Re: Universal grammar

Herman Rubin wrote:
Rob Freeman <groups@xxxxxxxxxxxxxxxxxxx> wrote:

The question is does any grammar say everything?

No...

Motivated by the analogy with natural language, I would like to get
down below predicate calculus and think about how it is defined in
terms of automata.

... A simple automaton ... is a device
which operates on a fixed set of rules to produce results. ...

To cut a long story short. Try to think of automata as a sequence of
symbols defining a set of rules, rather than as a set of rules
operating on symbols.

Natural language appears to be a sequence of symbols of this kind. The
same string of symbols can specify many grammars (just as a set of
examples can be considered to specify many "rules" of use for the
German definite article.)

Perhaps the different "results" of mathematics governed by each
different "particular set of precise axioms and rules" can be projected
out of a single string in this way. Each operation in a proof selecting
(overloading?) the "rule" which is most appropriate to it, at the time
the operation is performed.

-Rob

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