[Corpora-List] ad-hoc generalization and meaning

[Rob Freeman]

Yorick,

I include the quibbling at the bottom of this message just to clarify my use
of the terms "incompleteness" and "decidability" in these last two threads.
Should there be any doubt, I am very happy to distinguish the two.

To others:

The issue of incompleteness is indeed very technical, but it is also very
important, and central to the point I've been trying to make.

For those who have trouble understanding why it should matter (or what it
is!) I suggest you just look at the examples I have given in recent
messages. By this I mean the generalizations which I have pointed out can be
said to be true _and_ not true of word associations in corpora*. What is
important about these is they express generalizations which can be
considered to be true _and_ not true. Think of the fact they can be said to
be true _and_ not true as "incompleteness", and that should be enough.

My assertion is that the fact you can find generalizations which are both
true _and_ not true in this way among word associations in corpora, may tell
us something interesting, fundamental, about natural language. Indeed, that
it may be the single important fact we have been missing which will let us
model the detail of collocation, phraseology, and even semantics (because it
lets us select different meanings for text, and govern different
combinations of text, by searching for these patterns ad-hoc.)

*(The observation that "supported" = "accompanied" but also "supported" !=
"accompanied" a couple of messages back was one. The observation in the last
thread that "done" and "made" are in the same class in the context of
"study": "do/make a study", but they are not the same class in the context
of "attempt", was another.)

On 9/14/07, Yorick Wilks <Yorick at dcs.shef.ac.uk> wrote:
>
> RobNone of this matters much for most of us who read this list, but I
> think your reference from 1950 is not quite right, or rather its a
> non-standard way of putting it:
> A Remark Concerning Decidability of Complete Theories, Antoni Janiczak,
> The Journal of Symbolic Logic, Vol. 15, No. 4 (Dec., 1950), pp. 277-279:
>
> "A formalized theory is called complete if for each sentence expressible
> in this theory either the sentence itself or its negation is provable."
>
> Completeness normally (see e.g. Wikipedia) means that for every sentence S
> expressible in a language either S or ~S is derivable from the associated
> axioms, and that all sentences so derived are true (i.e. theorems). That
> is not the same at all as the system/set/language being decidable--i.e.
> that for any S there is an effective procedure for determining whether or
> not it is derivable. "provable" in that quote fudges this issue. For some
> reason I dont follow you seem to want to conflate completeness and
> decidabilty...
>

I don't want to conflate completeness and decidability. You did this in your
first message to the "completeness" thread when you gave your paper on
decidability as a reference for the issues I raised about incompleteness:

YW> Well, the topic, of completeness/decidability and grammars, has been
thought about and long, long ago; if modesty didnt forbid I would
mention"Decidability
and Natural Language" in Mind, 1971, easily downloadable from the web. A
crappy paper by Mind standards, but in the target zone.

I was happy to follow you in this because the issues are related. I thought
it best to discuss the one most familiar to linguists.

Later you wanted to separate them again:

YW>just for the record (because John cares about these things), I didnt mean
to equate decidability to completeness, only to say that the second is a
necessary condition for the first for a calculus (but not vice versa).

To my knowledge I haven't mentioned decidability since then, and have
continued to talk about incompleteness only.

I'm not quite sure why you are introducing decidability into the
conversation again. Particularly when I deliberately excluded Janiczak's
immediately subsequent comments on decidability as irrelevant.

If you find Janiczak's definition of completeness a "non-standard way of
putting it" that is not to be helped. Personally I can't see any substantial
difference between your statement of completeness and Janiczak's.

Best,

Rob
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