The Lishmah of Interpersonal Mitzvos

I recently noticed a paradox when it comes to mitzvos bein adam lachaveiro (interpersonal mitzvos). What is the purpose of such mitzvos? To develop feelings of love and caring toward others; to expand our natural focus on ourselves to include others. Does the lishmah (lit: for itself) mean doing the mitzvah for the sake of doing a mitzvah? If it does, then we are not focusing on caring for other people, we are focusing on Hashem. On the other hand, if we define lishmah as being "for the purpose for which we were given the mitzvah (as best we can understand it)", we would conclude that mitzvah bein adam lachaveiro "for itself" means doing it without thought to its being a mitzvah. As I said, a paradox.

(Along these lines are the Chessed Projects many girl schools require. Obviously the point is that "from doing it not lishmah, one is brought to doing it lishmah." But what is the school trying to encourage?)

The paradox seems to be addressed by the Torah by giving two overarching principles that motivate chessed. The first is "ve'ahavta lerei'akha kamokha -- and you shall love your neighbor as yourself." The other is "vehalakhta bidrakhav -- and you shall walk in His ways", to which Chazal comment (Sifri ad loc, among many other places), "Just as He is described as Merciful, so too must you be merciful. Just as He is described as Kind, so must you too be kind. Etc...."

(Note that the Sifri does not actually call G-d "kind" or "merciful". The Sifri clearly is ascribing the attributes to our perception of Hashem, not to Hashem Himself. See "The Attributes of G-d".)

Ve'ahavta obligates us to act out of love for the other. Vehalakhta, out of love for and obedience to G-d. Which one is fulfilling in a given act, which could mean both as well, could very well depend on the intent of the person.