(ד) הַמִּתְעַסֵּק בִּתְקִיעַת שׁוֹפָר לְהִתְלַמֵּד לֹא יָצָא יְדֵי חוֹבָתוֹ. וְכֵן הַשּׁוֹמֵעַ מִן הַמִּתְעַסֵּק לֹא יָצָא. נִתְכַּוֵּן שׁוֹמֵעַ לָצֵאת יְדֵי חוֹבָתוֹ וְלֹא נִתְכַּוֵּן הַתּוֹקֵעַ לְהוֹצִיאוֹ אוֹ שֶׁנִּתְכַּוֵּן הַתּוֹקֵעַ לְהוֹצִיאוֹ וְלֹא נִתְכַּוֵּן הַשּׁוֹמֵעַ לָצֵאת לֹא יָצָא יְדֵי חוֹבָתוֹ. עַד שֶׁיִּתְכַּוֵּן שׁוֹמֵעַ וּמַשְׁמִיעַ:
One who is blowing on the shofar simply for practice, has not fulfilled their obligation to hear the shofar. Relatedly, one who listens to the aforementioned shofar-blower has not fulfilled their own obligation. If the listener intends to fulfill their obligation, but the shofar-blower does not intend to fulfill on behalf of the listener; or if the shofar-blower has proper intention, but the listener does not - in either case, the listener has not fulfilled their obligation. Both parties must have proper intention.
(ג) אָכַל מַצָּה בְּלֹא כַּוָּנָה כְּגוֹן שֶׁאֲנָסוּהוּ עַכּוּ''ם אוֹ לִסְטִים לֶאֱכל יָצָא יְדֵי חוֹבָתוֹ.
One who eats matzah without proper intention (to fulfill the mitzvah); ie were one forced to do so by idolaters or bandits - such a person has (nevertheless) fulfilled their obligation.
What distinguishes between these cases?
Two types of answers are given:
A. The Maggid Mishneh states that the person being forced to eat must neverthless know that today is Pesach and there is an obligation to eat Matzah.
B. The Kesef Mishna notes that the case of Matzah is different, for it is intrinsically enjoyable; and something which is enjoyable does not require additional intention.
--> The Maggid Mishneh also inquires as to Maimonides' approach to the general question of whether mitzvot require intention.
3. Rav Soloveitchik, Har'rei Kedem 15:1
Maimonides' position is that the mitzvah of shofar isn't the act of blowing, but rather the simple hearing of it. Yet if this is so, why does it matter if the blower has intention or not? The listening is all that matters, so as long as the listener has intention, shouldn't that be sufficient? Why must the shofar-blower also have intention?
Our rabbi wrote in the name of Rav Chaim (Brisker): I have heard.... the question of why does Maimonides require intention on behalf of the blower... there are two possible answers. A. Even though the mitzvah requires hearing, nevertheless the action of the mitzvah is the blowing, and therefore we need intention for the blower and the listener. B. If neither were to have intention, then the listener would simply be sitting there doing nothing.
But these two answers join as one. Listening on its own is not enough of a mitzvah - we need to combine the blowing for there to be a more active component, so that the mitzvah act isn't reduced to a purely passive act.
This is to say that with regards to the fulfillment of the mitzvah (kiyum hamitzvah) of hearing the shofar, we don't require the intention of the listener, because the fulfillment will come on its own through hearing. But with regards to the act of the mitzvah (maaseh ha-mitzvah) we require the listener's intent, in order to connect the listener to the action of the blowing....So the rule of the blower needing intent is not because of a generalized rule that mitzvot require intention, but rather we need to connect the act of the blowing to the listener..
We can add to this a proof, from the argument between the rishonim as to what the proper phraseology of the blessing is, "to blow" or "to hear" the shofar. Ostensibly, it seems clear we should recite "to hear", for if one hasn't heard, they haven't fulfilled the mitzvah! But according to this explanation we have offered, we see how the action of the mitzvah is the blowing, and it's only the fulfillment-element which requires hearing. This must be what the argument centered over - the "act" of the mitzvah versus the fulfillment of the mitzvah.