17:
The rest of our present mishnah is comparatively simple to explain and understand. Our mishnah teaches that Jews are forbidden to eat vegetables cooked by a non-Jew. The basic reason for this prohibition is again the fear that in some way or other the non-Jew has dedicated the food to some deity or other. However, when we have explained the other items in the list we shall return to this matter.

18:
Our mishnah itself explains the reason for the prohibition of pickled vegetables: in Talmudic times it was customary to use wine (or vinegar derived from wine) in the pickling process. You will recall that all non-Jewish wine is forbidden. (See AZ 024.)

19:
The problem with herring that has been minced by a non-Jew is that bits of other fish may have been included in the mince and the Jew has no way of telling whether the added fish - if any - was of a permitted kind or a forbidden kind.

20:
The brine referred to in our mishnah is fish brine. If there are no pieces of fish left in the liquid the Jew has no way of telling whether the fish used to make the brine was of a permitted kind or of a forbidden kind. Hence brine of that sort is forbidden.

21:
We cannot precisely identify the fish which our mishnah designates as Ĥilak. There are two problems in this regard. Firstly, this is a fish which does not produce proper fins and scales until it reaches maturity. The physical signs of a fish which is permitted is that it has both fins and scales. Once the Ĥilak has been cooked by a non-Jew there is no way of knowing whether it was already mature when it was caught and cooked. The second problem in this regard is one that we have already encountered: it was customary to cook this fish together with other breeds of fish and so the Jew has no means to determine whether those other fish were of a permitted kind or not.

22:
Asafoedita, or asafoetida, is known by many popular names: devil's dung, stinking gum, food of the gods, Kaayam, Hing Gujarati, Hilteet, and giant fennel are some of them. It has a pungent garlic smell when raw, but in cooked dishes, it delivers a smooth flavor, reminiscent of leeks. It is used as a digestive aid, in food as a condiment and in pickles. Its odour is so strong that it must be stored in airtight containers; otherwise the aroma will contaminate other spices stored nearby. It is used in most vegetarian and lentil dishes to both add flavor and aroma and reduce flatulence.

23:
Rambam's commentary on our present mishnah is quite extended and he introduces matters that derive from our mishnah even though they are not specified in it. He begins his dissertation by saying what we have been saying throughout this chapter:

Rambam then goes on to explain - and his explanation is, of course, derived from the Gemara - that anything cooked by a non-Jew is forbidden. Certainly if the cooking were done in the utensils of the non-Jew but also even if the cooking were done in the Jew's utensils and even if it were done in the presence of the Jew. However, the Gemara [AZ 38a] does make certain exceptions to this blanket prohibition. Anything that is eaten raw may be eaten if prepared by a non-Jew. Also, anything - even if it is cooked - that would not be served at a royal banquet may be eaten (assuming that all the ingredients are kosher).

24:
The matter of the 'royal banquet' seems to be a way of determining whether the food might have been dedicated to some deity or other. In any case, it seems to me (and to several of my colleagues) that a Jew may certainly eat in an non-Jewish restaurant that is strictly vegan or in a vegetarian restaurant a dish that is strictly vegan.

In AZ 032 I replied very briefly to a question about cheese. I was referring specifically to the parmesan cheese mentioned in the question. Oren Steinitz has been so kind as to offer the following response which is much more detailed:

Even strictly Orthodox authorized cheese uses rennet that comes from a kosher-slaughtered animal, as it falls under the category of batel b'shishim [a minute quantity that may be ignored - SR]. Moreover, in North America this is one of the main points of difference between Conservative and Orthodox standards of kashrut, as Conservative authorities ruled that every commercially produced cheese is by definition kosher, as industrially produced rennet went through so much processing that it cannot be classified as food anymore, and is therefore a davar ĥadash [a new creation, not derived - SR]. This is the view presented in Rabbi Isaac Klein's responsa. Stricter Orthodox authorities claim that it may be davar ĥadash but since it is a substantial ingredient in cheese-making, it is also classified as davar ha-ma'amid [coagulant - SR].

I respond:

All this is, of course, correct about cheese in general. However, nowadays more and more kosher cheeses are coagulated using enzymes that are plant-based, to avoid any doubt. Those interested may care to look up Wikipedia to learn why parmesan cheese made by non-Jews cannot be kosher.

Discussion on this topic is now closed.

I wish everyone a very happy Ĥanukah!