Re: Universal grammar

Rob Freeman wrote:
Tak To wrote:

Rob Freeman wrote:

Tak To wrote:

(and I am personally convinced that is for the same reason we
have not been able to find universals of language or meaning.)

And the reason is?

Because I think there are many distributions which cannot be reduced to
logic, Tak.

I am not sure I understand what "distribution" and "reduced to
logic" means in the above statement.

By "distribution" I mean any pattern, like a string. By "reduced to
logic" I mean the string can be produced by a set of rules.

If you mean that some (infinitely long) strings cannot be
produced by a formalism with finite axioms, then it is true.
There are aleph-1 many of the former and only aleph-0 many of
the strings that can be produced by the latter, QED.

----- -----

In any case, I think "a universal representation of meaning"
exist, which is the collectively state of neurons in one's brain.
It is just that it is not that convenient to "use".

Well, that is true in a way. The point is it now seems what we
have in our heads is not a representation in the sense we have
been looking for.

Obviously this begs for the definition of "representation of
meaning". I submit that the only feasible definition is a
procedural one, sort of like a Turing test -- namely that if
you have a representation of the meaning of X, you can answer
questions about X and your answer would be the same as that of
some reference. For example, if you have a representation of
the meaning of "bird", you would be able to answer questions
such as "Can birds fly?", "Is a bat a bird?", or "Is a penguin
a bird?", correctly.

In this context, I take "representation of meaning" to be the
same as "representation of knowledge"; and in this sense,
the state of the brain itself is a representation of the
knowledge that it contains.

I understand many people tend to think of representation of
meaning as a single point in an "epistemological space" of
sorts. Well, one of the things that the AI/CogSci field has
found out rather quickly was that this notion of meaning was
an intractable one.

It is a "representation" which can represent contradictory
"truths", and so is illogical (though it can be
modeled by incompressible strings, like natural language.)

Well, "meaning" is not that same as "truth". I know the
meaning of the statement "1 = 2" and understand it to be
untrue.

By "universal" people have traditionally meant something which
is both logical and complete. That is what is not possible.

Not in the context of "universal grammar"(*), in which case it
simply means "common to all languages".

(*) also the context of the original post.

I don't see how this is related to Goedel's Theorem.

Think of Goedel's Theorem as a proof some strings are
incompressible. If some strings are incompressible, it will not
be possible to produce them by rules, which means they will not
have a (single, complete) logical description.

If you mean "cannot be described by a system with a finite
number of axioms", then yes.

Without Goedel's proof you would not be able to
have contradictory "truths" in a single representation.

Without Goedel's theorm there are still a number of equivalent
theorems in mathematical logic -- but it is neither here nor
there. Again, human knowledge is not the same as "truth".
The entire body of human knowledge is generated by a finite
number of brains each with a finite number of neurons(*).

(*) That is, if you buy into Church's Thesis instead of
Penrose s idea of "Quantum Computing". If you think
otherwise than there is really very little left for
discussion. :-(

would be logical, and Chomsky, you, and I, would all be
talking to our computers already.

That is of an entirely different issues -- that of engineering
practicality.

I have the impression that you are conflating several different
issues here.

Tak
--
----------------------------------------------------------------+-----
Tak To takto@xxxxxxxxxxxxxx
--------------------------------------------------------------------^^
[taode takto ~{LU5B~}] NB: trim the xx to get my real email addr

.

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