We are trying to define what "lomdus" is or the "Brisker derech" is working through a real example, so if you missed part I scroll down for the background of the machlokes R"I and R"M M'Rotenberg whether an onein would be obligated to say havdalah on Sunday after kevuras hameis. Rather than a specific approach, I would say there is a spectrum between what a yeshiva guy would call a "balebatish sevara", i.e. a theory a layperson would think of, and what is considered a "lomdish" analysis, which is something the yeshiva guy would pat himself on the back for thinking of and expect to find in a R' Chaim, R' Elchanan, Baruch Ber, R' Shimon, or other yeshivishe seforim. I would like to tentatively suggest the difference is that former focusses on the CASE, the latter focuses on the PRINCIPLE.
The R"I argued that havdalah should be similar to a lame person who once exempt from aliya l'regel on the first day of yom tov is not obligated on any subsequent days, which are just makeup days for the first day. The opportunity to say havdalah on Sunday is just a makeup for Motzei Shabbos - if an onein was not obligated then, he cannot become obligated during the makeup period. Why would the R"M M"Rotenberg argue? What is the locus of disagreement?
Balebatish approach #1 - distinguish between the CASES: by aliya l'regel, the days subsequent to the first are all makeup days. By havdalah, Sunday is not just a makeup, but R"M M'Rotenberg understood that the obligation of havdalah was extended through Sunday. You can make this more sophisticated and add a little sevara to explain why this should be so: by aliya l'regel, each day is a discreet unit. By havdalah, there is no seperation between motzei shabbos and Sunday that would warrant treating them as separate periords with different parameters on the obligation.
We can slide a little further down the "lomdus" spectrum with a distinction still rooted in the cases. You might contrast aliya l'regel, which is a pure positive commandment (actually, maybe not, but that's a complicated aside) with havdalah, where there is an issur to eat before havdalah - you might dispense with a mitzva, but not with a matir. If we generalize that into a rule, we can test it in other examples, and we are well down the road of dealing with principles.
Real "lomidus" would focus exclusively on the PRINCIPLES: even assuming the facts of the cases are similar, the time periods are similar, and all the practical details are the same, you can still distinguish between the fundemental principle which exempts aliya l'regel and the principle exempting an onein. No chiyuv of aliya l'regel ever applied on the first day of yom tov to the lame person, but perhaps by an onein there is a chiyuv of havdalah, but the mitzva of kevurah and tending to the meis overrides that obligation. Once the burial is complete, the latent obligation of havdalah which existed motzei shabbos now could be fulfilled. Once one has moved beyond CASES and into analyzing PRINCIPLES, one has opened the pandora's box to looking at many other cases with the same analysis: no obligation whatsoever, or a latent obligation overriden by some other concern? For example, see Y.D. 341 in the Taz and Shach in Nekudas haKesef regarding whether someone who misses davening because he was engaged in communal mitzva work is obligated in a tefilas tashlumin - was there never an obligation of tefila so no makeup is required, or was there an obligation overridden by another mitzva?
We are already pretty far down the "lomdish" spectrum, but I think a Brisker would go a step further. If you've heard Brisker analysis, you probably have heard the jargon of "gavra" vs. "cheftza", "tzvei dinim", or other such terms. In a nutshell, Brisk takes even the PRINCIPLES and breaks even those down into substrata to be contrasted and compared. Perhaps the R"M M'Rotenberg would not argue practical differences between the cases, perhaps he would agree that the operant exemption should be the same, but still there is a distinction that could be drawn. There are actually two elements to havdalah: the obligation on the person to say havdalah, and secondly, the "kos shel bracha" the halachically acceptable cup with beverage over which it is recited. Until now we have treated the PRINCIPLE exempting the onein as a whole unit, yet we can actually break it apart. It could be that the exemption has nothing to do with the onein being obligated or not obligated in havdalah - instead, it relates wholly to the nature of the "kos shel bracha" of an onein being unacceptable. The cheftza shel mitzva is lacking, not the chovas hagavra. When the kos becomes acceptable on Sunday, the onein is then free to fulfill his chovas hagavra which was never dispensed with. (NOTE: I am using this example for theoretical purposes only. I don't think you can realistically interpret every exemption of an onein from mitzvos as a ptur in the cheftza shel mitzva).
I haven't exhausted every possibility, but the purpose was more to dramatize the chiluk between lomdus and non-lomdus. In actaulity, sometimes the case by case method is best. In this case, I think the Brisker approach is a stretch. But ultimately, the goal of a "lamdan" is to discover those fundemental questions and principles that cut across multiple cases and issues.
Up next: another test case... oto be continued.