The narrator believes himself to be sane because he wisely executes his plan to kill the old man
In the tell-tale heart, the narrator describes how he killed an old man because this man had a vulture-like eye. This action seems quite insane but the author explains he is not mad.
About this, the author mentioned "Now this is the point. You fancy me mad. Madmen know nothing. But you should have seen me. You should I have seen how wisely I proceeded"
This shows the author considers he is not mad, because he wisely executed his plan.
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