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Re: splitting PA into multiple selma'o
>If you turned a grammarian loose on Lojban they'd come up with a
>different grammar from the official one, because Lojban has fiddled
>the initial data. The current official grammar overgenerates.
And natlang "official grammars" undergenerate if they follow Jacques Guy's
principle and exclude center-embedding, or overgenerate if they follow
Chomsky's and include fully-recursive center-embedding.
Lojban's grammar is no more overgenerating than any Chomskyan grammar that
doesn't explicitly rule out center-embeddings that no one finds understandable.
Yet, some people consider that Jabberwocky is fully grammatical, even though
it is nonsense, so that a natlang grammar may not exist that isn't in some
There ARE strings of PA that are ungramamtical, but surprsingly small
percentage if you venture off into the realmsof MEX-space. And part of
PA and its grammar is designed to include the needs of MEX. Mathematics allows
all sorts of weirdness in the name of precision and unambiguity.
WhatIS the case is that there exists grammatical Lojban text using PA that
has no defined and agreed-upon semantics - that does NOT mean that it is
utter gobbledygook (unless, like me, you find moth mathematical expression
to be utter gobbledygook %^).