  Whether or not these sentences exhibit the kind of infelicity associated with category mistakes depends on context: (11) and (12) are perfectly felicitous in a context where it is clear that the thing I am thinking about/referring to is a pen, but not so in a context where it is the number two. Similarly, (13) is felicitous in a context where it is clear that the property I’ve just mentioned the property of being prime, but not so if it was the property of being green. This is a problem for the syntactic approach, because whether a sentence is syntactically well-formed or not is a context-invariant property: it cannot vary according to context in this manner.