They are disputing which has greater significance, the
potential or the actual.
Beit Shammai holds that the potential is more significant.
The miracle of Chanukah took place over a period of eight
Immediately, on the first day the oil had the potential
to last for eight days. Each succeeding night this
potentiality was reduced; i.e. on the first night the oil
miraculously was able to last for eight, and the second day it
was able to last for seven days, etc. Therefore, to emphasize
this aspect of the miracle, we decrease by one each night.
According to Beit Hillel, primacy is given to the actual
miracle. After the first night, the Jewish people witnessed
a miracle of the oil lasting one night, the second night, two
nights, etc.; therefore we increase one candle because in
actuality, the visible miracle increased from night to night.