The gemara darshens from the words "V'asu lahem tzitzis" that the string of tzitzis must be owned and not stolen. Minchas Chinuch asks why a special pasuk is needed for this din -- stolen string should be excluded based on the din of mitzvah haba'ah b'aveira? (Obviously this is not a question according to the Rishonim (Tos. Sukkah 9) who hold mitzvah haba'ah b'aveira is only a psul derabbanan.) The M.C. explains that the din of mitzvah haba'ah b'aveira means that the mitzvah action is not acceptable to Hashem, it is not "l'ratzon." The limud from the pasuk goes a step further. Not only is wearing stolen tzitzis something Hashem funds unacceptable, but more than that -- it is like not wearing tzitzis at all. It's not just a lackof a kiyum mitzvah, i.e. like wearing a four cornered with tzitzis but getting no credit for it, but it's a biutl aseh as well, like not having tzitzis on the garment at all.
The Minchas Chinuch uses this same reasoning to explain why a limud is needed to exclude a stolen sukkah. Not only is eating in a stolen sukkah not a kiyum mitzvah because of mitzvah haba'ah b'aveira, but more than that -- it is like eating outside the sukkah, a bitul mitzvah. (See R' Yosef Engel in Asvan D'Oraysa #11 who rejects this chiddush.)
Ordinarily the shulchan aruch deals only in practical halacha, not philosophy. Tzitzis, tefillin, and sukkah are exceptions to the rule and the shulchan aruch tells us the reason for these mitzvos as well as how to perform them. Achronim explain that besides the regular din of kavanah required for all mitzvos, these mitzvos also require having in mind the reason behind them while doing the mitzvah.
R' Elchanan Wasserman, using similar logic to the Minchas Chinuch, raises the question of what happens if a person wears tzitzis without kavanah: does he simply lose the kiyum mitzvah, or would we go a step further and say it is as if the person was wearing a four cornered garment without any tzitzis, a bitul aseh?