Only arm tefillin are a sign?

Question

The four parshas of tefillin appear slightly differently each time when the Torah describes the mitzvah.

Shemos 13:9

וְהָיָה֩ לְךָ֨ לְא֜וֹת עַל־יָדְךָ֗ וּלְזִכָּרוֹן֙ בֵּ֣ין עֵינֶ֔יךָ לְמַ֗עַן תִּהְיֶ֛ה תּוֹרַ֥ת יְהוָ֖ה בְּפִ֑יךָ כִּ֚י בְּיָ֣ד חֲזָקָ֔ה הוֹצִֽאֲךָ֥ יְהֹוָ֖ה מִמִּצְרָֽיִם׃‏

“And this shall serve you as a sign on your hand and as a reminder on your forehead—in order that the Teaching of the LORD may be in your mouth—that with a mighty hand the LORD freed you from Egypt.

Shemos 13:16

וְהָיָ֤ה לְאוֹת֙ עַל־יָ֣דְכָ֔ה וּלְטוֹטָפֹ֖ת בֵּ֣ין עֵינֶ֑יךָ כִּ֚י בְּחֹ֣זֶק יָ֔ד הוֹצִיאָ֥נוּ יְהוָ֖ה מִמִּצְרָֽיִם׃ (ס)‏

“And so it shall be as a sign upon your hand and as a symbol on your forehead that with a mighty hand the LORD freed us from Egypt.”

Devarim 6:8

וּקְשַׁרְתָּ֥ם לְא֖וֹת עַל־יָדֶ֑ךָ וְהָי֥וּ לְטֹטָפֹ֖ת בֵּ֥ין עֵינֶֽיךָ׃‏

Bind them as a sign on your hand and let them serve as a symbol on your forehead;

Devarim 11:18

וְשַׂמְתֶּם֙ אֶת־דְּבָרַ֣י אֵ֔לֶּה עַל־לְבַבְכֶ֖ם וְעַֽל־נַפְשְׁכֶ֑ם וּקְשַׁרְתֶּ֨ם אֹתָ֤ם לְאוֹת֙ עַל־יֶדְכֶ֔ם וְהָי֥וּ לְטוֹטָפֹ֖ת בֵּ֥ין עֵינֵיכֶֽם׃‏

Therefore impress these My words upon your very heart: bind them as a sign on your hand and let them serve as a symbol on your forehead,

All four cases the Torah refers to the arm tefillin as being a sign.

Why is only the arm tefillin referred to this way and NOT the head tefillin- which instead is referred to as totafos or a remembrance?

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Edit: I guess you could conversely ask why only the head tefillin are called a remembrance or totafos, but I don't see this as as big a question. According to Menachem ibn Seruk (cited by Rashi) and the Ibn Ezra on Shemos 13:16, totafos means remembrance. Rashi explains that you'll see the head tefillin, talk about it, and remember the miracles of Egypt. This wouldn't apply to the arm tefillin, which are supposed to be covered. As well, according to the other explanation that Rashi brings, that totafos refers to the four parshiyos, this could apply more to the head tefillin which have four compartments. (Although you could then ask why only the head tefillin have four compartments, but that's probably too tangential to be a relevant question)

Answer 1

In R' Samson Raphael Hirsch's commentary on Shemot 13:9, he distinguishes the functions of the two tefillin as:

• לְאוֹת עַל יָדְךָ - "a guide for all your acts"

• לְזִכָּרוֹן בֵּין עֵינֶיךָ - "the basis of all your thoughts"

The tefillin serve as physical tokens of, respectively, our dedication of our actions (hand) and our thoughts (head) to God. In turn, the actions we take, themselves, demonstrate ("sign") our dedication to God, while our thoughts are our medium for considering God's, as R' Hirsch puts it in his commentary on Devarim 6:8, "theoretical truths and teachings" ("reminder").

He points out that the first phrase echoes what God had commanded a bit earlier, in Shemot 12:13:

וְהָיָה֩ הַדָּ֨ם לָכֶ֜ם לְאֹ֗ת עַ֤ל הַבָּתִּים֙ אֲשֶׁ֣ר אַתֶּ֣ם שָׁ֔ם וְרָאִ֙יתִי֙ אֶת־הַדָּ֔ם וּפָסַחְתִּ֖י עֲלֵכֶ֑ם וְלֹֽא־יִֽהְיֶ֨ה בָכֶ֥ם נֶ֙גֶף֙ לְמַשְׁחִ֔ית בְּהַכֹּתִ֖י בְּאֶ֥רֶץ מִצְרָֽיִם׃

And the blood on the houses where you are staying shall be a sign for you: when I see the blood I will pass over you, so that no plague will destroy you when I strike the land of Egypt

Just as the blood was a physical demonstration of our dedication of our homes to God and His mission, so are the hand-tefillin, and all of the Commandment-fulfilling actions we take with those hands, physical demonstrations of our dedication of our actions. In Egypt, we submitted to God's "hand" to enact our salvation; now, we have to dedicate the agency we gained thanks to God's actions to His service.

Of course, there's a lot more on related themes, connecting to many aspects of the rules of tefillin, in those two comments, especially the one on Devarim 6:8. I recommend reading them in full.

Answer 2

We read in Shmoth 33.6 "And the children of Israel stripped themselves of their ornaments from mount Horeb onward." And in Shabbat 57b: "Rather, Rav Yehuda said in the name of Abaye: A totefet is an appuzainu, an ornament worn on the forehead."

When we say a Bracha over the Hand tefillin we say it with the intention that the Bracha covers the Head tefillin as well. It is explained that the single bracha covers both because, it says, "bind them for a sign upon your arm and let them be for a remembrance between your eyes;" and them is written in the plural -

See also Ibn Ezra to Shmoth 13.9 citing Koheleth (Proverbs) 1.9, 3.3, 6.9

How can the Shel Rosh (head tefillin) serve as a sign if we do not discuss the Torah when we see it? The passuk says, "and as a reminder on your forehead—in order that the Teaching of the L-RD may be in your mouth" Shmoth 13.9

Obviously, if seeing the Shel Rosh initiates discussion of the Exodus, (as Ibn Ezra elaborates) then the head tefillin serves as a sign right along with the hand (arm) tefillin - The Torah stipulates that they are to be worn together, "in order that the Teaching of the L-RD may be in your mouth" Shmoth 13.9

I understand the mitzvah as: "and it shall be for a reminder between your eyes [and my eyes,"] that is, when each person sees the totafoth (shel rosh) on the head of a fellow Jew it shall serve as a reminder to discuss the Exodus; for "with a strong Hand, HaShem took you out of Mitzrayim."

Shmoth 13.8 stipulates that during the Pesach season we are to discuss the Exodus: "And thou shalt tell thy son in that day, saying: It is because of that which the L-RD did for me when I came forth out of Egypt."

Obviously, Shmoth 13.9 is teaching us that seeing the Shel Rosh serves to initiate discussion of Pesach and the Exodus; something the shel yad cannot do once it is placed opposite the heart!