Can the sentence Dan Brown isn't my favourite writer for no reason mean that he is in fact my favourite writer?
The context is that someone else had just pointed out how thrilling she found Dan Brown's The Da Vinci Code.
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The statement is ambiguous. It first seemed to me to mean that Dan Brown wasn't your favorite author, but you had no reason for that. The more subtle interpretation is that Dan Brown is your favorite author, and there is a reason for it (i.e. not for no reason). This is actually a more elegant reading, but it's not clear that is what is meant.
A sentence with two negations is ambiguous, depending on the scopes of the two negative elements. For instance,
has two meanings:
This is because the scope of no reason in (1) is outside the scope of didn't arrive, whereas the reverse is true in (2), which would have quite a different intonation pattern in speech, implying knowledge of a hidden motive.
Contrary to popular myth, two negatives do not cancel out each other just because they're in the same sentence, unless they apply to exactly the same constituents with exactly the right scoping. This is pretty rare, in fact. More negatives simply create more ambiguity.
In the OQ example, the scopes are arrayed a little differently, and since Dan Brown is a good example of a terrible writer, I got one of them immediately, paraphrased
The other meaning is less likely:
because favorite implies some decision already, thus justifying a reason.
Note that there is an invited inference in some of these senses of irony or hidden meanings in other contexts. These are all common effects of negation, which depends on listener presuppositions.