I appreciate the fact that my post was deemed worthy of serious comments, both positive and negative, by eminent academic scholars such as Rabbi Carmy and Dr. Unterman and I am humbled by their taking the time to respond to my post which was merely an attempt to unlink the previously posted idea that women studying Talmud and using Biblical criticism when studying Tanach are comparable and are, to use Dr. Unterman's terminology, "comparing apples to making bread".
Offline I responded to my colleague Rabbi Zev Farber's fair question about lumping together all types of literary analysis together with biblical criticism by stating that I was merely trying to point out there are types of applications of deconstructionism that are incompatible with Traditional Orthodox beliefs. I certainly apologize for my inexact term interchanging and I thank both Rabbi Farber and Dr. Unterman for their correctly pointing this out. I leave it to Rabbi Farber's discretion as to whether to share our offline exchange with the larger forum.
I agree fully that certain types of literary analysis can be used in defense of tradition and expand the pursuit of truth seeking that should underpin all study. The contemporary scholars that use modern study methodology such as the "Tanach beGovah Aynaayim" approach often defend tradition and are compatible with tradition. These approaches are similar to the Rambam quoting Aristotle at times under the banner of "seeking truth wherever it is", which is the one Halachic authority I know of actually advocating study of sources outside the Torah to interpret the Torah.
I think it is important to differentiate between traditional Yeshiva approaches that require an interpretation of the Torah to be proven by an existing Torah source (as Rav Kook put it, "Kimat Mefurash BaRishonim"

, the more lenient approach of the Rashba that Rav Yaakov Weinberg quoted as being that one may say interpretations of the Torah that are logical as long as they don't contradict any of the Torah's axioms such as Torah MiSinai etc., when considering the validity of these types of literary analysis.
I personally hired a teacher with expertise in the teachings of Dr. Nechama Leibowitz to teach our high school students specifically because she had the wisdom and experience to know what students should be exposed to and when. Any superficial study of her writings reveals that only a small part of her actual teaching was dedicated to non-traditional approaches to the study of Tanach. I view her writings as similar to Rav Hertz's commentary on Chumash as being selective and filtering of heretical notions unless it is for the sake of debunking them.
As far as not using cars to get around since the ancient scholars didn't use them either I could claim that this is like comparing apples to making bread. A precise analogy to my promoting caution using methods that aren't approved by leading contemporary Halachic authorities would be advising caution regarding one's method of transportation as recommending we should drive cars while wearing a seat belt and turning the headlights on and having airbags, but I wouldn't recommend driving Harleys on a wet road at night with the lights off while wearing no helmet.
Be Well,
Elisha Paul