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