Keitzad merkadim lifnei ha'kallah? Beis Hillel hold that one can say "kallah na'ah v'chasudah" no matter what the kallah looks like; Beis Shamai holds that one must tell the truth. (Kesubos 17)
One could learn that the point of disagreement here is whether one can bend the truth for the sake of shalom. You don't want the chassan to feel bad, so no matter what the kallah looks like, you pay a compliment.
R' Yaakov Kaminetzki explained the sugya differently. The issue is not whether one has a license to bend the truth, but rather the issue is more fundamental -- what is truth? Beis Shamai hold there is an objective standard of truth, and therefore, if the kallah is ugly, we have to call it like it is. Beis Hillel, however, holds that truth is relative. To the chassan, the kallah is the most beautiful girl in the world. Relative to his way of thinking, one is being entirely truthful in saying "kallah na'ah v'chasudah."
R' Yaakov uses this yesod to explain another gemara (Eiruvin 14) l'shitasam. Beis Shamai were sharper than Hillel's school, but Beis Hillel were more numerous. Does the halacha follow smarts or rov? A bas kol from Heaven declared that although eilu v'eilu divrei Elokim Chaim, the halacha follows Hillel. Tosfos asks: "lo bashamayim hi" -- why should the bas kol carry any weight?
Hillel l'shitasam was interested in subjective truth. Since the majority of people saw things their way, that defined the "correct" answer. Shamai was interested in objective standards. Therefore, l'shitasam they had to follow the bas kol, the objective voice of truth that stood outside the fray.
What does this idea of relative truth being truth come from?
The Midrash writes that Hashem took a poll among the angels to see whether He should create man. It was a tie score among the different groups, with shalom and emes being opposed to man's creation because we are quarrelsome and can't be truthful. To break the tie G-d took the angel of emes and cast him down to earth.
Why did G-d cast down the angel of truth and not the angel of shalom, since both were opposed? And how does throwing the angel down to earth, removing him from the scene, address his objection? It doesn't seem like a fair way to address the problem.
R' Yaakov explains that Hashem was not disregarding concern for truth. What the Midrash is saying is that truth can be defined in different ways. There is Heavenly truth, the truth of the bas kol and angels, objective truth -- man cannot live up to that standard. But G-d revealed that there is also a truth based on human perception, a subjective truth. Hashem said that to be fair to man we have to look at truth the way it appears on earth, through man's eyes. That is a truth man can be held to and which he can live up to. And if we go with that definition of truth, there will be shalom as well. When all we know is subjectivity, then eilu v'eilu prevails because right and wrong can never be established with objective certainty.
Now we can get back to the question from yesterday's post: given that chazakah is proof even for dinei nefashos, why is it a chidush to say that a kohen can become tamei for his father, who we identify based on rov/chazakah, any more than his mother, who we can identify with certainty?
R' Yaakov suggests that the Torah's allowance for tumah is tied to the emotional need to mourn for the loss of one's closest relatives (My 2 cents: see Rambam Hil Aveil 2:6 "kamah chamurah mitzvas aveilus she'harei nidcheis lo ha'tumah... k'dei she'yisasek imahem v'yisabel aleihem." Note that the Rambam does not say that tumah is allowed in order to *bury* the dead, but rather he says that it is tied to *aveilus.*) Therefore, what matters is not the objective definition of paternity, but rather what matters is the subjective emotions of the mourner. In that regards, a mother b'toras vaday trumps a father whose identity is established only by rov and chazakah. These may be objective proofs, but that is not sufficient when the question on one of subjectivity and emotion.