QUESTION: The Mishnah states that one who makes a Neder not to derive pleasure from his friend is prohibited from walking through his friend's land. The Gemara says that the Mishnah follows the view of Rebbi Eliezer who maintains that "Vitur" (any use of another person's property which the owner does not mind) is nevertheless prohibited to one who is Asur with a Neder.
The Gemara clearly understands that it is commonly accepted that a person does not mind when others walk through his courtyard without explicit permission.
The Rishonim question the Gemara's assumption here from the Gemara in Bava Basra (57b). The Gemara there says that only partners who jointly own a piece of land do not mind if the other walks on the field, but landowners generally do not allow any other person to walk on their field without explicit permission. How is the Gemara here, which implies that a person does not mind if others walk though his field without explicit permission, to be reconciled with the Gemara in Bava Basra?
(a) The RAN quotes the RAMBAN who answers that the Gemara in Bava Basra refers to one who sits down and loiters in the courtyard. Most people do not want others loitering in their courtyard without permission. The Gemara here, on the other hand, refers to one who merely walks through the courtyard and uses it as a shortcut. Most people do not mind if their property is used as a shortcut.
(b) TOSFOS in Bava Basra quotes RABEINU TAM (see also Tosfos here in brief) who answers that the Gemara in Bava Basra refers specifically to a courtyard. People do not want others walking through their private courtyards. The Gemara here, on the other hand, refers specifically to a Bik'a (a large, open field, not used for personal purposes), and therefore the owner does not mind if people walk through it.
HALACHAH: In practice, it seems that the Ramban would permit using someone else's property as a shortcut without explicit permission, while Rabeinu Tam would prohibit walking through someone else's courtyard without permission. Since today one cannot assume that every owner of property permits everyone to take shortcuts through his property, every situation needs to be evaluated individually. (E. KORNFELD)