Re: Universal grammar

In article <1161400222.396768.4770@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>, "Rob
Freeman" <groups@xxxxxxxxxxxxxxxxxxx> wrote:

It is another story with pinning down the human cognition, and find
a logical (= mathematical) representation of that.

You make such a close association between formal and human language on
the one hand, and logic and mathematics on the other, Hans:

formal language <-> human language
logic <-> mathematics

It may be impossible for you to see we can make other associations:

formal language <-> logic
human language (and cognition) <-> mathematics

Don't you see that solves our problems with language description, and
your mysterious cognitive "factor X" of mathematics?

You have the "<->" associations above wrong. :-)

It should be:

  Human natural language <-> human written mathematics.
because both involve human cognition.

Working pure math reasons about objects like integers and real numbers and
so on. In working math, one uses usual human language, and so called
"naive set theory".

Then there is a formal description of that, called metamathematics. The
most common approach is to view object mathematics as strings of symbols.
This way one can develop axiomatic theories for natural numbers and so
called axiomatic set theory. It is believed that this gives a sufficient
logical foundation for most (but not all) working math.

--
Hans Aberg
.

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