With Edah's demise and partial merger into Yeshivat Chovevei Torah (YCT), the members of the Union for Traditional Judaism (UTJ) email discussion list raised the old question of why Edah & UTJ were separate groups, why Edah didn't merge into UTJ rather than YCT.
Two ideas to which I respond below:
a) practice is more important than theology;
b) labels are so divisive.
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Thoughts on the current debate...
1) Rabbi Berman (spiritual leader and founder of Edah) told Bill Moyers that Judaism is about practice, not belief. In that, he follows Moses Mendelssohn, who asserted, in debate with non-Jews, that Judaism has no dogmas. I have to believe, given that there is some mandated belief (see Rambam in various guises, including Hilchos Teshuvah, where he legicizes (neologue-ism?) the ideas expressed in the 13 Principles), that this was stated more for effect than as an actual halachic definition.
2) Yes, practice is paramount, particularly as regards individuals. But there are three ways in which things happen: thought, speech and action. Speech sins are not generally punishable. Thought sins are few and far between (piggul being about the only one I can think of at the moment), but can affect practice.
Misguided thoughts (e.g. coveting, atheism, etc.) are not generally actionable until expressed as speech (again, see Sefer haChinuch for various attitudinal sins, such as coveting). So belief is a problem insofar as incorrect belief leads to incorrect actions (improper prayer, expression of improper ideas).
3) There has to be a difference between judging individuals (which has to be on the level of practice, praxis if we want to get all Hellenistic about it), and institutions (which has to be on the level of expressed ideas alone, including expressed support for various actions).
That's where labels become most important, because institutions don't have actions, they have ideas. (Yes, yes, yeshiva fraud, but that's a failing of the officers, for all that they can hide behind the corporate structure, not a failing of the institution). Institutions can, however, put their ideas into action, and that then becomes a basis for judgment as well. E.g., a yeshiva tells its teachers not to teach evolution - that's an action, based on a idea espoused by the institution. That institution could then be labeled as "anti-modern", "obscurantist", "chareidi", or whatever labels fit.
This connection flows both ways: just as the institutions ideas are reflected in the praxis of its employees and members, so too its leadership's ideas become associated with the institution. Thus, if an institution is devoted to a religion, the religious ideas of its leaders are validly associated with the institution: e.g. Mordechai Kaplan's Epicureanism with JTSA, or in this case R' Halivni's maculate textualism with UTJ/Metivta.
4) Orthodoxy, unlike Reform and Conservative (although Conservative is starting to go this way too), is an attribute of a movement, rather than a movement itself. Reform is defined by its institutions: HUC/UAHC/CCAR. Conservative is defined by its institutions: JTSA(&UJ?)/USCJ/RA.
Orthodoxy, well, you have yeshiva orthodox, modern orthodox, chasidic orthodox, mussar orthodox, etc. Orthodox is an attribute all these movements share in common: fealty to Rambam's 13 principles in some form. All of them require synagogues to have a mechitzah. They may not kick out synagogues that don't have one any more, but the rule is on the books.
Each of the other movements defines itself in part by denying one or more of Rambam's principles (pace Marc Shapiro - they may stretch, but the quoted Rishonim don't actually deny any): Reform by denying the binding nature of halacha, Conservative by denying the Divine origin of the Oral Torah, and increasingly, the Divine articulation of the Torah we have today, to within a few letters or words.
And the weakening of these principles leads to, apparently, a weakening of a group's attachment to tradition. Is it any wonder that the greatest liberalization of Conservative halacha has come at the same time as the weakening of attachment to an accurately-transmitted Biblical text? If the tradition is human, then we human rabbis have the authority to change it.
To be Orthodox, then, a movement has to have the attribute Orthodoxy, which is about ideas, or belief. (this idea due to Rabbi Micha Berger)
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So where does that leave our debate? We have to use different criteria for corporate entities and for persons. We know, since the court cases and responsa of the 1950s, that mechitza is the sine qua non of an Orthodox synagogue. A synagogue movement that refuses to articulate a coherent pro-mechitza policy, therefore, is going to have a hard time convincing anyone that it has the attribute "Orthodox". A religious movement, whose primary ideological leader holds by a theory of the Biblical text that denies the accurate transmission of the Sinaitic document, is going to have a hard time convincing anyone that it has the attribute "Orthodox."
I have to figure that the UTJ has something serious invested in not being Orthodox, or they would clarify these issues.
If I had to speculate, I might venture into the ad hominem and wonder if some of the UTJ rabbis who broke with the Seminary might still retain some loyalty to the institutions which trained and nurtured them. Certainly Conservative Judaism of the past 50 years has made itself consciously "not-Orthodox", much as contemporary American Orthodoxies in part define themselves as "not-Conservative". But that's a different essay.