[Corpora-List] ad-hoc generalization and meaning

[Yorick Wilks]

Rob
None of this matters much for most of us who read this list, but I  
think your reference from 1950 is not quite right, or rather its a  
non-standard way of putting it:
A Remark Concerning Decidability of Complete Theories, Antoni  
Janiczak, The Journal of Symbolic Logic, Vol. 15, No. 4 (Dec., 1950),  
pp. 277-279:

"A formalized theory is called complete if for each sentence  
expressible in this theory either the sentence itself or its negation  
is provable."

Completeness normally (see e.g. Wikipedia) means that for every  
sentence S expressible in a language either S or ~S is derivable from  
the associated axioms, and that all sentences so derived are true  
(i.e. theorems). That is not the same at all as the system/set/ 
language being decidable--i.e. that for any S there is an effective  
procedure for determining whether or not it is derivable. "provable"  
in that quote fudges this issue. For some reason I dont follow you  
seem to want to conflate completeness and decidabilty---in general  
you cant do that even though there are fudges round completeness like  
"semidecidable". The proof of this is that are systems which are  
complete but not decidable (i.e. arithmetic) as well as systems  
decidable but not complete--some roccoco bits of modern algebra...
Yorick



On 14 Sep 2007, at 07:17, Rob Freeman wrote:

> On 9/14/07, Paula Newman <paulan at earthlink.net> wrote:
> ...
> So the question, Rob, is what are you proposing?  Is it a new  
> approach to linguistic investigation, or to NLP, or to ??
>
> A better understanding of syntax and semantics.
>
> That's the glib answer, Paula, but really, does the study of  
> language have to be divided up in the ways you describe?
>
> Your comments conjure in me a rather odd picture of science where  
> we assume everything which can be known, is already know, and it  
> only remains to select what we want to do with that knowledge.
>
> It somehow reminds me of the reputed comment of some Chinese  
> emperor or other who when presented with a collection of Western  
> clocks and navigational instruments, sent them back saying "We  
> don't need such things in China."
>
> Is science now not to be the study of the world, but only the  
> selection of purposes?
>
> Yes, there are a plethora of little "schools" out there all doing  
> their own thing. But I don't think an analysis of reasons for  
> studying language gives us a exhaustive guide to the possibilities  
> for understanding language. People don't analyze language  
> statistically or symbolically just because their goals are different.
>
> Anyway, that is the philosophy of science. I hope that's not an  
> area where we need to do a lot of work.
>
> By the way, as I remember, the words "informal grammar" were John  
> Sowa's. I don't think I've ever used them. I did think of asking  
> him to define it, but he later back-tracked from his extreme  
> rejection of formal analysis, so there was no need.
>
> I think the idea of "informal grammar" is a muddle too. I don't  
> think grammar is "informal", I think it is "necessarily incomplete".
>
> I found a nice definition for "incomplete" by the way.
>
> A Remark Concerning Decidability of Complete Theories, Antoni  
> Janiczak, The Journal of Symbolic Logic, Vol. 15, No. 4 (Dec.,  
> 1950), pp. 277-279:
>
> "A formalized theory is called complete if for each sentence  
> expressible in this theory either the sentence itself or its  
> negation is provable."
>
> -Rob
> _______________________________________________
> Corpora mailing list
> Corpora at uib.no
> http://mailman.uib.no/listinfo/corpora

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