[SCL] two comments

[pat hayes]

>pat hayes wrote:
>[...]
>>Guys, I was using the term 'abstract syntax' in 
>>a precise sense. It is a technical term 
>>introduced by John McCarthy; its not just a 
>>handy English phrase. See 
>>http://www-formal.stanford.edu/jmc/towards/node12.html
>>for a succinct introduction.  This approach was 
>>later formalized and systematized in the 
>>specification literature as 'term algebras', I 
>>believe, but we don't really need to get that 
>>formal.
>
>Pat,
>
>I understand what you're saying. But are you *absolutely sure* that
>there is such a thing?

Yes, quite sure.

>That *perhaps* that even within the concept of
>an 'abstract syntax' there may be more levels/gradations of meta? All
>of the programming languages I know have various levels of meta-ness,
>but what is a primitive at one level (at what McCarthy would call the
>"abstract syntax") may often be further broken down once you look at
>it in a different context.
>
>I don't want to sideline the conversation down this road,

Neither do I. Yes, there is such a thing for all 
known formal languages, which SCL is. Please lets 
try to avoid this kind of philosophical debate, 
or at any rate keep it off this list.

>  but I think
>we may rely too heavily on the existence or possibility of some 'ur'
>level. (I'm not really even so sure that there any *actual* distinctions
>between meta-levels that exist absent any context, that it may be more
>a continuum than true levels). I think that both "meta" and "context"
>are recursively defined.
>
>>  The key motivational point is stated economically there:
>>
>>  " The predicates and functions whose existence and relations define the
>>  syntax, are precisely those needed to translate from the language, or to
>>  define the semantics. That is why we need not care whether sums are
>>  represented by a+b, or + ab, or (PLUS A B), or even by Gödel numbers 7a11b."
>>
>>  which is exactly the utility for us, since we want to allow things like
>>  CG diagrams to count as logical syntax. In Murray's terminology, the AS
>>  is the highest meta-level anyone needs to go to in order to define a
>>  syntax and a model theory.  (Splicing together documents, now, is
>>  another matter....)
>
>The problem here is that the link between the "abstract" and the "concrete"
>is always one of interpretation at some level/context, and I think I'd
>have to take it on faith that there is a mode in which one can define a
>*true* abstract syntax, something absent of context. But I suppose this
>road has a lot of potholes (or I've got it all wrong), so perhaps it's
>better we just stick to driving.

Quite. We don't have time to rewrite the 
philosophical foundations of semiotics before dec 
17th. Lets return to this interesting debate 
later, maybe.

Pat


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