Hallel means to bring Hashem’s light into this world as in Beis Hillel.
Hodo’oh means to self-nullify oneself to Hashem to raise oneself out of this world like Beis Shamai.
To Hashem.
Likkutei Torah Shir Hashirim 48 end of column 2
Where the Alter Rebbe explains what the word Hillel means and what the word Shamai means. That if one was to study the inner meaning of these two Hebrew words one will already know everything one needs to know regarding these two people, their yeshivahs and their personalities.
The name Hillel is the same as the word Hallel – to shine Hashem’s light into this world, which is Beis Hillel’s tendency – Chessed.
Drawing Down Hashem’s Light into the World
Drawing down Hashem’s light into the world, ‘from above to below’ (אוֹר וְהַמְשָׁכָה מִלְמַעְלָה לַמַטָה).
Whereas by contrast, the name Shamai comes from the words in the Talmud that mean he who appraises his own ways (הוּא מִלָשׁוֹן הַשָם אוֹרְ חוֹתָיו), meaning to consider one’s own ways and thus where one is currently.
This, in effect, is an elevation ‘from below to above’ (הָעֲלִיָּה מִלְמַטָה לְמַעְלָה).
And so, it turns out that this is the fundamental [conceptual] basis underlying the two [contrasting] opinions of Beis Shamai and Beis Hillel.
Appraising One’s Ways
Sotah 5B (Moed Koton 5a) And Rabbi Yehoshua ben Levi says: Whoever appraises his ways in this world, i.e., whoever carefully considers all his actions before deciding on the proper mode of conduct, merits and sees the salvation of the Holy One, Blessed be He, as it is stated: “And to him that orders his way aright [vesam derekh] will I show the salvation of God” (Psalms 50:23). Do not read it as “vesam,” “that orders”; rather, read it as Vesham dereCh, that appraises his way.
To judge, like the famous story of Reb Hillel that hears the Alter Rebbe telling someone that a young man who has questions in the Talmud tractate Erchin which deals with estimations and values, that before he judges the world he should judge himself.
One’s lifestyle, how one does things, what one does do, and what one does not do.
Judging oneself, and analysing oneself, and focusing on the minutia of oneself is not about bringing Hashem’s light down into one’s life but it is an elevation from below to above; it is about purifying, cleansing and making oneself more transparent so that Hashem can come into one more.
Beis Shamai and Beis Hillel: Two Paths
Beis Shamai represents one’s Avodah in raising oneself out of this world.
Beis Hillel represents one’s Avodah in bringing Hashem into this world.
This is exactly what Chanukah is about: bringing Hashem into this world in the minutia of the theme of the verse “Ner Havaya Nishmas Odom” – “Man's soul is Hashem's lamp” or raising oneself out of this world through the Bittul (self-abnegation) of the verse “Ner Havaya Nishmas Odom” – “Man's soul is Hashem's lamp.”
Which does not mean G-d forbid that there is more Klipah (Darkness) – Less light means that one has raised oneself above this world and there is less of a need for the light.
In other words, both opinions of Beis Hillel and of Beis Shamai are both right.
