Women that are Obligated to Wear Tefillin

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*******  WARNING: ACADEMIC HUMOR.  *******
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The Gemara in Shabbos 70b talks of a person that has lost track of time and does not know when Shabbos is.  היה מהלך בדרך או במדבר ואינו יודע אימתי שבת.  The Gemara says that he must do whatever is necessary to survive, but that in order to maintain his sense of Shabbos he should designate one day out of seven to be his Shabbos.  

The Gemara asks, but if every day might be Shabbos, his restriction to only doing what is necessary for survival applies to every day, including his designated special day; אלא כל יום ויום עושה לו פרנסתו אפילו ההוא יומא.  So how would his special day be different?  וההוא יומא במאי מינכר ליה?  The Gemara answers   בקידושא ואבדלתא.  On the day that he calls Shabbos he should make kiddush and havdala.

The Achronim discuss whether and when he should wear Tefillin.  Assuming that it is assur to wear Tefillin on Shabbos, can this lost person wear Tefillin on any day, or not?

For the purposes of this post, I want to quote a comment of the Mishna Berura in the Biur Halacha in 344 DH אפילו, where he says, and I quote:

ועוד יש סברא לחייבו דהלא פטור דשבת הוא מפני שהם עצמם אות וא"כ זה שעושה בו מלאכה לפרנסתו אין בו היכר

There is another reason to obligate him: After all, the rule that one does not wear Tefillin on Shabbos is because (Shabbos is an Os,a sign, and) Tefillin themselves are a sign, (and wearing the sign of Tefillin belittles the holy Os/sign of Shabbos.)  But for this person who is doing work on Shabbos, as is necessary to survive, Shabbos is no sign at all, (so Tefillin would be appropriate.)

But, you ask, doesn't he make Kiddush and Havdala?  So there is a sign pf Shabbos on that day, and that Os/sign should render his Tefillin superfluous!  To this he answers

דלא מסתבר לומר דבקידוש לבד הוא ההיכר דהא עיקר האות הוא דהקב"ה שבת ממלאכתו ביום השביעי והוא ג"כ שובת

that is is not reasonable to say that his Kiddush alone is a sign, because the main sign is that Hashem rested from work on Shabbos and he too rests from work, (and since this person is working on that day like every other day, his Kiddush is not much of a sign and does not interfere with wearing Tefillin.)

Of course, there is much to talk about regarding this opinion.  One might say that the rule of Os is a siman, not a sibbah, and the day is pattur no matter what this person is doing.  The Mishna Berura himself only uses this as a side thought, not the foundation of his opinion.  But again, for the purposes of this post, let us assume that this reasoning applies as he states it.

Now, why is it that women are not obligated to wear Tefillin?  Because it is a Mitzvas Asei She'hazman Gerama, a mitzva caused by time- it is operative only on a particular season, hour, or day.  We pasken that as far as the Torah rules, Tefillin are worn at night just as they are in the day.  It is only because the mitzva of Tefillin does not apply on Shabbos and Yomtov that it is Zman Gerama.

But what of a person that believes that one is allowed to do melacha on Shabbos and Yomtov, like Reform Jews?  They certainly don't believe that the Torah commands us to refrain from working, and they do whatever they want on Shabbos.  So as far as Issur Melacha is concerned, Shabbos is no more of an Os/sign for them than it is for the hypothetical מהלך בדרך או במדבר.  Well, then, according to the Biur Halacha, Reform Jews are obligated to wear Tefillin on Shabbos.

If a mechallel Shabbos is chayav to wear Tefillin on Shabbos, then for them it is no longer a Mitzvas Asei She'hazman Gerama.  Therefore, Reform Jewish women, for whom Shabbos is not an Os, are chayavos to wear Tefillin.