The Gemara (17b) states that in order to make up the 18 decrees R' Meir counts food and utensils that were contaminated by liquids as a single decree, whereas R' Yose counts them as two decrees.
Now the Gemara earlier (14b) said that the decree of foods contaminated by a liquid must cannot refer to a liquid that was a Rishon Mi'de'oraisa (Baim Machmas Sheretz), since such a liquid contaminates food Mi'de'oraisa and there is no need for a decree. Rather, the decree applies to liquid that came into contact, for example, with unwashed hands (Baim Machmas Yadayim); the decree is that the liquids revert to a Rishon and can then turn the food into a Sheni (Sheni Oseh Sheni Al Yedei Mashkin).
Regarding the decree of utensils contaminated by a liquid, in contrast, there is a need for a decree even for liquids that were a Rishon Mi'de'Oraisa, since Mi'de'oraisa a Rishon cannot contaminate utensils at all. Therefore the Gemara (14b) says that that decree refers to liquids contaminated by an Av (Baim Machmas Sheretz), which are a Rishon Mi'de'Oraisa, and the decree was that they can contaminate utensils.
The Rambam and the Raavad (Hil. Avos HaTumah 7:2) disagree regarding whether this decree applies even liquids that came in contact with a Rishon or Sheni, and reverted to a Rishon. The Rambam takes the Gemara at face value and rules that only liquids that came in contact with an Av, such as a sheretz, can contaminate utensils.
The Raavad, however, brings proof against this view from a Baraisa in Berachos (52b) which says that Beis Shammai require one to wash one's hands before pouring the wine at a meal lest one's unwashed hands (which are a Sheni) contaminate liquids on the backside of the cup which will in turn contaminate the cup. Clearly even liquids that became contaminated by a Sheni can contaminate utensils. (Beis Hillel disagree with Beis Shammai for unrelated reasons.)
What I don't understand is how, according to the Rambam, R' Meir could possibly count food and utensils that were contaminated by a liquid as a single decree, when they refer to two different types of liquids: The decree of food that was contaminated by a liquid refers to liquids that came into contact with a Rishon or Sheni and reverted to being a Rishon (Baim Machmas Yadayim) (and the substance of the decree is the very fact that they so revert) whereas the decree of utensils that were contaminated by a liquid refers exclusively to utensils that were contaminated by a liquid that was a Rishon D'oraisa (Baim Machmas Sheretz) (and the substance of the decree is that a utensil can become a Sheni when contaminated by a liquid)?
Perhaps one could suggest that this is exactly the point of issue between R' Meir and R' Yose. R' Yose maintains that after they decreed that utensils could contract tumah from liquids that are a Rishon (Barim Machmas Sheretz), they then incorporated utensils in the decree that liquids that become contaminated by a Rishon or Sheni revert to a Rishon and can in turn render food (or, now, utensils) a Sheni. This therefore counts as one decree. But R' Yose maintains that even after they decreed that utensils can contract tumah from liquids that are a Rishon, they did not include utensils in the decree that a liquid can revert to a Rishon and contaminate food. Therefore these are two decrees.
The Gemara (14b) which states that the decree refers to liquids that came into contact with a Sheretz follows the view of R' Yose, since the rule is that in a dispute between R' Meir and R' Yose the halacha follows R' Yose. Likewise the Rambam rules like R' Yose, as the Kesef Mishnah states in Hil. Mikvaos ch. 4.
This would solve the Ra'avad's proof against the Rambam, as well. We could say that the Baraisa in Berachos follows R' Meir's view, that utensils were included in the decree of food that was contaminated by a liquid (Baim Machmas Yadayim) . But the Rambam rules like R' Yose that these are separate decrees and the decree of utensils applies only to utensils that were contaminated by a liquid that was a Rishon on a d'Oraisa level.
Eli Shulman
Y'yasher Kochacha! Beautiful idea. It seems, though, a bit Dochek to say that both Beis Hillel and Beis Shamai in Berachos are going according to Rebbi Meir and not according to the way the Gemara concludes le'Halachah (Tosfos discusses this question in our Masechta, 14b, DH Ela b'Mashkin, and sides with the Ra'avad because of the Sugya in Berachos).
The words of the Rambam are difficult to understand and require further analysis, as you mentioned.
M. KORNFELD