Re: The Asymmetry of Identity

Jan Burse wrote:
John Jones schrieb:
Mitch Harris wrote:
On Oct 31, 10:35 pm, John Jones <jonescard...@xxxxxxx> wrote:
Dan Christensen wrote:
Now, I am confused. Again, you seem to be making things unnecessarily
complicated.
Yes, I am. I was indicating that syntax is given its meaning by a
commentary that falls outside mathematics. Assuming, which I don't, that
syrastiline syntax in mathematics is perceived as essentially divorced
from meaning.

What does 'syrastiline' mean (outside the current context)?

Mitch

Crystalline I meant to say. The idea, myth even, of syntax being divorced from meaning in a pure realm of its own.

You can also view it as a marriage of two mathematical
abstract entities which are not found immediately
in natural language and thus there was never
a divorce of such concepts.

Look see, there are models of natural language processing
which consists of a multi-step pipeline. Here is my
favorite pipeline:

Step 1: Input: Sentence, Dictionary, Grammar
Output: Parse Tree
Process: Chart Parser
Step 2: Input: Parse Tree, Thesaurus
Output: Intralingua
Process: Substitution
Step 3: Input: Intralingua
Output: Normal Form
Process: Logical Inference

Mathematically Parse Tree, Intralingua and Normal Form
are all syntax. Mathematically the processes Chart Parser,
Substitution and Logical Inference can all be viewed
as meanings.

The better word than meaning would be semantics. How
can semantics define a process? Easy, semantics can
be viewed as defining a notion of thruth, thus we can
relate input/output via truth, and thus we have
processes.

The details are here:
- Chart Parser truth is that of being the parse of a
string of tokens. The dictionary and grammar serves as parsing
postulates. (Examples of this meaning interpretation of
parsing can be found plenty, see for example DCG)

- Substitution truth is that of being the intralingua
of a parse tree. The thesaurus serves as substitution
postulates. (Examples of this meaning interpretation
of parsing can be found as well plenty, see for example
lambda calculus)

- Logical Inference truth is that of being the normal
form of an intralingua. (Example of this meaning
interpretation of logical inference can be found as
well plenty, see for example computer algebra)

Now how can we counter your claim of mathematical syntax/
semantic doing harm to natural language? In two ways:

- First of all: You are true, the immediate relationship
between natural language and mathematical syntax/semantic
is a myth. Nobody ever claims that there is any direct
relationship.

The example pipeline above shows that mathematical syntax/
semantic might be the briks which is used to model
natural language processing steps. But the pipeline
also shows that there is not a trivial relationship
between natural language and any syntax/semantic.

On the contrary the relationship is very multi-layer
and syntax/semantics is needed in many flavors. On
request I can give you real world examples that show
that it is needed, assuming a certain target normal form.

- Second: Any model we create is just a model. We cannot
open the brain of someone and look for a normal form
or what ever. Even if we talk to someone he will answer
in natural language, so all we have is the surface.

Any model that goes below the surface, is created
by us, because we have some purpose in mind. It cannot
directly be validated. And also it might have some
rival pipeline models, which might eventually also
satisfy our purpose.

Even if we venture into the validation of such a model
and its parts we will face our limmited resources. How
long will it take to build the needed dictionary, grammar,
thesaurus? How will we vaidate its performances? If we
know the How Long and How, the next question will be the Who?
Who will do the Job?

But the Job will never be done by attacking innocent
mathematics notions like syntax/semantics. Instead of using
these notions in creating explanations of phaenomena.

That is what the purpose of mathematical logic is. To give
one a set of recurring basic tools. Which will hopefully enable
one to sally forth and dabble into more complex problems,
which are typically interdisciplinary.

Bye


Here's the deal. There are two things in this world - familiar objects and names. There are no in-betweeny lands like 'abstractions', 'beneath the surface's. These are names, names for 'I have not understood'.

Mathematical syntax is about familiar objects behaviours. Logic is about familiar object behaviours. There's nothing else on offer in logic or maths, nor is it possible, analytically, and contingently, that there could be anything else on offer. That is why I feel comfortable in writing what I write.

To say that 'there are things we don't understand' is to utter a contradiction.

Admittedly, we can throw together a system that we cannot make sense of. But our 'failure' to make sense of it is because what we have built is senseless, and not because of a failure, or a consequence of our 'limited' faculties.
.

Relevant Pages

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