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Full Idea
The embedding data (such as 'John said that the number two is green', compared to '*John said that me likes apples') strongly suggests that category mistakes are not syntactically ill-formed.
Gist of Idea
Embedded (in 'he said that…') category mistakes show syntax isn't the problem
Source
Ofra Magidor (Category Mistakes [2013], 2.4)
Book Ref
Magidor,Ofra: 'Category Mistakes' [OUP 2013], p.39
A Reaction
Sounds conclusive. The report of John's category error, unlike the report of his remark about apples, seems perfectly syntactically acceptable.