How many degrees of separation from food does one have to kasher?

Question

I understand that the sink, the dishwasher, and sponges, etc. all need to be kashered, presumably because they touch things (plates, utensils) that also touch food.

But how many degrees of separate objects/surfaces need to be kept kosher in such a way? For example, if I am using hot rocks to kasher my counter or dishwasher, do the rocks first need to be kashered? If not, why not?

Supposedly, tabletops and counters need to be kashered and/or covered. Do placemats? Trivets? Vases that sit on the table? If not, wouldn't they treyf up the table and thus the food?

Related: Knife sharpening - can it be done anywhere?

Does a kosher pot become non-kosher after you kasher utensils in it?

Transfer of taste to/from non-food items

Answer 1

There isn't any real halakhic requirement to kasher items that are any degrees of separation from food. You only need to kasher items that are directly being used to cook food.

The only time we are required to apply the Koshering Process is on items that are normally used directly on the fire, or are in contact with hot foods that are directly on the fire. These are called Keli Rishon and Iruy Keli Rishon respectively.

Sinks, refrigerators, trash cans, counters, dishwashers, stovetops, tables, cutting boards, mixmasters, silver kiddush cups, and anything not used with hot foods from the fire do not need any koshering.

Silverware are typically kashered because on occasion one uses them in the cooking process, therefore it's easier to kasher them along with anything else. But nothing else "needs" to be kashered, or even covered since:

1) it's not being used in the cooking process

2) the temperature of its involvement is diminished to the point it can't absorb, or it can't transfer what it has absorbed back into any of your vessels

So there aren't any degrees of separation to worry about, one only needs to kasher the item directly involved with cooking food.

Source: http://kashrut.org/halacha/?law=kashering

Answer 2

I found a relevant comment here:

Some have the custom to kasher in a dedicated “kashering pot” which is not used for anything else, but most kasher in any pot which is clean and has not been used for 24 hours.

It seems, therefore, that there is not a legal stringency to keep items used in the kashering process kosher. This would answer the "hot rocks" part of my question above, and goes partway toward answering the general question of "degrees of separation."

Generally, I will add that last time I kashered my kitchen I asked the rabbi about my dining room table, and he said I didn't have to worry about it. He was aware it would be used uncovered. He certainly didn't mention the kashrus of placemats, trivets, or vases.

Finally, I am assuming the sink/dishwasher/sponges only need to be kashered because of the hot and wet conditions and, possibly, the potential for contact with davar charifs etc. This raises the question of why a dishwasher would need to be kashered, but not the items used for koshering, which I can't answer.

Answer 3

One --at least as far as bosor b'cholov is concerned. This page answers the question in its own terms:

[...] [The mixture] is 100% permissible to eat, for there was no direct contact between the meat and the cheese, only a weak secondary contact. This is known as Nat Bar Nat. In order for this hetter to occur, the meat and milk must be at least twice removed from each other: (Think of the branches on a family tree – Uncle Earl might be directly related to you, but that does not really make him related to Cousin Edna.)

[...] [I]t is not considered bassar b’chalav, since there are (at least) two degrees of separation in-between them. Please note that this leniency only applies to bassar b’chalav; it does not apply by bleeyos of issur or treif1.

The page goes on to discuss the halachos of nat bar nat and--to some extent--how they relate to issues of kashering in the kitchen. However, it neglects to discuss the roles that issur and treyf (and potentially other non-bosor b'cholov considerations) might play in this discussion, so its answer "one" is only provisional.