz <yahya@...>
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