Beitzah 9 - A ladder
Beit Shammai prohibit moving a ladder from one dovecote to another, even though his intention is to fetch some doves for slaughter and consumption, which by itself is permissible on a Holiday (Yom Tov). Beit Hillel disagree and allow moving the ladder.
They must be talking about a ladder specifically designated for dovecotes, and yet Beit Shammai do not allow moving it. Why? - Because an onlooker might still think that he is going to plaster his roof. And Beit Hillel, what do they say? - That his ladder and his dovecote are proof enough of his intention.
Rav Chanan further qualifies this disagreement: it is only a ladder in the street that they argue about, but if nobody sees him, in the privacy of his home, then it should be allowed by everybody. But how can Rav Chanan say so? We know that there is a rule that "Whatever the Sages prohibited to do in public, because of what an onlooker might think, is equally prohibited inside his most private room!?" - It turns out that not everybody agrees to this rule, and Rav Chanan thus has his source. Furthermore, this rule only applies when it looks like he may be violating a Torah prohibition, but when an onlooker may think that he is violating a rule of the Sages - that is allowed in private.
Art: The entrance to a large barn, a ladder leaning against the wall by Giovanni Battista Tiepolo