God's Preferred Pronoun

Disclaimer: I know it's bad form to apologize for what I write, but I feel I have to in this case. When I set out to write this post, it was going to be a simple question with a simple answer. However, once I started writing, I kind of got carried away with spelling out all of the premises and ramifications. The post ballooned into more fundamentals than I anticipated, and would have continued to do so had I not exercised restraint and brought the post to a close when I did. Suffice it to say, this is not my cleanest writing. I hope that the ideas are still enlightening and useful.

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God's Preferred Pronoun

The Pronoun Question 

Consider the following questions:

"Why don't we refer to God as 'she'?" 

"If God isn't male or female, why don't we use the pronoun 'It' instead of 'Him'?"  

"Shouldn't we avoid all gendered terms in relation to Hashem, since Hashem has no gender?"

These are all different formulations of the same question - a question that I am asked from time to time, usually by my 9th or 10th grade female students. [1] These students know that God has no gender.  They're not asking childish questions like, "What if God really IS female?" or "What if God has BOTH genders?" Their question is terminology - not metaphysics. They are bothered by the masculine terminology we use to describe our non-physical, non-anthropomorphic, unknowable Creator. 

My intention in this post is share the philosophical answer that I give my students when asked questions about why we use masculine terminology in reference to Hashem. But first I must dispel another answer.

The Linguistic Answer 

I say that I plan on giving a "philosophical answer" to distinguish this from the linguistic answer, which I have heard some people give to such questions. I will now summarize the linguistic answer and explain why I believe it to be inadequate.

The basis of the linguistic answer is the fact that, like it or not, Hebrew is a language with grammatical gender. Every noun in Hebrew is either masculine or feminine. For example: "sefer" (book) is masculine; "kenesset" (synagogue) is feminine; "shulchan" (table) is masculine; "simchah" (joy) is feminine. Many nouns can take on both forms. For example: "par" means bull (masculine), whereas "parah" means heifer (feminine); "ish" means man, whereas "ishah" means woman; "melech" means king, whereas "malkah" means queen.

This is the reality of the Hebrew language. As far as I know, these differences in grammatical gender for single-gender nouns do not stem from philosophical, psychological, biological, social, or sexual considerations. They are what they are, and nothing short of a reinvention of the entire Hebrew language will change that.

Similarly, all verbs and adjectives must conform to the gender of the noun they modify. For example: "sefer gadol" means "big book," whereas "kenesset gedolah" means "big synagogue." Again, "gender identity" has nothing to do with any of this. These are just the rules of the language.

How does Hebrew deal with situations which call for gender-neutral language? By using the gender-neutral mode in Hebrew, which is masculine. When referring to groups of objects or persons which include members of both genders, the masculine form is used as the gender-neutral default. For example, "ben" means "son" and "banim" means "sons"; "bas" means "daughter" and "banos" means "daughters." If you wanted to refer to a group which included sons and daughters, Hebrew doesn't offer a gender-neutral form of the pluralized noun (i.e. an equivalent to the English word "children" or "progeny"). Instead, you would say "banim," using the masculine pluralization as the gender-neutral form.

The same is true when the gender is unknown or otherwise inapplicable. If I were task someone, "Do you have a child?" I would say, "Yesh lecha yeled?" using the masculine form of the word "child" ("yeled" as opposed to "yaldah") even though my question was asked without any specific gender in mind.

There isn't even a word for "it" in Hebrew. If you're going to say "it," you'll have to either say "he" or "she." Similarly, there's no way to say "they" or "them." The only options are "they (masculine)" or "they (feminine)."

On this basis, the linguistic answer to the question, "Why do we use masculine terminology in reference to Hashem?" is: "We use masculine terminology because this is the only gender-neutral way we can refer to Hashem in the Hebrew language."

According to this answer, when we speak about Hashem, we should have in mind that we are speaking in a non-gendered way, despite the fact that we are using masculine verbs, adjectives, and pronouns. Just as we refer to a group of boys and girls with the masculine "banim" with full awareness that we intended this in a gender-neutral way, so too, when we make statements about Hashem such as "ve'hu Rachum" ("He is Merciful") and "Melech ha'olam" ("King of the universe"), we should really have in mind, "the genderless God is merciful" and "Monarch of the universe."

The Inadequacy of the Linguistic Answer

I believe that the linguistic answer is inadequate for several reasons. First and foremost, it's disingenuous. True, we don't think "masculine" when describing a group of five boys and five girls as "banim," but we do relate to the pronoun "He" and terms such as "melech," "shofet," "gibor," etc. as masculine in reference to Hashem. This is by design, as I will attempt to explain when I give the philosophical answer.

Secondly, there are dozens - if not hundreds - of anthropomorphic descriptions of Hashem in Tanach and in the words of Chazal which portray Him specifically as masculine - not as a non-gendered being. For example: "Hashem is a man of war" (Shemos 15:3), "Is He not your father?" (Devarim 32:6), "But like a woman who has been unfaithful to her male companion, you have been unfaithful to Me, O house of Israel - the word of Hashem" (Yirmiyahu 3:20). The entire Shir ha'Shirim is an allegorical love song, depicting Hashem as the man and the "beloved" seeking Him as the woman. To claim that all of these examples of vivid imagery and description are intended to be understood as "gender neutral" is, to my mind, dishonest and absurd. Chazal clearly followed this pattern with their numerous masculine allegorical depictions of Hashem.

Lastly, even if we were to explain the Hebrew use of masculine terminology in relation to Hashem, we still remain with the question of how we should speak of Him in English, and in other languages which do offer a gender-neutral alternative. To my knowledge there are no baalei Mesorah who have advocated for the use of gender-neutral terminology when speaking about Hashem in languages which allow for this. In other words, I do not know of any reputable Torah scholar who would suggest that we should refer to Hashem with the pronoun "It" in English. Everyone agrees that we should refer to Hashem as "He" - not "It," and not "She." I do not think that this is arbitrary.

By exploring the weaknesses of the linguistic answer, we have strengthened our original question. Not only must we answer why the Torah uses masculine terminology to describe Hashem, but we must also explain why He is depicted specifically using masculine imagery, and why we don't use non-gendered terminology when speaking about Hashem in languages that allow for it, such as English.

Predicating Attributes of God

Since gender is an attribute, the philosophical answer to our question requires an understanding of how we ascribe any attribute to God. Because this topic is exceedingly broad and deep, I will focus our discussion on a short excerpt from the Chovos ha'Levavos, by Rabbeinu Bachya Ibn Paquda. [2] He begins by making an important distinction between different types of Divine attributes:

The meanings of the Divine attributes are very many, just as the creatures – and the kindnesses upon them – are many. They can be divided into two classes: [attributes] of essence and [attributes] of action.  

The reason we call [the first class] “[attributes] of essence” is that they are abiding attributes of God, May He be exalted; [they were His] before [the existence of] all created things, and [they are His] afterwards. They are befitting of the Essence of His glory. These attributes are three: that He Exists, that He is One, and that He is Eternal and unpreceded.

The reason we describe Him with these attributes is to convey some conception of Him and of the true nature of His existence; to call attention to His glory; and to help men understand that they have a Creator Whom they are obligated to serve.

We find it necessary to describe Him as existing, since all evidence points to His existence: the signs of His handiwork in the universe testify to this, as it says: “Lift up your eyes on high and see! Who created these? He Who brings out their host by number, He calls them all by name; by His great might and strong power, not one is missing” (Yeshayahu 40:26). We must therefore attribute to Him existence, as it is clear to our minds that no action or work will issue from that which does not exist. Since His works and creations are evident, His Existence is evident to our minds.

We describe Him as Eternal, for all arguments led to the conclusion that this world had a beginning before which there was no other beginning, a first cause before which there was no other cause; it became clear that there cannot be an infinite series of causes [extending back]. It follows necessarily that the Creator, May He be exalted, is the Beginning before which there is no beginning. That is what is meant by [His] eternity, as it is said: “From eternity to eternity, You are God” (Tehilim 90:2); “Before Me no god was formed, nor will there be after Me” (Yeshayahu 43:10). 

Why we describe Him as One has already been explained in exhaustive fashion through solid arguments. It was proven by incontrovertible evidence that the notion of absolute Oneness is bound to the Essence of His Glory. The meaning of this oneness is the inapplicability of plurality to the Essence of His glory and the exclusion of change, metamorphosis, accident, creation and destruction, combination and separation, resemblance, association, transformation, and all other types of multiplicity from the true Essence of His glory.

It is vital that you understand that the meaning of these attributes [which we ascribe to God] is not to predicate of the Creator’s Essence change and diversity; rather, the meaning is to deem their opposites [i.e., the opposites of the three attributes of essence] inapplicable to Him, May He be exalted. What we have in mind by their attribution is that the Creator of the world, may He be exalted, is neither plural, nor nonexistent, nor created.

To summarize: when we ascribe these three "attributes of essence" to God - namely, Existence, Oneness, and Eternality - we are not attributing positive qualities to Him, since He has no qualities, and we cannot have any knowledge of His Essence. Rather, we are negating the opposite attributes (i.e. non-existence, plurality, and createdness).

All of this is in contrast to what Rabbeinu Bachya defines "attributes of action" as "those that are ascribed to the Creator as a result of His actions." Examples include: merciful, kind, righteous, jealous, awesome, gracious, slow to anger, mighty, etc. These attributes are intended to convey positive knowledge - not of God's Essence, but of His actions, His creations, and everything else that is involved in His governance of His world. In other words, when we say, "Hashem is merciful," we mean, "Hashem acts in a manner which, if a human acted that way, we would describe as 'merciful.'" When we say, "Hashem is jealous," we mean, "Hashem acts in a manner which, if a human acted this way, we would describe as 'jealous.'" And so on.

Rabbeinu Bachya emphasizes his point about negative "attributes of essence" one more time at the end of this section:

What you must understand in regard to the Creator is that nothing is like Him. When you ascribe attributes to the Creator, you should understand only that their opposites are inapplicable to Him. As Aristotle said, the negative attributes of God are truer than the positive ones; for all positive attributes ascribed to the Essence of His Glory cannot escape the characteristics of substantial or accidental properties, and the Creator of substance and accident is not subject to their properties. The negative attributes ascribed to God, however, are undoubtedly true and befitting of Him; for He is above all quality and description, resemblance or comparison. What you must therefore understand from the three attributes of which we have spoken is the inapplicability of their opposites to the Creator, may He be exalted. 

In other words, when we say "Hashem Exists," we really mean "Hashem doesn't NOT exist, but the nature of His Existence is unknowable to us." When we say "Hashem is One," we really mean "Hashem does not partake of plurality or multiplicity, but the nature of His Oneness is unknowable to us." When we say, "Hashem is Eternal," we really mean, "Hashem is not created, but the nature of His Eternality is unknowable to us."

One might ask: "If the nature of Hashem's Existence is unknowable to us, then what difference does it make if we describe Him as 'existent' or 'non-existent'? Strictly speaking, both are inaccurate, since the term 'exist' in relation to Hashem is completely different from what we mean when we say that anything else 'exists'!" The same goes for the statement that Hashem is "One" or "Eternal": since we cannot have any positive knowledge of what we mean by these terms, then why use them at all? What makes them superior to their opposites, or to using neither term?

The answer, to put it bluntly, is that we use these specific "attributes of essence" as the lesser of two evils, in that they are more conducive to developing a more accurate way of thinking about Hashem than their opposites. One can say that of any pair of "attributes of essence," we choose the lesser of two evils. We choose the term which conveys the least inaccurate conception of Him - or, if you prefer, the term which conveys a conception of Him which lends itself more to an accurate grasp of the truth than the alternative.

For example, although we cannot have any positive knowledge of the nature of Hashem's Existence, we nevertheless say that He "exists" because the term "existence" lends itself to a more accurate understanding of Hashem than "non-existence." If we did not ascribe "existence" to Hashem, then people would think of Him as non-existent, which would be extremely detrimental. The same is true of Oneness: although we do not have any positive knowledge of what we mean when we say Hashem "is One," that statement is more developmentally beneficial to our understanding than speaking of Him in terms of plurality or multiplicity. Similarly, saying that He "is Eternal" is more developmentally beneficial than if we didn't use this term, since the only alternative is to think of Him as "finite" or "created" or "existing in time" - all of which would do more harm than good to our understanding of Hashem.

The Rambam [3] applies this to other attributes as well. For example, he writes that Hashem "has neither death nor life like the life of a physical creature, neither foolishness nor wisdom like the wisdom of a wise man." Note how he negates one set of qualities in an absolute manner (i.e. death and foolishness), but he negates the other set of qualities in a qualified manner ("nor life like the life of a physical creature ... nor wisdom like the wisdom of a wise man"). This follows the same pattern as the attributes of essence mentioned by Rabbeinu Bachya (i.e. He has no plurality nor does He have Oneness like the oneness of any unities in the world, etc.).

The Philosophical Answer to the Pronoun Question

Now that we recognize Rabbeinu Bachya's distinction between attributes of essence and attributes of action, the question is: What about gender? When we describe Hashem as "He," or use masculine verbs or adjectives when speaking about Him, do we treat this gender-predication like an attribute of essence or an attribute of action?

I am of the opinion that we should treat gender as we would an attribute of essence - not to imply that it is on par with Existence, Oneness, and Eternality, but in the sense that we should view the attribution of gender to Hashem not as an affirmation of positive quality, but as a negation of its opposite. And what quality, exactly, are we negating when we describe Hashem in masculine terms and with masculine imagery? Objecthood. Allow me to explain.

In English we distinguish between an object and a person by our use of the pronoun "it" vs. the pronouns "he" or "she." In Hebrew, even though we don't have the option to express this distinction in language, we still mentally classify everything as either an object or a person. The human mind is simply wired that way. My dad is a person. The chair he's sitting on is an object. I am a person. My shoes are objects. The landlord is a person, and the apartment I'm renting is an object. The ship is an object when I am speaking literally, but is a person when I speak figuratively about "taking my ship out on her maiden voyage."

The Torah goes out of its way to anthropomorphize Hashem in order to ensure that we do not relate to Him as an object. If we avoided all anthropomorphic terminology, we would default into thinking of Hashem as an object - as a force, as a characteristic of the universe, or an abstraction like "existence" or "reality" or "truth" - all of which would be far more detrimental to our conception of Him than relating to Him as a person. [4]

Once we are referring to Hashem in anthropomorphic terminology, we have no choice but to characterize Him as either masculine or feminine (as explained above in the section about the linguistic answer). So why do we characterize God as masculine if He actually has no gender? Because of the two options, it is the most developmentally beneficial way of arriving at a less inaccurate conception of Him.

Masculinity is associated with qualities that are more accurate in relation to Hashem than their alternatives. For example, it is more accurate to think of Hashem as strong rather than weak, and masculinity is more associated with physical strength than femininity; it is more accurate to think of Hashem as active than passive, and masculinity is associated with the active role than the passive role; it is developmentally beneficial to think of Hashem as provider, protector, ruler, judge, etc. - roles which are more associated with masculinity than femininity.

This is not to suggest that these roles are intrinsically more masculine than feminine. It is certainly possible for women to be stronger, more active, and have greater leadership roles than men. It just happens to be that in most societies for most of human history, these qualities are more associated with men than with women.

By characterizing Hashem as masculine in our language and imagery, all of these associations automatically become attached to Him. Although they cannot be applied to Him in truth, since He is One and His Essence is unknowable, they are nevertheless more accurate than their opposites, which is why we ascribe masculine attributes to Him instead of feminine.

Summary

Allow me to summarize the answer in a single sentence:

Hashem has no gender, but we refer to Him in anthropomorphic terms in order to avoid characterizing Him as an object - and once we ascribe human qualities, we use masculine terminology and imagery because the qualities associated with masculinity are more developmentally beneficial to our conception of Him. 

Of course, one need not be aware of this explanation in order for this characterization to have its effect. Indeed, it is somewhat of a pity that we are forced to explicate the Torah's reasoning in this regard, since this might have the effect of diminishing the intended goal of these descriptions, rather than letting the effects of these terms occur naturally to our minds.

[1] While these questions have no doubt been raised and addressed by past generations of Torah educators, they have taken on a new degree of intensity and urgency in the milieu of 2018 America. Our culture is abuzz with LGBTQ+ issues, and gender identity is one of the "hot topics" which continuously generates both passion and controversy. 

I happen to live in a rather conservative bubble, but judging by what I see on the Internet, it has become an accepted - if not obligatory - practice on college campuses, when making a new acquaintance, to ask, "What is your preferred pronoun?" We now live in a world where someone who looks like a "he" insists on being called "she," where some individuals prefer the pronouns "they," "them," and "their" so as to avoid gender altogether, and where some have even gone so far as to try standardizing new pronouns, such as "ze," "zem," and "zir." 

I am not bringing up these social issues in order to voice an opinion about them. Regardless of what opinions you hold about politics, psychology, or medicine, the reality is that when Modern Orthodox teenagers ask questions about God and pronouns, this is where these questions are coming from, and if you are going to attempt to answer their questions, then it behooves you to know what premises they are operating with. 
[2] Rabbeinu Bachya ibn Paquda, Chovos ha'Levavos 1:10
[3] Rabbeinu Moshe ben Maimon (Rambam / Maimonides), Mishneh Torah: Sefer ha'Mada, Hilchos Yesodei ha'Torah  1:11
[4] If you're wondering why - that answer will have to wait until another time. I was originally going to address it in this post, but I realized that it deserves its own treatment.

Parashas Bechukosai: Why are Women Worth Less than Men?

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Preface: I struggled with the title of this blog post. I wanted it to be attention-grabbing in the same way as the pesukim themselves are attention-grabbing, but I also wanted a title which will be read in one way by a reactive person (who will likely dismiss it), and in another way by someone who is more open-minded and is willing to investigate before drawing conclusions - since that is one of the major points of this blog post. 

Artwork: Ardent Plea, by Chippy

Parashas Bechukosai: Why are Women Worth Less than Men?

The Facts

The final chapter of Sefer Vayikra begins with the laws of arachim - a type of vow which allows a person to donate the monetary equivalent of the value of one's field, one's house, one's animal, or the value of a human being to the building fund of the Beis ha'Mikdash. 

In the case of a pledged field, house, or animal, the Kohen evaluates the worth of the item on an individual basis. However, when it comes to pledging the value of a human being, the Torah establishes fixed amounts based solely on age and sex. This valuation of human beings doesn't take into account any other qualities: wealth, health, appearance, mental capacity, tribe, or even whether a person is a Jew or a gentile.

The Torah she'bi'Chsav explicitly states the value for each age/sex combination:

The valuation of a male shall be: for someone twenty years to sixty years of age, the valuation shall be fifty silver shekels, of the sacred shekel. If she is female, the valuation shall be thirty shekels. And if from five to twenty years of age, the valuation of a male shall be twenty shekels and of a female ten shekels. And if from one month to five years of age, the valuation shall be five silver shekels; and for a female, the valuation shall be three silver shekels. And if from sixty years and up, if for a male, the valuation shall be fifteen shekels; and for a female, ten shekels (Vayikra 27:3-7)

Here is the same information in the form of a table, incorporating some modifications from Torah she'baal Peh:

The Questions

I presented these facts to some of my students today. As I anticipated, one of them reacted by exclaiming: "WHAT?! HOW CAN THE TORAH SAY THAT MEN ARE WORTH MORE THAN WOMEN? THAT IS INCREDIBLY SEXIST!"  

To this student, and to anyone else who might respond in a likewise fashion, I would say the following: "Clearly, you are bothered by what the Torah says, and you have a legitimate question. Let's see if we can formulate your question in a clearer and more precise fashion."

Thankfully, the Abravanel does an excellent job of articulating the questions. He writes:

1. Why did the Torah establish the values of arachin vows for human beings? It would have been more fitting to entrust [this task] to the Kohen to evaluate each person in accordance with his or her value. For example, there might be a person who is worth 100 [shekels] and another person who isn't even worth 10. Just as the fields, and properties, and animals are evaluated by the Kohen, why aren't people evaluated in the same manner?  

2. Why did the Torah differentiate between the value of a male and the value of a female, seeing as how both of them are human beings, as it is stated, "male and female He created them" (Bereishis 1:27) "and He called their name 'man'" (ibid. 5:4)? In the realm of damages we see, "If the ox shall gore a slave or a maidservant, thirty silver shekels" (Shemos 21:32) - without making a differentiation between male and female. Why is the matter like this in this mitzvah? 

3. Why don't these valuations have a specific and set ratio between the male and the female? Between the ages of 20 and 60 the value of a female is 3/5ths the value of a male. From age 5 to 20 the value of a female is half the value of a male. From one month to 5 years the value of a female is 3/5ths the value of a male. And from 60 years and up the value of a female is 2/3rds the value of a male. It behooves us to investigate why this is the case. 

Let's take a moment to appreciate the difference between my student's initial reaction and the Abravanel's questions. The student was bothered by these facts and immediately jumped to a conclusion that the Torah was being sexist (i.e. discriminating against women out of the belief that they are inferior). In contrast, the Abravanel approached the area with the objective mindset of a scientist, looking for patterns, anomalies, and clues which might lead to deeper insight. This step of formulating the questions is critical. Even if we don't end up finding satisfactory answers, we will still have moved one step forward towards understanding.

An Approach

I would like to present Rav Hirsch's explanation, which answers the Abravanel's questions. His answers might not appeal to everyone, but I believe this is a good example of a valid and fruitful type of approach or method.

Rav Hirsch begins by examining the facts in search of some foothold from which to develop a comprehensive theory. He writes:

The eirech (valuation) of a male in these stages of life is 5, 20, 50, and 15 shekels, respectively. The eirech of a female is 3, 10, 30, and 10 shekels, respectively. These fixed amounts surely were not chosen arbitrarily, without reason. Since they do not take into account the physical, spiritual, moral, and social uniqueness of each nefesh (soul/being), and they vary only according to gender and age, it must be that they represent some common factor that is equal in all the nefashos, and that varies only according to age and gender.

Rav Hirsch's first deduction is a solid one. Unlike other areas of halacha, where we factor in a person's qualities, background, or circumstances, the laws of arachin are only interested in the subject's age and gender. Whatever these numbers represent, they must somehow be tied only to gender and age. Rav Hirsch continues:

Furthermore, since we are dealing here with erkecha nefashos la'Shem, with the national valuation of persons for God and His Sanctuary, it follows that this factor - common to all the nefashos and modified only by age and gender - pertains to the relation of these nefashos to God and to His Sanctuary. If we are not mistaken, then there is no factor that is common to all the nefashos as regards their relation to God and His Sanctuary, and that varies only according to age and gender, other than the task and mission of life that are given to every nefesh. On this basis we can explain the meaning of the numbers given here by Scripture, which rise and fall according to age and gender. 

This is the crux of Rav Hirsch's theory, namely, if we are evaluating eirech nefashos la'Shem ("the value of souls to Hashem"), and if this valuation is determined solely on the basis of age and gender, then these numbers must have something to do with "the task and mission of life that are given to every nefesh" - irrespective of any other personal quality. We will now see how he develops this approach:

Let us compare the numbers fixed for a male, namely, 5, 20, 50, and 15, to the numbers fixed for a female, namely 3, 10, 30, 10. Bear in mind that the full eierch amount for an adult male from the age of 20 to the age of 60 is 50 shekels, whereas the full eirech amount for an adult female is 30 shekels and that both these numbers - 30 and 50 - are 10 times the eirech of an infant girl or boy, whose eirech is 3 or 5. It appears, then, that we are not mistaken in proposing that the key to the whole scale is the numbers 3, 5, and 10. 3 is the signature of the female's life mission; 5 is the signature of the male's life mission; and 10 is a sign of completion and perfection.

Allow me to repeat this last point for emphasis: Rav Hirsch infers that 5 represents man's life mission; 3 represents woman's life mission; 10 signifies completion and perfection. How do these values make any sense? Rav Hirsch explains:

We venture to suggest that the home and the family - man, woman, and child - are represented by the number 3, whereas the society is represented by the number 2, as we often find in the Torah. Accordingly, the family and the society together would be represented by the number 5. The number 3 is the signature of woman's mission, namely, the family and the home, whereas the number 5 is the signature of man's mission, namely, the family and the society.

Rav Hirsch is working with the premise that a woman's life-mission pertains primarily to realm of the home, whereas a man is responsible for his home and his community. The number 3 represents the home, insofar as the smallest family unit is three people (man, woman, and child). I don't know where Rav Hirsch gets the idea from that society is represented by the number 2, but he seems to maintain that this is a recurring theme throughout Torah, and - for the purposes of this blog post - we'll take his word for it. Thus, woman's number is 3 (home) whereas man's number is 5, which is the sum of home (3) + community (2).

Now Rav Hirsch explains how these numbers account for all of the different values at each stage:

The eirech of an infant boy and of an infant girl starts with these two numbers, which signify the mission of man and woman. This eirech remains fixed for them, until they reach a trainable age, at the end of their 5th year.

From the end of the 5th year to the end of the 20th year are the years of training and completion in preparation for their mission. The preparation of the woman is on one level - preparation for the home; and its signature is 10. The preparation of the man is on two levels - preparation for the home and for the society; and its signature is 20. 

From the end of the 20th year to the end of the 60th year are the years of the full attainment of the male and female missions. The signature of this full attainment - as regards the woman's mission - is the product of 10 and 3: 30; whereas as regards the man's mission, it is the product of 10 and 5: 50.

From the end of the 60th year until the end of a person's life are the years of ziknah (old age) - the years of the harvest of life. As regards one's work as an individual, one can look back with satisfaction at the completed edifice of his life. As regards one's work in society, one can look back at least at a substantial contribution to the community. Hence, for the woman, whose work is in the individual realm, the signature of ziknah is a number representing completion: 10; whereas for the man, whose work is in the individual realm and also in the societal realm, the signature of ziknah is a number representing completion, plus partial completion: 10 + 5 = 15.

If one accepts Rav Hirsch's initial interpretation of the key numbers (i.e. 3, 5, and 10), then his interpretation of each of the stages fits quite nicely. To sum it up:

• 1 month to 5 years - pre-training: at this stage, prior to embarking on the preparation for one's life mission, we have the "base value" representing the life-task of each gender: the value of the male (5) and the value of the female (3), without any degree of completion (no 10s)
• 6 to 20 years - training for the mission: since 10 signifies the process of perfection, the woman's value lies in her single track of perfection (i.e. the realm of family) whereas the man's value lies in his dual-track of perfection (i.e. the realm of family and community); therefore, the woman's value at this stage is represented by a single 10, whereas the man's value reflects his dual track, and is a double-10 (i.e. 20). 
• 21 to 60 years - full attainment of mission: the Torah signifies a completed life-task as a product of the number representing completion (10) and the number representing the life-task of that specific gender. Thus, the man's value during this time is 10 x 5 = 50, whereas the woman's is 10 x 3 = 30.
• 61 years and up - the harvest of life: this value reflects what has been accomplished after the prime of one's life; the woman can look back at her contribution as being totally complete; in contrast, the man can only claim total completion in his family life, but only partial completion in the realm of his societal contributions; thus, the woman's value is the number of completion (10) whereas the man's is full completion plus partial completion (10 + 5 = 15).

This answers all three of the Abravanel's questions. 

1. Why did the Torah establish the values and not leave it up to the Kohen? Because the values here signify the life-missions of the age and gender to which the individual belongs - not the particular qualities of that individual, as is the case in the valuation of animals, houses, and land.

2. Why did the Torah differentiate between the valuation of men and women? Because their life-missions lie in different realms: the woman's is in the home, and the man's is in the home and in the community.

3. Why the differing ratios? Because the numbers are significant because of what they represent at each stage of life - not the intrinsic value of each gender. 

Upon hearing Rav Hirsch's explanation, my student said, "But the man is still worth more than the woman!" I responded that Rav Hirsch isn't necessarily learning that the monetary value of the ararchim-vow is an actual appraisal of the worth of the human being in the same way that a price tag indicates the value of the item. Rather, he is learning these arachim-valuations as symbolic - using fixed numbers as symbols to reflect ideas about the respective life-tasks of men and women.

An example of this type of numerical symbolism can be seen in the common Jewish practice of making donations in multiples of 18, which represents the numerical value of חי (chai = life). Imagine if everyone who would have donated $18 would donate $20 instead. From a strictly fiscal standpoint, $20 donations are much better. Nevertheless, people often want the amount they donate to represent something, or to convey a message. Donating $18 might provide less monetary value than donating $20, but it is superior in the message it conveys through the significance of the number 18.

I believe that is how Rav Hirsch regards these arachim-valuations. Yes, it is true that a woman who pledges her eirech will, in fact, be donating less money to the Beis ha'Mikdash than her male counterpart, but I think that it is a mistake to view this as indicative of women being inferior to men. This is especially true considering that this explanation comes from Rav Hirsch, who emphasizes the equality of men and women elsewhere in his Torah commentary.

Guess what? The student who objected ended up saying that she liked Rav Hirsch's explanation, and didn't find it to be sexist. That's great, but even great is the value of the methodology lesson that the student gained: things aren't always as they first appear, and if you take the time to formulate good questions, and approach your analysis in a deliberate and thoughtful manner, perhaps you'll find something you didn't expect.

Afterthought (5/30/19): 

Upon revisiting this post, I thought of another analogy. Women have two X chromosomes in each cell, whereas men have one X and one Y. Imagine if, upon first learning this fact, a student exclaimed, “THAT IS INCREDIBLY SEXIST! Why should a MAN get TWO types of chromosomes and a woman get stuck with just an extra of the same type?” We would all recognize such a question as being immature and misguided – and yet, when a person asks a question like this about the structure of a mitzvah, then it is often treated as a legitimate critique of Torah. 

This double-standard reveals a difference in the way people approach the empirical sciences versus the way they approach the analysis of Torah and mitzvos. This difference can be boiled down to two points: (1) in the sciences, people accept facts as facts, and (2) they recognize that these facts are determined by chochmah (wisdom) – namely, the lawfulness of nature. But when it comes to Torah and mitzvos, (1) people often refuse to even accept the facts as facts, and (2) they attribute the facts to social causes (e.g. “primitive beliefs about the world,” “outdated social norms,” “Old, white, cisgendered rabbis upholding the patriarchy under the guise of religion in order to oppress women and rob them of their power”). 

Ultimately, when analyzing Torah and mitzvos, the question is this: Do you regard the facts of Torah as being authored by the same Creator as the facts of nature? If so, then you should approach them with the same analytical objectivity, letting your investigation be guided by the facts and the nature of the subject matter, unencumbered by preexisting prejudices. If not, then on what basis do you make this distinction? If this latter question cannot be answered, then chances are it stems from some form of emotional prejudice or bias rather than from a genuine analysis of what Torah and mitzvos are.