Chacham: Someone specifically asked Rav Schachter in a Shiur a few years ago that according to the Rashba who Rav Schachter holds by for Bal Tigrah (he didn’t quote any opposing Rishonim if I recall correctly) that Bal Tosif and Bal Tigrah are not at all opposite sides of the same coin. In fact, they are very different. You cannot be Over on Bal Tigrah according to the Rashba unless you also fulfill the Mitzvah but not Bishleimusah.
Menu