On the subject of Majority I have been working on an absolutely fascinating and fundamental Talmud which may shake entirely the way I have understood Majority up till now. The Talmud in Zevachim 72a is discussing a herd of animals in which an animal that is condemned to die got mixed in (it was either condemned to die because it was a Chatas or because it was an animal that was sentenced to be stoned since it had relations with a person). Even if the condemned animal is outnumbered a thousand to one, the Mishna teaches us that all the animals must be treated as condemned and killed. The Talmud asks the obvious question: why is the one condemned animal not negated by the Majority of acceptable animals? The Talmud end up answering that an animal is considered a significant minority and is therefore not negated.

Now first things first, from the language of the Talmud here we see that the principle of Negation applies even to distinct entities that just happen to be in proximity; because truth be told, I might think that the concept of Negation would only apply when items are truly mixed in with each other, such as when liquids are mixed together or if solids are ground or cooked together. When these elements are truly combined it is much easier to understand why we would apply the concept of Negation; but from the Talmud here we see that even just being in a vague proximity is enough to consider items as Combined and thus allowing Negation to be applicable.

The Talmud then asks, well why should all the animals be forbidden, why can't we take one out from the group and thus apply the principle that Separated Items Separate From The Majority, meaning that if we have a Majority and Minority present in a group, and an item is separated from the group, we can assume that it separated from the Majority.

Now, this question from the Talmud is quite interesting in light of the fact that the Talmud just finished telling us that animals are considered a Significant Minority and therefore cannot be negated. Because if this is so, then why should separating an animal from the group help, isn't it still a Significant Minority and thus the principles of Majority should not apply!

So based on this Talmud it must be that the principles of Majority Negates Minority and Separation From A Majority are two completely different concepts. And this actually makes a lot of sense. The principle of Majority Negates Minority is dealing with a group that definitely contains a forbidden minority; thus, although normally we can "negate" the minority via the majority and therefore consider this group as if it does not contain anything forbidden at all, when the Minority is Significant then it cannot be negated and we are left with a group that contains a definite forbidden minority and thus the whole group becomes forbidden. But when we are dealing with Separation From A Majority, the separated item is no longer a part of the group, and thus when we say that we can assume it came from the Majority there is no certainly forbidden minority present to "poison" the item under consideration, and thus even though an animal is considered a Significant Minority we would still permit it via Separation From A Majority.

The Talmud then says that we can't just separate an animal from the group, because the animals are Established Things and we have a principle that Established Things Have 50/50 Odds.

Now, this is really interesting, because it is well known that the principle of Established Things only applies when the item under consideration was known and identifiable to us at the time that our uncertainty occurred. For example, when it comes to nine kosher stores and one non-kosher one where someone purchased meat from a store and they can't remember which store it was, we would consider the stores as Established Things since not only were they "established" in a given location, but their identity was "established" as well and we are always aware which of the stores is the non-kosher one, we are just unsure which store the person went into. And this is why by the famous case of three pieces of meat before us we say that we follow the Majority and you can eat the meat: because the meat would not be considered an Established Thing since we don't know which of the pieces is the forbidden one. But given all of this, then why by the case of the Talmud here would we consider the animals as Established Things? After all, we don't know which which animal is the forbidden one!

But there's an even more significant problem here. Namely, that we only have a single verse of After The Majority To Incline which teaches us the principles of Majority. So if it's the case, as we asserted above, that Separation From A Majority is a completely different principle than that of Negation, then how in the world can we learn the principle of Separation From A Majority from the verse of After The Majority To Incline which is discussing a court: by the court there is no separation that occurs at all! The principle of Negation we can understand how you could learn in out from the courts, but how can we learn the principle of Separation From A Majority?In Depth

I would suggest the following, which I think beautifully answers our questions, explains the flow of the Talmud, and also explains some other commentaries quite nicely (the only downside is that none of the later commentaries appear to agree with a key point I make, and I will explain what that point is).

I would start by pointing out that the concept of "negation" is less logical than the concept of "separation". What I mean by that is that the idea that even though we know for a fact that there is a forbidden minority present we can still treat it as if it wasn't there at all is not all that logical; to come up with this principle we would certainly need a verse. However, the concept of "separation" from a majority is, by contrast, fairly logical: we have an item before us, it either came from the Majority or the Minority, so logically we can assume that it came from the Majority.

Given this, I would suggest that the principle of Separation From The Majority is a purely logical principle that does not require any verse! Whereas the principle of Negation - which does need a verse - is actually the very principle that we learn from After The Majority To Incline! And this would explain the opinion of Rashi and the Rosh quite nicely, who both maintain that the principle of Negation is deduced from the verse of After The Majority: because if it's true that Separation From The Majority is purely logical and requires no verse, then the only principle that the verse could be coming to teach regarding Majority would be the principle of Separation!

And perhaps with this understanding we can explain the Talmud's position on Established Things. Because I would suggest that maybe the principle that Established Things Have 50/50 Odds is also something that could be determined logically; and if so, then perhaps from a purely logical perspective we should not differentiate between an item that is part of a group and an item that has been separated from the group; regardless, the minority is considered Significant and cannot be negated or ignored, and in all cases we have to be concerned for it. However, once the Torah uses a verse to teach us that Majority Negates Minority, then we ought to assume that this is a comprehensive, sweeping ruling and would apply to all situations, even when we are dealing with Established Things; therefore, the Torah has to bring another verse to teach us that we still apply the principle of Established Things; however, for whatever reason, the Rabbis understood that when the Torah taught us that this principle applies, the Torah distinguished between where the item is still part of a group versus where it has been separated from a group.

So to summarize, while it's true that Established Things only apply when we the forbidden minority is known and identifiable, this is only true by cases of Negation; but by cases of Separation - which is a purely logical principle - we would say that logically Established Things applies in all scenarios, even where the item under consideration is not known and identifiable.

A freilichin Purim!!!

What a wonderful end to the Jewish calendar! Since the Jewish holidays begin with Passover, then the holiday right before it - Purim - must be the last, the final holiday, the culmination of the year. And what an interesting note to end on: not the holiness and abstinence of Yom Kippur, but the feasting, partying, gift-giving and drunkenness of Purim. In fact, the Rabbis point out that Yom Kippur can be read as "Kippurim", meaning "like Purim", as if to say that everything that Yom Kippur is is but a shadow of Purim itself.

And the question of course is why and how is Purim so special that it is the culmination of all our holidays, and something that Yom Kippur itself can only be a faint shadow of?

I believe that the answer lies in the rather shocking fact that nowhere in the Bible is the Afterlife mentioned. Christianity, Islam, and most other religions lead with descriptions of Heaven and the eternal reward that waits for us. But in Judaism we find almost nothing in the entirety of Scripture. So what rewards are promised by the Jewish God? Well, the chapters of Shema describe eloquently how if we follow God's commandments then the rains will come at the ideal times, and the crops will grow, and we will eat and be satisfied. That is to say, that the promises of the Torah are material and tangible. And in fact, even the later writings that do discuss a world-to-come see it as just an anteroom of sorts, where we await the resurrection of the dead and a life in a material world wholly dedicated to God. So even in the ultimate goal of God's plan, our final place is in a physical world where we worship freely, and not in some purely spiritual plane.

The Hassidic masters make a big point around how our purpose in this physical world is to uncover the "sparks" of spirituality which are the core around which the meat of the physical world depends. And even once the Messiah comes, we will continue to dwell in a material world where we must constantly work at revealing these "sparks". Unlike Christianity for example, who sees abstinence from the physical world to be holier than involvement with it, Judaism sees the material plane as something to be embraces and upraised. After all, if someone believes in an all-powerful deity who is the sole "reality" in existence, then it must be that all things in existence are a part of that God, even the material component which may seem to us to be separate.

Thus is Purim the culmination of the Jewish calendar. On this day we celebrate an excess of the material in anticipation or our ability to one day achieve the highest level of perception in which we will at last realize that the material is just as much of God as is the spiritual.

So much has happened in the world of Majority! I have to share some of the big, monumental things that have come up since I last wrote.

This biggest by far is that it turns out that my original understanding of the classic case of Majority is actually correct: namely, that if there are three pieces of meat in front of you and you know that two of them are kosher and one is non-kosher, but you don't know which is which, you are allowed to eat the meat and rely on the Majority of Odds.

Now, the reason I thought that this was incorrect was because I later came across the principle of Established Things Have 50/50 Odds. As soon as I learned of this principle I immediately had the question: why are the pieces of meat not considered Established Things and thus we should not follow the Majority? And when I looked at the commentaries I noticed that they discussed how the items under consideration are "mixed together", which I took to mean that they were physically all mixed up and blended together until no individual component was recognizable.

However, in my discussion with Rabbi Lang it became clear that he agreed with my original understanding. And in fact, there is a Tosafos in Zevachim 73b (Ela Amar Rava) who clearly explains that we only apply the principle of Established Things when the status of the item is Established at the time of our uncertainty: meaning, for example, that by the case of the nine gentiles and one Jew, we knew who was the Jew and who were the gentiles, and thus at the moment of uncertainty (when the killer randomly threw their weapon at the crowd) we had an Established Jew and nine Established Gentiles and thus we consider it 50/50 odds. Another example would be by the nine kosher stores and one non-kosher store, where a person purchased meat from one of them but doesn't remember which one they purchased from: over there as well, when the uncertainty happened the person knew which store was non-kosher and which ones are kosher, it's just that right now they don't remember which one they purchased it from, and thus the uncertainty was birthed amongst items with an Established Status. Thus, by the case of the three pieces of meat, where we don't know which one is non-kosher and which are kosher, we would not consider them Established Things.

However, Tosafos in Pesachim 9b (Haynu Tesha Chanviyos) at the end asks from the Talmud in Zevachim 73b that we see from the Mishna that even if a single forbidden animal was mixed in a herd of 10k we must kill them all - and the Talmud explains because the animal is an Established Thing - but the question is, we don't know which animal is which and thus it should not be considered an Established Thing! Tosafos answers that it must be that the Mishna is merely teaching us a Rabbinic stringency, but indeed we would say that Biblically this is not a matter of Established Things.

And in fact the Talmud there does indicate that the Mishna is discussing just a Rabbinic stringency, as seen on 71b where the Talmud asks that it appears that we already learned this principle that there is no negation by sacrifices from another Mishna in Temura 28a which appears to reiterate the principle that a forbidden animal is not negated, and the Talmud answers that if we had only said one case or the other I might have thought that there was a special stringency which explained why just that case was forbidden. But the takeaway is that the Talmud is clearly implying that the animals are forbidden as a result of a Rabbinic ruling, since if it was Biblical why would have I originally thought that the distinctions between the cases make a difference; if it's just a Rabbinic stringency then this kind of assumed distinction makes a lot more sense.

I had a truly wonderful insight over Shabbos.

I was learning through Rabbi Shimon Shkop in the Shaarie Yosher (Shaar 3, Perek 3) where he writes his incredible premise that the world of monetary law runs according to its own laws of logic and common sense, and thus Biblicaly-based laws like Majority would not be applicable.

My problem with his premise is that while this is a beautiful explanation of Shmuel's opinion by monetary law, it does not sufficiently explain (to me, at least) how Rav and Shmuel also seem to carry the same disagreement into non-monetary cases. For example, we find that Rav and Shmuel disagree about us following the Majority when it comes to saving human life; but according to Rabbi Shimon Shkop, why would Shmuel also disagree here? Even stronger than this, we find that Rav and Shmuel disagree about Majority in Bava Basra 23b where we find a barrel of wine floating in the river near a city which is Majority Jewish, and the question is do we say that the principle of Proximity instructs us that the barrel likely came from this city and is thus permitted, or do we say that maybe the barrel came from upstream where the general population is majority gentile and thus the barrel of wine is forbidden? Rav maintains that a river has lots of nooks and crannies where a barrel would get stuck, and thus the fact that the overall population is majority gentile is irrelevant since we don't assume the barrel came from upriver, whereas Shmuel disagrees and says there is a possibility that the barrel fell into the middle of the river and got carried all the way here, and thus we do have to take into account the fact that the Majority of the general population is gentile and thus we must forbid the wine. Once again, per Rabbi Shimon Shkop, how do we explain this disagreement of Rav and Shmuel? They are clearly disagreeing over whether we are concerned for the minority of chances that the barrel came from upstream; but how would Rabbi Shimon Shkop explain their disagreement?

Based on this, I would suggest an alternative approach that I think not only answers this quite elegantly but also neatly explains some other tricky concepts such as the fact that Majority is considered stronger than Proximity and Status Quo.

Essentially, I would suggest that Rav and Shmuel are arguing about whether Majority is a revelation of the truth or just an arbiter of uncertainty. What I mean, is that perhaps the Torah is telling us that a Majority can be used as a proof to determine what the real and actual state of something is, thus resolving our uncertainty; or, perhaps our uncertainty is not resolved, and the Torah is merely giving us a guideline as to how we should act when in the presence of uncertainty. I would suggest that Rav maintains that Majority is a revelation of the truth, and thus everywhere that a Majority is present we say we know for certainty what the truth is, and I would suggest that Shmuel maintains that Majority is merely an arbiter of uncertainty and thus there are situations where we would not follow the Majority.

Based on this, we can say that perhaps Shmuel generally maintains that since there is always a real uncertainty, we follow the Minority to be strict; meaning, if following the Majority would result in a lenient ruling we would not follow it. This would explain why by the case of the barrel of wine Shmuel maintains that we are strict to forbid the wine.In Depth

And as for monetary law, the reason Shmuel says that we follow the Minority not only to be strict but also to be lenient is because we see from the Talmud in Bava Kama 46b that the reason for Shmuel is because the Burden of Proof Is On The Claimant, which is a purely logical principle that requires no verse. I would suggest that what this principle means is that we require "certain" proofs, such as witnesses, where there is no uncertainty at all, and thus Majority - which according to Shmuel does still have uncertainty - would be insufficient.

This approach could also answer why it is that we say that Majority is stronger than Status Quo and Proximity: by Status Quo (and I believe by Proximity as well), nobody says that it is a revelation of truth; it is clearly merely an arbiter of uncertainty. Therefore, Majority - which according to some opinions is a revelation of truth - has to be assumed to be stronger.

I later found that the Kreisi Upleisi (Hilchos Basar Shenisalem Min Ha'ayin, Samech Gimmel) gives my exact same answer in explaining the disagreement between Rav and Shmuel!

I have some solid proofs that Rabbi Meir - who says that we are Concerned for the Minority - is just a Rabbinic principle and is not Biblical. Because Rabbi Meir does not actually say whether their principle is Rabbinic or Biblical and there is some discussion about it among the commentaries.

In the Talmud in Chullin 6a we find that Rabbi Gamliel agrees with Rabbi Meir that we are Concerned for the Minority. And yet in Eruvin 64b the Talmud discusses a case where someone is traveling down a road and finds a piece of bread, Rabbi Gamliel says it is forbidden to be eaten. The Talmud says we learn from here that we follow the majority of travelers who are non-Jews and we assume that the bread came from that Majority. The Rashash there asks, isn't it obvious that we follow the Majority?! That's the universal rule that we follow! The Rashash answers that since we see that Rabbi Gamliel agrees with Rabbi Meir that we are concerned for the minority, I might have that that was true both to be stringent and to be lenient, and so Rabbi Gamliel teaches us that no, this principle is only to be stringent but not to be lenient and permit eating this bread. Now, it is well known that Biblically we do not distinguish between strict and lenient. Therefore, this is a strong indication that being Concerned for the Minority - where we do differentiate between strict and lenient - is purely Rabbinic.

Another proof is that we see that Rabbi Meir differentiates between normal minorities and extremely unlikely minorities, and says that by extremely unlikely minorities - such as that a divorce scribe does not know how to write a divorce document - we do not concern ourselves for the minority. This is in contrast with the Talmud where we discuss the source for Theoretical Majority and say that one proof is that we permit slaughtered animals to be eaten even though there is a possibility that there was a mortal wound in the neck directly where the knife ended up passing through and thus really the animal was not kosher. Now, surely this is an extremely unlikely possibility and yet clearly Biblically we do not distinguish between how likely a minority is or not; so from the fact that Rabbi Meir does make this distinction is yet another proof that his principle is only Rabbinic.

There is a very fascinating language that we use for certain types of Majority.

For example, there is a principle that the majority of people do not repay their loans before the official due date. Now, the Talmud does not actually call this a Majority, rather refers to it as a "Chazaka", which is generally used to mean a "Status Quo" (Rabbi Shimon Shkop in Shaar 3, Perek 3 makes this point). This same language of "Status Quo" is used for a number of Majorities throughout the Talmud; and the question of course is why are we using this language? A Majority is something very different from a Status Quo; why is the Talmud mixing up the terminologies?

Well, the first thing we can do is to examine how these types of Majority are different than a standard Majority. Rabbi Shimon Shkop points out that even though Shmuel classically says that we do not follow the Majority by financial matters, even he agrees that we do apply these "Status Quo" Majorities, because we find that the Talmud regularly asserts that by financial matters we do apply the principle that people do not repay their loans before the due date, and the Talmud never mentions that Shmuel argues!

But why would Shmuel agree by "Status Quo" Majorities? What is different about them?

I would suggest that "Status Quo" Majorities are actually what we can call "super-majorities". It's where the Majority is so strong, and the minority so tiny, that we consider the Majority to be almost like a rule of nature, like an established fact, which is why we refer to these Majorities as "Status Quo", since they are like the default status that we can assume things follow.

And in fact I would bring the Talmud in Nidda 29a where Ravina makes use of interesting language when discussing two Majorities that are competing: one Majority is that most animals give birth to viable offsprings, and the other Majority is that most animals that are about to have a viable birth have a discharge and this animal did not. Now, Ravina says that the Majority re discharge weakens the Majority about viable offspring. However, the way he says it is very interesting: he prefaces his statement by saying that "because one could say that that the majority of animals give birth to viable offspring and a minority birth something which is not viable". Now, this preface is strange: of course we know that every Majority also has a Minority, so what it Ravina trying to tell us?

I would suggest that we see from here that Ravina had to point out that there is a real minority here, because sometimes we are dealing with a Majority where there is no real minority and thus the Majority is a "super-majority" or what we would call a "Status Quo" Majority, and this type of Majority is almost like a law of nature and therefore the second Majority would not be able to weaken it.

The following is a list of places in the Talmud where we discuss Majority.

The Talmud in Yoma 84b says that when it comes to saving a life we do not follow the principle of following the Majority.

The Talmud in Kesubos 16a/b discusses a case where we are unsure if a women who got married was a virgin. The Talmud points out that there should be a Majority here, since the majority of women who get married are virgins. The Talmud answers that this is true, however there is a competing majority here: that a majority of virgin marriages a publicly known as being virgin marriages, and here there was no widespread knowledge of her virginity, and thus this majority "weakens" the other majority and thus we cannot rely on it.

The Talmud in Bava Basra 23b says that when we have two conflicting proofs, one of which is a proof of Majority, and one which is a proof of proximity, we say that the Majority beats proximity. The Talmud subsequently in 24a discusses blood that is found in the cervical canal: we have an uncertainty whether it came from the uterus in which case she is impure, or whether it came from an area of the body called the "attic" in which case she is not impure. Now, the "attic" is closer to the location where the blood is found, yet still the Sages rule that we assume the blood came from the uterus which contains much more blood, thus proving that when a Majority confront proximity we follow the Majority. Rava disagrees with this proof and points out that there is another proof here bolstering the Majority: namely, the principe of frequency, since blood flows from the uterus much more frequently that from the attic; thus we have no proof that a Majority all on its own can beat a proximity. The Talmud there also brings to light a remarkable insight into the opinion of Shmuel who generally holds that we do not follow Majority when it comes to financial matters: the Talmud says that if there is a case where a barrel is found in a river by the banks of a city that is majority Jewish, Rav holds that we follow the Majority since the barrel was found in close proximity to the city, and Shmuel disagrees and says that there's a possibility that the barrel came from somewhere upstream where a majority of the city is non-Jewish. What this indicates to me is that Shmuel's opinion has something to do with being Concerned for the Minority, since that is effectively what he's doing in this case of the barrel.

The Talmud in Kesubos 15a makes an interesting statement around the principle of Established Things Have 50/50 Odds. The Talmud writes that regarding a woman who had illicit relations with a stranger, if the majority of the city is of pure ancestry then we can assume that her child is pure, but if the stranger came from a traveling caravan then we do not follow the majority of members of the caravan who come from pure ancestry and we declare her child to be impure. The Talmud asks on this that if anything it should be the opposite: we have a general principle that Established Things Have 50/50 Odds, and thus the people from the city should be considered Established Things and thus we should consider the minority to have equal odds to the majority and in the presence of the 50/50 odds we should be strict and rule the child impure, whereas by a traveling caravan it should not be considered an Established Thing since it is moving and therefore we should follow the Majority! My problem with this is that since the case is where she went to where the caravans were, who cares that they generally tend to travel, when she went there she was visiting something that was Established relative to her and thus we should consider it to be like Established Things. Otherwise, by the case of 9 Jews and one gentile who got trapped under rubble on the Sabbath why do we say we consider them to be Established Things, why don't we say that of course they don't permanently dwell in this building rather they travel between different buildings in the city and therefore we should not consider them to be Established Things?!

The Talmud in Brachos 53a says that if someone was walking outside a city on Saturday night and wishes to make the Havdalah blessing on the lights they see in the city, if the majority of the city is gentile he may not recite the blessing, but if the majority is Jewish then he can. My question is, why don't we say that since the city is an Established Thing the odds are considered 50/50 and he may not recite the blessing? The answer comes from the subsequent lines of the Talmud where it clarifies that if the city was exactly 50/50 you would be permitted to make the blessing.

The Talmud in Pesachim 7a may reveal to us a very interesting exception to the general rule that Majority is stronger than other kinds of proof (such as Status Quo and proximity). The Talmud discusses a new kind of principal called "Recency": the idea is, if we have a group of something and we aren't sure whether the items in the group are of Type A or Type B, and the case is where we know that while this group certainly used to mostly consist of Type A, it recently has been cleaned up and starting consisting of mostly Type B, we say that we can assume any given item currently in the pile belongs to Type B. The Talmud then asks from a Braisa where Rabbi Yosei bar Yehuda says that in a case where we have a box of coins that people use for sacred and non-sacred coins (switching off usage, sometimes exclusively for sacred, sometimes exclusively for non-sacred), we determine the status of all the coins based on whether the majority of usage overall is for sacred or non-sacred coins; the Talmud asks, well why don't we just look at what the most recent usage of the box was and say that whatever it was being used for we can assume that any given coin in the box has the same status? The Talmud gives several answers, all of which clearly accept the premise that Recency is stronger than Majority.

The obvious question is why in the world does the Talmud assume this? We always say that Majority is the strongest of proofs, beating both Proximity and Status Quo. So why is it so obvious to the Talmud that Majority would lose to Recency?

My first thought is along the lines that if we say that Majority as well as Proximity and Status Quo are not "revelations" of truth, rather they are just "arbiters" of what to do in the presence of uncertainty, then perhaps it is obvious to the Talmud that Recency is different, and that it actually is a "revelation" of what the actual truth is. My problem with this is that I just don't understand why logically Recency is a revelation of truth: it seems to me clear as day that it is just another tool in our arsenal to determine what to do in the presence of uncertainty.

The Talmud also appears to maintain that this principle of Recency is purely logical and does not require any verse. The only other place where I see Recency discussed is in Baba Metzia 26a, and there just like here we take the principle for granted and do not discuss any verse as the source. This would strongly imply that Recency must be a revelation of truth, since when it comes to "arbiters" of uncertainty we do require verses (this is for sure true for Status Quo and Majority, although as I write this I'm not sure if it's also true for proximity). The fact that we need verses for these other proof is indicative that they are just legal arbiters and thus need explicit verses because they are not purely logical revelations of truth, whereas Recency is purely logical and thus does not need a verse.

This would also fit in beautifully with the fact that by financial matters we do not follow the Majority, because the Talmud also says that the reason we do not follow the Majority is because of the principle of The Burden of Proof Is Upon the Claimant which the Talmud says is purely logical and does not require a verse. This fits in beautifully because both by Recency and Burden of Proof we determine them purely logically with no verse needed which is indicative that they are "revelation" of truth and not just "arbiters" of uncertainty.

But of course this still brings us back to our original question which is why in the world is Recency considered purely logical? It seems to me obvious that it's just another "arbiter" in the face of uncertainty.

After learning through this a bit more, it's actually fairly clear why Recency is considered so strong. It appears to me that Recency is actually just a standard form of Majority that we have come across before. For example, the Mishna in Machshirim 2:3 - 2:11 gives many examples where we care about "relevant" Majorities: for example, if someone found bread then we look at whether the majority of bakers are Jewish or not, but if the bread they found was made of pure flour then we ignore the majority of bakers and instead focus on just the majority of bakers who bake using pure flour. I would argue that this is the same principle here: it's true that overall over the course of the year the majority of coins may be non-sacred, but we know for a fact that more recently the box was being used to store sacred coins and thus the Majority of the most recently added coins are sacred, and thus this is a more relevant Majority and we follow it over the general Majority of the rest of the year.

In the Talmud Berachos 46a-46b discusses the fact that a baby is considered fully born when just it's head emerges even though the majority of the body has not been birthed yet: and not even the whole head, just the majority of the head (the forehead) is considered sufficient.

The Talmud in Eruvin 64b brings a story where Rabbi Gamliel found bread on the road and said that it was not allowed to be eaten. The Talmud says that we can learn from here that we follow the majority of travelers who are non-Jews, and thus we can assume that the bread came from that majority. The Benayahu asks that why is this a novel principle: of course we follow the Majority! This is just a standard case of an item that has separated from a Majority and we know that universally we always follow the Majority! I would suggest that the language of the Talmud implies that the Majority of local inhabitants were Jewish, but Rabbi Gamliel is teaching us that since the bread was found on the road we follow the more relevant majority of the road-travelers.

The Rashash gives a beautiful answer, that the Talmud in Chullin 6a clearly says that Rabbi Gamliel agreed with Rabbi Meir that we are Concerned for the Minority. Given that, I might have thought that therefore Rabbi Gamliel would say that even though the majority of travelers are non-Jews, still we can rely on the minority of Jews to permit eating the bread. In response to that the Talmud taught that even Rabbi Gamliel who agrees with Rabbi Meir would still not rely on the minority to be lenient.

The Talmud in Gittin 2b seems to give us a new view on the opinion of Rabbi Meir who as we know is generally Concerned for the Minority. The Talmud says that most Jewish people know that a divorce document must be written for the woman's sake, and even Rabbi Meir would agree even though usually he's Concerned for the Minority, because here the scribes who are the ones who write the actual divorce papers can be assumed to be knowledgeable. What we see from here is that even Rabbi Meir has his limits. He would not be concerned for the minority if the minority is vanishingly small, such as the chance that the scribe who wrote the divorce papers is not aware of such a basic law.

The Talmud in Sotah 31b informs us of an interesting principle: normally, we only accept "valid" witnesses, and when it comes to valid witnesses it doesn't make a difference if there's a hundred witnesses on one side and only two on the other, we still consider the two sides as equally balanced. However, there are specific kinds of cases where we do accept invalid witnesses, and in these types of cases we would follow the one hundred witnesses over the two!

My question on this is, why do we not say that these invalid witnesses are Established Things and thus we should consider their odds to be 50/50? I would answer similar to the way I answered by judges, where by judges we also do not consider them to be Established Things, because both by judges and witnesses they themselves are not the primary matter of our consideration, rather their is some question like did this woman cheat on her husband which is actually our main focus and the judges and witnesses are just external proofs that we are bringing to bear, and thus they are like the case of the meat found on the street where our primary question is around the source of this meat, and the 10 stores in the area - even though they are Established Things - are just external evidence and thus we make use of the Majority of kosher stores to help us make a decision about the meat that has been found.

The Talmud in Bava Kamma 119a tells us of a dispute between Rav and Shmuel by a case where someone wishes to purchase something from a known thief. Rav says that the only time it is permitted to purchase something from a thief is when we know that a majority of items in his possession are not stolen, and Shmuel disagrees and says that even if the majority of items are stolen it is permitted to purchase things from the thief and to rely on the fact that this particular item may have been from the minority of unstolen items.

My problem with this is that the way I explained Shmuel's opinion that we generally do not follow the Majority by financial matters is because financial matters are civil matters, and by civil cases there have to be two parties and thus the side that does not currently have the funds must bring extremely strong proof - like witnesses - in order to even be considered a valid party and for there even to be a court case at all. The problem is, that if this is true, then why by this case is Shmuel asserting that we do not follow the majority? The case here is where a person is being faced with a choice whether it is permissible for them to purchase something from a known thief: this question has nothing to do with whether there is a court case here or not. This is actually a strong indication that Rabbi Shimon Shkop's understanding is correct, and that generally speaking by all financial related matters we have to follow purely logical based rules and not Torah-created principles like Majority.

It is possible however to say that we find that Shmuel does not only argue by financial matters but also for example life and death matters that we do not follow the Majority. So perhaps theft is just yet a third, separate place where Shmuel argues with Rav. But this answer is not nearly as clean as Rabbi Shimon Shkop.

The Talmud in Nidda 29a uses an interesting language that I believe may shed some light on how minority works. The Talmud is discussing an animal that went out to pasture while pregnant, and returned not pregnant, having given birth. Our uncertainty is whether the animal gave birth to a viable offspring, because if it did then we would consider that offspring to be the firstborn and consecrated and thus the subsequent offspring would not be consecrated, or perhaps it did not give birth to a viable offspring in which case we would consider the subsequent offspring to be the legitimate firstborn and thus consecrated. The Talmud says that the law here is that we consider the subsequent offspring to be a "possible" firstborn. The Talmud asks on this that Rabbi Yehoshua ben Levi maintains that there is a Majority here: namely, that the majority of animals give birth to viable offspring; and if so, then we should apply the majority and say that the subsequent offspring is not considered the firstborn and would not be consecrated.

Ravina answers the Talmud's question as follows: "Because one could say that that the majority of animals give birth to viable offspring and a minority birth something which is not viable, and all animals that are about to give birth discharge liquids, and since this animal did not discharge liquids it weakens the majority". Now, let us analyze what Ravina said: the crux of his answer is that the Majority that most animals give birth to viable offsprings is weakened by a counter Majority that most animals discharge prior to a viable birth and this animal did not discharge. My question is, what in the world is the first half of Ravina's statement, where he says that true, there is a Majority, but there is also a minority? What is he trying to say? Of course every majority also has a minority, he's not saying anything new here, and how is it relevant to his actual answer which he gives in the second half of his statement?

I would suggest that based on the Talmud in Gittin 2b that we brought above, we see that even Rabbi Meir who is Concerned for the Minority would agree that there are certain types of minority which are so vanishingly small that we don't have to consider them at all. Rabbi Shimon Shkop makes a similar point that Shmuel who usually says that we do not follow the Majority when it comes to financial matters, does agree that certain Majorities - for example, that the majority of people do not repay loans early - are so strong and their minority so vanishingly small that we would follow them even by financial matters. So based on this, perhaps the point that Ravina is making here is that there is a real and certain minority of animals that do give birth to non-viable offsprings and therefore this would not be considered a "super-majority" and therefore we can say that the majority is weakened by a counter majority. So according to my explanation, if the Majority that most animals have viable births was a "super-majority", then we would not be able to weaken it using a counter majority.

The Talmud in Bechoros 45a says that if one found the bones of a dead person, if the majority of their skeletal structure or the majority of their bones are present then it imparts impurity. The Talmud elaborates that a majority of the skeletal structure would be where two calves and one thigh are present since this constitutes the majority of height in an adult, and the majority of bones would be when there are one hundred and twenty five bones present.

But the interesting thing we see here, is that Majority is not just "simple", meaning like the majority of bones. Rather there is also such a thing as a "conceptual" majority, like the majority of the height of the person, where this attribute of a person's height is considered a defining attribute to the extent that a majority of bones that comprise that height results in us considering as if the entire skeleton was present.

The Talmud in Beitza 15a explicitly says that the opinion of the Mishna is to be Concerned for the Minority. The case is where a person found Tefillin that were laying on the ground outside on Shabbos, and our concern is that thieves in the area might find the Tefillin and steal them (and therefore a person should pick them up and carry them into the city). The Talmud says that even in a case where the majority of thieves are Jewish, and thus we don't have to be concerned that they would steal a pair of Tefillin, still, the Mishna comes to teach us that we are Concerned for the Minority here.

This is very interesting because the implication is that the Mishna is agreeing with Rabbi Meir that we are Concerned for the Minority. It could be argues that this is a special exception by Tefillin, but the question of course is why would Tefillin merit this special ruling over everything else?

It is possible to say that technically by donning the Tefillin so as to carry them to safety, the person is not violating the Shabbos. I believe that this may be how to understand the Talmud, that while we prefer that a person not don the Tefillin at all on Shabbos, it's technically OK (I believe, from my reading of the Talmud), and therefore we say that a person should be concerned for the minority.

If this is the case, then it is a good indication that Majority is not a revelation of truth, rather an arbiter of uncertainty, because if it was a revelation of truth then we should be confident that nobody is going to disturb the Tefillin.

The Talmud in Sotah 476b is discussing the fact that when we are dealing with non-optimal witnesses who are disagreeing with each other, we follow the Majority (by optimal witnesses it does make a difference if there's a thousand on one side and only two on the other, we consider them balanced). The Talmud says that the Mishna is coming to teach us an important principle: I might have thought that we only follow the Majority to be stringent, so the Mishna teaches us that even if following the Majority of witnesses will result in a leniency we should still follow the Majority.

This is interesting because why should the Talmud have assumed at all that we would only follow Majority to be strict?

I think the likely answer is that since accepting the testimony of non-optimal witnesses is itself very novel, we might have thought that following the majority of them is limited solely to being stringent. But I think the question is better than the answer.

The Talmud in Berachos 48a gives us a potentially huge insight into Majority. It introduces the idea that a Super Majority is different from a Simple Majority. The case is where there are 10 men eating together and they want to know if they can join to make a Zimun; however, if only nine of them ate bread and one ate vegetables, I might have thought that the one could not join together with the ten, so the Talmud teaches that since the majority did eat bread it's fine for the one to join them in the Zimun. The Talmud then asks well what if only six of them ate bread, can the other four join with them? Rabbi Yirmiyahu says of course they can join, after all, we see from the case of nine bread-eating men that a Majority is sufficient for Zimun, so if Majority work then who cares whether it's a Super Majority or Simple Majority? But Rabbi Zeira disagrees and says that there needs to be a "Noticable Majority", e.g. a Super Majority.

This is really, really interesting because where in the world does Rabbi Zeira get this from? Who says that a Super Majority should be any different from a Simple Majority?

We find another example of a "Noticeable Majority" in the Talmud in Chullin 29a where Rava says that with regard to asserting that an animal has a fatal defect in its trachea or esophagus that renders it non-kosher, it must be that the defect encompasses a Noticeable Majority of the pipe, but even if it does extend to the majority of the pipe, if it is not clearly noticeable then we do not consider it a valid Majority (although I would note that the Ramban explains this to mean that strictly 50/50 does not suffice, but any majority - even a tiny bit - is sufficient to be considered a noticeable majority and thus a defect).

We see from the Talmud in Bechoros 20b the Rabbi Akiva agrees with Rabbi Meir that we are Concerned for the Minority.

We see from the Talmud in Avoda Zara 34b that even though Rabbi Meir is generally Concerned for the Minority, he is not concerned for a minority of a minority. The specific case is where we forbid cheese produced in the city of Beis Unyaki because we suspect that the cheese may have made use of rennet that was produced from the stomach of a calf that was slaughtered for idol worship. The Talmud says it must be that according to Rabbi Meir the majority of calves in the town are slaughtered for idolatrous purpose. On this the Talmud asks, even if it was just a minority it should still be forbidden according to Rabbi Meir who maintains that we are Concerned for the Minority. The Talmud answers that if only a minority of calves were slaughtered for idolatry then we would be confronted with a minority of a minority, since when we are considering the rennet that came from the stomach of an animal of that town, most animals of that town are not calves, and of the calves, most of them are not slaughtered for idolatry. And since there is only a minority of a minority even Rabbi Meir would not forbid.

The Ritva says something interesting here, that the reason Rabbi Meir is not concerned for a minority of a minority is not because the chances are so low, but rather because it is a double uncertainty: first whether the animal was a calf, and even if it was a calf maybe it was not slaughtered for idolatry. The Ritva brings proof that Rabbi Meir is concerned even for tiny minorities since we see that he is concerned that maybe a minor will never enter puberty and thus never be valid for a Levirate marriage. My question on this is that we see from Rabbi Meir in the Talmud in Gittin 2b that when the minority is extremely unlikely - namely, the chances that divorce scribes are not familiar with the laws of divorce - we do not concern ourselves for the minority.

The Talmud in Zevachim 72a discusses the case of the Mishna where a single animal which is forbidden for use because it was a sin offering that must be left to die or it was an animal which must be stoned, if such an animal got mixed up in a herd of other animals, even if the permitted animals are a huge super majority we would still say that they are all forbidden and must all be killed. The Talmud asks on this that why do we not follow the principle that Majority Negates Minority? (And the language the Talmud uses in quite interesting: it says that the forbidden animal should be "Negated" by the Majority, which is an indication that my understanding of this topic - namely, that all cases of Majority work via the power of negation - is correct). The Talmud answers that since animals are sometimes sold by unit instead of just by weight or volume they are therefore considered "significant" and cannot be negated.

The Talmud then says that this actually is subject to a general dispute over whether something can be considered "significant" (and therefore can't be negated) if it is exclusively sold by unit, or even if it is just generally sold by unit. Rabbi Meir is the one who says even if it is just generally sold by unit it cannot be negated. My question on this is, that we know that Rabbi Meir famously maintains that we are Concerned For The Minority, and if this is the case then even if an item is not generally sold by the unit we should still say that we are Concerned For The Minority and thus everything should be forbidden!

The following is a complete list of all places that Majority is discussed in the Mishna.

The Mishna in Nidda 3:5 explicitly discusses the principle of Majority (and see the Talmud Nidda 29a). The case is where a woman gives birth and we need to determine when the moment of birth is, because only from that moment and on must she count her days of impurity. If the baby came out chopped up or feet first we say that when the majority of limbs have existed we consider it like the baby is born; however, if it came out normally, then it is considered born as soon as the majority of the head exits the mother - and the Mishna specifies that the majority of the head means when the forehead exists the mother.

This is fascinating because I would think that Majority should always mean the majority of the limbs, meaning the majority of the baby. But the fact that when the baby is being born normally we focus on just the head and we ignore the fact that the majority of the body is still in the mother, suggests that the Mishna considers the head to be a significant minority and thus we do not follow the majority of the rest of the body that is still in the mother.

But what's interesting is that it's almost like we're dealing with a majority of the majority here: meaning, we're saying that the head is important and thus when it exits we consider it like the baby is born, yet we don't need the whole head to come out because even just a majority of the head is sufficient!

The Mishna in Kilayim 9:1 clearly describes the principal of Majority Negates Minority. The case is the law that prohibits wearing clothing that contains a mixture of wool and linen; the Mishna says that lets say you mix camel hair together with sheep's wool, if the camel's hair is in the majority then it is fine to mix to entire mixture together with linen. This is clearly because the camel hair negates the minority of sheep's wool.

The Mishna in Kesubos 1:10 clearly describes relying on a majority when it comes to determining whether a woman was raped by someone who had a valid lineage. The Mishna says that if the majority of the men in that area have a valid lineage then we follow the majority (the commentators point out that the Mishna actually would only follow the majority if there are two majorities - which in this case is a majority of the local population plus a majority of a band that was traveling in the area - do we follow the majority to be lenient when it comes to matters of lineage.)

The Mishna in Machshirim 2:3 - 2:11 discusses at length many cases where we follow the Majority. For example, if someone found a lost item, if the majority of inhabitants were non-Jews he does not need to announce it, but if the majority were Jews he does have to announce it. And the Mishna also keeps repeating that if it's 50/50 we must be strict. The Mishna also makes an interesting point that sometimes we don't follow the simple majority but rather the relevant majority: meaning, if someone found bread we have to look at who the majority of bakers are, but if the bread was made of pure flour then we don't look at the full majority of bakers, rather just at the bakers who bake with pure flour.

The Mishna in Kelim 11:4 discusses unclean iron that was smelted together with clean iron, we follow the majority.

The Mishna in Chullin 2:1 says that if one slaughters the majority of either the trachea or esophagus in a bird then it is considered a valid slaughtering (and for an animal it would be the majority of both the trachea and esophagus)

The Mishna in Mikvaos 4:4 says that if a aajority of kosher mikva water mixed with a minority of non-kosher mikva water before the combined waters entered the mikva, then we consider the whole thing to be kosher. However, if the majority was non-kosher or the waters were 50/50, then we consider it non-kosher. The Mishna adds a very interesting point: let's say the waters only mixed after they entered the mikva, then even if the majority is kosher we would not say that the entire mixture is kosher, rather it would be considered non-kosher! I have looked at the commentaries and I'm trying to understand this, but potentially this may shed a very important light on how Majority works; because, really, why should it make a difference if the waters mixed after they entered the mikva: there's still a majority of kosher water here which should negate the minority and allow us to consider the entire mixed waters as kosher!

One could theorize whether the reason that a minority is negated is because of a weakness in the minority or because of a strength in the majority. Meaning, do we say that when something is in the minority it is inherently considered to be non-existent and thus we are left with solely the majority, or do we say that a minority is not inherently weak rather a majority is strong enough to subsume the minority and effectively negate it.

I would argue for several reasons that the principle is based on the majority being strong and thus actively negating the minority.

One elegant argument for this approach is in the terminology of Majority. In Hebrew the word we use is "Rov"; now, Rov means Majority but it also is uses to mean "a large size/quantity". For example, the Mishna in Berachos 7:3 says that "According to the size of the crowd they recite the blessings"; the word "Rov" is used here to mean size. The fact that the term Rov is used to mean both Majority and Size indicates to me that the essence of what makes something a Majority is wrapped up in the fact that it has a substantial size; that is to say, that the mechanism of Majority is dependant on the fact that the overwhelming size of the majority subsumes the minority. And even stronger, Rabbi Samson Raphael Hirsh defines "Rov" as meaning "fight", so this is clearly an "active", subsuming force that overwhelms the minority.

Another proof is that in my opinion the Torah maintains that based purely on logic we would always respect and acknowledge the minority to the point that we would always consider the minority to be 50/50 odds. My proof to this is that both for Tangible Majority and Theoretical Majority we require verses to teach them to us; but if the principle of following the Majority was purely logical then the Talmud would have said Why I do I need a verse, it's just logical! But from the fact that we do require verses means that the Talmud understood that without the verse I would not have followed the Majority, meaning that we would have given the minority equal weight to the majority and said that we were facing an even 50/50 odds. Given this, then the simplest explanation of what the verse is teaching us is not a complete repudiation of basic logic, rather a new principle that while yes, the minority is significant, still, the Majority is able to overwhelm and subsume it.

The strongest argument for this approach is that to my understanding the way the Torah constructed the mechanism of Majority is that it works via an active negation of the minority. Now, if the minority was just fundamentally weak I would not need the Majority to actively negate it: I would just say that a minority all on its own has no value and is considered like it's not here at all! And yet the the principle of Majority Negates Minority is derived from the very same verse by the courts where we learn the fundamental principle of following the Majority. To me, this is a clear indication that the minority fundamentally has an equal weight as the Majority, and it is only because the Torah teaches us a new principle of negation that we are able to consider it as if there was only the Majority present.

This approach also makes the entire subject of Established Things Have 50/50 Odds a lot more palatable and understandable. Because if it's the case as we're saying that the Torah's starting position is that purely logically we would always consider the minority to be 50/50 odds because we consider it to be significant, then even after the Torah taught me that Majority is strong enough, if we are facing a minority which is unusually strong - as in the case of Established Things - then it's easier to understand how we revert to the fundamental principle that the minority has an equal weight to the Majority and thus we are faced with 50/50 odds!

I decided to trudge out to the BMG library today in the Yoshon building to go through their set of the Encyclopedia Talmudis to look up the principle of The Burden of Proof Is Upon The Claimant (Hamotzei mechavairo alav haraya).

What I found is fantastic.

The Talmud in Bava Kama 46b quotes the verse in Shemos 24:14 that when Moshe was preparing to ascend to Mt. Sinai he told the elders that Aharon and Chur would stay behind, and "whoever has a legal matter should approach them". The Talmud says that the language "approach" ("yigash") can also be read as "submit", and thus the verse can be read as "whoever has a legal matter should submit to them", meaning that the claimant who is initiating the proceedings by coming to the court must be the one to submit evidence to the court.

Rav Ashi responds to this and says that there is no need for a verse; it is common sense! Because "someone who suffers from illness goes to the doctor".

Now, the way I understand Rav Ashi is that he is referring to the classic distinction in law between civil and criminal matters. When it comes to civil matters there are always two parties involved: the claimant and the defendant. If either of them is absent then there is no case here at all. Whereas by criminal cases we don't need any party to exist outside of the defendant: as soon as Person A kills Person B we have a criminal case on our hands: we don't need the family of Person B to bring a suit against Person A in order for there to be a case against him.

It is in this manner that Rav Ashi says "someone who suffers from illness goes to the doctor". A doctor doesn't just point to random people on the street and start diagnosing them: after all, how can he, he doesn't even know what their symptoms are until they proactively tell him! So before the doctor can diagnose anything, he needs the patient to first describe and demonstrate their symptoms. The same is true for civil (specifically financial) cases: until the claimant brings absolute proof (like witnesses) that the money is theirs, we don't see them as even being part of the court case yet, and thus we are missing the claimant party to this civil case and thus there is no case here at all!

And what's absolutely fascinating is that right before the Talmud explains the source of The Burden of Proof is Upon The Claimant, it brings the disagreement between Rav and Shmuel regarding Majority by financial matters, and says that the reason that Shmuel maintains we do not follow Majority by financial matters is because of the principle that The Burden of Proof is Upon the Claimant!

Now, there are many places in the Talmud where we mention the principle of The Burden of Proof, and yet out of all those places the Talmud picks here to explain the reasoning behind it - immediately after we attribute the principle of Burden of Proof to be the reason behind why we do not follow Majority by financial matters. I would suggest that this is not at all accidental. The Talmud is trying to explain why it is that the principal of Burden of Proof means that we do not follow the Majority by uncertainty; and to this the Talmud explains that the court does not consider there to be a civil case here at all unless the claimant can demonstrate that they have an actual side, which can only be accomplished by bringing witnesses as proof.

Now, if there is no case here at all, then it makes a lot of sense that Majority is unable to work by financial matters but does work by criminal matters, even if they are life-and-death, because by financial matters there is no court case here at all until the claimant brings rock solid evidence, and therefore since there is no case things like Majority or Status Quo are unable to work, whereas by criminal matters there is a court case here, and therefore we can make use of the proofs of Majority and Status Quo etc.

And this fits in very beautifully into the language of the Talmud. Because you might object to my approach and say that the principle of "going to the doctor" is a metaphor for how the claimant cannot demand things from the defendant without strong proof (meaning, the "doctor" represents the defendant); but the court is not part of the discussion here. Meaning, you could argue that of course we consider there to currently be an ongoing court case, just that we have a principle that the claimant must bring extremely strong proof. But to this I would point out that the verse that the Talmud initially brings is explicitly addressing the courts, and says that the claimant must "submit" proof since the burden of proof is on the claimant. Given this, then when Rav Ashi replies that I don't need a verse for this since it is purely logical, he must also be discussing along the same lines, where the "doctor" in his metaphor is not the defendant, rather the court! And it is the court, in Rav Ashi's metaphor, who doesn't know that the defendant is even "sick" at all until he brings forward definitive proof that he is even involved!

I do really like this explanation, and it strikes me as being very true; but it is important to point out that some of the Rishonim do not appear to agree with my approach; the way they explain that we do not rely on Majority by financial matters is because the minority joins together with the Status Quo and together they beat the Majority. Now, according to my answer, this is not the case at all: there isn't any kind of "battle" at all with Majority on one side and Status Quo and minority on the other side, rather we consider it like there's no court case here at all and thus Majority is not even relevant.

I had an extraordinary insight; extraordinary in the sense that I think it's quite good, but also extraordinary in the sense that it's kind of wild. Either way it's a real swing and I've just got the outline of it worked out now. I need to spend some real time fleshing it out, and the odds are good (pun intended) that along the way I'll find some flaws in the theory. But either way, here it is:

So one of the big, outstanding questions in the entire topic of Majority, is that the Talmud in Bava Kama 27b says that by financial matters we do not follow the Majority, whereas we know that by everything else - including capital punishment - we do. And the question is, how does this make sense? If Majority is not strong enough to take somebody's money away from them, then it certainly should not be strong enough to take their life away from them!

So here's what I think. I'm going to just write it out, and then afterward I'll flesh out all the places where I believe we can find proof to my theory.

My theory is based on the source of the famous principle of Established Things Have 50/50 Odds. The Talmud in Sanhedrin 79a discusses a case where there are nine Jews and one gentile in a group, and somebody throws a rock at one of them with deadly intent and it ends up hitting and killing one of the Jews. The Talmud says that I would assume that since we generally follow the Majority, then we should say that the group should be considered entirely Jewish (since Majority Negates Minority) and thus we should say that the perpetrator threw with deadly intent at a group that was 100% Jewish and therefore should certainly be liable to the death penalty. In response to this, the Torah wrote a verse in Devarim 19:11/12: "And when there will be a man who hates his fellow and lies in wait for him and rises against him and strikes a fatal blow and kills him, and then flees to one of these [sanctuary] cities. The elders of his city shall send and retrieve him from there, and put him in the hands of the blood-avenger and he shall die." The Talmud deduces from the emphasis on "him" in the words "wait for him and rises against him", that the assailant has to actually be 100% sure that their deadly action will result in a death sentence, and that in the specific kind of case we are discussing here, where the Majority is Jewish and the minority gentile, since the minority is Established we will apply the principle of Established Things Have 50/50 Odds and say that since the odds are an even 50/50 here, it is like the case where there is one Jew and one gentile where we say that we are lenient by capital punishment and thus the assailant cannot be held liable for murder.

Now, one of the big questions that is asked on this Talmud, is what in the world does the principle of Majority have to do with a person's intent? We are trying to determine whether the assailant intended to kill a Jew or not; given this, then what role does the abstract principle of probability play? We're trying to figure out what the person's intention was when they threw the deadly missile, which has nothing to do with the general, abstract principles of probability. Just because we have a principle that we follow the Majority in matters of uncertainty, what does that have to do with the mindset of this particular individual at the moment that they threw the rock?!

And even more puzzling is the Talmud's conclusion, that the Torah is teaching us a new, general principle by all matters of probability that Established Things Have 50/50 Odds. Because if anything, I would say that the Torah is teaching me a limited principle that only applies to people's intent: namely, that when I see physically in front of me 10 things, then because human perception does not follow the abstract principles of probability it is quite possible that for me the 1 object holds just as much importance in my mind as the 9, and therefore we must default to assuming that the odds are only 50/50 as regards my intent. But this should not be generalizable as a principle for all probability; this should just be considered a niche accommodation for human intent!

So here in short is the outline of my theory: the idea is, that when it comes to probability, the Torah introduces a new concept that human perception plays a role. Meaning, that even though from the perspective of mathematical probability something has 90/10 odds, if the human perception is potentially focused on the minority, then it gives that minority an equal significance to the Majority. The idea being that the Torah's rule are very human-centric: after all, the laws of the Torah were made to be followed by humans, and thus things like measurements for example are all done in ways that an average human could perform with no special equipment. So that same approach is taken by probability: the Torah's principle are not just absolute abstractions, but rather are entirely wrapped around human activity: thus, when we are trying to determine the probability of Jews vs gentiles in a group, the human perception of the probability is pivotal! And since when something is physically in front of you it plays a much larger role in your perception, and is harder to simply "negate", the Torah says we must apply a principle that Established Things Have 50/50 Odds.

Now we can answer both questions nicely. It makes sense now that the principle of Majority is connected to a person's intent, since it is the person's perception that affects how we consider the actual odds.

And it also makes sense that we learn from here a general principle to all cases of probability: because by all cases of probability we do care very much what was in the person's mind: after all, their perception changes how we calculate the odds!

And now we can answer the huge question we started with, namely why it is that by financial matters we do not follow Majority. There is a disagreement whether this principle is Biblical or Rabbinic (meaning, the Rabbis instituted a decree that by financial matters we do not follow the Majority). I would suggest that it's both! Meaning, that it's true that Biblically there is no distinction between financial matters and everything else, and that therefore we would follow Majority even by financial matters; however, a thousand years later the Rabbis instituted a number of decrees dedicated to protecting people in financial matters, and as a result of these Rabbinic decrees, human perception about minority odds for money changed, and people began to focus on the minority possibility that the money might belong to Person A, and as a result of this change in human perception the Biblical principle of considering the odds to be 50/50 came into play! Now of course, money is not considered an Established Thing, and it is not because of the principle of Established Things that by money we do not follow the Majority, but rather it is because of the underlying principle of human perception which is the reason that Established Things Have 50/50 Odds, and is therefore also the reason that by money we consider the odds to be 50/50 and that the minority odds are not negated!

To elaborate even further on my insight: I believe that fundamentally the Torah is concerned for the minority. Meaning, that if no laws had been issued either way, the Torah considers it basic common sense that we would err on the side of caution and be concerned with the minority. This is evidenced by the fact that the verse of "After the majority to incline" had to be written to teach us that the minority is negated: because without the verse I would say it is not negated and we err on the side of caution. Given this, it means that we actually have a fairly low bar to pass to have something be considered 50/50 odds: so long as the minority is not completely negated then we revert to our fundamental principle of being concerned with the minority and considering the odds to be 50/50. Thus, if human perception views the minority as being more tangible than the norm, the result is that we do not consider the minority negated and revert to 50/50 odds.

There is a very interesting principle with regard to kosher and non-kosher food which was mixed together which requires some real research. The principle is called Same Types (Min B'Mino). The idea is that there is a difference in negating a minority depending on if the minority is of the same type as the Majority or is of a different type (exactly what constitutes "same" and "different" is an entire topic of its own (hint: is it based on a difference in "name" or a difference in "taste")). When substances are of a Different Type then the negation of the minority happens based on simple Majority. However, if the substances are of the Same Type, then we require the Majority to have a ratio of at least 60:1 in order to negate the Minority.

Now, the question is, why in the world is there a principle of 60:1? We have determined that there is a principle of Majority Negates Minority and that this suffices with a simple majority (with the exception of the death penalty which requires a Majority of 2 judges). So why would the Majority have to be 60:1 to negate the minority?

The answer is, that the Talmud in Pesachim 44b quotes the verse from Bamidbar 6:3 that a Nazir must abstain from "All grape-steeped products"; meaning, that if grapes were merely steeped in a liquid and then removed, then the remaining liquid is still forbidden. The Talmud deduces a principle from here that Taste is Like Substance; meaning, that Taste is considered like its own physical entity, and the Torah's forbidding of physical grapes extends as well to the taste of grapes, and thus even if you remove the physical grapes after having steeped them in a liquid, since the taste of grapes remains in the liquid they are still considered forbidden.

Given this, then the principle of 60:1 makes sense. Because when it comes to the actual, physical grapes, it's easy for us to tell whether the Majority consists of a forbidden or permitted substance, but when it comes to taste there isn't really any physical "thing" here that we can measure. So how can we determine Majority? To this the Talmud in Chullin 98b deduces from the verse in Bamidbar 6:19 which says "and the priest shall take the cooked foreleg of the lamb" that the foreleg - which is reserved exclusively for the priest and is forbidden to be consumed by non-priests - was cooked together with the rest of the ram and even so we say that the rest of the ram is permitted to non-priests. The Talmud deduces that the proportion of the foreleg to the rest of the ram's body is 1 to 60, hence we see that 1 part of a forbidden mixture which is steeped inside 60 parts of a permitted mixture does not forbid that permitted mixture.

So now we can understand better the principle of 60:1. The regular rules of Majority do apply by taste; the problem just is how do we determine what the Majority taste is? There's no real scientific way of determining this. For this reason we rely on the verse that tells us that we can assume for sure that when the ratio is 1:60, the taste of the 1 is definitely in the minority and thus negated.In Depth

Based on everything I have been working on, it's become clearer and clearer to me that the source of Majority Negates Minority is from the verse of "after the Majority to incline", like the opinion of Rashi and the Ran. There are 3 primary reasons for this:

1) The source can't be from the Talmud in Menachos 22a because the Talmud there does not explicity say that the Sages derive from the verse in Vayikra 16:18 (re blood of a bull and goat) a global principle of Majority Negates Minority (even though Rabbi Yehuda there does derive a global principle that Majority does not negate minority)

2) We have a principle that a court requires a specific number of judges in order to be valid (3, 23, or 71). And yet, we have another principle that if just a majority of judges vote we can follow their vote. The problem is, that let's say with a court of 3, we require 3 judges in order for the court to function and yet we are going to follow the ruling of only 2 judges!In Depth

3) The strongest proof in my opinion is the proof I brought from how we err on the side of caution in capital cases when there is just a majority of 1, but when there's a majority of 2 we do follow the Majority. The only way this makes sense is if the mechanism of following the Majority is accomplished via negating the minority, otherwise we should continue to err on the side of caution even when there's a majority of 2 judges.

An interesting thought:

What happens if I have a pot of kosher food and then non-kosher food gets added and mixed in bit by bit until the majority of the pot contains non-kosher food. Do we say that as each small piece of non-kosher food was added it got negated, and therefore even though technically the majority of the food in the pot is non-kosher, since each individual piece was negated as it was added therefore we consider it like the entire pot is kosher, or do we say that no, physically the majority of the food in the pot is non-kosher and therefore maybe it's true that as it was added we applied Majority Negates Minority, but now after the fact that the majority of the food is non-kosher we would not say Majority Negates Minority?

I have a proof that Negation of the Same Type cannot be the same principle as Majority Negates Minority. By Majority Negates Minority we clearly require the elements to be completely mixed together and indistinguishable in order for the negation to take place. However, by Negation of the Same Type, the Talmud in Yoma 58a applies the principle to when a bowl is placed inside another bowl, that because both bowls are the same "type" we should apply the principle of Negation of the Same Type (the Talmud also gives an example of a foot on top of another person's foot, that would also be considered Negation of the Same Type). But by the bowls they are clearly separate from each other and thus would not have the principle of Majority Negates Minority applied at all!

But I believe that this is actually not the case. And that we are just using similar sounding terms here, but the underlying principles are unrelated. Meaning that true, in both cases it is true that things of the Same Type are all mixed together, but by food the reason we permit it is under the standard principle of Majority Negates Minority, whereas by the bowls we have a different principle that materials that are of the Same Type can be considered singular and thus it is considered like the priest is holding the inner bowl directly.

Some interesting sources:

• The Talmud in Horayos 3b discusses at length whether a court is responsible for an incorrect ruling, including when there is a minority of judges who differed. (I really have to work on this whole thing in Horayos in depth, it really goes into a lot of detail around Majority and courts, which is key.)

• The Talmud in Berachos 47a says that after a person says a blessing they should wait until everyone finishes answering Amen before beginning to eat. Rav Chisda says you just need to wait until the Majority finish saying Amen, because "anyone who answers Amen longer than normal is just making a mistake". My question is, why didn't Rav Chisda just say that Majority Equals Entirety and therefore since the Majority answered Amen it is like everyone finished saying Amen and therefore you can begin to eat?

• The Talmud in Kiddushin 73a says that we know that a Mamzer (someone of invalid lineage) is not allowed to marry non-Mamzer Jews. The question is, what if a person is only possibly a Mamzer? The Talmud says that we derive from the verse of "A Mamzer shall not enter into the congregation of the Lord", that only a certain Mamzer cannot join, but a "possible" Mamzer can. I see this as a strong proof against the opinion of the Rambam who says that Biblical Uncertainties are permitted Biblically - because if this was true, then why do we need a special verse here, why can't I just say that this is a Biblically Uncertain Mamzer and therefore they are Biblically permitted?! So this is a proof that Biblical Uncertainties are forbidden Biblically.

• The Talmud in Gittin 70b quotes the opinion of Shmuel that if two witnesses saw Person A slit Person B's throat or the majority of their throat but they didn't see Person B actually die, they can still testify with certainty that Person A killed Person B. Now, this language about the "majority of their throat" is extremely similar to the language we employ regarding ritual slaughter where we say that slitting the majority of the throat is considered as if the whole throat was slit. And by ritual slaughter we say that the reason is because of "Majority Equals Entirety". But here, by killing someone, how can the logic of Majority Equals Entirety work? The implication is that the reason they can testify to certain death is not because when a majority of the throat is slit then it is certainly fatal - rather, the implication is that it is simply because of the principle of Majority Equals Entirety and thus it as if the whole throat was slit, which is indeed fatal. But this means that potentially, from a medical perspective, the majority of the throat being slit is not fatal, and yet still because of the principle of Majority Equals Entirety the witnesses can treat the case as if the entire throat was slit! And in fact, even without this Talmud we really should have to say the same idea purely as a result of the principle of Majority Equals Entirety. But of course, it is wild to say this! After all, how can they testify to certain death if the majority of the throat being slit is survivable?! The Meiri here does note that even when just the majority of the throat is slit it is fatal and this is why we say they can testify to a certain death.

• I have an EXTREMELY strong question against those who maintain that Experimental Probability is not a revelation of truth, rather just a Torah law that by fiat we follow the majority. If so, then the Talmud in Sotah 31b is extremely difficult to understand: the Talmud there brings the opinion of Rabbi Nechamia that in cases where the Torah allows us to rely on witnesses that would normally be invalid (for example, female witnesses testifying that man's wife secluded herself with another man), then if there are multiple competing witnesses we follow the majority of the witnesses: so if majority are saying she did seclude herself then we follow them, but if the majority say she did not seclude herself then we follow them. The question is, is that this is an Experimental Probability, and if an Experimental Probability is not any kind of revelation of truth, then how in the world does it make sense that witnesses - whose entire purpose is to reveal the truth - are given greater trust if they are in the majority?! After all, Experimental Majority is not evidence of anything!! And this is even a bigger question on the Talmud in Makkos 5b that says that even though there is principle that if two witnesses come and testify, another two witnesses can come afterwards and impeach the first two, I would have thought to say that let's say there were a hundred witnesses in the first group and only two in the second group that the two should not be able to impeach the one hundred. To refute this the Torah had to teach a verse that "By the hand of two witnesses or three witnesses shall the condemned be executed", with the added language of "three witnesses" coming to teach us that just like two witnesses can impeach two witnesses, so too can two witnesses condemn three witnesses. My question is, why in the world would I not have said this even absent the verse?! After all, there is a principle that Established Things Have 50/50 Odds, and if so then of course I wouldn't follow a Majority here by the testimony of witnesses since they are all Established! For this second question we can actually give a great answer similar to how we answered the question of why by the court is there not a principle of Established Things Have 50/50 Odds: by the court I answered that a court is similar to the case of 10 meat stores where a piece of meat was found on the street, where we do not apply the principle of Established Things even though the meat stores are established, because the item under consideration is not the meat stores directly, rather the found piece of meat, and the stores are just external proofs; and the same is true by a court: the item under consideration that we are uncertain about is the case that came before them, and the judges themselves are just external proof. So we can say the same thing by witnesses: the item under consideration is the case that they are testifying about, but not the witnesses themselves, therefore we would not apply the principle of Established Things and we would follow the Majority, and thus the Torah has to have an explicit verse against that. But my first question still stands and is very strong in my opinion. Perhaps you could say that witnesses are a kind of Theoretical Probability in the sense that the whole reason we believe testimony at all is because most people can be relied upon to tell the truth most of the time; but to this I would say that from the fact that the Torah requires explicit dedicated verses to teach us that we can accept testimony from witnesses implies that without these verses we would not accept testimony since there is no Theoretical Probability that most people can be believed (because if this was a valid Theoretical Probability then why would need a verse at all?)

• There is an interesting observation from the language of the Talmud in Berachos 50a that we make a distinction in our blessings based on the size of the crowd; the details are unimportant, but what matters is that the Talmud uses the language "Rov" to mean "size". Now, normally "Rov" is used to mean Majority, and clearly that is how it is related to the usage here of "size", but I wonder if there's some deeper significance that we can extract from this usage of "Rov" to mean "size".

• Just a note so I don't forget the source: the Talmud in Sotah 47b quotes Ulla that wherever one witness is believed, it is henceforth considered as strong as two witnesses; thus, if a second witness comes later on we will not believe him (so only when competing witnesses come simultaneously will we have a problem with their competing testimony).

• The Talmud makes an interesting inference in Sotah 47b: the Talmud understand that the Mishna is teaching a principle that when we are dealing with invalid witnesses who are disagreeing with each other, we follow whichever side has a larger number of witnesses. The Talmud asks, why does the Mishna have to give me two cases that teach me this; and the Talmud answers, because if there was just one case I might have thought that we only apply the principle of Majority when we are being strict, but not when we would be lenient; thus, a second case is mentioned in the Mishna to teach that even when the Majority of witnesses will end up delivering a lenient judgment, still we follow the Majority. My question is, since the Majority by invalid witnesses is just a standard Experimental Probability, then why in the world would I think that it only applies to "strict" judgements? To my knowledge, we never distinguish elsewhere between strict and lenient judgements by Experimental Probability, so why would we do so here?

Just an interesting observation:

Experimental Probability has both a unique strength and unique weakness when compared with Theoretical Probability.

It is uniquely strong because by Experimental Probability there is a certain Majority - meaning that we know that the Majority for sure exists and is present; whereas by Theoretical Probability it is possible that there is no Majority present at all. For example, by the case of 10 meat stores, the Majority of kosher stores certainly exist. Whereas by the case of a child who performed a Levirate marriage, it is possible that for his generation no children will attain puberty - of course this is extremely unlikely but it is possible. Thus, Experimental Probability has an advantage.

However, the same concept also presents a unique weakness for Experimental Probability: because it means that we know that the minority is for sure present as well! By Experimental Probability, we know for sure that there is 1 meat shop which is not kosher. Whereas by Theoretical Probability, it is possible that all children of this generation will attain puberty, and thus there is no minority at all!

Yesterday was absolutely jam-packed!

I met and learned together with Rabbi Simcha Lang who publishes the Chezkas Hashmatza seforim that BMG uses each zman that contains all the sources for the sugyas that they are studying. Similar to the goal of my website, Rabbi Lang is working to make deep sugyas more available and streamlined to people who want to learn them. I hope to continue working on these topics together with him and his kollel.

Because he is an expert on sources, it was very illuminating to discuss a number of points that I have made on the topic of Majority. A lot of new sources were thrown at me and I am now actively working my way through them and through their ramifications, but I will now write about some of those sources here.

But before I get to these sources we discussed, I just came across a wonderful proof in what the nature of a court's ruling is. Because there are 2 ways that a court's ruling can work: 1) we have a requirement to follow individual sages, and a court is merely a collection of those sages of whom we follow the majority opinion, or 2) that a court has its own, distinct requirement to be followed.

Now of course, you might ask how option 1 makes sense: if what powers our requirement to obey the courts is merely the individual commandments compelling us to follow each individual member of the court, then why is the context of a "court" important at all? After all, even if the majority of the court votes one way, we should still take a poll of what all the Sages across the entirety of the Jewish people maintain, and just follow the majority of those opinions! So it must be, that even according to option 1, while it's true that the power that is compelling us to follow the court is merely the requirement to follow the individual judges, the form in which that power can be formally expressed according to the Torah is only in the form of an established court with a specific number of judges. So if the majority of the court rules one way, then even if the majority of Sages at large disagree with them, until those other Sages form a formal court of their own their opinion is not materialized as something that we must obey. The only time we must actually obey the individual Sages is when they issue their ruling in the context of a formal court.

All this being said, I have a clear proof from an open verse that option 2 is correct. The Mishna in Sanhedrin 2a says that the source for the court of 71 sages is from the verse in Bamidbar 11:16/17 where Moshe is begging Hashem to not make the burden of the Jewish people be on his shoulders alone, and Hashem tells him to "gather to me 70 men from the elders of Israel... and have them stand with you. And I will descend and speak with you there and I will reserve from some of the spirit which is upon you and I will place it on them; and they will share with you the burden of the people and you will not have to bear it alone." Rabbi Shamshon Raphael Hirsch points out that the language of "placing the spirit on them" is distinct from the normal language employed when discussing the spirit of Hashem, such as in Shemos 31:3, where the verse describes the spirit of Hashem as "filling up" a person; because when the spirit "fills" someone up, it is an internal inspiration and while it is an empowerment of a person, their utterances are still their own, merely divinely inspired. Whereas here, by a court of 71, the verse uses an external language that the spirit of Hashem is "placed on them": meaning, that when the court of 71 rule, they are doing so purely as a conduit of this distinct "spirit" of Hashem - this prophecy-type of spirit. This it is clear that option 2 is correct, and that when a number of Sages gather together to form a court, they tap into a distinct power of prophecy, and it is this "spirit of Hashem" which is the power compelling us to follow them.

And if this is so, then it is also a proof that a courts ruling is not merely a legal resolution in the face of uncertainty, rather the court's ruling is along the lines of prophecy which is clearly a revelation of the actual truth!

This does contradict the approach I have taken in my piece on Majority where I asserted that the way we learn the general principle of Majority from a court is because the reason we follow a court is purely due to the global principles of following the Majority. But according to what we are saying now, the reason we have to follow the court if via a distinct commandment and not just because of the principle of Majority.

I also realized a good explanation of why Experimental Probability is so weak. Imagine if I flip a hundred coins and 51 of them are heads and 49 are tails: if I close my eyes and point to any coin at random, I have a real Biblically valid Majority that asserts that I can assume it is heads, since the majority of coins are heads. But clearly, in the real world, this is a very weak proof! After all, there's only a 1% difference between the minority and majority, and yet still we say that we follow the Majority. And this is why the Torah had to teach me a special lesson that Majority Negates Minority by Experimental Probability, because otherwise in cases like this where the difference between minority and majority is so slight, it would seem impossible to actually rely on the Majority!

A question occurred to me.

There is an accepted principal that Majority does not work when it comes to financial matters. The commentators give different explanations, but the principle is universally agreed upon.

My question is, that the whole source for Majority is from the verse that deals with a court voting: so that means that certainly by a court we should not be able to apply the principle of Majority to cases that deal with money! And yet obviously we do! So how is it that Majority does not work by money, and yet if the majority of a court rules that Person A must surrender money to Person B, we follow the majority and take the money away?!

Today I started on something really exciting! Shaar 3 of the Shaarei Yosher!

The reason it's so exciting is that this is the Shaar that focuses specifically on Majority. And in looking over his summaries of the chapters in Shaar 3, I see that a lot of them have some really substantive and juicy arguments with the Shev Shmaatza in Shmaatza 4 that I just finished learning! So it's going to be quite exciting to see where the Shaarei Yosher disagrees with the Shev Shmaatza.

I still have to go back and complete my summary of the piece of Majority. Maybe today or tomorrow (this Shaarei Yosher is just too interesting to put down!)

In the Majority topic I've written a section about how the elements that comprise a majority must be mixed together.

I think, though, that this section should not be the second one in the Majority piece. I think we still need to spend some more time upfront outlining the fundamental principles.

For example, I'm thinking that we should first tackle Experimental and Theoretical Probabilities. This will lay the groundwork for seguing into the Talmudic discussion surrounding Theoretical Majorities which the Talmud in turn segues into Resolvable and Unresolvable Uncertainties.