[Avodah] Halizah (or is it better for one person to do a vadai mitzva...)

[Chana Luntz]

RYG writes in response to RMB:

> What's your source for the assertion that Halizah is only 
> kiyumis / materes?  The Hinuch concludes his discussion of 
> Yibum(598) with the statement that:
> 
> ve'over al zeh ve'lo yibem yevimto, kelomar shelo ba aleha 
> biah ahas shehi ikar mizvas aseh zeh o she'lo patrah 
> be'halizah, bitel aseh zeh
> 
> and his discussion of Halizah (599) with:
> 
> ve'over al zeh ve'lo razah le'yabem yevimto ve'lo la'haloz 
> be'ro'a le'vavo, bitel aseh zeh
> 
> They seem pretty parallel to me.  Additionally, the Minhas 
> Hinuch (598) writes (regarding Halizah):
> 
> zarich le'chavein la'zeis ye'dei ha'mizvah, ki hi mizvas aseh 
> ve'hi ke'kol ha'mizvos

Well you seem to both be right.  The Encyclopedia Talmudit brings as a
machlokus rishonim whether or not chalitza is a mitzva chiyuvis or not.
The Mordechai, inter alia, appears to agree that it is a mitzvah
chiyuvis, and therefore even if neither yevam or yevama wants to do
chalitza, and the yevama has no intention of getting married, they
should be forced like other mitzvos aseh.  On the other hand others
appear to hold that if she does not want to get married again, and he
does not mind the zika remaining, there is no need to do chalitza as the
chalitza is only a heter for her to get married to somebody else, just
like shechita is a mitzvah to permit the animal to be eaten.  See there
(it is under section aleph, on the facing page to the beginning).  The
Encyclopedia Talmudit does not (as is its way) provide any conclusion,
and it would seem from the sources quoted that the machlokus extends to
the achronim, so why not to Avodah.

>
> Yitzhak

Earlier RSM wrote:

> My example of 4 black balls and one white one indeed did not 
> completely correspond  to the case of yevamot, and was merely 
> designed to illustrate the difference between selecting with 
> replacement and without replacement, to show why the number 
> of possible selections is five factorial and not five to the 
> fifth power.   A complete match to the yevamot case is the 
> follows: A box has 5 balls of the following colors: black, 
> white, brown green and grey. 5 people, who happen to be named 
> Mr. White, Mr. Black, Mr Brown, Mr. Green, and Mr Grey choose 
> balls, one after another without replacenment, from the box. 
> A "match" is when someone chooses a ball from the box whose 
> color corresponds to his name (this is like a yavam marrying 
> his yevama). A perfect match is all five doing so, which will 
> happen on average in only 1/120 of the cases. Clearly it is 
> possible that there will be no matches, or one or 2 or 3 
> (only four matches is impossible, sin ce if the first 4  
> match, the fifth one must be a match as well). I have been 
> unable to devise a general formula for calulating the 
> likelyhood of a certain number of matches for any given 
> number of brothers; 

This of course is what I was after - or more specifically, what I wanted
to do was compare the probability of getting one or more yibumim in the
case of five yevamas as opposed to the case of six yevamas.

As you say, if getting five yibumim occurs via five factorial, ie 1/120
or 0.833% then if there are six yevamas, the equivalent would be 1/720
or 0.139%.  But what I really want to know is what is the probability of
getting one or more yibumim occuring (which could be calculated if we
can work out what the probability of getting all chalitzos, because then
we could subtract that figure from 1).

 RER did an empirical calculation for five and concluded: 
 
>5     Yibumim      1     possibility
>3     Yibumim    10     possiblities
>2     Yibumim    19     possibilites
>1      Yibum       46     possibilities
>0     Yibumim     44     possibilities
 
>We see that out of the 120 there are 76 cases (120-44), i.e a 63%+
possibility that will be at least one Yibum and 30 cases (1 + 10 +19),
i.e. a 25% 
>possibilty that there be more than one.

I am not quite sure how one would go about doing this for six.  Again 6
yibumim would be 1 possibility out of 720, and there would be no chance
of their being 5 yibumim but how you get to the equivalent of that 44
figure (how did you even get the first one RER, I am struggling to keep
the alternatives straight?).  There must be some sort of formula that
gets you there - don't we have some mathematicians on this list?

Getting back to the substance of our discussion, RSM writes:

> That means, as I understand it, that while there may be a 
> whole debate about Reish Lakish's principle and whether it is 
> d'orisa or d'rabbanan, elsewhere, that debate does not start 
> to apply to yibum/chalitza, because chalitza is already 
> discounted as a mitzvah when one is discussing yibum, so the 
> whole Resh Lakish principle does not apply if the option is 
> chalitza as opposed to yibum. 
> >>
> Reish Lakish makes his statement (or more accurately *could* 
> make his statement - "amar l'cha Reish Lakish") that 
> "chalitza b'makom yibum lav mitzva hi" in order to save his 
> whole principle, which the gemara suggests is refuted (leima 
> tehavei t'yuvta d'Riesh Lakish) by the case of chayvei lavim 
> and yibum. To present this tentative suggestion that Reish 
> Lakish could conceivably make to avoid being entirely refuted 
> as a fundamental principle universally accepted and 
> applicable to our case is IMO something of a stretch.

Why?  As you agree, the gemora makes it clear that Reish Lakish's
principle would appear to be completely refuted by the case of chalitza
and yibum, if we understood the halacha as you understand it, ie that
chalitza is a real mitzvah alternative.  Given that we appear to hold
like Reish Lakish's principle in other places, this is more than an
academic discussion.  If Reish Lakish's principle can be refuted here,
there we can't hold like it elsewhere.  So the gemora comes riding to
the rescue of Reish Lakish's principle by explaining that in the face of
yibum, chalitza cannot be considered a mitzvah.  There appears to be no
disagreement proposed to this statement, and this is where the sugya
concludes.  If you do not say that this is a fundamental principle
universally accepted, you then have to reject Reish Lakish's priciple
elsewhere wherever it appears.  You would also surely need to show
somebody else who holds differently, otherwise you appear to have a stam
gemora without refutation.  

 I am 
> happy with my statement that "lav mitzva" means "lav mitzva 
> kol kach" even according to RL. 
> My proof from the case where when appropriate the yavam is 
> persuaded to do chalitza instead of yibum is still valid;

But the gemora in Yevamos 101b brings a braisa that derives this aspect
(ie that the judges are required to persuade the yavam where
appropriate) from the pasuk "v'dibru elav".  In fact the authority of
the court to pursuade the yavam could be argued to be proof in the
opposite direction.  If it were true that yibum and chalitza are
alternative mitvos, with yibum merely being the more preferable, then
why is there a need for a specific posuk to tell the judges to tell him
not to bring strife into his home - obviously shalom bayis should take
precedence and the judges would logically of their own accord tell him
that if he couldn't work it out himself.  Only if you say that in the
face of yibum chalitza aino mitzvah does it seem absolutely necessary
that the Torah brings a pasuk specifically telling the judges that they
have authority to, and should, counsel the yavam that if there is a risk
that he is going to bring strife into his home, because on the face of
it the couple do not seem compatible, he should not do yibum.  Otherwise
everybody's inclination, in the face of a vadai mitzva aseh with no real
alternative, would be to take the risk.

 the 
> case of safek is merely another case where chalitza is a 
> proper procedure, and one who does so is m'kayem a mitzva. 

As far as I can see, the way one should be thinking about it is this.
Yes one who does chalitza is m'kayem a mitzvah (whether a mitzvah
chiyuvis or kiyumis seems to be a machlokus as set out above), but that
when one is faced with a yibum/chalitza choice, one should not take into
account the fact that chalitza is a mitzvah in its own right, but should
ignore that in the face of yibum.  Thus, all one must consider is
whether it is appropriate for yibum to be performed or not, and only
once that decision is made, does the question of chalitza come into
play.  It therefore seems to me that the same analysis ought to be being
applied to the case of safek - and hence the idea of "going for max" in
terms of doing a vadai mitzvah ought to be generalisable (unless of
course you agree with the Aruch L'Ner who appears to hold that one
should generally go for the vadai mitzvah, and the only reason that this
is not done here is not really because of the gemora's reason about
everybody getting a chance to get their yevama, but because one yavam
cannot marry five yevamos in any case).

> Saul Mashbaum

Regards

Chana