I do want to get to more Chanukah stuff, but we were in the middle of borer and I want to finish that topic. Lots of interesting comments to the last post, but I want to do this slowly before jumping to the answer. The Aruch haShulchan (319:9) asks a fundamental question. If borer involves any sort of selecting, then it seems we run into trouble at every turn on Shabbos. For example, you have three suits in the closet and want to take out one to wear; you have three spoons in front of you at your place setting and want to use one of them -- why in each of these cases is taking the desired item not a violation of borer?
The Aruch haShulchan gives two answers. The first answer hinges on the rules we learned last time. Quick review: Borer means selecting between items and is permitted if three conditions are met:
1) ochel is being removed from psoles
2) it is for immediate need/consumption
3) a special utensil (e.g. a strainer) is not being used
As we learned, ochel does not mean exclusively food, nor does psoles mean bad stuff. Ochel simply means the item you want; psoles is the item being discarded. If you take the spoon that you want or the suit that you want, that is ochel m'toch psoles for immediate use and is therefore permissible.
The second answer of the Aruch haShulchan (actually, it's the first one he suggests) is that we don't even need to refer to the three criteria here because, as I mentioned, there is another condition that needs to be met before we even begin speaking about borer and it almost goes without saying: we need a mixture. Where each individual item is clearly recognizable, e.g. I can clearly tell one suit from another; I can clearly tell the difference between each spoon at the place setting in front of me, taking one item is not called borer. The Aruch haShulchan writes that this is called netilah, taking a desired item, and it has nothing to do with the melacha of borer which entails sorting between different items, .
So now for a little test with a case that appears in many handbooks and which was given by my daughter's teacher. You sit down to your Shabbos chicken soup and suddenly notice something is wrong. "Waiter, there's a fly in my soup!" Can you remove that fly on Shabbos?
Most handbooks will tell you (based on a Ta"z) that that the correct procedure in this case is to take a little soup out along with the fly. Removing the fly alone would be taking psoles from ochel, which violates rule #2 in our list of three criteria. However, shlepping the fly along with a little soup, which is ochel, avoids separating between fly and soup and is therefore OK.
If this was your answer, I'm afraid you failed the test. Based on the basic rules of borer this approach makes no sense. First of all, as we learned, ochel does not mean food; ochel means the item that you want, as opposed to psoles, which you are just taking to discard. If the whole purpose of taking some soup with the fly is to discard that soup in the trash with the fly rather than eat it, that spoon of soup itself becomes psoles! Instead of violating borer by separating a fly from soup, you now have violated borer by separating a fly+soup that you don't want to eat from the soup you do want to eat. That does not seem to accomplish anything.
The second point I guess depends on your soup. I like my chicken soup pretty clear, with maybe some noodles or a matzah ball floating along in it. I am pretty confident that I can tell the difference between clear chicken soup and a fly even if I took off my glasses. Why should removing the fly not be considered what the Aruch haShulchan calls netilah? We shouldn't even need to speak about borer in this case because we haven't met the most basic criteria required to talk about it: we don't have a mixture. We have two distinct items and are just removing one from being nearby the other.
(Just for the record, one can defend the Taz, but doing so involves some elaboration. My point for now is that taking the Taz at face value [as many people do] 'flies' in the face of the basic rules of borer and is therefore not a good illustration if you want to understand or teach principles.)