Hotza'ah and the Sanctity of Shabbos in the Rebbe's Teachings
In the Hadran on Maseches Eruvin, the Rebbe explains the distinctive relationship of hotza'ah to Shabbos as a whole. Carrying can appear less visibly creative than other melachos, which makes public care especially important.
Hotza'ah among the melachos of Shabbos
In the Hadran on Maseches Eruvin, the Rebbe develops the distinctive place of hotza'ah among the melachos. Most melachos visibly alter an object; hotza'ah can consist simply of moving the same object from one domain to another.
The melacha is defined by the domains of Shabbos and by the act of taking an object across their boundary. That makes the ordinary appearance of carrying especially deceptive: nothing seems to have been created or changed, yet a full melacha may have been performed.
Why Maseches Eruvin centers on public practice
An eruv permits certain forms of carrying only after halacha has changed the status in which that carrying takes place. The enclosure and communal eruv must be valid; otherwise the familiar act of walking with a key or pushing a stroller remains hotza'ah.
The hadran was delivered during the period of the Manhattan eruv controversy, when these laws had become an immediate public question in New York.
The visible character of Shabbos
A public eruv changes what a neighborhood looks like on Shabbos. Once people see carrying become ordinary, they reasonably assume that a reliable psak, boundary, inspection system, and method of public notice stand behind it.
Where the Rabbonim have not accepted the eruv, that visible practice creates the opposite of the intended result. It turns a disputed route into an appearance of communal permission.