Are women equal to men in respect to prayer?

I just read “Gender Equality and Prayer in Jewish Law” by Rabbis E. Tucker and M. Rosenberg. It is an excellent thoughtful book. Whether a reader agrees with the two rabbis who authored the book or not, he or she will find a wealth of information in the book that will prompt thought.
Whether the Hebrew Bible disparaged women or not is still a subject that scholars debate even though there is no clear negative statement in the Torah about women, and even though there are female heroes in the Tanakh and a female prophet. Furthermore, there is no indication in the Torah that women are excluded from biblical mandated activities. True, current Jewish law is that women do not have to observe certain positive commands that come at a certain time, not always, such as the blowing of a shofar or dwelling in a sukkah, but not all of them. Shabbat is an example of an exception. But this rule is not in the Bible. One commentator, Luzzatto, for example, contends that women are biblically required to observe all biblical laws, just as men, for the Bible does not exclude them from what it mandates, but in a later age women were allowed to refrain from observing certain positive laws because it interfered with the many other more necessary activities they were engaged in, such as raising and educating children.
In this book, the two rabbis discuss the issue whether women may participate in and lead public prayer. When did the idea arise that they should not do so? Is praying a biblical requirement? What different ideas were offered to support a female prohibition? Are these reasons applicable today, such as men being embarrassed that a woman prayer leader knows more about leading prayers than them or that they would be sexually aroused by hearing women singing?
We also learn about the origin of the idea that some prayers need ten males before they are recited, a concept that is also not biblical, although some biblical language is used to support the practice, and why women are not included in the ten. They also discuss, among much else, why some rabbis insist that women should be treated as slaves and children in respect to some laws.
The authors end their book by quoting Sifre Bemidbar 133 which compares humans to God: “Flesh and blood show greater goodness to males than to females, but the One-Who-Spoke-the-World-into-Being is not so, but is good to all, as it is said… ‘The Lord is good to all and shows kindness to all creatures’ (Tehillim [Psalm] 145:9).”

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