Experienced Fregeans will recognise a number of places in which I simplify or omit. Some Fregeans doubt that his theory was meant to apply to natural language, that his remarks were only to explain his artificial symbolic language, his Begriffsschrift(concept-script). I think he thought that his Begriffsschrift more exactly mirrors what goes on more vaguely in natural language, namely the expression of thoughts, of propositions.
G. Kemp, What is this thing called Philosophy of Language?(2018) pp. 47-48
Considering the context, I think that for the correct explanation, the sentence bolded should mean the followings:
Some Fregeans do not think that his theory was meant to apply to natural language.
Those Fregeans do think that his remarks were only to explain his artificial symbolic language.
But it seems to me that some readers might think that some Fregeans doubt both.
So, I wonder if this use of "doubt" is proper and common or not. Thanks.