IF A MAN LIVES IN A COURTYARD WITH A HEATHEN OR WITH ONE WHO DOES NOT ACKNOWLEDGE THE PRINCIPLE OF ERUB, EITHER OF THEM CAUSES HIM TO BE RESTRICTED IN THE USE OF THE COURTYARD. R. ELIEZER B. JACOB RULED: NEITHER CAN RESTRICT HIM UNLESS THERE ARE TWO ISRAELITES WHO IMPOSE RESTRICTIONS UPON EACH OTHER.
There is a lot of discussion on this point, about the legal validity of a shared eruv where one party does not share it. And is R. Eliezer b. Jacob right or wrong? Perhaps it hinges on what kind of agreement can be made between them? Or perhaps whether the non-Jew is at home at the time or not.
Rab Judah stated in the name of Samuel: The law (halachah) is in agreement with R. Eliezer b. Jacob; R. Huna stated: The custom (minhag) is in agreement with the ruling of R. Eliezer b. Jacob; while R. Johanan stated: The public act (nahagu) in agreement with the ruling of R. Eliezer b. Jacob.
The difference being who widely promulgated the ruling is. Halachah can be taught publicly. Minhag is taught privately. Nahagu is not taught, but anyone who practices it is allowed to.
Quite a difference!
Said Abaye to R. Joseph: We have a tradition, that ‘the teaching of R. Eliezer b. Jacob is small in quantity but well sifted.’
I like that analogy – the law is not written or invented, it is “sifted” from the all the excess.