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The syntactic account of computation is not very popular.
In this syntactic account of computation, the notion of representation is not used at all.
And if so, the syntactic account of computation collapses into the semantic account.
The Nagel-Schaffner approach to theory reduction assumes a syntactic account of theory structure such that they are axiomatized systems formalizable in first order predicate calculus.
Since Stich's account of syntax is ultimately aimed at grounding computational theories of cognition, Stich's account of syntax also provides an (implicit) syntactic account of computation.
The syntactic account demands that only physical states that qualify as syntactic may be mapped onto computational descriptions, thereby qualifying as computational states.
The syntactic account may be seen as adding a restriction on acceptable mappings that replaces the semantic restriction proposed by the semantic account.
Although Stich does not use the term "computation," his account of syntax is aimed at grounding a syntactic account of mental states and processes.
Instead of a semantic restriction, the syntactic account imposes a syntactic restriction: only physical states that qualify as syntactic may be mapped onto computational descriptions, thereby qualifying as computational states.
A proof system for first-order logic provides a direct syntactic account of when φ is a consequence of Γ, in terms of derivability using rules (and perhaps axioms) sensitive only to the form of the formulas involved.
(Computability theorists call any set of words from a finite alphabet a language, but that broad notion of language should not be confused with the narrower notion — inspired by grammars in logic and linguistics — that Stich employs in his syntactic account of computation).
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com