More on rabbinic interpretation of the biblical text and the rules about how that works - by means of gezarah shavah, kal va-chomer, hekesh. What happens when the sages themselves aren't sure that they're inferences and analogies work in the derivation of halakhot? When can logic triumph over textual inference?

Shifting focus to the guilt-offering (the "asham"), and the fact that it too is to be slaughtered in the northern part of the Temple courtyard - along with the blood collection and sprinkling and so on. And, again, the details are derived from the Torah's verses and inferences from one verse to another. Also, the guilt-offering slaughtered by the person who is coming off tzara'at also needs to be in the north of the Temple courtyard. And this derivation is then used to understand certain exegetical rules that apply to elsehwere in the Torah as well. The claim is that the Torah is written in this way to make sure that we learn the halakhah in this way.

The sin-offerings and others needs to be slaughtered in the northern part of the Temple courtyard -- as derived by biblical verses. Plus, the collecting of the blood, the sprinkling of the blood, and the placement of the person collecting the blood. Also, the way "he shall slaughter it" comes to exclude. And the laying on of hands comes into play as a possible exclusion, rather than it being about the northern location for the slaughtering. With a deep dive as to whether the person handling the offering needs to stand in the north too.

Finishing the 4th chapter, with a new mishnah: A sacrifice is slaughtered for the sake of 6 things -- all of which are far less tangible than the animal itself. The kohen's intentions have been preoccupying the Gemara for all these chapters, but now the shift, at the very end, is to the owner's intentions - that is, those of the person offering the sacrifice, even though it's handled professionally, as it were, via the kohanim. Also, starting the 5th chapter, with a new mishnah: The worship of certain sacrifices, from slaughter to collecting of blood to sprinkling of blood, needs to be specifically located in the Temple - in the northern part of the courtyard. To the extent that failing to do so correctly disqualifies the offering. But if the disposal of the blood is not as prescribed, it won't disqualify the offering. Specifically, the bull and the goat of Yom Kippur. Plus, what seems to be the carcasses would be removed to the ash pile outside of the Temple.

How is sacrificial blood excluded from the prohibition against "notar" and impurity? As derived from verses, that is. Likewise, how is blood not subject to me'ilah, after atonement (or even before atonement). Also, how these details are derived from verses that seem indirect or insufficient, when we might have wanted more. Also, why does the Torah mention "karet," the punishment of being cut off, three disctinct times? Each teaches another factor - with a dispute between Rabbi Yochanan and Shimon.

Two mishnayot! When an idolator brings an offering in the Temple... yes, that turns out to be something that could happen. Jewish people can't get benefit from those offerings, but there's no "misuse" of consecretion in those offerings. Likewise, there's no concern of impurity or exchanging the offering. The Gemara, of course, has some level of dispute over the stringencies applied to this kind of case. Also, those practices that were not subject to a violation of pigul may still be relevant for concerns of "notar" - leftovers, in terms of timing - and impurity.

Anything that has permitting factors - specifically, in this case, for the consumption of the consecrated offerings - will, depending, avoid the complicating factor of pigul. If pigul is established with regard to the peace-offering (shelamim), how can it apply to other offerings that aren't quite parallel to the shelamim? The Gemara explains it all very clearly, and pigul indeed is extended even to the oil that the person recovering from tzara'at offers (including non-shelamim meat offerings, bird offerings, and grain offerings). Such a clear delineation of pigul! Also, how it is that kohanim can eat from bird offerings. Plus, the grain offerings and atonement coming from the less likely source of the grain and the birds. With verses to teach it all.

A new mishnah! With a list of cases that would not make a person liable for pigul. The flour of the minchah offering won't become pigul. Likewise, the frankinscense. That is, the offerings themselves may become pigul, but not the ingredients thereof. Those ingredients are what make the offering possible to begin with. Also, on the case of the consecrated food to be eaten by a person who is ritually impure - why is there a need to state both the lenient cases and the stringent cases? Either side of that "equation," as it were, should be inferrable from the other. Note that "Ze'irei" doesn't have a title of "rav" or "rabbi."

Following the dispute about pigul for a meal-offering, the Gemara investigates all the permitting factors for an offering to be accepted, before there are any considerations of pigul. Note that the sprinkling of the blood on the inner altar needs to be done correctly. Also, the count of blood worship tasks: 43 or 47 or 48? If the bloods of two animals mingles, there is room to be lenient, in terms of how many placements there were on the altar.

"With the bull" - looking at the comparison between the goats that would be brought for unwitting communal idolatry and the unwitting sin in other fields. Via the juxtaposition of verses. Also, putting the sacrifices into the context of the Jewish people being beloved by God. With more details on the curtain too.