[Avodah] talis qoton

[Mandel, Seth]

Daniel Israel:
<Which would seem to me to imply that if you are choshesh for the Mordechai's position you shouldn't wear a talis katan outside on  
Shabbos where there is no eruv.  I've never heard anyone suggest that chumra, although I was once advised to be machmir in the minimum shiur  
to avoid the issue of hotza'ah.>
It is well-known (or should be) that R. Chaim Brisker did not wear a talis qoton outside on Shabbos, because he was choshesh that one is not yotze any mitzvah with one, for a variety of reasons.  He also did not make a brokho on wearing one, but following the Gra and others that the brokho should be made on the talis godol.

Rabbi Seth Mandel