Meta-Goedeling...

From: Alex Ferguson <abf_at_cs.ucc.ie>
Date: Sun, 2 Nov 2003 02:07:37 +0000

Julian wanted to keep the other thread on matters Gloranthan (though 'back to' doesn't really apply), so I've snipped the bits where we get yet more tangential, to here...):

> It's a bit like mathematics in this sense, except that the bases are
> uncomfortably vague (from the hard science POV).
                                                                                

That is itself a rather uncomfortably vague statement; maths doesn't have 'untestable tenets', it has (on a branch-by-branch, and indeed flavour-by-flavour) axioms. If one removes them, one doesn't get something 'anti-mathematical', one just gets a different type of mathematics. (Whether said maths describes anything in the RW is another question entirely, of course. Keep watching this space (as it were) for the parallel postulate...)

> To get to the superficial point of the objections, too, Linguistics
> can provide no testable and therefore "scientific" model, because
> language and meta-language (which is used to discuss language)
> share many common features, which are impossible to analyse
> because of their shared inherently linguistic nature.

Sorry, I don't see how that applies at all. Linguistics positively _abounds_ with testability, but the existence of an ur-language (in the Proto-World sense) is beyond the scope of same (according to most reckoning, at least). So if you want to be a scientific linguistic, you leave that out of your model; nothing else much goes wrong, AFAIK. The problems of expressing (as opposed to testing) hypotheses are no different in linguistics merely because of the subject matter, however. (Which isn't to say they don't exist, but they have nothing to do with the meta-quality you're citing.)

(And to another objection to the above:)

> This is incompatible with the definition of what a meta-language is,
> I'm afraid. "Language discussing language". It implies an objectivation
> of the target language(s), where it or they are deprived of the ability
> to actually communicate, and are instead studied for their physical
> qualities. the core tools used remain linguistic though, which engenders
> a certain number of unavoidable paradoxes. However :

Unless you're using meta-language in some narrower sense than I'm familiar with (in which case, I await enlightenment (though somewhat in a more-in-hope state)), I see no such incompatibility. One can describe BNF in BNF, or French in French, without any major calamities (or at least beyond those of describing BNF in some other formal language, or French in Basque, or any other alternative that springs to mind).                                                                                 

[Goedel's Theorem]                                                                                 

> A theorem I myself fail to accept.

Assuming you don't mean that you flunked that course (if so, commiserations), or that your have a refutation/counter-example (in which case, congratulations!), I suspect what we have here is an applicability objection (or misunderstanding).

The incompleteness theorem proves (note, proves, hence the 'theorem' part; this isn't a matter of preference or opinion) that in a given formal system, there are certain 'true' things you won't be able to prove inside that system. Now, where things get wooly is where people want to extrapolate what this means in practice, about say, computational systems, or people (as this requires further assumptions about the 'things' and the 'systems' being described). (e.g., that both are limited in some sense, or that one is more limited than the other, typically.) Whether it says anything about (a given) language depends on whether you think you could write down a complete set of rules for a/the language, or believe that in principle it's possible so to do.

> Mostali is doubtless its own meta-laguage ... :-)
                                                                                

In practice, most languages are, or at least can be, beyond a certain threshold of complexity and expressivity. I'm sure Mostali is very precise and reductionistic when it comes to expressing knowledge about languages (and everything else). Mind you, fixing (other) languages may be a somewhat moot point, given the drastic nature of some of their other 'fixes'.

Cheers,
Alex.

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End of Glorantha Digest

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