Hullin, Chapter Two, Mishnah Four
In our mishnah Rabbi Akiva and Rabbi Yeshevav argue about whether an animal that has been improperly slaughtered is a nevelah or a terefah two terms that I explained in the introduction to Hullin. While neither animal can be eaten, the nevelah causes impurity while the terefah doesnt. Thus there is some practical difference between the two. Today, since neither animal can be eaten, it doesnt really matter whether an animal is a nevelah or a terefah.
1) If one first sliced the esophagus and then cut away the windpipe, or first cut away the windpipe and then sliced the esophagus; or if he sliced one of these organs and paused until the animal died; or if he thrust the knife underneath the second organ and cut it:
a) [In all these cases] Rabbi Yeshevav says: the animal is nevelah;
b) Rabbi Akiva says: it is terefah.
2) Rabbi Yeshevav stated this general rule in the name of Rabbi Joshua: whenever an animal is rendered invalid by a fault in the slaughtering it is nevelah; whenever an animal has been duly slaughtered but is rendered invalid by some other defect it is terefah.
a) And Rabbi Akiba [ultimately] agreed with him.
Section one: Slicing is how I have translated shachat which means to validly slaughter. Cut away is my translation of the verb pasak and it is an invalid method of slaughter. So if one properly slices one of the two organs and then improperly slices the other one, or if he slices one of the organs and then doesnt slice the other one and the animal dies, or if instead of slicing the organ he thrusts the knife under the organ and slices up (this is called haladah, burrowing), the animal cannot be eaten. The rabbis argue as to the status of the animal.
According to Rabbi Yeshevav the animal is a nevelah. As we in section two, Rabbi Yeshevav says that whenever an animal cannot be eaten because it was slaughtered improperly, the animal has the status of nevelah.
Rabbi Akiva says that it is a terefah.
Section two: Rabbi Yeshevav provides a general rule for determining what is a nevelah and what is a terefah. We have already explained nevelah above. A terefah is an animal that was slaughtered correctly but couldnt be eaten because there was some other previously existing problem with it. We shall learn what causes an animal to be a terefah in chapter three.
Ultimately, Rabbi Akiva agrees with Rabbi Yeshevav. My definitions of nevelah and terefah in the introduction to Hullin reflect this mishnah.