Ohalot, Chapter Twelve, Mishnah Eight
1) If an olive-sized portion of a corpse is stuck to the threshold:
a) Rabbi Eliezer declares the house unclean.
b) Rabbi Joshua declares it clean.
2) If it was placed beneath the threshold, the [case] is judged by the half [in which the uncleanness is found].
3) If it is stuck to the lintel, the house becomes unclean.
a) Rabbi Yose declares it clean.
4) If it was in the house, a person touching the lintel becomes unclean.
5) [As for] a person touching the threshold:
a) Rabbi Eliezer declares him unclean.
b) Rabbi Joshua says: [if he touches it at a point] below a handbreadth [from the
surface] he remains clean; above that handbreadth he becomes unclean.
Section one: According to Rabbi Eliezer, the threshold is part of the house. Therefore, if a source of uncleanness is found on the threshold, the house is impure.
Rabbi Joshua holds that the threshold is not part of the house. Therefore, if the impurity is found on the threshold, the house is clean.
Section two: If it is found underneath the threshold, then whether it is considered to be in the house depends on whether it is under the inner half of the threshold or the outer half. The house is impure if the impurity is in the inner half.
Section three: The impurity is stuck to the outer section of the lintel. Most sages consider the lintel to be included in the house. Rabbi Yose considers the outer side of the lintel to be outside the house.
Section four: As a corollary, if the impurity is inside the house and a person touches the lintel, he is defiled.
Section five: Rabbi Eliezer is consistent with his opinion above. Since he considers the threshold to be part of the house, if someone touches the threshold (when the impurity is in the house) he is impure.
Rabbi Joshua says that he is impure only if he touches a space on the threshold that is at least one handbreadth above the ground. If it is less than a handbreadth above the ground, then he is pure because less than a handbreadth is considered part of the ground (see 9:15 where Rabbi Joshua says the same thing concerning a coffin).
Rabbi Joshua’s opinions seem to be inconsistent. In section one he holds that the threshold is not part of the house, but here he holds that it is, at least one handbreadth over the ground. One explanation is that since in this case the impurity is found in the house, the impurity goes out through the threshold and thereby defiles it. In other words, it is not that the threshold is part of the house, rather that the impurity goes out through the threshold and thereby defiles it.