[hist-analytic] What do we need to represent syntax?

Richard Grandy rgrandy at rice.edu
Wed Feb 25 14:42:55 EST 2009


You are correct, I was thinking of too narrow and standard a range of cases.

Richard

>On Wednesday 25 February 2009 05:38:14 Richard Grandy wrote:
>>  OK,  can we separate two questions?
>>
>>  1.  What is the minimal metalanguage we need to represent syntax of
>>  another language.
>
>Depends on what you want to do with the representation.
>
>For the kind of metatheory which I engage in I would state the
>minimal requirement as:
>
>     It must be possible to define in the metalanguage
>     an algebraic structure isomorphic to the abstract syntax
>     of the object language.
>
>This entails that there is an injection from the abstract syntax
>of the object language into the things over which one can
>quantify in the metalanguage.
>
>It does not entail that there is an injection from the syntax
>of the object language into that of the metalanguage.
>This may be seen in my own most recent technical work
>(see: http://www.rbjones.com/rbjpub/pp/doc/t024.pdf)
>which involves formalising the syntax and semantics of
>an infinitary set theory using as metalanguage
>a higher-order set theory. In this case the syntax of
>the metalanguage is countable, but that of the object language
>is inaccessible, so there is no possiblity of an injection
>from the object language syntax into the metalanguage syntax.




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