(Recorded in advance of Tisha B'Av) The Gemara claims that non-Jews were considered contaminated - why? They never had the contamination from the Garden of Eden serpent removed, as Bnei Yisrael did. It's a difficult presumption in a world where we generally claim that people are born good, or at least innocent (which would mean not contaminated!). And what about converts? The implication is that they were always going to be part of the Jewish people. Also: Making a hole in a cask of dates - depending on how it's done, either you're strengthening the cask or your preserving it. Likewise, opening up a house... depending on your actions, impurity will or will not be removed... again, the difference between strengthening and preserving. Which also brings us back to intention, but in these cases, the physical manifestation of the action reveals the intent more than any verbalized statement. Plus: a cloth that can be a blanket or a cloak - depending on the fabric, you can wear it (or not) on Shabbat. The Gemara provides the rationale for the dispute here, including when one is lenient.