Principle of the Excluded Middle
The Sun either contains hydrogen or it doesn’t contain hydrogen. There is no third possibility. As two separate statements, one is true and the other is false. As a single ‘either-or’ statement, it is definitely true. And so it is with all similar pairs of statements (or compound ‘either-or’ statements) where there are only two possibilities and both are presented. One statement is the negation of the other and one is true and one is false.
This is a rough explanation of the Principle of the Excluded Middle. There is no middle. The Moon is either made of green cheese or it isn’t made of green cheese.
There is also a Fallacy of the Excluded Middle (it has several other names) in which there is a third (or more) possibility that is not presented in the ‘either-or’ statement or in either of two statements. The water is either hot or it isn’t hot. Not a true statement since warm water is neither not nor not-hot.
With this simplified, amateurish presentation of one (or two) of the classic laws of thought (or logic), let us examine some mitzva-pairs of the Torah and some statements from Pirkei Avot.
Let’s start with a statement in this week’s Perek: R’ Yosi says, One who honors the Torah, will be honored by mankind. One who disgraces the Torah, will be disgraced by mankind. Here’s another:
R’ Yochanan the sandal maker says, Every gathering that meets for the sake of heaven will have an enduring effect. One that is not for the sake of heaven will not have an enduring effect.
Does the Principle of the Excluded Middle apply in these cases, or does the Fallacy?
Does one by his/her behavior either honor the Torah or disgrace it, or is there a neutral position - a third possibility of neither honoring nor disgracing?
Is every gathering either for the sake of heaven or not for the sake of heaven? Or is there a ‘pareve’ position between the extremes?
It can be suggested that if only the first of the pair of statements were made, then we might conclude that there is a negative and a neutral midpoint. But with the statement of the opposite side of the coin - perhaps the Tana is implying that we have an either-or issue. You either respect the Torah or - if you don’t, then that is tantamount to disgracing it. Your meetings are L’SHEIM SHAMAYIM or they are not - no middle.
In perhaps a different manner, we find many mitzva-pairs - one being an ASEI, a positive command and the other being a LAV or LO TAASEI (prohibition). In Parshat Emor we have the command to fast on Yom Kippur and the prohibition of eating and drinking on Yom Kippur. A person either fasts or he doesn’t. One cannot say that he didn’t fast but he didn’t eat or drink either. I don’t work that way. Excluded middle.
But now let’s try to apply some of the above to a very significant mitzva- pair in this week’s sedra.
You shall observe My commandments and perform them… And you shall not desecrate My holy Name, rather I should be sanctified among the Children of Israel - I am HaShem Who sanctifies you.
The mitzva of Kiddush HaShem and the prohibition of Chilul HaShem are as serious and powerful as mitzvot get.
They both - one in a positive sense, the other in a negative way - have a wide range of behaviors and actions that exemplify them. They range from giving up one’s life when called upon for the sake of G-d, to performance of mitzvot (or violation of them) with certain attitudes, to dropping a candy wrapper on the ground at the bus stop or picking one up and dropping it into the waste basket.
There are countless situations - big and small, earth-shaking and mundane that present themselves to each of us all the time.
Is there an Excluded Middle when it comes to Sanctifying G-d’s Name, or are there other possibilities?
We might suggest that a missed Kiddush HaShem is in some way a Chilul HaShem. Too simple a statement, but the stakes are so high that we cannot ignore the possibility. Why didn’t Mordechai just hide behind a convenient pillar when Haman was around so he could avoid the consequences of refusing to bow? We must be pro-active with Kiddush HaShem.
In This Issue of Torah Tidbits
- Lead Tidbit
- Candle A Day
- Gold from the Land of Israel
- Aliya-by-Aliya Sedra Summary
- Sedra Stats
- Maharal on the Sedra
- Vebbe Rebbe
- Portion of the Portion
- Oz Torah
- Parsha Points to Ponder
- TTriddles "Report"
- Person In The Parsha
- Word of the Month
- The Trade and Commerce of the Talmid Chacham- Tamari
- Chizuk and Idud
- Divrei Menachem
- "From Machon Puah"
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