Question: If one or more strings of the ‘p’sil’ tear – either partially or completely – does that invalidate the fringe?
Answer: Maybe yes and maybe no. First let us explain what is clear and then what is disputed in this matter. All agree that the twelve thumb-breadths which are required for the initial length are not required in the event that a string tears. How much must remain? A string – i.e. one of the eight singles - that still has the remaining length of ‘k’dei aniva’ (lit. enough length to wrap around a fringe, i.e. approximately two thumb-breadths) can still be regarded as a valid remnant. The dispute is how many remnants are allowed and how many strings must be completely intact.
Before we present the two dissenting opinions, let us point out something very crucial for understanding how the strings are constructed. The way we tie our tzitzis, we keep the two halves of each string on separate sides of the last knot. Thus, if we hold a fringe and separate the strings by splitting them at the knot, we are looking at half of the original four strings on one side of the knot and the other half of those same stings on the other side of the knot. Got it?
Now, here are the two opinions, regarding how many remnants are allowed:
Lenient opinion: There is no minimum number of the four strings that must remain completely intact. As long as each one of the four strings has a remnant of ‘k’dei aniva’, the tzitzis are still kosher. Let’s apply this now: Suppose one of the eight half-strings tore off completely. Its other half is still intact – on the other side of the knot, right? Right! In fact, according to that logic, even if all four half-strings on one side of the knot tore off – and ‘k’dei aniva’ remained to the four half-strings on the other side - the tzitzis are still valid. Do you see why? Because each one of the completely-torn half-strings has its other half with ‘k’dei aniva’ on the other side of the knot. Since each of the original four whole strings has a remnant of at least ‘k’dei aniva’, the fringe is still kosher. The only time there would be a problem is if one half-string on one side and one half-string on the other side tore off completely. Then, we would be in doubt that perhaps those two halves were part of the same whole, and there would be one entire string without a remnant of ‘k’dei aniva’! (Ed: I think it would be easier to just go buy another talis than to try and understand the lenient opinion, don’t you?!)
Strict opinion: Of the four whole strings, two must remain complete (i.e. twelve thumb-breadths) and the other two are allowed to remain ‘k’dei aniva’. According to this view, as soon as three half-strings tear partially – on either side of the knot - we must assume the worst - i.e. that each half-string that tore is from a distinct one of the four whole strings, and thus no longer do two strings remain completely intact.
To review and summarize: Lenient opinion: No one string must remain completely intact, and all four must remain ‘k’dei aniva’ Strict opinion: Two strings must remain completely intact, and the other two must remain ‘k’dei aniva’
Which opinion do we follow? The Shulchan Aruch teaches us to uphold the stricter opinion, but that we may rely on the more lenient opinion if it will be difficult (i.e. even if not impossible) to obtain new tzitzis.
The “last resort” opinion: There is a minority opinion that holds that the measure of k’dei aniva does not begin with the loose strings of the ‘p’sil’. Rather, even the string that is wrapped up in the ‘g’dil’ (the braided part) is included in the ‘k’dei aniva’ remnant. That would allow us to consider even a string which was torn down to the bottom knot as a valid remnant! The Shulchan Aruch permits reliance on this opinion only when no other tzitzis are available.
Note: According to all opinions, if even one string is broken at the loop between the garment and the first knot, the entire fringe is invalidated and must be repaired. This part of the fringe should be included in the daily inspection of the tzitzis.