We've got a couple of problems here, I think. I won't tell you that this sentence is never uttered as is, but 'doubted if' is a doubtful construction, and the present tense in the 'if' clause sounds odd even if you want it to mean what you suggest-- because the sentence makes no mention of present belief whatsoever. You would be referring to possible pigheadedness if anything.
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Mister MicawberFrankly, I think a completely separate statement of pigheadedness is required; as it stands, it's a question of when the doubt is, not when the pigheadedness is. (And haven't I said that already?!)Thanks so very much, MM. I just had to confirm it with you, as I was not too sure I understood you. Thanks.