“Why?” you ask. “I am wearing a garment; that’s not carrying!”
Your garment is not the problem. The problem is not even the fringe(s) that is/are not kosher. The problem is the fringes that are still kosher! This takes us back to our lessons on Hilchos Shabbos, regarding the laws of carrying. You see, something that is attached to a garment and is insignificant can be regarded as secondary to the garment, and therefore does not create a violation. Something that is significant cannot, and if it is not clothing or ornamental in its own rite, may not be carried, even if it is attached to a garment. Thus, the invalid fringe, which is insignificant, does not cause a violation of carrying. But the valid ones, which are significant, do. Now you may ask: So why is a kosher set of tzitzis not a violation of carrying? That is because kosher fringes – when they fulfill the mitzvah – are ornamental due to the fact that they “adorn” the garment with the mitzvah! But think about it: kosher fringes, which are not currently part of a kosher set (i.e. because at least one fringe is invalid, and it takes four kosher fringes to make a kosher talis) are not presently adorning the talis with the mitzvah, on the one hand, but are too significant to be secondary, on the other! Isn’t this incredible!!!
Question: OK, now let’s get really deep: If a full set of kosher tzitzis-fringes adorn the garment only because they fulfill the mitzvah, then why isn’t it a violation of carrying on Shabbos, if it is nighttime, according to the opinion that there is no mitzvah at night, even for daytime garments (see dispute in lesson MBY 8:16-17)?!
Answer: What a great question! The answer is that a kosher set of tzitzis adorns the garment even at a time when the mitzvah is not applicable. The fact is that this is a kosher talis and a mitzvah object, and that fact, in and of itself, is enough to keep the tzitzis as an adornment all the time!
Question: Based upon our discovery today, it would seem that one would be required to inspect his tzitzis (e.g. talis katan, which is most likely what he would be wearing outside of the eruv) every time he wishes to go out of the eruv an Shabbos, for fear that one of the fringes is not kosher, and he would be carrying. It would be similar to having to check one’s pockets before going out, is it not?
Answer: Yes and no. If the person checked his tzitzis in the morning before davening (or the previous day before putting his talis away), then he does not have to check it again before going outside. Otherwise, he does.
Question: So, if a person is walking outside of an eruv, and suddenly he discovers that his tzitzis are invalid, must he take them off immediately – no ifs ands or buts?
Answer: Not necessarily. Remember the principle of ‘kavod habriyos’ – i.e. where the rabbis waived their restrictions in order to preserve human dignity? That applies here as well. Thus, if the person discovers the invalid tzitzis while walking in a ‘karmelis’ (i.e. not a bona fide reshus harabim – public domain – so that the prohibition against carrying is only rabbinic, as is the case with most of our streets), the principle dictates that he may continue to wear the non-kosher tzitzis until he gets to a private place where he can remove them without embarrassment. (Note: On a weekday, he would be required – by Torah law - to remove them and fix them before continuing his walk, but on Shabbos that is not an option.) In fact, even if he was sitting in shul on Shabbos, wearing his talis when he discovered that one of the fringes was invalid, he would not be required to remove it immediately, if doing so would cause him embarrassment!