Boundaries For Yourself

The possuk (19:12-13) says וְהִגְבַּלְתָּ֤ אֶת־הָעָם֙ סָבִ֣יב לֵאמֹ֔ר הִשָּׁמְר֥וּ לָכֶ֛ם עֲל֥וֹת בָּהָ֖ר וּנְגֹ֣עַ בְּקָצֵ֑הוּ כׇּל־הַנֹּגֵ֥עַ בָּהָ֖ר מ֥וֹת יוּמָֽת׃ לֹא־תִגַּ֨ע בּ֜וֹ יָ֗ד כִּֽי־סָק֤וֹל יִסָּקֵל֙ אוֹ־יָרֹ֣ה יִיָּרֶ֔ה אִם־בְּהֵמָ֥ה אִם־אִ֖ישׁ לֹ֣א יִחְיֶ֑ה בִּמְשֹׁךְ֙ הַיֹּבֵ֔ל הֵ֖מָּה יַעֲל֥וּ בָהָֽר.  A few pessukim later (21-24) it says וַיֹּ֤אמֶר י״י֙ אֶל־מֹשֶׁ֔ה רֵ֖ד הָעֵ֣ד בָּעָ֑ם פֶּן־יֶהֶרְס֤וּ אֶל־י״י֙ לִרְא֔וֹת וְנָפַ֥ל מִמֶּ֖נּוּ רָֽב וְגַ֧ם הַכֹּהֲנִ֛ים הַנִּגָּשִׁ֥ים אֶל־י״י֖ יִתְקַדָּ֑שׁוּ פֶּן־יִפְרֹ֥ץ בָּהֶ֖ם י״יֽ׃ וַיֹּ֤אמֶר מֹשֶׁה֙ אֶל־י״י֔ לֹא־יוּכַ֣ל הָעָ֔ם לַעֲלֹ֖ת אֶל־הַ֣ר סִינָ֑י כִּֽי־אַתָּ֞ה הַעֵדֹ֤תָה בָּ֙נוּ֙ לֵאמֹ֔ר הַגְבֵּ֥ל אֶת־הָהָ֖ר וְקִדַּשְׁתּֽוֹ׃ וַיֹּ֨אמֶר אֵלָ֤יו י״י֙ לֶךְ־רֵ֔ד וְעָלִ֥יתָ אַתָּ֖ה וְאַהֲרֹ֣ן עִמָּ֑ךְ וְהַכֹּהֲנִ֣ים וְהָעָ֗ם אַל־יֶֽהֶרְס֛וּ לַעֲלֹ֥ת אֶל־י״י֖ פֶּן־יִפְרׇץ־בָּֽם׃.  Why is the warning repeated (see Rashi?) Furthermore, why the second time around is there an additional warning for the kohanim? And the Gemorah Sanhedrin (daf 15a,41a) learns from כִּֽי־סָק֤וֹל יִסָּקֵל֙ אוֹ־יָרֹ֣ה יִיָּרֶ֔ה the rules of סקילה, clearly going on the mountain is a capitol punishment administered by man, yet in the second time around it says פֶּן־יִפְרֹ֥ץ בָּהֶ֖ם י״י, a punishment meted out by G-d, which one is it?  The first time it says a warning on animals as well, but the second time animals aren't mentioned, why?

We see that there were two separate warnings not to approach the mountain.  The first time was during the three days of הגבלה.  This was not to breach the sanctity of the mountain.  A violation of this is punishable by death through ב"ד.  The second warning was during the time Moshe went up to the mountain.  This wasn't a warning to violate the kedusha of the mountain, rather it was a warning for everyone to retain there respective places that they were designated to.  As the meforshim say there were different levels of closeness to the mountain.  This warning was not to violate one's place of designation.  A violation of one's personal boundaries isn't subject to death by ב"ד, rather death by G-d.  This may be the intent of the Or Hachayim (possuk 22) explaining why the kohanim are mentioned here: או ירצה על פי דבריהם ז״ל (מכילתא) כי הגביל ההר עד כאן משה עד כאן גבול אהרן עד כאן גבול הכהנים, כפי זה אומרו הנגשים אל ה׳ פירוש שגבולם בהר נגשים מה שאין כן ישראל, יתקדשו, פי׳ יעמדו בקדושתם ולא יוסיפו לעלות עוד פן וגו׳.  That's why the first time animals are included for they also can't go up the mountain, however they aren't included in the commandment of a personal boundary. (Based upon חבצלת השרון, see די באר that also explains they are two dinim, but with a different approach.)

Why is the giving of the Torah introduced by a commandment of boundaries?  This is the intro. to Torah.  The many vast laws and restrictions aren't methodologies of torture but an exercise in self control.  As Rav Shirkin recounts: