The "Law of the Excluded Middle" is one of the basic laws of logic. It means that for any proposition A, either "A" or "not A" is true. For example, let's take as our proposition that bumble bees cannot fly. The law of the excluded middle says that either it is true that bumble bees cannot fly (A), or it is true that bumble bees can, indeed, fly (not A); there is no third possibility. That principle is the foundation of many logical proofs, because it is often easier to prove (or disprove) "not A" than "A"; after which one simply invokes the law of excluded middle to claim a victory.
Understandably, the strict laws of classical logic do not apply to apply to all situations (as any man who has been married for more than an hour or two can surely testify). It doesn't mean there is anything illogical about the situation, it simply means that the over strict laws of classical logic have been applied incorrectly to the situation (as any woman who has suffered being married for more than an hour or two to aforementioned man can quite passionately testify).
Here's a concrete example from a recent TftD regarding the Mishna Brura's stance on using putting raw food into a כלי שלישי on Shabbos. In siman 318, sk 39, the Mishna Brura states unequivocally that it is forbidden to put uncooked food into a כלי שני on Shabbos. Great! So no problem using a כלי שלישי on Shabbos; right? Well... the Mishna Brura then goes on to explain -- in great detail -- how to make tea sense before Shabbos, in order to avoid any issues with cooking the tea leaves on Shabbos. So... sounds like using any vessel -- including a כלי שלישי -- on Shabbos is a problem. There seems to be quite a canyon here where there ought not to be a middle position at all.
Don't get frustrated; just look further. In sk 45, the Mishna Brura decries the practice of putting bread into a hot bowl of soup on Shabbos. What's the problem? The bowl is a כלי שני, and while the halacha is אין בישול אחר בישול/a solid food that has been cooked can be reheated without concern that one is cooking, none the less we are stringent with baked foods because there are opinions that יש בישול אחר אפיה/a baked food can still be cooked in hot liquid. (In halacha, בישול/cooking means heated by/in a liquid; אפיה/baking means heating in a vessel without liquid, צלי/roasting means directly on a fire without an intervening vessel.) Therefore, says the Mishna Brura one must either let the soup cool to a point where it surely will not cook or כל הפחות/at the very least use an intermediate vessel between the pot and the soup bowl so you will have a -- TADA -- כלי שלישי! Hah! You see quite clearly that the Misha Brura holds there is no issue of cooking in a כלי שלישי. QED
Well.... perhaps, you may argue, the Mishna Brura is only lenient in this case because we are talking about bread and the issue of cooking is really only a stringency. Fine, fine, fine; you have a point. Read a bit further in that same sk 45 and you will find that the Mishna Brura says that you need to take that precaution all the more so when putting raw onions or garlic into the soup. Hah! Not baked; just plain, raw vegetables, and the Mishna Brura (grudgingly, perhaps, but I am not looking for stringencies here) says that a כלי שלישי is fine. QED
Well... another chaver suggested that I really needed to check that last bit of reasoning out with R' Fuerst. Fine, fine, fine; if it will make you happy. After all... what else could it possibly mean? So I asked, and R' Fuerst told me, "No, of course you can't use a tea bag on Shabbos; even in a כלי שלישי." But... but, what about sk 45? (At this point, I choose to pat myself on my shoulder, even though that is a strain on this old man frame... because R' Fuerst asked me to get him a Mishna Brura as he wanted to review the details before answering. Cool! It was worth getting up that morning to have found asked a question that at least required a review.) "Ah," replied the rabbi, "In that case the onions are being used as a spice, and we allow spices to be used in a כלי שלישי." But, I persisted, the onions are a vegetable, and so it is being cooked. "Yes," replied R' Fuerst patiently as ever, "but the onions are not being cooked for themselves, but only to flavor the soup. That's why we can be lenient."
Bottom line: the Mishna Brura states clearly and unequivocally that it is forbidden to put uncooked food into a כלי שני on Shabbos. Regarding a כלי שלישי, moreover, the Mishna Brura is only willing to be lenient when there is another factor (סניף) that tips the scales toward a leniency; such as being previously baked (bread, for example), being used as a spice/flavoring (onions and garlic, for example), or being previously roasted (Starbucks Via brand instant coffee, for example). Lacking that, though, R' Fuerst holds that the halacha is to be stringent; after all, we are dealing with Shabbos!
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